Valuation & Modelling

September 7, 2017 | Author: Faizan Maqsood | Category: Discounted Cash Flow, Valuation (Finance), Cost Of Capital, Mergers And Acquisitions, Private Equity
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Valuation and modelling for investment bankers

Valuation and modelling for investment bankers

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Published by The Corporate Training Group 2008

Copyright © 2008 The Corporate Training Group All rights reserved. No part of this work may be reproduced or used in any form whatsoever, including photocopying, without prior written permission of the publisher. This book is intended to provide accurate information with regard to the subject matter covered at the time of publication. However, the author and publisher accept no legal responsibility for errors or omissions in the subject matter contained in this book, or the consequences thereof.

The Corporate Training Group 52 Kingsway Place Sans Walk London EC1R 0LU www.ctguk.com At various points in the manual a number of financial analysis issues are examined. The financial analysis implications for these issues, although relatively standard in treatment, remain an opinion of the authors of this manual. No responsibility is assumed for any action taken or inaction as a result of the financial analysis included in the manual.

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About CTG

About CTG The Corporate Training Group (CTG) has been in existence since 1994 and has grown to become one of the pre-eminent organisations in the world of finance training. Although we take pride in our success, we know that to remain the first choice for our clients, we must constantly provide value, excellence and innovation. For this reason, our approach is to channel our expertise into providing the best in-house tailored finance training in the industry. CTG has one of the largest and most experienced trainer faculties in our field. We draw upon full time, dedicated finance professionals who specialise in training. Our overriding philosophy is that for training to be effective it needs to be relevant and enjoyable. However, such an approach must be backed up by the necessary expertise. All our tutors have extensive market experience as well as excellent technical understanding. CTG has • Specialists in all aspects of valuation who work with global corporates and Investment Banking teams • Accountants who are renowned within their fields and are able to analyse credit and valuation fundamentals without getting bogged down in the jargon • Experts in capital markets who are equally expert in making it practical, interactive and interesting • Modellers with a depth of experience in creating robust and flexible models for many different purposes • Unparalled experience in delivering to cross-cultural audiences And many, many more people who love to make training a fun and valuable experience.

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Contents

Contents

Executive summary Comparable company analysis Precedent transaction analysis Discounted Cash Flow (DCF) Leveraged Buy Out analysis (LBO) Merger analysis (combination)

1 2 3 4 4

1 • Introduction to valuation

5

An Investment Banking perspective Mergers and acquisitions Demergers and spin offs Private equity valuation IPO valuation Some common pitfalls Seeing the big picture DCF Comparable company analysis Precedent transactions Accretion / dilution analysis

5 5 8 8 9 10 10 10 11 14 15

2 • Comparable company analysis

17

Introduction Why use comps? Reasons for popularity Potential pitfall areas Structured approach to comps Output – a pure market driven valuation excluding the value of a control premium

17 17 18 18 20 20

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Contents

An overview of the comps process Step 1 − Identify the comparable universe of companies Step 2 – Focus on the appropriate financial metrics and ratios What level of valuation are we seeking – equity or enterprise value level? Minority interests Net debt Non-operating cash balances Understanding what drives EV / EBITDA multiples (EV multiple model) Growth adjusted multiples Typical sector specific multiples Sources of information Step 3 – Standardise the metric to ensure comparability Is the metric consistently defined? Is the metric consistently calculated? Pension scheme deficits The impact of adjusting for pension deficits on BA’s EV multiples Exceptional / extraordinary items The impact of adjusting for operating lease on BA’s EV multiples Valuing the target European airlines and airports – valuation multiple Selecting an appropriate comparable multiple Explanation of premia / discounts to peers Consistency of the target earnings metric Breakdown to equity value Common errors made in comps modelling Process checklist for comps

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22 26 28 28 32 34 35 37 42 45 47 48 48 49 52 54 55 59 64 64 64 65 66 66 69 70

Contents

3 • Precedent transactions

73

Introduction Structured approach to precedent transactions Identifying the comparable universe Collecting data Comparable universe parameters Using SDC to extract an initial comparable universe Common SDC search fields Issues using SDC Sources of information Calculating the relevant multiples Analysing the results and valuing the target Understanding the control premium Why pay a premium? Synergies Premium paid analysis Trading comparables vs. precedent comparables

73 75 76 79 80 80 81 83 84 86 89 90 90 90 91 92

4 • Discounted Cash Flow (DCF) fundamentals

93

Introduction to DCF Free Cash Flow to the Enterprise model Free Cash Flow to the Enterprise Calculation of FCFE Forecasting FCFE Key drivers of FCFE Length of the FCFE forecast period Weighted Average Cost of Capital Cost of debt

93 95 96 96 100 101 103 106 107

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Contents

Empirical approach Synthetic approach Risk-free rate of return Credit risk premium Interest tax shield Cost of equity The Capital Asset Pricing Model Risk-free rate of return Equity Market Risk Premium Beta factor Calculating the beta factor Published vs. synthetic beta factors Weighting Calculating the Weighted Average Cost of Capital Year-end vs. mid-year discounting Terminal value Perpetuity growth method Terminal multiple method Cross-checking the two terminal values Calculating the present value of the terminal value Enterprise value Key terminal value drivers Lengthening the explicit forecast horizon Adjusting enterprise value to equity value FCFEq methodology and pitfalls

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107 108 108 111 114 114 115 116 116 118 119 125 127 129 129 131 132 133 133 135 135 136 136 136 140

Contents

5 • Dividend Discount Model (DDM) Dividend Discount Model Constant dividends Constant growth in dividends Two-stage growth model

6 • Advanced DCF valuation Introduction Delevering betas Creating a synthetic (delevered beta) The WACC formula APV valuation Terminal value and growth rates International cost of capital

7 • Rothschild standard models Introduction Discounted cash flow models Excel set-up Side by side analysis of the 3 DCF models DCF II Overview Model structure How to complete the model The control sheet (In) The broker and in-house sheets (In) The WACC sheet (In) The check sheet (In)

141 141 141 143 147

151 151 152 152 158 164 169 173

179 179 180 180 182 182 183 183 184 188 188 189

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Contents

Segmental sales flexibility Capex driver flexibility Detailed WACC Beta deleveraging Mid year discounting Mid year valuation Subsequent period discounting Cash flow perpetuity with mid-year discounting Review points Assumption inconsistency (graphical review) 70 / 30 split on EV Inconsistency on the exit scenario Implied exit multiples vs. peer group Updating of data tables The merger models Merger I Merger II Overview Comps model Overview Starting the model Company inputs Sector-specific ratios Inserting additional companies Workings sheet Control (In)sheet Output sheet Inserting additional currencies

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192 192 192 194 197 199 201 204 206 206 206 207 208 208 210 210 215 215 225 225 225 229 231 232 235 235 236 236

Contents

Financial modelling 8 • Financial modelling

239

Introduction Meeting user needs Excel vs. modelling Excel set up for efficient modelling Autosave Model set up Design Model structure Sheet consistency Using and managing windows in Excel Referencing Relative vs. absolute references Naming (cells & ranges) Transpose Formatting Sign convention Colours, size and number formats Styles Conditional formatting Text strings Regional settings IF and some other logical functions Common problems with IF statements and some simple solutions Nested statements Data retrieval – the LOOKUP school

239 239 240 241 241 245 245 247 255 258 260 260 261 268 270 270 271 274 279 281 282 282 284 286 287

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Contents

CHOOSE MATCH INDEX OFFSET VLOOKUP HLOOKUP Volatile functions Excel’s volatile functions Arrays Rules for entering and changing array formulae Expanding an array formula Adding logic to arrays Advantages and disadvantages of arrays Dates Date formats Date functions Consolidating time periods Switches Two-way switch Multiple options Formality Sensitivity Goal seek Data tables Enterprise Value – £m sensitivity Validating data Data validation – with inputs Data validation – with outputs Conditional formatting Conditional statements

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288 289 290 294 297 300 301 302 303 305 305 307 308 309 310 310 313 316 316 317 320 320 320 321 323 325 325 327 328 328

Contents

The ISERROR function Model completion Group outline Protecting the model Report manager Tracking editing changes Historic financials The income statement The cash flow The balance sheet Forecast financials Ensuring balancing balance sheets Setting up the reconciliation Debt modelling The problem A solution Auditing and error detection tools Error values Auditing a formula Finding links The F5 Special Other auditing tips Auditing a model – a process Upon opening Coding clarity index Troubleshooting Modifying models

329 330 330 331 332 333 334 334 335 335 336 336 338 341 341 341 343 343 344 346 347 349 351 351 352 355 356

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Contents

Appendix Excel tricks Excel function keys

9 • Financial modelling – transition to Excel 2007 Introduction and objectives Audience Microsoft migration tools New layout The ribbon Developer Larger worksheet area Page setup View functionality The office button Excel options One click quick access commands Formatting Styles Conditional formatting Paste special Workbook setup in 07 Creating a workbook setup template Formula assistance New functions Resizable formula bar Function AutoComplete Using Excel names

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358 358 364

367 367 368 368 369 371 373 374 375 375 378 379 382 383 384 388 392 393 396 398 399 399 399 401

Contents

Creating names The name manager Using names Auditing and associated issues Protection Saving a workbook as a pdf file Finalising a workbook Inspecting a workbook Comments Using the VBA forms What if analysis (data tables etc.) Data functionality Data validation Sort and filter Charts Inserting charts Design chart tool Layout chart tool Format chart tool Valuation summary diagrams in 07 Data connections Run compatibility checker

Index

401 402 403 404 404 404 405 405 406 407 408 409 409 409 410 410 411 412 413 414 415 415

417

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Executive summary

Executive summary This manual examines the main techniques used by investment bankers to value companies, including the use of Excel for modelling. It focuses on valuation for M&A transactions, rather than valuation and analysis for ongoing equity research. The three main techniques employed in valuing a target company are covered: • Comparable company analysis, or comps • Precedent transactions analysis • Discounted cash flow, or DCF (both fundamental and advanced) The common pitfalls and key issues with each of these methods are also considered. (Note: Leveraged Buyout (LBO) analysis is covered in detail in the ‘Financial Products’ manual.) Best practice for successful modelling is explored, along with an introduction to the Rothschild standard models. The manual also provides an introduction to Excel 2007, which should prove a useful aid in the near future.

Comparable company analysis Overview The chapter takes a four step approach to comps: Step 1

Identify the comparable universe of companies

Step 2

Focus on the appropriate financial metrics and ratios

Step 3

Standardise the metric and calculate the comparable multiple

Step 4

Use the multiple to value the target

In essence the approach is to decide on a group of comparable companies, take the market value of the equity and debt for each and divide by an appropriate figure from the income statement or cash flow statement. The extracted figures may require ‘cleaning up’ for accounting inconsistencies,

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Executive summary

before being used to calculate an average sector multiple. The average multiple is then applied to the target company to establish a value. For example, if one of the comparable universe of companies has a market capitalisation of $5bn and debt with a market value of $1bn, its enterprise value or EV is $6bn. This figure would be adjusted to take account of associates, joint ventures, pension deficits and the like (all covered in detail later). This EV would then be divided by an appropriate figure, such as the forecast EBITDA. So if EBITDA was $500m and EV was $6bn, EV/EBITDA = 12

This multiple of 12 would be used alongside the multiples of the other comparable companies to gauge the sector average EV/EBITDA multiples. These sector averages can then be used to calculate the indicative values of the target company. For example, with an average range of EV/forecast EBITDA from the comparable universe: EV/EBITDA High 13

Target company forecast EBITDA $100m – implied value $1.3bn

Low 10

Target company forecast EBITDA $100m – implied value $1.0bn

Precedent transaction analysis Overview The way precedent transactions are analysed is similar to comps, the key difference being that rather than looking at comparable trading companies’ multiples, the multiples (often EV/EBITDA) are drawn from previous relevant transactions. The price paid for similar companies in the past is used to determine the value of the target. If the relevant precedent transactions were for listed companies, the premium paid over the pre-bid share price can also be used for valuation. For example, if relevant, recent transactions have been completed at an average premium of 35% over the pre-bid (or pre-rumour) share price, the target company shareholders will be expecting a similar premium – so the price offered per share will have to incorporate this to have a chance of success.

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Executive summary

Discounted Cash Flow (DCF) Overview The major way that discounted cash flow is used for valuation is to discount the unlevered free cash flows expected from the company, at the weighted average cost of capital (WACC) to establish an enterprise value (EV). The WACC is calculated by weighting the cost of equity (Ke) and the posttax cost of debt (Kd) according to the relevant proportions of equity and debt in the target company.

The calculation of free cash flow EBIT

5,000

Add back Depreciation

600

Amortisation

100

EBITDA

5,700

Deduct 1,000

Capex Tax (on operating profit)

700

Increase in working capital

500

Free Cash Flow (FCF)

4,500

Each future year’s free cash flows are calculated, and then discounted at the WACC to determine the present value. The sum of all of the present values of the future free cash flows results in an implied enterprise value. This is usually achieved by forecasting a number of years’ free cash flows discretely (often 10 years), and then using a perpetuity formula to establish a terminal value for the cash flows anticipated beyond the forecast period. This process will establish a ‘standalone’ value for the company, valuing it independently of any synergies that may arise if it were acquired. Indeed, the value must be ‘standalone’ because the WACC used to discount the cash flows is based on the target’s capital structure, not the potential acquirer’s. Other DCF valuation techniques, such as discounted dividend valuations and FCF to equity, are examined separately.

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Executive summary

Merger analysis (combination) Overview For acquisitions by listed companies, it is important to forecast the impact of the combination on key metrics such as EPS and credit ratings. At this stage, the potential synergies of bringing the two companies together need to be considered. The merger model will deliver forecast EPS, together with the implied credit rating. The credit rating itself will be dependent upon the capital structure of the combination.

The manual then moves on to review the models used by Rothschild to use these valuation methods in a robust and integrated way. The final two chapters highlight the key features of Excel that are used when modelling, including both Excel 2003 and Excel 2007.

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1 • Introduction to valuation

1 • Introduction to valuation An Investment Banking perspective From an investment banker’s perspective, valuation is performed for a number of different reasons. These reasons will often differ from the per share valuations that occupy equity investors, the focus of published equity research. The key reasons investment bankers are interested in valuation are: • Mergers and Acquisitions The target company is valued by the acquirer. There are numerous techniques for performing this valuation, but, in essence, the aim is to determine a fair value for the operations of the target business. • Demergers and spin offs A business unit is valued independently of the parent (which itself may be listed). • Private equity valuations This involves valuation of the company for a private equity transaction. The target company could currently be listed and be taken private or it could be an unlisted company. • Initial Public Offer (IPO) In this instance the investment banker’s perspective is closer to that of the equity research analyst in that the target audience for the valuation is the general investment community. However the techniques for valuing a newly listed company will differ from those used for valuing existing quoted securities.

Mergers and acquisitions Rothschild will act on both the buy and sell side of M&A transactions. In each instance a number of different valuation techniques will be employed to derive a range of values which will form the basis for negotiation between buyer and seller.

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1 • Introduction to valuation

Acting on the buy side Objectives: • To advise the acquiring company on the range of values for the target and the likely impact of paying those values on the acquirer’s EPS, internal rate of return and other metrics • To assist the directors of the acquiring company whose duty it is to consider the impact of the acquisition on shareholder value. The target company is usually valued as a standalone entity. This means that valuing the earnings (usually based on a comparable multiple such as EV / EBITDA) or cash flows (Discounted Cash Flow or DCF techniques) of the target, assuming any growth is organic. Standalone valuation does not take into account the impact of future acquisitions by the target nor interference by the buyer (i.e. no synergies). If the buyer is using listed company information to value a private company the buyer will push for a discount to take account of the illiquidity of the private company compared to quoted comparables. Any potential synergies from the combination will be appraised separately and may form part of the overall valuation. It is then usual to look at previous transactions in the sector and to consider the premia paid by other acquiring companies over the ‘normal’ valuation multiple for the targets they have acquired. This will give the buyer the price the target’s owners will be ‘expecting’ as a return for selling the business (this will usually include the ‘control premium’, the compensation for passing over control of the business). The next technique employed will usually be an LBO valuation. Based on the returns required by private equity (say 25% p.a.) it is possible to work out the maximum price which could be paid and still achieve this return. This will provide an indication of the likely amount to be offered by the private equity buyers in any auction. Trial capital structures will be input based on the lending constraints of the period. If the structures are robust (loan repayment terms met, borrowing limits not exceeded) then the returns to equity can be checked.

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1 • Introduction to valuation

If the returns are acceptable then the bid premia input into the model can be converted to a valuation and used as a benchmark on the football pitch. The output of all of this valuation work is the “Football Pitch”. Summary valuation (um) Current EV Discounted cash flows

2,010

Precedent transaction multiples

1,830

Comparable company multiples

2,200

1,530

2,010

Control premium (25%-40%)

1,950

LBO 12 month share price performance

2,610

1,950

1,770

1,410

1,200

2,130

1,770 1,450

1,700 1,950 2,200 Enterprise value (um)

2,450

2,700

The merger model With a suitable range of potential values for the target company, the next stage is to run the merger model. This will make use of the potential purchase price (based on the above valuation range) and produce a combined EPS (this is most relevant for listed buyers) for the new entity. The model will take into account the financing of the acquisition together with the forecast synergies. Ideally, the transaction should be EPS enhancing (accretive) rather than dilutive. The accretion (based on forecast numbers) is often seen in the year following the acquisition (or the year at which full synergies have been attained) – given the disruption in the year of acquisition and integration required. The merger model will, in taking account of the financing of the transaction through cash or equity (or both), forecast the credit rating of the new

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1 • Introduction to valuation

combination based on a new capital structure which may be very relevant for some sectors, but not a key part of analysis for other sectors.

