Chapter 10: Business valuation

Chapter learning Objectives

Upon completion of this chapter you will be able to:

  • Explain the issue of overvaluation and outline the problems it can cause
  • Estimate the potential near-term and continuing growth levels of a firm’s earnings using internal measures such as the earnings retention model
  • Estimate the potential near-term and continuing growth levels of a firm’s earnings using external measures such as extrapolation from past dividend patterns
  • Describe the potential risks of an acquisition or merger on the acquirer, distinguishing between business, financial and other risks
  • In a scenario question, identify and analyse the impact on the risk profile of the acquirer in a Type 1, Type 2 and Type 3 acquisition
  • Calculate and discuss the value of an acquisition of both quoted and unquoted entities using asset based approaches:
    • Without considering intangibles
    • Including the valuation of intangibles using the calculated intangible value method
    • Including the valuation of intangibles using Lev’s knowledge earnings method.
  • Calculate and discuss the value of an acquisition of both quoted and unquoted entities using market relative models:
    • PE ratio model
    • Earnings yield model
    • Market to book ratios.
  • Forecast a firms’ free cash flow and its free cash flow to equity (i.e. after deduction of debt interest and repayments and addition of new debt finance)
  • Calculate the dividend cover for a firm using free cash flows to equity and interpret the result
  • Forecast a firms’ terminal (or residual value) assuming cash flows are discounted in perpetuity with no growth
  • Forecast a firm's terminal (or residual value) assuming cash flows are discounted in perpetuity with growth
  • Forecast a firm's terminal (or residual value) assuming cash flows can be expressed as a lump sum using a PE ratio  
  • Calculate and discuss the value of an acquisition of both quoted and unquoted entities using cash flow approaches:
    • Dividend valuation model
    • FCF and FCFE models
    • Economic value added
  • Discuss the value of a Type 2 and 3 acquisitions of both quoted and unquoted entities using:
    • The adjusted net present value approach
    • Iterative revaluation procedures.
  • Describe the procedure for valuing high growth start-ups.

1 Introduction to business