Acting on the sell side / defence The bank’s role can vary here, Rothschild may be: 1. Acting for the seller in a private auction Objectives To help secure the best price and to maximise deal certainty. 2. Acting for the seller in a public takeover Objectives To help secure the best price and to maximise deal certainty. 3. Acting for the defence in a public takeover Objectives To help defend the target against an unwelcome predator. In all three instances the valuation techniques discussed above will be employed. The valuations will be based on management forecasts, with estimates made for potential synergies and for private equity capital structures. The valuations will be used to appraise the fairness of the buyer’s bid price and to give shareholders an indication as to whether or not to accept the offer.

Demergers and spin offs The valuation of a division is similar to valuing a private company although there may be publicly available information from equity research analysts who have valued the entire company on a sum of the parts basis, showing an implied value for the division in question. The demerger will usually result in the listing of the division in question, with forecast numbers being produced by management. The main techniques of DCF and comparable company analysis should provide the basis for valuation.

Private equity valuation The private equity buyer will be seeking a return of 25%-30% on the investment. The purchase will be highly leveraged with the aim of paying off the debt burden through the cash flow generation of the target company. The target will be valued using an LBO (leveraged buyout) model.

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1 • Introduction to valuation

The model will trial differing capital structures with various constraints placed on the level of debt introduced (minimum equity component, ‘Senior A’ debt paid back after 7 years, etc.). If the target can service the debt and the return to the private equity fund is in the region of 25% then the transaction may be viable.

IPO valuation The flotation of a company will generally involve a bookbuilt marketing process. This is a two week period when the investment bank goes on the road with the company, meeting many leading institutional investors. During this period the valuation methodology will be outlined (comparable companies, Dividend Discount Model, etc.) and the market appetite for the shares will be assessed. The equity sales team will be in constant dialogue with the investors and the final price will be determined as a result of the demand for the stock.

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1 • Introduction to valuation

Some common pitfalls The following is a quick run through some of the valuation aspects that can trip up the unwary. It is an anecdotal section based on many years experience of reviewing valuations prepared in practice and / or simulations.

Seeing the big picture Occasionally, analysts will become absorbed in the detail and produce final valuations that simply don’t make sense. It is vital to step back from the detail and look at the final position, particularly with regard to inconsistencies that can arise as different parties produce different parts of the football pitch. Watch out for: 1. Inconsistent net debt numbers between comps and DCF 2. EBIT numbers in comps and DCF that don’t tie up with one another 3. Football pitches that confuse equity and enterprise value 4. Lack of reference to the current share price of the target on the football pitch 5. Bid premia in the merger model that don’t tie in to the football pitch 6. Different seasonalisation of financials between methodologies 7. EV adjustments.

DCF It is a well known cliché that the DCF model will not produce a ‘right’ answer – however there can be major inconsistencies in models which can undermine the integrity of the entire valuation. Watch out for: 1. Timing of cash flows – be careful with the first period, especially if not a full year 2. Capex – think carefully about maintenance and expansionary capex and their relationship with growth 3. Tax – follow the tax calculations through the model (e.g. if Income from JVs is excluded from FCF what is the impact of the tax on this income?)

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1 • Introduction to valuation

4. Tax rates – if the company is paying an effective tax rate which is less than the country rate, consider the impact on both cash flows and the cost of debt – should the rate eventually be the same for both? 5. Net debt – this will feature as a part of the WACC calculation (target leverage), part of the synthetic beta calculation (target leverage) and as part of the conversion from enterprise to equity value calculation. There should be some reconciliation between these numbers 6. Synergies – generally the target is valued as a standalone entity; synergies would not be part of the DCF 7. Synergies – occasionally these are valued in a DCF as a separate calculation – it is conventional to discount these at the acquirer’s WACC 8. Terminal growth rates – whilst growth rates from year 10 onwards are a guess, it is important to cross reference them to reinvestment levels and to historic growth rates 9. Exit multiples – it is important that the implicit growth rates in the multiples are made explicit and sense checked 10. Mid-year discounting and the terminal value – for the exit multiple approach, use end-of-year discounting (assuming the company is sold on that date), for the perpetuity growth approach continue with midyear discounting 11. Normalised FCF (capex = depreciation) and tax.

Comparable company analysis Valuing a target using traded comparables will provide a market based benchmark, without any built in acquisition premium. The comps models are detailed and rigorous, but it is still possible to create confusion in the valuation. Watch out for: 1. Adding an arbitrary premium (30% control) to the valuation without any explanation. The range on the football pitch should have a transparent audit trail and if possible should be presented without amendments 2. Ranges – too wide a valuation range is unhelpful 3. Models not kept up to date with most recent information. Update comps regularly for:

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1 • Introduction to valuation

• Daily share prices • Earnings announcements • Corporate events such as M&A deals, share issues, buybacks Keep source documentation for verification purposes Make notes in the comps model to back up source information and adjustments made to historic and broker information 4. Financials not adjusted for exceptional items • Exceptional items are not just what the financial statements disclose as exceptional. Analysts should be able to make a judgment call on whether an exceptional item is truly exceptional or not (and conversely whether an item not disclosed as exceptional should be treated as such) 5. Ignorance of different GAAPs • Financials will need to be adjusted to a consistent set of accounting rules 6. Companies with different year ends not calendarised 7. Foreign currency figures not converted to a common currency 8. Corporate actions taken since the publication of the most recent set of financial statements. Always check regulatory filings and reflect this in the comps numbers 9. Blindly using broker numbers without understanding the definitions they have applied and ensuring that historics and broker information are consistent • Always reconcile the broker historicals to the published historicals – this will help to understand how the broker has defined key metrics e.g. EBITA and EPS, so that the historics and the forecasts can be input using consistent adjustments 10. The free float figure not being adjusted for significant shareholdings

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Other things to bear in mind: 11. Understand the industry by reading analyst reports and news stories • What are the industry specific statistics (sales / employee, etc.)? • What are the most important performance ratios? • What are the most important market multiples? 12. Select the universe of comparable companies carefully – more is not necessarily better 13. Use only the most appropriate brokers • Ensure that the research is recent and subsequent to any company result announcements • Ensure that the forecast numbers are similar to global estimates • The recommendation is to use a consensus 14. All source documentation should be marked to show from where information has been extracted with both a post-it showing the page and a highlighter showing the numbers used 15. Use footnotes • To disclose adjustments made to the numbers • To explain unusual operating and financial trends 16. Ensure that the numbers are comparable – potentially, the more adjustments made for special situations (true exceptionals / non-recurring items, dilution, associates, etc.), the more comparable, but the more time to input the comps • The less likely that all the desired adjustments will be visible in the brokers’ research forecasts • The more chance of errors 17. Keep the comps analysis up to date • Check the web site and the financial calendar of the individual companies to ensure that the most recent published financial information is used • Update share prices • Update exchange rates

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1 • Introduction to valuation

18. Check the work • Double check for data entry or other processing mistakes • Step back and look at the finished product – do the results make sense? • Get someone else to check the work 19. Understand the results of the analysis and be prepared to discuss them. The numbers can be meaningless without solid analysis to back up the metrics 20. The comps model will calculate average metrics and multiples for the comparable universe. Do not just rely on using an average for the target company valuation • Review the comparables and exclude outliers from any average calculations. Make sure there is justification for using a comparable multiple that is above or below the average (mean or median).

Precedent transactions The precedent transactions databases are notoriously unfriendly to users and care must be exercised in establishing the real transaction multiples. When the groundwork has been done and the valuations prepared there is still scope for error. Watch out for: 1. Blind reliance on numbers taken from databases without reference to the original source data 2. Not spending enough time ensuring that the comparable universe is comparable – this can be frustrating but again you cannot necessarily rely on the data provider 3. Insufficient footnoting of assumptions or unusual data items 4. Premia incorrectly calculated (this is a common occurrence). It is vital to track back to the date before any rumours hit the market in order to accurately calculate the actual premium paid on the transaction 5. Inconsistent use of different accounting regimes – US GAAP vs. IFRS as with the comparable company analysis 6. Financials not adjusted for exceptional items – accounting or analyst viewed exceptionals

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7. Transaction values not equal to the enterprise and equity value ( 51 x 1 share Consequently, transaction multiples are higher than the trading multiples of the company. It is theoretically not correct to compare an acquisition of 5% of a company with a full take-over since, in the latter case, the Bidder would have to pay a larger premium to gain control. Consequently, purchases of small stakes, i.e. less than 25%, are likely to be excluded from the analysis. Do not compare crossing the 50% threshold (or achieving control) with a minority position.

Why pay a premium? The ability to control a company has a value, but value in a corporate sense must be represented by future cash flows. When the equity markets value a company, they are assessing the PV of its future cash flows.

Synergies The control premium must be justified by higher future cash flows to the new owner. The additional cash the bidder can earn from the target arises through synergies that are not available to: • The market; or • The current owner (in a private transaction) Synergies mean that the cash flows discounted by bidders are higher than the cash flows being discounted by the market (or current owner). The synergies set a limit on how much the bidder could pay. If the acquisition

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3 • Precedent transactions

is going to add any value to the bidder, then the amount actually paid needs to be less than this maximum. Consequently, precedent transaction multiples are impacted by the value of synergies, and the split of these synergies between target and bidder.

Premium paid analysis The premium is calculated as: = (Offer price / Target’s share price) −1 It is common to use various time frames to calculate the premium in order to remove the impact of any price sensitive leaks to the market. Common time frames are: • 1 day prior • 1 week prior • 1 month prior • One may also use averages or volume weighted averages over 10, 20, or 30 trading days prior. The idea is to calculate the premium paid using an undisturbed share price (i.e., a price unaffected by the deal announcement or before market speculation).

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3 • Precedent transactions

Trading comparables vs. precedent comparables Trading comparables

Precedent transactions

• Reflect current value in public markets

• Reflect value at time of transaction

• What investors are willing to pay for company at this point in time

• What the acquiror was willing to pay for the company at the time of the transaction

• Often forward-looking (i.e. EV / 2009 EBITDA), although can use last twelve months (LTM) figures • Can be influenced by other factors than cash conversion, risk and growth • Size and liquidity • Easier for large institutional investors to invest in • Large controlling shareholder • Could put smaller shareholders at disadvantage, or block valuecreating takeover • High dividend payout • Reduces ability of management to re-invest earnings in value destructive activities • Market sentiment • Companies who clearly articulate their “story” to investors may trade at premium • Management teams with a track record of executing on plans earn the confidence of investors and may trade at a premium.

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• Often based on historical figures (LTM) figures), although can use forward estimates at the time of transaction • Should, in theory, contain “acquisition premium” that acquiror was willing to pay • Premium reflects synergy potential of combined businesses • As a result, all things being equal, precedent transaction multiples will be higher than trading comparable multiples • However, this is not always the case. It is dependent on current market sentiment.

4 • Discounted Cash Flow (DCF) fundamentals

4 • Discounted Cash Flow (DCF) fundamentals Introduction to DCF It is a fundamental principle of asset valuation that the future cash flows expected to be generated by an asset discounted at a rate adjusted for the risk of those future cash flows will yield the intrinsic value of that asset. Time

0

1

2

3

...

n

Cash flows



X

X

X

...

X

Asset value

X Discounting @ risk-adjusted rate

This principle can be applied to the valuation of the debt and equity instruments issued by a business, and by extension to the business itself. This methodology has the advantage that it is based on cash flows, and so is unaffected by many of the accounting issues that hamper earnings-based valuation approaches. It has the disadvantage that it is highly sensitive to the underlying assumptions used in the calculation of the cash flows and the discount rate. Calculating a DCF valuation raises some key questions which must be answered: • Cash flows • Which cash flows should be used? • How should these cash flows be correctly calculated? • How should the cash flows be forecasted forwards? • For how long should these cash flows be forecast? • Discount rate • Which discount rate should be used?

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• How should this discount rate be correctly calculated? • How should this discount rate be appropriately applied to the future cash flows in order to calculate their present value? To answer the first of each of these sets of questions, it needs to be understood that DCF valuation techniques, as with other methodologies, can be used to generate valuations at both the equity level and the enterprise level. If calculating the equity value, the cash flows must be those attributable to the equity-holders, i.e. dividends or the free cash flow to equity (FCFEq). The discount rate must be the rate of return required by the equity-holders, i.e. the cost of equity (Ke). Conversely, if calculating the enterprise value, the cash flows must be those attributable to both the debt- and equity-holders, i.e. the free cash flow to the enterprise (FCFE). The discount rate must be the blended rate of return required by both the debt- and equity-holders, i.e. the weighted average cost of capital (WACC). It is essential that the cash flows and discount rate are NOT mismatched. Equity value

Enterprise value

Cash flows

Dividends FCFEq

FCFE

Discount rate

Ke

WACC

The three main DCF approaches are: 1. Dividend Discount Model 2. Free Cash Flow to Equity Model 3. Free Cash Flow to the Enterprise Model.

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Three main DCF valuation approaches

Dividend Discount Model (DDM)

Free Cash Flow to Equity Model (FCFEq)

Free Cash Flow to the Enterprise Model (FCFE)

The following sections will focus on the Free Cash Flow models in turn, highlighting the remaining issues on cash flows and discount rates. Please refer to Chapter 5 in relation to the DDM model.

Free Cash Flow to the Enterprise model The Free Cash Flow to the Enterprise Model is the most commonly used version of the available DCF models. As with all valuations, it is based on the following three fundamentals: 1. Cash • In the form of free cash flow to the enterprise (FCFE). 2. Risk • In the form of the weighted average cost of capital (WACC). 3. Growth • Principally in the form of the terminal value (TV). Three fundamentals of FCFE valuation

Cash (FCFE)

Risk (WACC)

Growth (TV)

Each of these three fundamental issues will be looked at in order. Finally the method to adjust from the resultant enterprise value (EV) to the equity value, and an implied share price, will be covered.

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4 • Discounted Cash Flow (DCF) fundamentals

Overview of FCFE DCF model Time



n

0 1. FCFE

EV

3. TV

2. WACC

4. A D J S Equity value and implied share price

Free Cash Flow to the Enterprise With regards to free cash flow to the enterprise, the three key questions that need to be answered are: 1. How should FCFE be correctly calculated? 2. How should forecasts of FCFE be correctly driven forward? 3. For how long should forecasts of FCFE be continued?

Calculation of FCFE The FCFE model uses a very specific definition of FCFE. However, this can still be calculated in a number of ways. The most commonly used method is as follows: FCFE – calculation 1. EBITA

X

2. Depreciation

X

EBITDA

X

3. Capex

(X)

4. Working capital (investment) / release 5. Tax paid (unlevered) FCFE

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(X) / X (X) X

4 • Discounted Cash Flow (DCF) fundamentals

1. EBITA The calculation starts with EBITA (earnings before interest, tax and amortisation of goodwill). As usual, this should be before any exceptional items, in order to arrive at the underlying earnings on which forecasts can be based. Generally any income from joint ventures and associates is also excluded. Under IFRS, this is normally reported using the equity method of accounting as a single number post-tax in the income statement. Given the lack of information in the published financial statements, it is usually very difficult, if not impossible, to convert this into its equivalent EBITA number. For that reason, it is generally easier to deal with the value of interests in joint ventures and associates as an adjustment at time zero. This approach may need to be reconsidered if the value of interests in joint ventures and associates is a significant proportion of the total enterprise value, or if proportional consolidation is used for joint ventures under IFRS. EBITA

Exclude exceptional items

Exclude income from JVs & Associates

2. Depreciation Depreciation of tangible and non-goodwill intangible fixed assets will have been deducted in arriving at EBITA, the starting point. Since, these are non-cash expenses and accruals-based rather than cash-based numbers, depreciation is added back to arrive at EBITDA. 3. Capex Having just added back the accruals-based cost of the longer-term assets, it is necessary to replace that by deducting the cash-based cost of those assets, so as not to ignore this real cost to the business and so over-value it. This capex deduction should include both replacement / maintenance capex (for which depreciation may be used as a proxy) and expansionary capex, as the FCFE model is predicated on growth and that growth is unlikely to be achieved without the necessary long-term investment in the business. The capex figure should, therefore, generally be higher than the depreciation

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4 • Discounted Cash Flow (DCF) fundamentals

figure. N.B. Bankers often use “normalised” cashflows in the terminal value calculation where capex is trended to equal depreciation. Generally, the capex figure should exclude M&A activity. It is difficult to predict such activity into the future and the model is normally based on organic growth, rather than growth through acquisition. Again, this approach may need to be reconsidered if the strategy of the business in question is primarily one of growth through acquisition. Capex

Replacement

Expansionary

✔ Organic

Acquisitive





4. Working capital investment / release

Since the model is based on growth, it is necessary to consider the need for continued investment in day-to-day working capital. As most businesses grow, more cash will become tied up in items such as inventory and accounts receivable, as compared to the cash made available through increased accounts payable. This will lead to an increased investment in net working capital. More cash being used in this way means that less will be available, or “free”, to provide returns to the debt and equity finance providers. Purchase

Purchase

Inventory

Payables

Sale

Receivables

Cash in

Cash out

Cash requirement grows as business grows Note: In this example, through each iteration of the operating cycle, cash has to be paid out to suppliers before it is received in from customers. This creates a cash requirement.

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4 • Discounted Cash Flow (DCF) fundamentals

It is worth noting that the above is not the case for all types of business. Retailers, for example, especially supermarkets, tend to release cash from their working-capital cycle as they grow, as the increase in payables tends to dwarf any increase in inventories and receivables. So, working capital becomes a source, rather than a use, of cash. Cash surplus grows as business grows

Purchase

Sale Inventory

Purchase

Cash in Receivables

Payables

Cash out

Note: Through each iteration of the operating cycle, cash is received in from customers before it has to be paid out of suppliers. This creates a cash surplus.

5. Tax paid (unlevered) Since the model requires the calculation of free cash flow to the enterprise or unlevered free cash flow, all of the numbers, including tax paid, must also be unlevered – i.e. they must ignore the capital structure of the business and its consequences. The calculation must not reflect the benefit of the tax-deductibility of the interest on the debt finance (the interest tax shield). This benefit will be built into the model later within the WACC (by using a post-tax cost of debt). The easiest way to achieve this is to apply an appropriate tax rate (this will be discussed below) to the EBITA figure (using EBITA as a proxy for pre-interest taxable profits). This automatically results in an unlevered tax number, i.e. the taxes on the operations N.B. If FCFE is being calculated using historical data or a fully-integrated financial-statements model, there is a problem. The tax paid figure will be levered (i.e. post-interest). The tax figure will be too low as it will have been calculated after deducting interest expenses. This would give too high a FCFE and would result in an over-valuation of the enterprise. This must, therefore, be adjusted for the interest tax shield. By multiplying the interest expense by the tax rate we can calculate the interest tax shield. This amount must then be deducted in arriving at FCFE, to remove the

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4 • Discounted Cash Flow (DCF) fundamentals

benefit of the tax-deductibility of the interest, reduce the FCFE and correctly lower the enterprise value of the business. Illustration – interest tax shield EBITA

500

Interest expense

(100)

EBT

400

Tax expense (30%)

(120)

Net income

280

Levered tax expense

120

Interest tax shield (100 x 30%)

30

Unlevered tax expense

150 Both methods arrive at the same answer for tax paid

Tax on EBITA (500 x 30%)

150

The following shows the overall FCFE calculation: Illustration – FCFE calculation EBITA

1,000

Depreciation EBITDA Capex

200 Tax is based on EBITA

Capex is greater than depreciation

Working capital investment Tax paid (30%) Free cash flow to the enterprise

Forecasting FCFE There are seven macro-level drivers of FCFE valuations. They are: 1. Revenue growth 2. Operating margins 3. Capex investment rate 4. Working capital investment / release rate 5. Cash tax rate

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1,200 (350) (50) (300) 500

4 • Discounted Cash Flow (DCF) fundamentals

6. WACC 7. Terminal growth rate. The first five of these relate directly to the forecasting of FCFE and are dealt with here. The final two are considered later.

Key drivers of FCFE A proper understanding of these first five drivers is essential in creating credible forecasts of FCFE: 1. Revenue growth Revenue growth is the single most important driver in the FCFE model. For a thorough valuation, it may be necessary to perform a full bottom-up forecast of future expected revenues, broken down, for example, by product / service lines and geographical locations. For a more “quick and dirty” valuation, top level growth percentages will suffice. While relatively high growth rates might persist for some years, they would be expected to decline over time, ultimately towards the long-term sector / GDP growth rate. It will also be necessary to take into account the target company’s strategy and any cyclicality in its sector. Long term sector / GDP growth rate

Year-on-year revenue growth

% Revenues

X

% X

% X

...

X

2. Operating margins Starting the FCFE calculation with EBITA, means the focus is on EBITA margins. Again, this analysis could be broken down further into, for example, labour and materials costs as a percentage of revenues. We use EBITA as a short rather then EBITDA as it is useful to have depreciation as a separate line item. Generally, the expectation is that these margins will be eroded over time, to a sector average. However, if a business has a strategy of selling more highermargin products / services in the future, its margins could actually improve.

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4 • Discounted Cash Flow (DCF) fundamentals

Revenues

X

X

X

...

X

EBITA margin

% EBITA

% X

% X

... X

Sector average margins

%

...

X

3. Capex investment rate Capex can be forecast in a number of ways, but most of them tend to relate back to revenues. The argument being, very simply, that the more products / services a business wants to sell, the higher the investment in assets. For example, depreciation could be forecast as a percentage of revenues and capex could then be forecast as a multiple of depreciation. This multiple would be expected to tend towards one over time, as revenue growth declines and capex becomes more about maintenance and less about expansion. This is very much an overview short cut. A more comprehensive model would have a number of separately calculated capex and depreciation sheets. Revenues

X

X

X

...

X

Depreciation / revenues

% Depreciation Capex / depreciation

Capex

%

X x

%

X x

X

...

X x

X

... ...

X

%

...

X Should tend towards 1.0x

x

X

4. Working capital investment / release rate As revenues grow, for most businesses, more cash will become tied up in working capital. This extra investment requirement is related to the increase in revenues from one year to the next. As such, the working capital investment will often be forecast based on a percentage of the increase in revenues from the current year to the following year. Again, this might be expected to tend to a sector average over time.

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4 • Discounted Cash Flow (DCF) fundamentals

In a fully-integrated financial-statements model, inventories, receivables and payables could all be forecast separately, based, for instance, on days ratios. r Revenues

r

X

X

%

%

X

X

r X

...

X

...

%

...

X

X

WC investment / CY-PY revenues

Working capital investment

X

Should tend to sector average

5. Cash tax rate The main choices are an effective tax rate (calculated from the published financial data) or the country tax rate. If these two are different (for example, if the effective rate is lower than the country rate), it should be considered why this is the case and whether the difference is sustainable. If the difference is due to creative tax planning / structuring it may be more sustainable. If it is due to tax losses brought forward, it would be expected that these losses would be used up over time. These net operating losses could be extracted and valued separately. There is no consensus on the appropriate discount rate for net operating losses (NOLs) but most commonly they would be discounted at the pre tax cost of debt as they are unlikely to fluctuate with earnings. In any case, a short-term low effective tax rate would not normally be expected to persist into the long term. It is most likely that the effective rate would tend towards the country rate. EBITA

X %

Tax paid

X %

X

X %

X

... ...

X

...

X Should tend to country rate

%

X

Length of the FCFE forecast period The final question to answer with regards to the FCFE is how long to forecast. Theoretically, the FCFE should be forecast explicitly for as long

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4 • Discounted Cash Flow (DCF) fundamentals

as the enterprise in question enjoys a competitive advantage and until it achieves a steady state of growth, at which point there is no longer any reason to forecast year-on-year individually. Revenues Competitive advantage

Steady state

Time 0

n



TERMINOLOGY

Explicit Visible

Forecast period / horizon

Terminal period

Discreet

However, the longer the explicit forecast, the less reliable those forecasts become. So, in practice, it is acceptable to default to a standard ten-year explicit forecast horizon. This length of time should be long enough to see the evolution of the firm, as well as enough time to trend the forecasts towards a more steady state of growth.

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Standard approach Revenues

10 year explicit forecast horizon

Terminal period

Time 0

10



To save time, it is possible to shorten the ten-year period to a five-year period. However, this poses a problem. One of the weaknesses of the FCFE model is that, commonly, the lion’s share of the enterprise value is derived from the terminal period, where the cash flows have not been forecast explicitly – they are invisible. This, therefore, raises the question of where the value is coming from. Shortening the explicit forecast horizon to five years is likely to exacerbate this problem, giving an even more disproportionate split between the present value of the visible cash flows and the present value of the terminal value. It is also less likely that the firm being valued will have achieved a steady state of growth.

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4 • Discounted Cash Flow (DCF) fundamentals

Alternative approach Revenues

Shorter visible period

Longer terminal period

Time 0

5

10



Some sectors, such as utilities and infrastructure, tend to use much longer forecast periods.

Weighted Average Cost of Capital As stated earlier, since the calculation is an enterprise value, the FCFE must be discounted at the weighted average cost of capital (WACC). To calculate the WACC, there are three elements required: 1. Cost of debt (Kd) 2. Cost of equity (Ke) 3. Weighting to blend Kd and Ke into a WACC. Cost of debt (Kd)

Cost of equity (Ke)

Weighting WACC

An issue dealt with later is whether to use year-end or mid-year discounting.

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Cost of debt The cost of debt is the return required by the debt finance providers of the business, i.e. the rate of interest that they will charge on the capital they lend. There are two main approaches to calculating the cost of debt: 1. Empirical 2. Synthetic. Calculating the cost of debt

Empirical approach

Synthetic approach

Empirical approach The empirical approach is only really possible if the business being valued has quoted debt instruments. In these circumstances, the yield on these quoted bonds can be observed. Assuming the bond market is reasonably efficient, this yield should be a fair approximation of the cost of debt of the business. It is important to remember that this yield is the required return of the bondholders of the business. It is, therefore, the pre-tax cost of debt of the business. Since FCFE is after tax, this yield must be converted into post-tax cost of debt. Post-tax Kd = Yield on quoted bond x (1− t) t = Tax rate

This is also essential as the FCFE has been calculated using unlevered tax figures and so does not reflect the benefit to the business of the taxdeductibility of the interest on its debt finance. This benefit is built into the valuation through the use of the post-tax cost of debt.

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Synthetic approach The synthetic approach involves constructing a post-tax cost of debt using the following three elements: 1. Risk-free rate of return 2. Credit risk premium 3. Interest tax shield. The formula takes the following form: Post-tax Kd = (Rf + CRP) x (1− t) Rf = Risk-free rate of return CRP = Credit risk premium t = Tax rate (marginal − see later)

Risk-free rate of return In a mature economy, such as the UK, the return on government debt is the best proxy for the risk-free rate of return. However, there will usually be numerous government bonds in issue at any point in time, so it is necessary to decide which one to use. The cost of debt, and the WACC, is going to be applied to all of the future cash flows of the business, i.e. both those from the explicit forecast horizon and those from the terminal period. The cost of capital, therefore, has to apply from time zero to infinity. This would suggest using the yield on perpetual / longer-dated (thirty to fifty years) gilts as the risk-free return. However, there may be no / few such gilts in issue. If this is the case, a thin market for the bonds will give an unreliable proxy for the risk-free rate of return. Therefore, the standard approach is to use the yield on a benchmark, midcoupon, ten-year gilt. This will normally be one of the more liquid gilts and should, therefore, give a more reliable proxy for the risk-free rate of return.

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UK GILTS – cash market Feb 14 Price (£) Tr 5pc ‘08 99.99 Tr 4pc ‘09 99.66 Tr 4.75pc ‘10 101.10 Cn 9pc Ln ‘11 114.65 Tr 5pc ‘12 102.58 Tr 8pc ‘13 117.23 Tr 5pc ‘14 102.79 Tr 4.75pc ‘15 101.14 Tr 4pc ‘16 95.80 Tr 4.75pc ‘20 100.78 Tr 8pc ‘21 132.01 Tr 5pc ‘25 103.91 Tr 6pc ‘28 117.39 Tr 4.25pc ‘32 94.92 Tr 4.25pc ‘36 95.33 Tr 4.75pc ‘38 103.64 Tr 4.25pc ‘55 96.91 War Ln 3.5pc 76.09

Bid yield 5.12 4.33 4.24 4.33 4.30 4.49 4.50 4.57 4.60 4.66 4.73 4.67 4.68 4.60 4.55 4.53 4.41 4.60

... Change in yield ... Day Week Month +0.01 +0.04 -0.06 -0.01 +0.23 -0.02 -0.01 +0.19 -0.01 -0.02 +0.19 +0.01 -0.01 +0.20 +0.05 +0.01 +0.18 +0.12 +0.01 +0.19 +0.14 +0.02 +0.20 +0.19 +0.01 +0.20 +0.20 +0.02 +0.20 +0.22 +0.02 +0.20 +0.22 +0.03 +0.20 +0.25 +0.03 +0.20 +0.25 +0.03 +0.20 +0.25 +0.03 +0.19 +0.24 +0.03 +0.18 +0.23 +0.03 +0.16 +0.18 +0.03 +0.18 +0.24

Year -0.30 -1.06 -1.09 -0.94 -0.90 -0.63 -0.57 -0.44 -0.35 -0.16 -0.11 -0.02 +0.09 +0.14 +0.16 +0.18 +0.28 +0.16

... 52 week ... Amount High Low £m 100.01 99.49 14,928 99.89 97.05 16,974 101.53 97.05 12,774 115.39 111.14 5,664 103.34 96.93 14,009 118.43 111.64 6,489 103.96 95.99 13,699 102.74 94.37 13,647 97.53 89.02 13,500 103.26 93.94 10,743 135.33 124.86 17,573 107.52 97.34 16,188 121.92 111.19 12,340 99.33 89.59 17,326 100.52 90.20 15,668 109.78 98.49 14,958 105.49 93.37 11,602 81.89 71.23 1,939

Source: www.ft.com 15/02/08 Note: These are the two closest gilts listed to the benchmark ten-year period

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4 • Discounted Cash Flow (DCF) fundamentals

Benchmark government bonds Feb 14 Australia Austria Belgium Canada Denmark Finland France

Germany

Greece Ireland Italy

Japan

Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK

US

Red date 09/09 02/17 01/10 03/19 03/10 03/18 12/09 06/17 11/09 11/17 04/09 09/17 01/10 01/13 10/17 04/35 12/09 10/12 01/18 01/37 03/11 07/17 04/09 10/18 06/09 10/12 02/18 02/37 03/10 03/13 12/17 12/27 01/10 07/17 07/09 12/17 05/13 05/17 07/09 10/17 07/09 01/17 12/09 08/17 11/09 01/18 03/09 06/12 08/17 03/36 01/10 01/13 02/18 02/38

Coupon 7.50 6.00 5.50 4.35 3.00 4.00 4.25 4.00 6.00 4.00 5.00 3.88 3.00 3.75 4.25 4.75 4.00 4.25 4.00 4.00 3.80 4.30 3.25 4.50 3.75 4.25 4.50 4.00 1.80 0.80 1.50 2.10 3.00 4.50 7.00 6.00 6.50 4.25 3.95 4.35 5.15 3.80 4.00 3.75 1.75 3.00 4.00 5.25 8.75 4.25 2.13 2.88 3.50 4.38

Source: www.ft.com 15/02/08 Note: This is the benchmark ten-year gilt

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Bid price 100.8550 97.7630 103.9410 101.0300 99.3200 97.8300 102.0540 100.7800 103.9750 99.0350 101.6900 98.1360 99.4400 100.5800 100.8800 101.7800 101.3800 103.0700 99.8500 91.6100 100.3600 99.2690 99.6370 102.1610 100.3500 102.0000 101.1280 86.0100 102.4920 99.2730 100.3000 99.9300 99.4400 103.0220 99.5200 96.8200 109.7400 98.5000 100.5660 100.3780 102.3630 97.4800 100.3360 97.1550 99.4700 101.0900 99.6450 103.4400 130.8500 95.2000 100.4297 100.4609 97.3125 95.4688

Bid Day chg yield yield 6.91 +0.08 6.33 +0.07 3.33 +0.07 4.23 +0.04 3.34 +0.06 4.27 +0.04 3.05 -0.03 3.90 +0.04 3.58 +0.07 4.12 +0.06 3.50 +0.07 4.11 +0.04 3.31 +0.06 3.62 +0.09 4.14 +0.05 4.63 +0.02 3.20 +0.05 3.52 +0.07 4.02 +0.04 4.53 +0.02 3.67 +0.07 4.39 +0.05 3.57 +0.06 4.24 +0.05 3.50 +0.04 3.81 +0.06 4.41 +0.05 4.97 +0.01 0.59 +0.01 0.95 +0.03 1.47 +0.04 2.11 +0.03 3.31 +0.06 4.10 +0.04 7.36 +0.04 6.44 +0.03 4.37 +0.05 4.45 +0.04 3.52 +0.06 4.30 +0.06 3.43 +0.09 4.14 +0.03 3.79 +0.06 4.12 +0.10 2.07 +0.03 2.87 +0.03 4.35 -0.01 4.36 -0.01 4.70 +0.02 4.56 +0.03 1.90 -0.01 2.77 +0.07 3.83 +0.12 4.66 +0.14

Wk chg yield +0.23 +0.15 +0.08 +0.12 +0.06 +0.13 -0.03 +0.05 +0.10 +0.12 +0.10 +0.16 +0.07 +0.15 +0.11 +0.10 +0.08 +0.20 +0.12 +0.09 +0.15 +0.09 +0.13 +0.13 +0.10 +0.17 +0.14 +0.08 – +0.03 +0.04 +0.04 +0.10 +0.09 +0.06 +0.04 +0.15 +0.12 +0.12 +0.14 +0.08 +0.12 +0.33 +0.21 +0.12 +0.10 +0.24 +0.19 +0.22 +0.19 -0.10 -0.01 +0.10 +0.16

Month Year chg yld chg yld +0.35 +0.77 +0.31 +0.54 -0.27 -0.65 +0.09 +0.10 -0.48 -0.65 +0.12 +0.11 -0.21 -1.05 +0.12 -0.24 -0.21 -0.49 +0.04 +0.03 -0.30 -0.44 +0.07 -0.02 -0.32 -0.68 -0.07 -0.43 +0.08 – +0.13 +0.37 -0.29 -0.76 -0.10 -0.50 +0.07 -0.08 +0.10 +0.31 -0.05 -0.39 +0.08 +0.04 -0.22 -0.52 +0.08 -0.09 -0.24 -0.51 -0.07 -0.31 +0.09 +0.09 +0.13 +0.41 -0.01 -0.19 +0.06 -0.31 +0.03 -0.27 +0.07 -0.07 -0.26 -0.66 +0.06 -0.02 +0.05 +0.74 +0.13 +0.40 -0.16 -0.25 -0.17 -0.12 -0.21 -0.50 +0.08 +0.06 -0.28 -0.43 +0.04 -0.02 +0.02 +0.02 +0.06 +0.15 +0.11 -0.44 +0.01 +0.25 – -1.17 +0.06 -0.91 +0.25 -0.26 +0.24 +0.17 -0.54 -2.97 -0.13 -1.95 +0.19 -0.90 +0.40 -0.17

4 • Discounted Cash Flow (DCF) fundamentals

World markets Interest rates US Gov 10 yr UK Gov 10 yr Ger Gov 10 yr Jap Gov 10 yr US Gov 30 yr Ger Gov 2 yr

Price 97.31 130.85 99.85 100.30 95.47 101.38

Yield 3.83 4.70 4.02 1.47 4.66 3.20

Chg +0.12 +0.02 +0.04 +0.04 +0.14 +0.05

Source: www.ft.com 15/02/08 Note: The yield on this benchmark ten-year gilt is shown on the front page of the Financial Times

Note: See bonds section in Financial markets and products for investment bankers page 28 onwards

Credit risk premium The credit risk premium represents the additional return, over and above the risk-free rate of return, required by the debt-holders of the business. This is due to the fact that the business is more likely to default on its debt than the government, and so the debt-holders expect this extra reward. If the business being valued has a credit rating, then the credit risk premium will be based on this rating. The worse the credit rating, the riskier the borrower and the higher will be the credit risk premium. Business risk / financial risk Financial risk profile Business risk profile

Minimal

Modest

Intermediate

Aggressive

Highly leveraged

Excellent

AAA

AA

A

BBB

BB

Strong

AA

A

A-

BBB-

BB-

Satisfactory

A

BBB+

BBB

BB+

B+

Weak

BBB

BBB-

BB+

BB-

B

Vulnerable

BB

B+

B+

B

B-

Source: S&P’s Corporate Ratings Criteria, 2006

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4 • Discounted Cash Flow (DCF) fundamentals

Global investment grade Red date Coupon

Feb 14 £ HBOS Network Rail Boots France Telecom Vodafone

04/08 03/09 05/09 03/11 11/32

Ratings S&P Moody’s Fitch

6.38 AA 4.88 AAA 5.50 – 7.50 A5.90 A-

Aa1 Aaa B2 A3 –

Bid Bid price yield

Day’s Mth’s Spread chge chge vs. yield yield Govts

AA+ 99.89 6.90 -0.13 AAA 100.14 4.68 -0.01 BBB 94.17 10.33 -0.02 – 104.65 5.82 -0.01 – 90.11 6.62 +0.17

+1.08 +0.03 +1.62 +0.16 +0.56

+2.68 +0.31 +6.00 +1.57 +2.09

Source: www.ft.com 15/02/08 Note: The table clearly shows the lower the credit rating, the higher the credit risk premium over and above the risk-free rate

If the business being valued does not have a credit rating then it is necessary to create a synthetic rating. This will involve performing a credit analysis on the financials of the business. The worse the credit metrics, the higher the synthetic rating and the higher will be the credit risk premium. Key industrial financial ratios, long-term debt Three-year (2002 to 2004) medians EBIT interest coverage (x) EBITDA interest coverage (x)

AAA

AA

A

BBB

BB

B

CCC

23.8

19.5

8.0

4.7

2.5

1.2

0.4 0.9

25.5

24.6

10.2

6.5

3.5

1.9

FFO / total debt (%)

203.3

79.9

48.0

35.9

22.4

11.5

5.0

Free operating cash flow / total debt (%)

127.6

44.5

25.0

17.3

8.3

2.8

(2.1)

Total debt / EBITDA (x)

0.4

0.9

1.6

2.2

3.5

5.3

7.9

Return on capital (%)

27.6

27.0

17.5

13.4

11.3

8.7

3.2

Total debt / total debt + equity (%)

12.4

28.3

37.5

42.5

53.7

75.9

113.5

Source: S&P’s Corporate Ratings Criteria, 2006

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Key ratios Higher-growth period 1. EBIT interest coverage

Earnings from continuing operations* before interest and taxes / gross interest incurred before subtracting capitalized interest and interest income

2. EBITDA interest coverage

Adjusted earnings from continuing operations** before interest, taxes, depreciation, and amortization / gross interest incurred before subtracting capitalized interest and interest income

3. Funds from operations (FFO) / total debt

Net income from continuing operations, depreciation and amortization, deferred income taxes, and other non-cash items / long-term debt§ + current maturities + commercial paper, and other short-term borrowings

4. Free operating cash flow / total debt

FFO – capital expenditures – (+) increase (decrease) in working capital (excluding changes in cash, marketable securities, and short-term debt) / long-term debt§ + current maturities, commercial paper, and other short-term borrowings

5. Total debt / Total debt + equity

Long-term debt§ + current maturities, commercial paper, and other short-term borrowings / long-term debt§ + current maturities, commercial paper, and other short-term borrowings + shareholders’ equity (including preferred stock) + minority interest

6. Return on capital

EBIT / average of beginning of year and end of year capital, including short-term debt, current maturities, long-term debt§, non-current deferred taxes, minority interest, and equity (common and preferred stock)

7. Total debt / EBITDA

Long-term debt§ + current maturities, commercial paper, and other short-term borrowings / adjusted earnings from continuing operations before interest, taxes, and D&A

* Including interest income and equity earnings; excluding nonrecurring items ** Excludes interest income, equity earnings, and non-recurring items; also excludes rental expense that exceeds the interest component of capitalised operating leases § Including amounts for operating lease debt equivalent, and debt associated with accounts receivable sales / securitisation programs.

Source: S&P’s Corporate Ratings Criteria, 2006

Much of this data can often be sourced from colleagues in the Debt Advisory team and the results of such analysis should be sanity-checked with them.

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4 • Discounted Cash Flow (DCF) fundamentals

Interest tax shield The pre-tax cost of debt of the business is calculated by adding the credit risk premium onto the risk-free rate of return. This must be converted from pre-tax into a post-tax cost of debt. The premium can be calculated over either the ten year government bond or the swap rate (obviously the premium will be different depending on the rate used). Pre-tax Kd = Rf + CRP

:

. Post-tax Kd = Pre-tax Kd x (1 – t)

This raises the question of the tax rate to use for this conversion. As discussed earlier, the cost of capital has to apply to the entire forecast period, from time zero to infinity. When discussing how to drive the FCFE forecasts forwards, it was stated that the tax rate was likely to tend towards the country rate over time. This is, therefore, the tax rate that is likely to persist over the majority of the forecast period and so is probably the most appropriate for the post-tax cost of debt calculation. This is an important point, as in many FCFE valuations a short-term effective tax rate, which is unlikely to persist over the longer-term, is mistakenly used. Illustration − Kd for Tesco Kd = (Rf + CRP) x (1– t) = (5.11% + 1.08%) x (1– 30%) = 4.33% Source: ABN AMRO, European Beta Book, 30 June 2006

Cost of equity The cost of equity (Ke) represents the return required by the providers of equity finance to the business. This should reflect all of the returns the equity-holders expect from the business, both in the form of income (i.e. regular dividends) and growth (i.e. capital gains), as well as any returns from special dividends and share buybacks.

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Returns required by equity-holders

Income Income

Growth

Dividends

Capital gains Special dividends & share buybacks

The Capital Asset Pricing Model (CAPM) is the method that the vast majority of valuations use to calculate the cost of equity. It is, therefore, worth remembering that the CAPM’s origins lie in Modern Portfolio Theory and the world of asset management, rather than in the fields of Investment Banking and equity research. As such, the model is built on the assumption that investors are well diversified, e.g. institutional investors, which may or may not be the case in the context of the valuations. There are alternative models, namely Arbitrage Pricing Theory (APT) and Multi-Factor Models (MFM), but these are used much less commonly. Here, the focus is on the CAPM, which is used in the Rothschild standard DCF models.

The Capital Asset Pricing Model The CAPM has three elements: 1. Risk-free rate of return 2. Equity market risk premium 3. Beta factor. The formula for the CAPM takes the following form:

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4 • Discounted Cash Flow (DCF) fundamentals

Ke = Rf + EMRP x ß Ke = Cost of equity Rf = Risk free rate of return EMRP = Equity market risk premium β = Beta factor

Applying this to a real example: Illustration − Ke for Tesco Ke = Rf + EMRP + β = 5.11% + 4.00% x 0.69 = 7.87% Source: ABN AMRO, European Beta Book, 30 June 2006

Risk-free rate of return The risk-free rate of return is one of the elements of the synthetic post-tax cost of debt. Therefore, for the sake of consistency, the same figure should be used when calculating the cost of equity. (See the discussion above with regards to the choice of an appropriate risk-free rate of return).

Equity Market Risk Premium The CAPM assumes that we are dealing with rational, risk-averse investors. Therefore, the higher the risk the investors take on, the higher the return they will require. The risk-free rate only gives investors a return commensurate with lending money to the government. However, the investors are investing in the equity of a business. This is a significantly more risky proposition and so the equityholders require a higher rate of return. The equity market risk premium (EMRP) reflects the incremental return, over and above the risk-free rate of return, which the equity-holders will require from their investment. The EMRP is usually based on historical data. This raises a number of questions:

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4 • Discounted Cash Flow (DCF) fundamentals

Returns

2. Equities

4. EMRP – average

1. Gilts

Time 3. Period

1. Risk-free rate of return How should the risk-free rate of return be measured over a relatively long period of time? If at any particular point in time, as suggested above, the return on a benchmark, ten-year, mid-coupon gilt is used, the relevant product will change over time. This will complicate the measurement of the return. 2. Equity market return Which equity market’s returns should be measured? If, for example, a business such as Tesco is being valued, is it more appropriate to use the FTSE 100 or the FTSE All-Share? A common alternative is to use to a global benchmark such as the Morgan Stanley composite index. However, the two choices will lead to different answers for the EMRP. 3. Period measured Over what period should the EMRP be measured? Different service providers, such as Ibbotson Associates and the London Business School Risk Measurement Service, measure the EMRP over various periods. Again, there is no single best answer to this question but, as with any economic metric, different periods can lead to very different answers. 4. Calculation of the average As well as considering when and how often the EMRP should be measured during the period, how should the average over that period be calculated? An arithmetic or a geometric mean could be used. Academics continue to

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4 • Discounted Cash Flow (DCF) fundamentals

argue over the relative merits of these two options. As always, they give different answers. Rothschild’s view is that geometric average must be used. Cumulative returns on UK asset classes in nominal terms, 1900-2005 Index value (start-1900 = 1.0; log scale) 100,000

Equities

9.7% per year

10,000

Bonds Bills Inflation

5.4% per year 5.0% per year 4.0% per year

18,187

1,000 100

267 184 62

10 1 0 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2006 Source: ABN AMRO, Global Investment Returns Yearbook, 2006

The available data seems to suggest an average EMRP in the range of 4% to 6%. It is not uncommon to use the mid-point of this range (i.e. 5%) in DCF valuations. This still begs the question of whether this past premium will continue into the future.

Beta factor The beta factor represents the fact that some businesses are more exposed than others to the risks inherent in the market. The beta factor acts as an adjustment to the EMRP, to reflect this difference in risk and so to give a different level of return. For example, if a business is twice as exposed as average to the inherent market risks, it will have a beta factor of two and investors will have a required return which incorporates twice the normal EMRP. It is important, here, to remember that the CAPM stems from Modern Portfolio Theory. As it assumes that equity investors are well diversified, the CAPM only rewards them for the systematic, or non-diversifiable, risk in their investments.

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Risk Not rewarded

Rewarded

Unsystematic Diversifiable Unique

Systematic Non-diversifiable Market

0

Diversification

This residual, systematic risk reflects the fact that, no matter how well diversified the investor, there is still uncertainty in investing in equity markets. The value of these markets can still rise or fall due to macro-economic factors, such as changes in interest rates. The beta factor measures how much a particular investment is affected by these macro-economic factors. Some investments are more affected than others. For example, the value of a highly leveraged business will be more affected by changes in interest rates than a business with little or no debt.

Calculating the beta factor The beta factor is usually calculated using historical data. This involves measuring the return on the equity investment in question versus the return of the equity market to which it belongs. As always, this raises a number of questions: 1. Equity market Which equity market should we use? As with the EMRP, if a business such as Tesco is being valued, is it more appropriate to use the FTSE 100 or the FTSE All-Share? There is not necessarily a correct answer to this question. However, the two choices will lead to different answers for the beta factor. 2. Period measured and frequency of measurements Over what period and how often should the returns on the investment and the returns on the market be measured? For example, a two-year, weekly approach was used, it would be based on just over one hundred observations.

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4 • Discounted Cash Flow (DCF) fundamentals

Alternatively, a five-year, monthly approach would give sixty observations, and could provide a very different result. Once obtained, these observations are then plotted on a graph and a linear regression performed to obtain a line of best fit: Ri Line of best fit

β Rm

Rm = Return on market Ri = Return on investment β = Beta factor

The gradient of this line of best fit is the beta factor. This can also be expressed as follows: ß=

im m2

σim = Covariance of the investment returns with respect to the market returns σm 2 = Variance of the market returns

It is worth noting that the co-efficient of determination (R-squared) of this relationship, which measures to what extent the beta factor is really due to the market risk of the investment, can be quite low, suggesting a relatively weak relationship. The result of the regression can be interpreted as follows: β > 1: The investment is more exposed to systematic risk than the market in general β = 1: The market itself has a beta factor of 1, so the investment has the same systematic risk as the market β < 1: The investment is less exposed to systematic risk than the market in general

This Bloomberg download shows the calculation process and the results of the regression process:

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The Bloomberg page offers two possible answers: 1. Raw beta 2. Adjusted beta. The relationship between the two is this:

§A = §R x 2 + 1 x 1 3

3

βA = Adjusted beta βR = Raw beta

The adjustment (often referred to as the Blume adjustment) gives a weighting of two-thirds to the observed beta and one-third to the market beta of one. The effect of this adjustment is to push all raw betas towards unity. There is much academic debate on this subject, analysis can be found in the LBS RMS quarterly report or on the Ibbotson website. Illustration − adjusted betas Raw

Adjusted

0.8 0.87 1

1 1.13 1.2

The argument for this is that as the business grows it will become more diversified and will more closely resemble the market in general. Therefore, its beta factor is expected to tend towards the market beta factor of one. In general, it is recommended to use adjusted betas. Although different sectors at Rothschild have different views: • Telecoms / Utilities: unadjusted • M&A team: adjusted The following extract shows some of the problems inherent in calculating beta factors:

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4 • Discounted Cash Flow (DCF) fundamentals

“Ideally risk measures are forward looking. In the case of beta, investors must rely on historical data over, say, the last five years. That is the problem; until recently, this period included the internet bubble, when the volatile and overvalued telecommunications, media and technology sectors comprised up to half of the S&P 500. Since the market as a whole must have a beta of one, the betas of other sectors slumped. McKinsey reckons that US food stocks’ observed beta reached zero, ridiculously implying that they had the same risk as Treasuries.” Source: www.ft.com 04/09/06 Lex article “Equity beta “

The following is another Bloomberg download of a beta factor for British Airways. This time, five-year, monthly observations have been taken, rather than three-year, weekly. The beta factor thus derived is quite different from the previous download. Use global index to calculate your beta from Bloomberg N.B. this is a pitfall as bloomberg default setting is local. Do not use Barra betas (methodology is not transparent).

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Published vs. synthetic beta factors The published beta factors seen above were based on historical data. These beta factors are driven by two elements: 1. Business risk 2. Financial risk. The business risk reflects factors such as the level of operational leverage (fixed costs versus variable costs); whether the business produces necessities or luxuries; whether the business’s customers are public sector or private sector; how highly regulated the sector is; among other factors. The other key element is the financial risk, or leverage. If the target capital structure that is used for the WACC calculation (see below) is different to the existing capital structure (i.e. the capital structure for the period over which the published beta factor was calculated), then the published beta factor may not be relevant for the valuation. It is necessary to adjust the beta factor to take into account the target capital structure. This can be done in two stages: 1. De-lever the published beta factor to remove the effect of the existing financial leverage. This gives us an unlevered, or asset, beta factor. Stage 1 – de-levering the beta factor βu =

βL

⎡1 + (1 – T) ⎣

⎛ D ⎛⎡ ⎝ E ⎝⎣

Existing capital structure N.B. market values

e.g. βu =

0.8

⎡1 + (1 – 0.3) ⎛ 30 ⎛⎡ ⎝ 70 ⎝⎣ ⎣

= 0.62 βu = Unlevered beta factor βL = Levered beta factor t = Tax rate N.B. The above assumes the beta of debt is zero

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4 • Discounted Cash Flow (DCF) fundamentals

2. Re-lever this asset beta to incorporate the target capital structure. This gives us a levered, or equity, beta factor. Stage 2 – re-levering the beta factor

⎡ ⎣

βL = βu x 1 + (1 – T)

⎛ D ⎛⎡ ⎝ E ⎝⎣

Target capital structure

e.g.

⎡ ⎣

40 ⎛ ⎡ ⎝ 60 ⎝ ⎣

βL = 0.62 x 1 + (1 – 0.3) ⎛ = 0.9

βu = Unlevered beta factor βL = Levered beta factor t = Tax rate N.B. The above assumes the beta of debt is zero

A similar approach can be taken when valuing private companies, which do not have published beta factors. A universe of comparable listed companies can be selected, their published beta factors de-levered for their existing capital structure and re-levered for the private company’s target capital structure, and an average then taken. The version illustrated above is a slight simplification, as it assumes that the debt finance of the business has a beta factor of zero. This is consistent with the approach seen in many textbooks (e.g. Damodaran, Fernandez and others). See the “Advanced DCF Valuation” chapter of this manual for a fuller discussion of this process. The following should clarify the alternative terminology used for beta factors: Terminology Levered

Unlevered

Geared

Ungeared

Equity

Asset

Dividend

Earnings

Published



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Weighting Once a cost of debt and a cost of equity are established, they must be blended together to produce a weighted average cost of capital. The key question that arises is the proportions of debt and equity funding to be used for this process. The following options are available: 1. Current book values of debt and equity 2. Current market values of debt and equity 3. Target book values of debt and equity 4. Target market values of debt and equity 5. Optimal capital structure. The merits of each of these will be addressed in turn: 1. Current book values of debt and equity The advantage of using the current book values of debt and equity is that they are known numbers, in that they can be found in the balance sheet of the business to be valued. However, the disadvantage of this is that it shows the existing position, rather than being forward-looking. Also, the balance sheet numbers are affected by differences in generally accepted accounting principles (GAAP). For example, under IFRS, convertible bonds are split into the debt portion, which is presented as a liability, and the equity portion, which is presented within equity. Under US GAAP, the full amount is shown as a liability (see “Accounting and analysis for investment bankers”, for further detail). Different GAAP could lead to different weighting proportions being used in the WACC calculation, even though there is no underlying difference in the economic reality. Therefore, trading values must be used. 2. Current market values of debt and equity Using market values of debt and equity avoids the accounting issues discussed above. However, this option presents other problems: • Market values of debt and equity will only be available for listed businesses • When they are available, they still show a current rather than a forwardlooking position

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4 • Discounted Cash Flow (DCF) fundamentals

• Market values suffer from volatility, which then leads to the issue of whether an average should be used. If so, what sort of average and over what period (again, historical rather than forecast)? For these reasons, the current market values of debt and equity are often best avoided as well. 3. Target book values of debt and equity If a forward-looking target capital structure is to be used it makes sense to think of this in market value terms (debt and equity as proportions of total enterprise value), rather than accounting, or book values. 4. Target market values of debt and equity Using target market values of debt and equity is possible if the existing management has announced such a target or if a prospective management team envisages a particular capital structure. This is the preferred approach. If no such announcement has been made or there is no clear preference, defaulting to the sector average capital structure can provide the solution. A key driver of how much a business can gear up is its ability to generate cash. Since it is reasonable to expect businesses in the same sector to have similar cash-generative characteristics, their levels of leverage will converge over time. Therefore, even if the business being valued does not currently share the sector average capital structure, it should tend towards this position in the long run. 5. Optimal capital structure The use of an optimal capital structure has several advantages over the use of book or market values of debt and equity: • It is forward looking • It is not affected by accounting judgements • It is not affected by market volatility. However, although theories regarding the optimal capital structure do exist (e.g. those of Modigliani and Miller), calculating it in practice often proves difficult and the situation can still change over time. Also, there is no certainty that the business will follow this financial strategy. For these reasons, the use of the optimal capital structure is also problematic.

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Book value

Market value

Current





Target





Optimal

Problematic

Calculating the Weighted Average Cost of Capital Once the cost of debt, the cost of equity and the weighting have been decided, the WACC can be calculated as follows: D + Ke x E D+E D+E

WACC = Kd x

D = Proportion of finance sourced from debt D+E E = Proportion of finance sourced from equity D+E

Let’s apply this to a real example: Illustration − WACC calculation for Tesco WACC = Kd x

D + Ke x E D+E D+E

= 4.33% x 0.25 + 7.87% x 0.75 = 6.99%

• An important aspect of the WACC analysis is also to benchmark the result against industry averages (from the companies themselves or brokers consensus)

Year-end vs. mid-year discounting Now the discount rate is established, it is necessary to consider whether it should be applied to the cash flows as at each year end or as at the mid-point of each year. Unfortunately, there is no right answer to this issue.

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Valuation is always going to involve a simplification of reality. This issue is just another example of that. It is simply necessary to decide when the cash flows for year one, for example, arise. If the total cash flow for the year is not likely to be available until the end of the year, year-end discounting should be used. Illustration − year-end discounting 0

1

2

3

...

n



X

X

X

...

X

X

The relevant discount factors will take the following form: Illustration − year-end discount factors 0

1

2

3

...

n



1 (1 + WACC) 1

1 (1 + WACC) 2

1 (1 + WACC) 3

...

1 (1 + WACC) n

If the cash flows for the year accrue evenly over the course of the year and therefore on average accrue half-way through the year, mid-year discounting should be used. Illustration − mid-year discounting 0



0.5

X

1

1.5

X

2

2.5

X

3

... n – 1

...

n

X

X

The relevant discount factors will take the following form:

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Illustration − mid year discount factors 0



0.5

1

1.5

2

2.5

3

... n – 1 n – 0.5 ...

1 1 1 (1 + WACC) 0.5 (1 + WACC) 1.5 (1 + WACC) 2.5

n

1 (1 + WACC) n – 0.5

Using year-end discounting will give a lower enterprise value, as all of the future cash flows are being discounted half a year more. Conversely, using mid-year discounting will give a higher enterprise value, since all of the future cash flows are discounted half a year less. It is possible to switch between the two approaches, depending on the circumstances of the valuation. However, in the prevailing regulatory environment, following a consistent approach to this issue is probably the wisest course of action.

Terminal value If the standard ten-year explicit forecast horizon is used, it is still necessary to place a value on all of the FCFE that will be generated by the business from time ten onwards, i.e. the terminal value. FCFE

Explicit forecast horizon

0

Terminal value

10



Time

There are two common methods of calculating this terminal value: 1. Perpetuity growth method 2. Terminal multiple method.

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4 • Discounted Cash Flow (DCF) fundamentals

Terminal value calculations

Perpetuity growth method

Terminal multiple method

The perpetuity growth method might be considered the preferred option, as it continues the use of the DCF methodology in the FCFE model. However, the terminal multiple method is also attractive, as it is relatively quick and easy to perform and provides a useful check on the terminal value produced by the perpetuity growth method. In fact, the two methods can be used as a cross-check on each other.

Perpetuity growth method The perpetuity growth method produces a terminal value by treating the FCFE generated during the terminal period as a perpetuity with constant growth. It is, therefore, the same approach as the Gordon Growth Model seen earlier. This also highlights why it is important that the explicit forecast horizon continues until a steady state – a stable growth rate – has been reached. This terminal growth rate is likely to be close to the long-term sector growth rate or GDP growth rate of the economy in which the business operates. Again, assuming the standard ten-year explicit forecast horizon, the terminal value will be calculated as follows: TVp = FCFE10 x (1 + g)

i.e. FCFE11

WACC – g e.g. TVp = 1,170 x (1 + 2%) 8% – 2% = 19,890 TVp = Terminal value, as calculated using the perpetuity growth method FCFE10 = Free cash flow to the enterprise at time ten g = Terminal growth rate WACC = Weighted average cost of capital Typically, one would look at growth rates in line with inflation (e.g. 2%) or nominal GDP growth (e.g. 4.5%). Also analysts need to cross check the perpetuity growth assumptions with the implied return on capital produced at the end of the forecasting period.

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It should be noted that this formula uses the FCFE at time eleven and so produces a terminal value as at time ten, i.e. at the end of the visible forecast period.

Terminal multiple method The terminal multiple method produces a terminal value by applying a relevant multiple to a relevant metric. Since the FCFE model is being used and an enterprise value calculated, then an EV multiple rather than an equity value multiple is used. As an EV multiple, the metric must be stated before interest, e.g. EBITA or EBITDA. Again, if the standard ten-year explicit forecast horizon is used, then the terminal value (as at time ten) will be calculated as follows: TVm = EV / EBITDA multiple x EBITDA10 e.g. TVm = 6.0x x 3,474 = 20,844 TVm = Terminal value, as calculated using the terminal multiple method EBITDA10 = EBITDA for year ten

This raises the question of the EV / EBITDA multiple to be used. Using the EV / EBITDA multiple as at time zero means applying a multiple at time zero to a metric for year ten. Intuitively, this would seem to be wrong. More analytically, if the valuation multiple is driven by the usual three fundamentals of cash, risk and growth, then the multiple at time ten is expected to be lower than the multiple at time zero, as the business will have now passed through its higher-growth phase and will have arrived at its steady state, or constant-growth phase. EV / EBITDA10 < EV / EBITDA0

Cross-checking the two terminal values The terminal values calculated by both methods can be used as a cross-check against each other. Firstly, calculating the terminal multiple implied by the terminal value arrived at through the perpetuity growth method:

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4 • Discounted Cash Flow (DCF) fundamentals

If TVp = TVm Then TVp = EV / EBITDA multiple x EBITDA10

. :

Implied TVp EV / EBITDA = EBITDA10 multiple

Implied 19,890 e.g. EV / EBITDA = 3,474 multiple = 5.7x

This implied terminal multiple can then be compared with the equivalent multiple for the business at time zero and the equivalent multiple for peer companies to check whether it is reasonable. Secondly, calculating the terminal growth rate implied by the terminal value arrived at through the terminal multiple method: If TVm = TVp Then TVm = FCFE10 x (1 + g) WACC – g

. : . : . : . : .

TVm x (WACC – g) = FCFE10 x (1 + g) TVm x WACC – TVm x g = FCFE10 + FCFE10 x g TVm x WACC – FCFE10 = TVm x g + FCFE10 x g TVm x WACC – FCFE10 = g (TVm + FCFE10)

:

Implied growth rate g = TVm x WACC – FCFE10 TVm + FCFE10

e.g. Implied growth rate g = 20,844 x 8% – 1,170 20,844 + 1,170 = 2.3%

This implied terminal growth rate can then be compared with the long-term sector or GDP growth rate for reasonableness. This highlights the point that the key driver behind the terminal value is growth. It is within the terminal value that this key driver has its greatest impact within the FCFE model.

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Calculating the present value of the terminal value Both of the methods described above have calculated a terminal value as at the end of the explicit forecast horizon, in the example as at time ten. In order to calculate the present value of the terminal value, these terminal values must be discounted back to time zero: PV of TV =

Perpetuity growth method PV of TV =

19,890 (1 + 8%) 10

TV (1 + WACC) 10

Terminal multiple method PV of TV =

20,844 (1 + 8%) 10

= 9,655

= 9,213 PV of TV = Present value of terminal value

Enterprise value At this point, an enterprise value can be arrived at by adding together the present value of the explicit cash flows and the present value of the terminal value. It is also worth checking what percentage of the enterprise value is contributed by each of these elements: PV of explicit cash flows

£ X

% X

PV of TV

X

X

EV

X

100

If it is deemed that the proportion of the enterprise value that is derived from the terminal value is too high, then there are two main options: 1. Review the key drivers of the terminal value 2. Consider lengthening the explicit forecast horizon.

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4 • Discounted Cash Flow (DCF) fundamentals

Key terminal value drivers If the terminal value has been calculated using the perpetuity growth method, the terminal growth rate should be reviewed. It may be too high. Check the final FCFE figure, especially numbers such as capex. If the final explicit capex figure is understated, then the terminal value will be overstated. Also check implied return on capital implicit on the multiple. If the terminal value has been calculated using the terminal multiple method, the terminal multiple should be reviewed. It may also be too high. It is also appropriate to check the implied ROCE implicit in the multiple.

Lengthening the explicit forecast horizon Lengthening the explicit forecast horizon will require some work in producing more discrete forecasts but will result in more of the enterprise value coming from the visible period and less coming from the less visible terminal period.

Adjusting enterprise value to equity value The enterprise value (EV) arrived at is, effectively, the net present value of the operations of the business. This excludes the value of any financial assets the business may have and, as it is an enterprise value, has not had any financial liabilities deducted from it. By making these adjustments, the equity value is determined. The key adjustments are as follows: 1. Add joint ventures and associates 2. Deduct net debt 3. Deduct un-funded / under-funded pension liabilities 4. Deduct minority interests.

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Enterprise value

1

2

Investments Net debt including Joint ventures & associates

3

4

Provisions including un/under funded pension liability

Minority interests

Equity value

1. Joint ventures and associates In EBITA and, therefore, in FCFE, any share of the income and cash flows from joint ventures and associates were excluded. Therefore, the enterprise value calculated excludes the business’ share of the value of those investments. This value must be added in separately at time zero. If these investments are listed, their market value can be used. If they are not listed, and the required information is available, a separate DCF or multiplebased valuation can be performed. Otherwise, the default option is using the book value of investments in joint ventures and associates. £m

2007 314

Investment in joint ventures and associates Source: Tesco plc Annual Report 2007, Balance sheet, p. 46

As this is an accounting number, it is the least favoured option. This is illustrated by the following extract: CHFm

2006

Book value

7,795

Market value

21,784

Source: Consolidated Financial Statements of the Nestlé Group 2006, Note 6, p. 30

The value of Nestlé’s investment in L’Oréal is significantly understated in the balance sheet under the equity method of accounting.

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4 • Discounted Cash Flow (DCF) fundamentals

2. Net debt Net debt is calculated as follows: Long-term debt

X

Short-term debt

X

Short-term investments

(X)

Cash and cash equivalents

(X)

Net debt

X

As these numbers are sourced from the balance sheet, they will be book values. For the purposes of valuation, they should be adjusted to fair, or market, values. This information should be disclosed in the notes to the financial statements under IFRS, although it may need to be updated if the balance sheet is not sufficiently recent.

Fair values Fair values of financial assets and financial liabilities are disclosed below: 2007 £m

Carrying value

Fair value

Short-term borrowings

(1,518)

(1,509)

Long-term borrowings

(3,999)

(3,949)

Primary financial instruments held or issued to finance the Group’s operations:

Finance leases (Group as lessor – note 31)

12

12

Finance leases (Group as lessee – note 31)

(183)

(183)

Cash and cash equivalents

1,042

1,042

Source: Tesco plc Annual Report 2007, Note 20, p. 77

By deducting net debt from the enterprise value, the effect is to add the value of the liquid financial assets and deduct the value of the standard financial liabilities. 3. Un-funded /under-funded pension liabilities The un-funded / under-funded pension liability represents the shortfall between the market value of any pension assets that are held and the present value of the pension obligations. This represents a claim by the company

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4 • Discounted Cash Flow (DCF) fundamentals

pension scheme, and / or the retired workers, on the future cash flows of the business. This is, therefore, a quasi-debt item and is treated as such. If the corridor method of pension accounting is being used, which is often the case under IFRS, care must be taken to ensure that the correct economic deficit is extracted from the financial statements and not the balance sheet deficit. 31 Dec 2004 Funded status

(4,827)

Unrecognised actuarial (gain) loss

2,593

Asset limitation due to uncertainty of obtaining future benefits

(1,186)

Net recognised liability

(3,420)

Source: Bayer Annual Report 2004

Also, in many countries, cash contributions into the company pension scheme, and cash payments to the retired workers, are tax deductible. This means that the economic pension deficit attracts a tax shield and should be adjusted for this, assuming the business is sufficiently profitable to take advantage of the tax deduction. Post-tax economic deficit = Pre-tax economic deficit x (1 – t)

:

. Post-tax economic deficit = €4,827m x (1 – 30%) = €3,379m

t = Tax rate

Most IFRS accounts will disclose the related deferred tax asset therefore there is no need to manually estimate the figure. 4. Minority interests Since the calculation of FCFE began with EBITA, which is before the deduction of the profit attributable to the minority shareholders in group subsidiaries, the resultant enterprise value includes the minority’s share of the value of those group subsidiaries. As the equity value looks at the business from the perspective of the group shareholders (i.e. the shareholders in the parent company only), the minority interest must be removed. As with the investments in joint ventures and associates discussed above, if the subsidiaries are listed, their market value can be used. If they are not listed, and the required information is available, a separate DCF or multiplebased valuation can be performed. Otherwise, the default option is to use

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4 • Discounted Cash Flow (DCF) fundamentals

the book value of minority interests. Again, as this is an accounting number, it is the least favoured option. £m

2007

Minority interests

65

Source: Tesco plc Annual Report, 2007, Balance sheet

For completeness, the equity value can be divided by the number of shares outstanding, in order to derive an implied share price. If the business is listed, this can be compared with the actual share price, in order to calculate a control premium. Enterprise value

41,534

Add: joint ventures and associates

476

Less: net debt

(4,415)

Less: pension deficit

(1,211)

Less: minority interests Equity value

(64) 36,320

Number of shares outstanding

7,900

Implied share price

460

Current share price Control premium

415 10.8%

FCFEq methodology and pitfalls It is theoretically possible to establish a value of the firm directly as the equity level. The cashflow to be discounted would be the levered cashflows (i.e. post interest) and the discount rate would be the cost of equity. However, this is rarely done in practice due to the difficulty of forecasting forward the level of debt in the company and the consequent interest on that debt. It is much more straightforward to assume a constant debt to equity ratio in the WACC and to establish an enterprise value rather than an equity value.

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5 • Dividend Discount Model (DDM)

5 • Dividend Discount Model (DDM) Dividend Discount Model The Dividend Discount Model (DDM) discounts the future dividends to arrive at equity value. Since dividends are the simplest of the cash flows that can be considered when valuing a business, the dividend discount model is consequently the simplest of the available DCF valuation models. Despite its simplicity, it is still a valid and useful valuation technique. In the post-Enron world, dividends have become more important, with the cash payments providing proof that reported profits are genuine. The DDM method is most often used for financial services businesses (free cash flows being notoriously difficult to calculate) and utilities, and businesses with similar characteristics. For example, the dividend discount model has been used for cable television businesses and for Eurotunnel. Generally, the model is most appropriate for more mature firms that pay regular dividends and have stable levels of growth and leverage.

Constant dividends If the future dividends to be paid by a business are expected to be constant and shareholders intend to hold their shares in the business in perpetuity, the equity in the business can be valued as follows: MVe = =

D D D + + ... + 1 + Ke (1 + Ke) 2 (1 + Ke) ∞ D Ke

MVe = Market value of equity D = Constant dividends Ke = Shareholders’ required rate of return

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5 • Dividend Discount Model (DDM)

The following illustration demonstrates the point: Illustration − DDM with constant dividends MegaBank is expected to pay dividends of £150m per annum for the foreseeable future. Its shareholders require an annual rate of return of 12%. The total market value of MegaBank’s equity is: MVe =

£150m 0.12

= £1,250m

If the total market value of MegaBank’s equity was already known, the above formula could be rearranged to reveal the required rate of return of MegaBank’s shareholders, as shown: Illustration − backing out the cost of equity D Ke

. Ke =

D MVe

:

MVe =

= £150m £1,250m = 12%

However, this is not a derivation of MegaBank’s cost of equity. It is simply the cost of equity implied by the expected dividends and the current market value of the equity. This implied cost of equity could, if so desired, be disaggregated further, using a model such as the Capital Asset Pricing Model (CAPM – see later). The implied beta factor could, for example, be found in this way. While useful, this version of the DDM is somewhat unrealistic, as it assumes no growth. As this state of affairs would be unacceptable to most shareholders, we must extend the model to incorporate growth.

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5 • Dividend Discount Model (DDM)

Constant growth in dividends We will start by assuming that dividends are expected to grow at a constant rate, in perpetuity: Gordon Growth Model MVe =

Do x (1 + g) Ke − g

MVe = Market value of equity Do = Latest dividend g = Constant growth rate of dividends in perpetuity Ke = Shareholders’ required rate of return

The following illustration demonstrates the model: Illustration − Gordon Growth Model Let’s assume that MegaBank’s most recent dividend was £150m and that they are expected to grow at 2% per annum in perpertuity. MVe =

£150m x (1 + 0.02) 0.12 − 0.02

= £1,530m Note: The annual growth of 2% adds £280m of value to the business’s equity.

If the total market value of MegaBank’s equity was already known, the Gordon Growth Model could be rearranged to allow us to find the growth rate implied in the value, as shown: Illustration − backing out the implied growth rate MVe =

Do x (1 + g) Ke − g

:

. MVe x (Ke − g) = Do x (1 − g) . MVe x Ke − MVe x g = Do + Do x g . MVe x Ke − Do = MVe x g + Do x g

: :

= g (MVe + Do) g= =

MVe x Ke − Do MVe + Do £1,530 x 0.12 − £150m £1,530 + £150m

= 2%

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5 • Dividend Discount Model (DDM)

Applying this process to a real example, substituting the share price for the total market value of equity: Illustration − HSBC − backing out the implied growth rate Share price x Ke − Do Share price + Do

g=

Banks

Alnce&Lei Alliedlr € Anglolr € ANZ A$ BankAM $ BankIre € BkNvas C$ Barclays BcoSantdr Brdford&B Canlmp C$ EFG Intl SFr EsprtoS € HBOS HSBC LlydsTSB MitsubTk Y NrthnRck RylBkC C$ RBS StandCh Trnto-Dom C$ Westpc A$

Price 492 £10.46 677.06 £10.36 22.13 713.67 £24.50 490 878 181 £33.40 £16.05 £13.90 646.50 745.50 428 438.34 96 £25.61 363.25 £15.58 £33.92 £10.57

Chng -36 +0.40 -10.56 -0.30 +0.18 +1.87 +0.23 +13 -12 -1.25 -0.13 +0.40 -0.28 -12.50 -10.50 -4 -19.63 – – -3.50 -0.30 +0.46 -0.35

... 52 week ... High Low £12.10 428 £16.40 923.63 £12.18 594.83 £14.05 £10.32 £27.68 £16.96 £12.68 £633.60 £24.53 £21.46 794 396 £10.87 776 £473.75 169 £49.98 £31.99 £25.03 £13.47 £23.80 £13.44 £11.76 587 972 676 622 354 760.01 411.61 £12.29 52.50 £28.41 22.48 724.93 317 £19.75 £13.21 £38.08 £30.32 £13.82 £10.45

Source: www.ft.com 15/02/08

Share price = 745.5p Ke = 4.5% + 1.1 x 5% = 10% (using CAPM − see later) Do = Dividend yield x share price

:

= 6.6% x 745.5p = 49.2p 745.5p x 10% − 49.2p . g= 745.5p + 49.2p = c. 3.2%

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Yld 11.2 5.4 2.2 8.8 5.7 6.7 3.7 6.9 5.5 11.6 5.0 0.9 2.2 6.9 6.6 8.1 1.5 29.6 3.8 8.9 2.7 3.3 8.2

P/E 8.0 5.5 6.8 10.1 12.9 4.9 12.0 7.6 9.5 4.7 7.1 18.9 13.7 6.0 9.3 7.7 16.7 – 12.1 5.1 17.1 12.1 13.1

Vol ‘000s 25,406 4,660 3,359 9,422 5,765 3,473 968 95,696 289 8,611 943 155 0 42,311 36,756 47,113 60,118 2,061 1,662 67,247 7,967 856 11,141

5 • Dividend Discount Model (DDM)

The implied growth rate can then be disaggregated using the following growth model: g=rxb r = Return on capital reinvested b = Reinvestment rate

The growth model shows that growth comes from reinvesting some of the profits and then generating further returns on the capital reinvested. The following examples illustrate this: Illustration − r x b model Assuming £100m is invested at time zero: A

Return on investment Reinvestment rate Time Investment Withdrawn

10% 50%

0 £100m

1 £110m (£5m) £105m

Withdrawn

2

£115.50m (£5.25m) £110.25m

The investment has grown at 5% p.a. (10% x 50%)

B

Return on investment Reinvestment rate Time Investment Withdrawn

10% 100%

0 £100m

1 £110m − £110m

Withdrawn

2

£121m − £121m

The investment has grown at 10% p.a. (10% x 100%)

The more that is reinvested and the greater the return on that reinvestment, the greater the growth.

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5 • Dividend Discount Model (DDM)

Returning to the real example: Banks Price 492 £10.46 677.06 £10.36 22.13 713.67 £24.50 490 878 181 £33.40 £16.05 £13.90 646.50 745.50 428 438.34 96 £25.61 363.25 £15.58 £33.92 £10.57

Alnce&Lei Alliedlr € Anglolr € ANZ A$ BankAM $ BankIre € BkNvas C$ Barclays BcoSantdr Brdford&B Canlmp C$ EFG Intl SFr EsprtoS € HBOS HSBC LlydsTSB MitsubTk Y NrthnRck RylBkC C$ RBS StandCh Trnto-Dom C$ Westpc A$

Chng -36 +0.40 -10.56 -0.30 +0.18 +1.87 +0.23 +13 -12 -1.25 -0.13 +0.40 -0.28 -12.50 -10.50 -4 -19.63 – – -3.50 -0.30 +0.46 -0.35

... 52 week ... High Low £12.10 428 £16.40 923.63 £12.18 594.83 £14.05 £10.32 £27.68 £16.96 £12.68 633.60 £24.53 £21.46 794 396 £10.87 776 £473.75 169 £49.98 £31.99 £25.03 £13.47 £23.80 £13.44 £11.76 587 972 676 622 354 760.01 411.61 £12.29 52.50 £28.41 22.48 724.93 317 £19.75 £13.21 £38.08 £30.32 £13.82 £10.45

Yld 11.2 5.4 2.2 8.8 5.7 6.7 3.7 6.9 5.5 11.6 5.0 0.9 2.2 6.9 6.6 8.1 1.5 29.6 3.8 8.9 2.7 3.3 8.2

P/E 8.0 5.5 6.8 10.1 12.9 4.9 12.0 7.6 9.5 4.7 7.1 18.9 13.7 6.0 9.3 7.7 16.7 – 12.1 5.1 17.1 12.1 13.1

Vol ‘000s 25,406 4,660 3,359 9,422 5,765 3,473 968 95,696 289 8,611 943 155 0 42,311 36,756 47,113 60,118 2,061 1,662 67,247 7,967 856 11,141

Source: www.ft.com 15/02/08

Illustration − disaggregating the implied growth rate Dividend Price

x

Price Earnings

=

Dividend Earnings

Dividend Yield

x

P/E Ratio

=

Payout Ratio

6.6%

x

9.3

=

61.4%

If payout ratio = 61.4%, reinvestment rate = 1 − 61.4% = 38.6% Rearranging the simple growth model, the implied return on equity can be backed out: g=rxb

:

. r= g b =

3.2% 38.6%

= c. 8.3%

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5 • Dividend Discount Model (DDM)

This implied return on equity can be compared with historical data and expectations in order to form a view on the current valuation of the business’s shares. The advantage of this constant growth model is that it highlights the three fundamentals that lie behind any valuation: 1. Cash 2. Risk 3. Growth. 1. Cash

MVe =

3. Growth

Do x (1 + g) Ke − g

2. Risk

The more cash a business can generate, the less risky those cash flows and the more those cash flows are likely to grow, the more valuable that business will be, and vice versa. One disadvantage of this model is that it does not work if the growth rate is higher than the cost of equity (the denominator, and consequently the value, become negative). Another is that it can be somewhat unrealistic. In the example, an implied growth rate of 3.2% per annum in perpetuity is debatable. These problems can be remedied by extending the model to a two-stage growth model.

Two-stage growth model The first model assumed no growth in dividends. The second model assumed constant growth. This third version assumes two stages of growth in dividends: a shorter higher-growth stage followed by a longer lower-growth stage.

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5 • Dividend Discount Model (DDM)

Constant dividends D

t Constant growth in dividends D

t Two stages of growth in dividends D

Lower

Higher 0

n



t

The formula for the two-stage growth model can be written as follows: MVe = Higher-growth stage + Lower-growth stage Higher-growth stage

0



Do x (1 + GHIGH) KeHIGH − GHIGH

n





Do x (1 + GHIGH) n + 1 KeHIGH − GHIGH (1 + KeHIGH) n

Lower-growth stage Dn x (1 + GLOW) KeLOW − GLOW (1 + KeHIGH) n

In the higher-growth stage, the first term calculates a perpetuity with constant (high) growth starting at time zero. The second term removes all of the value created after time n, the end of the higher-growth stage. This leaves just the value created during the higher-growth stage.

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5 • Dividend Discount Model (DDM)

In the lower-growth stage, the term calculates a perpetuity with constant (low) growth, starting at time n. This is then discounted back to time zero. If applied to the real example, assuming a 5 year higher period at 4% and then a lower growth period of 1%:

Higher-growth period Dividend

Price

%

209p

28%

538p

72%

747p

100%

49.3p

Cost of equity

10%

Growth

4%

No. of years

5 years

Lower-growth period Dividend

77.2p

Cost of equity

10%

Growth

1%

Total

Obviously, the DDM can be extended further to a three-stage model (with, for example, a higher-growth phase, then a transitional phase and finally a lower-growth phase) and beyond. Three stages of growth D

Higher

Transitional

Lower t

This approach can also be applied to the terminal phase of the full-blown free cash flow DCF models, if the business in question has not reached a steady state of growth by the end of the visible forecast period (see later).

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5 • Dividend Discount Model (DDM)

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6 • Advanced DCF valuation

6 • Advanced DCF valuation Introduction The subject matter of advanced DCF is no longer the sole province of business school academics, but is a live issue in the current M&A market place. Given that the academics are still debating many of the issues there are often no ‘right or wrong’ answers to many of the topics – however it is important to establish a consistent approach and to be conversant with the relevant issues. A number of the topic areas interrelate, in particular, delevering betas, the appropriate WACC formula and the APV calculations. The aim is for consistency and a robust approach. Other areas such as terminal growth rates, implied returns and cyclicality are also interrelated and will be treated in a similar way.

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6 • Advanced DCF valuation

Delevering betas The published beta obtained from most data sources will be a levered beta – that is to say it represents the systematic business risk of the share, plus the finance risk associated with the company’s level of debt finance. Delevering the beta involves removing the finance risk element and creating a synthetic or artificial beta which simply reflects the systematic business risk of the company on the assumption that it was all equity financed. The key reason for doing this is to establish a comparable universe when creating a synthetic beta for a company. This may be because the company doesn’t have a beta (IPO valuation or lack of reliable data in the country) or it may be because the banker feels that a beta based on comparable data is more reliable in the long term and less subject to short term market noise than a beta selected from a data provider.

Creating a synthetic (delevered beta) Many investment banks now have standard models for DCF (free cash flow) valuations which include, as part of the model, a delevering calculation. This will comprise a comparable universe with each company contributing a levered beta into the equation. These levered betas are then delevered to create an underlying delevered comparable beta. This comparable delevered beta is then relevered according to the required gearing ratio for the target company. The resulting beta is then inserted into CAPM to produce a cost of equity, which is then inserted into a second formula to create a WACC. There are a number of (often interrelated) issues to consider in this process: 1. Selection of the comparable universe 2. The delevering formula 3. The averaging process 4. The relevering formula 5. The WACC formula.

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6 • Advanced DCF valuation

Selection of the comparable universe The usual comparable issues will be considered – but since the aim is to determine an underlying industry beta, greater weight will obviously be placed on the nature of the business than on growth profiles, size of company, geographical location, etc.

The delevering formula There are a number of different formulae to be considered when delevering a beta and these can be reviewed in the academic literature – the following website is a useful start: http://ideas.repec.org/a/eee/jfinec/v73y2004i1p145-165.html The theories and their proof can become extremely mathematical with most work centering around the valuation of the tax shield, in particular the level of risk associated with it, and the stability of the long term relationship between the equity and debt of the company in question.

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6 • Advanced DCF valuation

Some of the most commonly expressed formulae are: βL = βu + (βu – βd) (D / E) (1 – T)

(ABN approach)

βL = βu + βu (D / E) (1 – T)

(Damodaran)

βL = βu (1 + D / E)

(No tax)

βL = βu + (D / E) (βu – βd)

(Harris Pringle)

βL = βu + (D / E) (βu – βd) [1 – T Kd / (Kd – g)]

(Myers)

βL = βu + (D / E) (βu – βd) [1 – T Kd / (1 + Kd)]

(Miles-Ezzell)

βL = βu + (D / E) [βu – βd + (T Kd / Pm) – VTS (Ku – g) / (D Pm)]

(Modigliani and Miller)

The above are taken from IESE CIIF working paper 488 revised May 2006 – “Levered and unlevered Beta”, by Pablo Fernandez.

The symbols and abbreviations are: βd = Beta of debt βL = Beta of levered equity βu = Beta of delevered equity = Beta of assets D = Value of debt E = Value of equity g = Constant growth rate Ku = Cost of delevered equity (required return to delevered equity) Ke = Cost of levered equity (required return to levered equity) Kd = Required return to debt = Cost of debt (pre tax) Pm = Market risk premium = Rm – Rf T = Corporate tax rate VTS = Value of the tax shields

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6 • Advanced DCF valuation

At Rothschild it makes sense to start with cost of capital research from ABN AMRO equity research (given the historic AAR JV) and to then consider possible issues (a more detailed review would require an entire text in its own right). The delevering formula used is:

βu =

⎡ βL + βd ⎛ D (1 – T) ⎛⎡ ⎝E ⎝⎣ ⎣ ⎛ 1 + D (1 – T) ⎛ ⎝ ⎝ E

This is a rearranged version of the first formula making the asset (delevered) beta the subject of the formula. Note that this is the same as the Damodaran formula, if the beta of debt is assumed to be zero. Many bankers make this simplifying assumption for investment grade companies. A key underlying assumption is that there is a fixed relationship between the book values of debt and equity (rather than the less realistic assumption as to a fixed market value relationship). McKinsey (Valuation) also cites this formula in appendix D to the fourth edition with the underlying assumptions being: • Dollar level of debt is constant (similar but not identical to the above) • Debt is risky (hence the debt beta) • The tax shields have the same risk as debt (rather than the same risk as operating assets). The assumptions can of course be challenged, but are not unreasonable. If the underlying academic assumptions are accepted, the next hurdle is the practical issue of establishing the inputs for the formula. These are: The equity (levered) betas to be delevered need to be sourced The ABN team produce their own beta estimates based on a 5 year monthly observation period regressed against a global market index using the FTSE world index as a proxy for the global market portfolio.

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6 • Advanced DCF valuation

The observed beta (raw) is adjusted based on the Blume adjustment: Adjusted beta =

2 1 x raw + x1 3 3

There are a number of immediate practical issues to consider: Issue

Resolution

Thin trading in shares

Companies removed if a period of no trading for 2 months

Dealing with outliers

Companies discarded if beta is negative or over 3

The estimation period

Difficult to resolve but it is a balance between more data and data becoming old

Reference day

A recent paper (Prof Daniela Acker, Bristol University) shows the actual day of reference (i.e. the date within the month selected as the reference point for measuring the relative change) will have a significant impact on the outcome

From the above there is already a degree of imperfection entering the analysis. This should be borne in mind when considering a ‘right’ answer to the cost of capital problem. The debt betas need to be calculated and sourced Academically the debt beta can be derived by decomposition of the debt premium for a company. This will involve separate identification of: 1. Default premium 2. Non credit risk factors such as liquidity, tax etc. 3. Systematic risk. It would appear that academic research in this area is thin. An alternative would be to regress bond returns against a market index – once again there is a distinct lack of data. In practice the approach often used is … βd = Debt premium / (Rm – Rf)

This in turn requires estimates for the risk-free rate, Rf. Rf The ABN research uses 10 year government bond yields for the country in which the company’s cash flows are denominated. These are adjusted if the rates are considered to be abnormally low (further subjectivity).

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Rm – Rf = Market risk premium As always a subject for debate. ABN uses a global premium extracted from the Global Investment Returns Yearbook (GIRY) produced by Dimson, Marsh and Staunton at the London Business School (LBS). Debt premium ABN derive their debt premiums “based on the cost of publicly traded debt and/or the cost of existing bank facilities and the company’s credit outlook. The analyst estimates the interest margin or debt premium the company pays over the risk-free rate. If there is a significant difference between the current debt and the target debt level then an estimate of the premium at the target level is used.” (Source: ABN beta book) Once again there is a large amount of subjectivity and potential noise entering into the calculation. The leverage ratio needs to be estimated D/E This can be calculated in a number of ways. The ABN research analysis looks at the likely future leverage of the company in question. This can of course be quite different from the existing leverage of the company. Corporate tax (T) This is the expected effective corporate tax rate over the forecast period. Once again this may need to be estimated.

The averaging process The ABN team delevers the betas to create an industry average delevered beta. For the averaging calculation, the individual betas are weighted according to the relative market capitalisation of the stocks. Once again the calculation will be subject to the state of the individual companies and the market at a particular moment in time.

The releveraging formula The target stock has a synthetic beta calculated for it based upon relevering the underlying asset beta for the sector. ABN uses the formula: βL = βu + (βu – βd) D / E (1 – T)

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All of the issues surrounding the formula have been covered previously. The obvious point is that it is consistent with the delevering formula and the tax rate used is the expected effective tax rate for the company in question. Once again the leverage is based on the analyst’s view of the forecast debt/ equity ratio for the company.

The WACC formula There are two main routes for calculating the WACC: 1. Weighting the cost of equity and cost of debt 2. Using the Modigliani and Miller formula.

The market weighting version By far the most popular method is the simple weighting formula with the WACC calculated as: WACC = Ke x E / (D + E) + Kd x (1 – T) x D / (D + E)

This requires both Ke and Kd to be calculated. Cost of equity, Ke This is calculated using CAPM: Ke = Rf + βL x (Rm – Rf)

Global estimates for the equity market premium and the local risk-free rate are used. The equity (levered) beta, βL, is calculated using the formula above. Cost of debt, Kd The cost of debt is calculated using the formula: Kd = Rf + βd (Rm – Rf)

Note: this is the same as Kd = Rf + debt premium, which is the most commonly used version. WACC The formula is: WACC = Ke x E / (D + E) + Kd x (1 – T) x D / (D + E)

The weightings are based on the analyst’s leverage forecast for the company in question.

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The above calculation is familiar and straightforward; however, the weighting proportions can be debated. Weighting proportions The proportions of equity and debt used in the WACC should be based on market values. However, there are a number of alternatives as regards market values: Current market value This has the advantage of being empirically correct. However the current position may be atypical. Also if the WACC is being used to calculate a market value there is a degree of circularity in basing one of the inputs on current market value. When using a WACC based on current market values to calculate an implied enterprise value it would make sense to deduct the current market value of the net debt when moving from enterprise to equity value. Optimum leverage ratio Using either Modigliani and Miller (M&M) or an empirical model, it is possible to derive the optimal capital structure for the company’s WACC. This capital structure can then be used in the WACC calculation. Obviously this assumes that the company can and will move towards this optimum position. When using a WACC based on an optimal capital structure to calculate an implied enterprise value it would make sense to deduct the same proportion when moving from enterprise to equity value. Target leverage ratio The board may have stated targets for their long term leverage. If these are publicly stated and deemed attainable, then it would make sense to use this ratio in creating the WACC. Alternatively, the target leverage ratio is calculated by the research analyst (per ABN AMRO). The target leverage ratio approach creates an issue when moving from enterprise value to equity value in a DCF. The issue is that the enterprise value is based on the capital structure created for the WACC, but the net debt deduction to establish the equity value is the current market value of

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the net debt which could be quite different to a deduction based on the target leverage ratio, leaving the resulting equity value open to question. Industry average In certain circumstances (for example in IPOs) there may be a lack of available data. In these instances it can be assumed that the company will tend towards the industry average debt to equity ratio. This can be used in a one-stage WACC model or as the stable ratio in a two-stage or three-stage model. Modigliani and Miller version Modigliani and Miller, two of the most eminent and respected of all financial strategists, created a model of leverage based on their famous underlying assumption of the ‘perfect capital market’. Their work, spanning three decades, provides a comprehensive coverage of the leverage debate. Their formula for deriving the WACC is: WACC = Ku x (1 – T x D / (D + E)) Where Ku = delevered cost of equity

A worked example Aiming to calculate WACC Assume: D = 200 E = 300 T = 30% βu = 0.9 Rf = 5% EMP = 4% Debt premium 1.5%

Following ABN to find βL βL = βu + (βu – βd) D (1 – T) / E

This requires βd βd = Debt premium / (Rm – Rf) βd = 0.015 / 0.04 βd = 0.375

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βL = 0.9 + (0.9 – 0.375) x 200 x (1 – 0.3) / 300 βL = 1.145 So Ke = Rf + βL (Rm – Rf) Ke = 5% + 1.145 x (4%) Ke = 9.58%

To find Kd Kd = Rf + βd (Rm – Rf) Kd = 5% + 0.375 x 0.04 Kd = 6.5% (needs to be post tax in the WACC formula)

The WACC Based on market weighting 9.58% x 300 / 500 + (6.5% x 0.7) x 200 / 500 = 7.568%

Based on M&M WACC = Ku x (1 – T x D / (D+E))

To find Ku = Rf + βu (Rm – Rf) = 5% + 0.9 x (4%) Ku = 8.6%

So WACC = 8.6% x (1 – 30% x 200 / 500) = 7.568%

The above relies on the pre-stated academic assumptions. These may be challenged but given the ‘noise’ attached to establishing the data and the fact that the WACC is always subject to sensitivity analysis in DCF valuations it would appear academically safe to follow the ABN approach providing one is aware of the underlying assumptions. The above will still work starting (as happens in practice) with the observed equity beta. The above is shown in the text box on the Rothschild standard DCF model allowing flexibility as the case requires.

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Beta 1.

If the company has a listed beta, then this figure can be chosen as the basis for the cost of equity and so WACC

2.

If a comparable beta is to be used, then different methods can be adopted to find the appropriate equity beta: a.

ABN approach βL = βu + (βu – βd) x D x (1 – T) / E

b.

Damodaran approach (per above assuming Beta of debt is zero). This assumption is made in the model βL = βu + (D / E) x βu (1 – T)

c.

Untaxed beta approach βL = βu x (1 + D / E)

Where: βL = target’s equity levered beta βu = ungeared comparable beta T = target’s corporate tax rate D = market value of target’s debt E = market value of target’s equity Cost of equity In all cases the cost of equity is calculated as: Ke = Rf + βL x EMRP Where: Ke = target’s cost of equity Rf = risk-free rate βL = equity beta calculated above EMRP = equity market risk premium

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WACC There are 2 approaches to the WACC calculation: a.

Modigliani and Miller approach:

⎛ ⎝

WACC = Ku x 1 – T x b.

D ⎛ D+E⎝

Weighted average approach:

WACC = Ke x

E D + Kd x (1 – T) x D+E E+D

Where: Ku = target’s delevered cost of equity Ke = target’s levered cost of equity Kd = target’s pre tax T = target’s corporate tax rate D = market value of target’s debt E = market value of target’s equity

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APV valuation The Adjusted Present Value (APV) valuation methodology has long been a favourite for academics. More recently, however, it has become a part of mainstream valuation analysis. The principle is to value the operations of the business and then separately to value the benefits of financing. This allows a much more flexible approach to financing than the plain vanilla DCF which assumes a constant (target) capital structure throughout the forecast period. The mechanics are straightforward: 1. Discount the free cash flow (delevered) at the delevered cost of equity to establish a present value 2. Then discount the relevant financing cash flows at an appropriate discount rate to establish their present value 3. Add the two present values together to arrive at the enterprise value. In practice this is quite frequently simplified into:

Adjusted present value =

Enterprise value if the company was all equity financed + present value of the tax shields

The above ignores, as immaterial, other incremental financing flows (fees, distress costs, etc.) The APV requires an understanding of: 1. Free cash flow (delevered) 2. Tax shield 3. Delevered cost of equity Ku 4. Discount rate for tax shield.

Free cash flow (delevered) This is the same as the normal definition when discounting at the WACC to establish an enterprise value.

Tax shield This will be the interest payments on debt multiplied by the firm’s effective corporation tax rate.

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Delevered cost of equity, Ku The calculations required for this are based on the M&M theories of the firm. The summarised position is that the total risk of the company’s assets must equal the total risk of the financial claims against those assets. So: Vu Vtxa D E Ku + Ktxa = Kd + Ke Vu + Vtxa Vu + Vtxa D+E D+E Operating Assets

Tax Assets

Debt

Equity

Where: Vu = Enterprise value if company was all equity financed Vtxa = PV of tax shields Ktxa = Appropriate discount rate for tax shields Kd = Post tax cost of debt

To establish Ku an assumption about the risk associated with the tax shield is required. 1. Assuming that the risk of the tax shield equals the risk of the operating assets the equation simplifies to: Ku =

D E Kd + Ke D+E D+E

2. Assuming the risk associated with the tax shield equals the risk of debt then the equation becomes (after a fair amount of re-arrangement and substitutions): Ku =

D – Vtxa E Kd + Ke D – Vtxa + E D – Vtxa + E

This second equation can be further refined (based on the assumption of the company maintaining a constant level of debt) with the value of the tax shield being D x T so Ku becomes: Ku =

(1 – T) D (1 – T) D + E

Kd +

E

Ke

(1 – T) D + E

This links back to the ABN formula for the delevering of the beta.

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An alternative route to calculating Ku is to use CAPM with the industry delevered beta: Ku = Rf + βu x (Rm – Rf)

Both cases start with an empirically observed number (Ke or βL) and apply the relevant delevering formula. Which formula to select Once again there is academic debate as to the most appropriate formula to use – the following should be borne in mind: 1. The equations are based on the M&M assumptions which simply don’t apply in the real world 2. Imperfections exist in collating the data 3. Flexibility: for example, if the company is managing a target capital structure, the value of the tax shield is more likely to have a risk profile aligned with the operating assets. If the company is managing a high debt level (a private equity transaction over infrastructure assets), then the value of the tax shield will be aligned with the debt level being maintained and the final formula is appropriate.

Discount rate for the tax shield The appropriate discount rate will depend on the risk profile of the tax shield. The possible options are: 1. The risk-free rate (Rf) 2. The pre-tax cost of debt (Kd) 3. The delevered cost of equity (Ku) 4. The levered cost of equity (Ke) 5. A combination of the above. There are two issues at this point – what discount rate makes intuitive sense and ensuring consistency with the assumptions made in deriving the Ku that has been used in discounting the free cash flows. However, given that the Ku calculation was based partially on the underlying assumption regarding the risk associated with the tax shield, it would make sense to follow the same assumption with the actual discounting of the tax shield.

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Provided this consistency is maintained it would be reasonable to suggest that the APV calculation be based on a case by case basis rather than having one overriding assumption.

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Worked example Summary Balance sheet Net working capital PPE Accum depn

0

1

2

3

4

5

640

688

824

880

898

916

2,560

2,880

3,680

4,160

4,661

5,171



320

720

1,152

1,593

2,042

Net fixed assets

2,560

2,560

2,960

3,008

3,068

3,129

Total assets

3,200

3,248

3,784

3,888

3,966

4,045

Debt

2,400

2,400

2,400

2,400

2,400

2,400

800

848

1,384

1,488

1,566

1,645

3,200

3,248

3,784

3,888

3,966

4,045

EBIT

672

1,088

1,184

1,224

1,248

Interest payments

192

192

192

192

192

PBT

480

896

992

1,032

1,056

Equity Total liabilities & equity

6

Income statement

Tax

168

314

347

361

370

PAT

312

582

645

671

686

EBIT

672

1,088

1,184

1,224

1,248

Add depn

320

400

432

441

449

Less increase in working capital requirement

-48

-136

-56

-18

-18

Less investment in fixed assets

-320

-800

-480

-501

-510

Tax (adjusted for interest tax shield)

-235

-381

-414

-428

-437

FCF

389

171

666

718

732

747

67

67

67

67

67

67

353

141

500

490

455

62

58

53

49

46

416

199

553

540

500

Cash Flow

Tax shield g

2%

βu

1

Rf

6%

Kd

8%

EMRP Ku

4% 10%

FCF (discounted at Ku) Tax shield (discounted at Kd) Total PV of above Terminal value of FCF Present value of Terminal value of FCF Terminal value of Tax shield Present value of terminal value of tax shield

2,208

9,337 5,797 840 572

Enterprise value

8,577

Debt

2,400

Equity value

6,177

The above is based on the assumption of a constant debt level with the tax shield discounted at the pre tax cost of debt.

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6 • Advanced DCF valuation

Terminal value and growth rates The terminal value calculation is the continuing or ongoing value of the business after the discrete or visible year by year forecast period. It is a critical element of the DCF valuation occasionally accounting for over 100% of the total value. Often it is captured in a single one stage calculation (which can be extended to cover two or even three stages). There are a number of different ways of performing the calculation. The most well known ones are: 1. The (McKinsey) value drivers method 2. FCF method 3. Exit multiple.

The McKinsey value drivers method Whilst this is the least used in practice it is the most robust method and will serve as a platform to critique the more popular practical approaches. The basic formula for estimating the Terminal Value (TV) is: NOPLAT T + 1 ⎛1 – TV =



g ⎛ RONIC ⎝

WACC – g

Where: NOPLAT = Net operating profit less adjusted taxes (adjusted for interest tax shield) NOPLAT T + 1 =

Normalised level of NOPLAT in the first year after the explicit forecast period

g = Expected growth rate in NOPLAT in perpetuity Note: As growth (g) comes from the return generated on new invested capital (RONIC), g / RONIC is one way of expressing the new investment rate (the proportion of NOPLAT reinvested) RONIC = Expected rate of return on new invested capital WACC = Weighted average cost of capital

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For example: NOPLAT = 1,000 WACC = 8% RONIC = 12% Net new investment = 30% (proportion of NOPLAT reinvested) FCF = 700 (NOPLAT less net new investment) Growth = 3.6% (based on RONIC x new investment rate)

The TV would be: = 1,000 x (1 + 0.036) x [1 – 0.036 / 0.12] / (0.08 – 0.036) = 16,481.82

It is interesting to see what happens when the RONIC falls to the WACC, classically assumed at the end of the competitive advantage period. Using the numbers above, but with RONIC = 8% Growth will fall to 2.4% The TV would be: = 1,000 x (1 + 0.024) x [1 – 0.024 / 0.08] / (0.08 – 0.024) = 12,800

The key point to observe here is this is the same as: NOPLAT (T + 1) / WACC = 1,000 x (1 +0.024) / 0.08 = 12,800

As McKinsey correctly states: “The fact that the growth term has disappeared from the equation does not mean that nominal growth in NOPLAT will be zero. The growth term drops out because new growth adds nothing to value as the return associated with the growth equals the cost of capital. The formula is sometimes interpreted as implying zero growth (not even with inflation), but this is not the case.”

The FCF method This is most commonly used in practice and is: FCF (T + 1) / (WACC – g)

Using the numbers above firstly with RONIC at 12% and growth at 3.6% we find:

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700 x (1 + 0.036) / (0.08 – 0.036) = 16,481.82

the same as the value drivers result. And with RONIC at 8% 700 x (1 + 0.024) / (0.8 – 0.024) = 12,800

the same as the value drivers result. The issue of difference only arises in the FCF valuation when growth is changed (often in sensitivity tables) without reference to the associated returns or required levels of reinvestment. Taking the above numbers if we keep RONIC at 12% and then arbitrarily increase the growth rate to 5% – the FCF TV becomes: 700 x (1 + 0.05) / (0.08 – 0.05) = 24,500

The value drivers formula gives us: 1,000 x (1 + 0.05) x [1 – 0.05 / 0.12] / (0.08 – 0.05) = 20,416.67

In effect the formula is automatically correcting for the required retention needed to deliver a 5% growth rate: i.e. if RONIC x retained investment = growth then g / RONIC = the retained investment level

In this instance 0.05 / 0.12 = 41.67%, thereby reducing the cash to be discounted and the terminal value. The danger therefore lies in the FCF TV approach overlooking the need to change the FCF to reflect the implied investment required to deliver a new growth rate.

The multiple approach One of the most common methods of estimating terminal value is to apply an exit multiple – usually to an income statement line item. The multiples seen most often are:

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EV / EBIT EV / EBITA EV / EBITDA

The creation and application of these multiples is comprehensively covered in the chapter on comparable company analysis. There are, however, interesting considerations when using this technique to establish the TV. Most of these surround the implied growth rate used in the multiple. If the multiple is simply selected from a contemporary comparable universe and applied to future cash flows (maybe in 10 years time) then the assumption is that the growth potential of the existing universe is the same as the growth profile of the target company in 10 years time. Ideally the comparable company selected should have the same growth profile (now) as the target will have in the future (10 years on). In practice this is difficult to establish and bankers will fall back on existing multiples. One key issue is to understand what Professor Aswath Damodaran refers to as the anatomy of the multiple – essentially the drivers of the multiple. Working with perpetuities FCF / (WACC – g) = EV So EBITA x (1 – T) x [1 – g / RONIC] / (WACC – g) = EV

where, as before, g / RONIC is the reinvestment proportion. If the second equation is divided by EBITA: EV / EBITA = (1 – T) x [1 – g / RONIC] / (WACC – g)

The benefit of this is that it allows a ‘back testing’ of the exit multiple used. Illustration: Assume: An exit multiple of 10.5 (EV / EBITA). Tax rate = 30% WACC = 8% Growth rate = 3% The formula can be rearranged to find the implied RONIC in the multiple. 10.5 = 0.7 x [1 – 0.03 / RONIC] / (0.08 – 0.03)

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Using goal seek or similar, the implied RONIC is 12%. This can be compared with the company’s actual RONIC to check the soundness (or otherwise) of the EV / EBITA estimate of 10.5. The above analysis is based on a single long term growth rate. It is possible to extend this to cover 2 or even 3 stage growth periods.

International cost of capital The key issues of cost of capital, cash flows and exchange rates are interrelated. There is no consensus on the correct solution to the problems, but it is important to establish consistency in the methodology used to value international assets.

General approach Assuming the UK to be the ‘home’ country, the most frequently used methods are: • Forecast cash flows in nominal terms in the overseas currency • Forecast exchange rates, based on purchasing power parity (inflation differential) • Translate cash flows into UK currency • Discount at a WACC incorporating a political risk premium. Using this approach the practicalities of forecasting the cash flows and the exchange rates are problematic. However, the most controversial issue is the incorporation of the political risk premium into the WACC.

WACC Taking the traditional approach to WACC, there are three components: • Ke calculated using CAPM • Kd calculated using risk-free rate plus a credit premium (adjusted for tax shield) • Weighting the Ke and Kd.

Ke The most frequently used approach is to add the political risk premium to one element of the CAPM. There are many variations on this theme.

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The CAPM has three components: • Rf • Beta • EMP.

Rf – the risk-free rate The risk-free rate is based on: • Bonds (shorter term instruments are possible, but less frequently used) • Government bonds (in some circumstances corporate bonds may be preferred) • 10 years (convention within the DCF diet) • Medium yield (zero coupon may be academically purer, but less frequently used). For a mature market, the above are straightforward. For less mature markets, there are two key issues: 1. Deriving a risk-free rate when no 10 year government bond exists 2. Determining whether the risk-free rate (actual or synthetically derived) includes all or part of the political risk premium. Deriving a risk-free rate If the country has some government bonds, but no 10 year bond, an artificial yield curve can be created by regressing the available bond data for the country against the mature market data. If the country has no sovereign bond then a synthetic risk-free rate can be calculated. The approach is: • Establish a country rating • e.g. Standard and Poor’s AA • Convert the ratings into percentage rates • e.g. 10.5% • Regress the percentage risk-free rates to compare against a mature market • Build a predictive model.

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Local risk-free rate and the political risk premium 1. If it is considered that the local risk-free rate (actual or synthetically derived) entirely captures the country political risk premium then no further additions should be made to the WACC calculation. The Ke based on CAPM will be calculated using the local market risk-free rate 2. If the conclusion is that the local risk-free rate does not accurately capture the political risk, then the political risk premium must be incorporated elsewhere in the CAPM. If the political risk premium is included elsewhere in the CAPM then the risk-free rate should be based on the mature market and not on the local (overseas) risk-free rate.

Beta (β) The beta selected and the equity market premium need to be consistent. There are many options. The most frequently analysed are: 1. Local beta measured against the local market index 2. Global beta measured against the global market index 3. Mature beta measured against the mature market index. Most academics agree that a local beta measured against a local market is fairly meaningless. There is more disagreement concerning a global beta measured against a global index, but the consensus appears to be in favour of using the mature beta measured against the mature market index. The arguments follow from the statistical data availability in terms of numbers of observations and lack of distorting data. The beta would be a bottom up beta, based on the industry average levered for the specific asset debt to equity ratio. Care must be taken to ensure consistency of debt to equity ratios and of tax rates when degearing and regearing the beta. Historic weekly betas with 2 or 3 year history (depending on changes in the nature or structure of the business) are generally preferred. Given the averaging process a raw beta may be preferred to the adjusted.

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Equity market premium Using a mature market premium the usual questions arise in terms of measurement. 1. Premium over bonds or bills 2. Historic or forecast premia 3. Number of years of measurement (historic) 4. Geometric or arithmetic averages (historic). There is no consensus here, but the premium is generally best calculated as far back as possible, over bonds. The statistical arguments with regard to geometric or arithmetic averages are complex and are far from trivial – assuming some form of correlation between periods, the geometric average is generally favoured. Cross checking the result to the implied equity return backed out of current market values is a valid reference point.

The political risk premium / country risk premium The political or country risk premium reflects the additional risk faced by investing in the overseas country – it aims to reflect the non-systematic risk associated with expropriation, currency blocks and capital market closures (it does not incorporate inflation which is incorporated into cash flows). The argument advanced by Damodaran is that “the default spreads that come with country ratings provide an important first step, but still only measure the premium for default risk”. Intuitively the country equity risk premium would be expected to be larger than the country default spread. To address the issue of how much higher, it is appropriate to look at the volatility of the country bond used to estimate the spread. This provides the following estimate for the country equity risk premium: Country equity risk premium = Country default spread x

σ equity σ country bond

This method has a good intuitive logic and will generally lead to a higher political risk premium than the more conventional uplift of the sovereign bond rate.

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If this approach is used there are a number of options as to the restatement of the CAPM: 1. 2.

Ke = Rf (mature) + β (mature, bottom up) x (EMP mature) + PRP Ke = Rf (mature) + β (mature, bottom up) x (EMP mature + PRP) Assuming the company exposure to country risk is proportional to its exposure to market risk

3.

Ke = Rf (mature) + β (mature, bottom up) x (EMP mature) + λ (PRP).

Assuming the company exposure to be a product of factors other than those influencing market risk. Many other approaches are possible, for example the Financial Strategy Group (FSG) at Citigroup published a paper (May 2002), in which a key conclusion included the recommendation of the following model: Ke = Rf (mature) + β (global, bottom up) x (EMP global) +

λ1 + λ2 + λ3 30

x (PRP)

λ1 = access to capital markets (score 0 to 10) λ2 = susceptibility of investment to political risk (score 0 to 10) λ3 = importance of the investment to the investor (score 0 to 10)

This method will generally lead to a lower political risk premium than with the uplift of the sovereign bond rate.

Kd The cost of debt should be calculated in a consistent fashion. A workable version being: Kd = Rf (inclusive of PRP) + credit risk premium x (1 – T) based on country tax rate

Weighting of Ke and Kd The options available are as usual: 1. Industry average capital structure 2. Optimal capital structure 3. Current capital structure 4. Long term target capital structure. Again, to maintain consistency it is important to reflect the leverage used when adjusting the beta factor.

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Cash flows and exchange rates The cost of capital logic detailed above assumes that the cash flows are forecast in nominal terms year by year in local currency. These cash flows are then translated year by year using forecast exchange rates. They are then discounted and the PV calculated. An alternative approach is to discount the cash flows in the overseas currency. In this instance it would be appropriate to increase the cost of capital to reflect the long-term inflation rate. For example: Ke =

Rf (mature) + β (mature, bottom up) x (EMP mature) + λ (PRP) + inflation differential

The inflation differential could be backed out of the different yields on 10 year government bonds, so using the local bond rate may be a sensible proxy here.

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7 • Rothschild standard model overview

7 • Rothschild standard models Introduction There are 18 standard models in total. These consist of: • Three DCF models • Two merger models • Two comps models • An LBO model • A precedent transactions model • Multiple models. The models can be found on the L:\ drive (in the CTG standard models folder) for UK investment bankers and emailed upon request to other offices. The comparable and precedent transaction models can be used to keep a running database for companies within sectors whereas all the others can be used as pitch models, with different outputs.

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7 • Rothschild standard model overview

Discounted cash flow models There are three DCF models, with different levels of complexity. The notes will concentrate on DCF II as this is the most useful model for illustration purposes. A comparison of the three models is given below.

Excel set-up Before using any of the standard models ensure that the following is done: Using the Tools / Add-Ins menu, ensure that “Analysis ToolPak” and “Report Manager” are both selected. (Go into tools menu then add ins- tick analysis toolpak)

As there are significant areas of conditional formatting using white text within all the models, a pale grey background should be used so that the white text can be seen. To do this right mouse on the desktop; Go to Properties; then Appearance; then (Advanced Appearance); then Item: choose Window and change Color (sic) one to pale grey.

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7 • Rothschild standard model overview

Back in Excel, the style drop down box should be added to your tool bar. • Tools; then Customise; ensure customise is selected • Drag the drop down box on to the toolbar.

This drop down box can then be accessed by using Alt ‘. (For screen tools menu, then customise, select format and style)

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Side by side analysis of the 3 DCF models DCF I

DCF II

DCF III

30 mins

60 mins

90 mins+

1 statement model (CFS)







Mid vs. end of year discounting flexibility







Exit multiple scenario management







Full sensitivity analysis







Time flexible DCF 1st stage forecasting







Detailed WACC calculation







Comparable beta funtionality







Broker input







Segmental sales flexibility







Minimum estimated completion time

Capex flexibility







Full operating scenario management







3 statement integrated model







DCF II Overview DCF II is a traditional discounted free cash flow to enterprise (FCFE) model. The cash flows are discounted using a weighted average cost of capital (WACC) which can be calculated using either service or comparable (relevered) betas. The model does not produce a set of integrated financial statements. If this is required DCF III should be used. The model does not explicitly deal with the treatment of tax losses. Therefore the effective tax rate as % of EBITA should be adjusted in the assumptions. The output of the model is an initial valuation of either a listed company covered by brokers, or a private company requiring Rothschild in-house forecasts.

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Model structure Output

Sensitivity analysis

Broker inputs

Cover Control sheet Pres

Assumptions

DCF FCFE Graphical output

In house inputs

Capex / sales flexibility

Checklist

WACC

Discounting convention Exit multiples

The model is modular in its structure. This allows for a straightforward flow of information through the model, as well as allowing the model to be treated as a template whereby additional modules can be added.

How to complete the model DCF II should take about 1 hour to setup and run an initial valuation. The sources required can be found in: • Annual and interim reports • Brokers research notes • Bloomberg beta information • The comps model used to estimate an appropriate exit multiple and link in key input information. The model requires input information in the following sheets:

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• Control (In) • Broker (In) • In-house (In) • WACC (In) • Check (In). Output

Sensitivity analysis

Broker inputs

Cover Control sheet

Assumptions

Graphical output

In house inputs

Pres

DCF FCFE

Capex / sales flexibility

Checklist

WACC

Discounting convention Exit multiples

All sheet tabs that require user defined inputs have the suffix (In) included in the sheet tab name.

The control sheet (In) A sensible starting point for DCF II is the control sheet. This sheet holds inputs for: • Transaction year end and completion dates This information will be used to calculate; the discount factors; how many days’ worth of the first forecast period to include using the transaction completion date as to.

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• Most recent balance sheet information for minority interest, net debt and joint ventures and associates This information will be used to calculate the breakdown of the implied enterprise value output from the DCF down to the implied equity value. This information should come from the most recent set of published information – annual, interim or preliminary reports.

Source: Extract from DCF II (Control sheet)

The minority interest value is normally taken as the book value per the balance sheet. This is used as an estimate of the present value of the future cash flows from the minority. Users can estimate the market value of minorities separately if desired. The joint venture / associate is normally taken as the book value per the balance sheet − this is used as an estimate of the present value of the future cash flows from the joint ventures and associates. Again market values can be calculated at the user’s discretion.

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Joint ventures – proportional consolidation Joint ventures can be accounted for either using equity accounting or proportional consolidation under IFRS. If the joint ventures are equity accounted, the implied equity value associated with the JVs will be excluded from the FCFE enterprise value, and so will need to be included in the breakdown to equity value as part of the final valuation output. Whilst equity accounting for joint ventures is a common method of consolidation in Europe (compulsory under US GAAP), the IFRS preferred method of JV consolidation is via proportional consolidation. This method will bring into the group accounts their contribution of the JV line by line into the financial statements. Therefore, all the metrics used to run a FCFE DCF will include the contribution from the JVs and as a result the value of the JVs will be included in the implied enterprise value. If the JVs are proportionally consolidated DO NOT include a JV value in the control sheet.

The most recent number of shares outstanding is used to calculate the implied equity value per share. Sources for this information could be FACTSET, Thomson One, Extel cards or Bloomberg. Whilst these sources are highly accessible, they are not always current. The alternative to these sources is to complete a roll forward. A roll forward involves taking the number of shares outstanding per the latest set of audited accounts and rolling this forward using stock exchange announcements for any equity issues or buybacks up to the transaction date. • Terminal value multiples and perpetuity growth rates (base, downside and upside cases). The model allows up to twelve terminal value drivers. However, only one driver is required to run the model, as long as the appropriate switch has been chosen.

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7 • Rothschild standard model overview

Source: Extract from DCF II (Control sheet)

• Basic WACC inputs (risk-free rates, risk premiums, target capital structures etc.). The WACC calculation itself is completed on the WACC sheet. The control sheet allows the user to choose one of four different methods of applying beta to the cost of equity calculation.

Source: Extract from DCF II (Control sheet) Note: See page 196 and following for details

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Target capital structure consistency – WACC and Betas DCF II ensures that the same target capital structure is used to weight the WACC and to relever comparable betas (when appropriate). The model will automatically convert the target D/E input into a target D/D+E proportion for WACC weighting purposes.

βL =

⎡1+⎛D ⎛ x (1 – T)⎡ ⎣ ⎝ E Target ⎝ ⎣

WACC = Ke x (1 –

D D ) + Kd x D + E Target D + E Target

The broker and in-house sheets (In) The broker sheet is used to input historical operating data and broker forecasts. The number of years of broker information to be used in the forecasts for the DCF will be defined in the broker information area on the control page (see extract below). The model will ensure that the broker and in-house information are amalgamated in the main free cash flow to enterprise forecasts contained within the DCF.

Source: Extract from DCF II (Control sheet)

The in-house sheet requires the user to define the necessary free cash flow assumptions in order to drive the DCF model. The key issues here are to make sure that the assumptions are consistent with the business model and the market. The graph sheet is a useful area to review the consistency of these assumptions.

The WACC sheet (In) The WACC sheet requires inputs if the user wishes to use comparable betas to drive the beta calculation. Otherwise the WACC calculation is driven off the basic WACC information contained on the control sheet.

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The check sheet (In) The check sheet is a sense checklist that ensures that all key inputs and considerations have been addressed before the model is reviewed.

Key elements and functionality of model DCF II is a traditional two stage DCF FCFE model, discounting the cash flow forecasts with a WACC. The terminal value can be calculated using either a FCFE cash flow perpetuity or an enterprise value exit multiple. The WACC is a weighted average cost of capital using cost of equity and debt weighted by a target net debt / net debt and equity proportion. The cost of equity can be calculated using a traditional service beta (Bloomberg or LBS for instance) or through deleveraging and releveraging comparable betas. Key functionality within the model: • Time flexible DCF FCFE 1st stage forecasting (between 1 year and 10 year forecasting periods) • Broker / in-house integrated inputs (number of broker years flexibility) • Segmental sales flexibility • Capex driver flexibility • Detailed WACC • Four methods for beta deleveraging • Mid year valuation and discounting • Terminal value discounting with mid-year discounting.

Time flexible DCF FCFE 1st stage forecasting The model allows the user to run a time flexible 1st stage forecasting period. The model is set up for a 10 year forecast period, although inserting additional columns and copying formulae across will allow the forecasting period to be extended beyond this maximum.

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7 • Rothschild standard model overview

Source: Extract from DCF II (Control sheet)

By entering less than 10 years into the length of DCF period (years) cell, the model will conditionally format the DCF output sheet to show the appropriate number of forecast years in arriving at the implied enterprise value. Care must be taken when running a short period (=

Greater than or equal to

=3.75,C5/C17,”N/A”) Note: it is not necessary to put an equals sign immediately before the logical test formula (C5/C17)>=3.75, nor before the value_if_true argument formula C5/C17. 3. Comments or “labels” – the label N/A is enclosed in inverted commas. If not in inverted commas, Excel will try to interpret the message as one of the following: a formula name; the name of a range; the address of a cell; or a logical value such as TRUE or FALSE. N/A is none of these and the formula will produce an error when Excel tries to return this as a result.

Common problems with IF statements and some simple solutions Using equals in a test 1. Although IFs are very useful, they can easily break down. If we are testing for a particular numerical value from a formula, =0 can give spurious results because Excel shortens decimals to store them and therefore cannot calculate exactly. As a result of Excel’s rounding, a formula which logically should give exactly zero as a result will often give a very small number, typically of approximately 0.000000000001 in value. This problem can easily be solved by using an AND statement to test to see if a number is nearly zero, i.e.

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8 • Financial modelling

=IF(AND(cell-0.001),“Effectively zero”,“Not zero”) Alternatively one of Excel’s rounding or other functions, such as ROUND(), ROUNDDOWN() or ABS() can be used instead. =IF(ABS(cell)>0.001, “Not zero” , “Effectively zero”) 2. Another potential problem in using equals is where the IF statement refers to a user input; for example where the user has to type “yes” or “no” into a cell and then using IF to switch to the relevant formula. Simple typing errors can cause big problems here: a typo in the cell entry will result in the second choice, i.e. the value if false being selected in error. This is a particularly insidious type of mistake because it will usually not result in an error message, but the wrong data or a wrong calculation being used in the model. Using data validation to limit data entry into the ‘switch’ input cell, so only the specific alternatives (for example, “yes” or “no”) can be selected, will solve this problem.

The AND and OR Statements Suppose we want to choose an option if two tests are passed. To deal with these more complex problems there are two other useful tools, the AND and OR function. These functions are often used as the logical test of IF statements. The syntax of an AND statement is as follows: =AND(test1,test2, test3….testn) In the case of the AND statement, Excel evaluates all of the tests in the formula (and there may be up to 30 of these) to see if they are TRUE or FALSE. If they are all TRUE, then the AND statement will give TRUE as a result. Otherwise it will give a FALSE. In the following illustration, u45m of debt is raised (DebtInitialIn) on 31 December 2005 and then is to be repaid following a 2 year grace period (DebtGraceIn) over the remaining 5 years of its 7 year term (DebtTermIn). One solution is to use AND as the logical argument, using the year counters to decide whether it is after 2 years and also within the 7 year period:

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The syntax of an OR statement is the same: =OR(test1,test2, test3….testn) In the case of the OR statement, if any of the tests are TRUE, the statement will result in TRUE. Another solution to the debt problem above is to decide whether the year is within the grace period or after the debt term. If this is the case, no payment is made:

Whether to use AND or OR depends on your thought process. • If you are an inclusive modeller, then your thought process is to define everything that falls within boundaries – AND is your solution. In the above illustration, the logical argument is to require all the criteria to be met / to fall within the boundaries. • If you are an exclusive modeller, then your thought process is to define anything that falls outside boundaries – OR is your solution. In the above illustration, the logical arguments were written so that if any were outside the limits, then no payment was made and if ‘value_if_false’ was returned, payments were made.

Nested statements Excel is a very simple and flexible language and it is very easy to combine formulae to write quite complex programmes in a single cell. For example, a corporate tax formula:

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If we make a loss, we do not pay tax, if we make a profit, then if our profit is less than 300,000, we will have a tax rate of 19%, if we have profit of 300,000 or more, we will be charged at 30%. This would be written as follows:

Tax charge = IF(profit
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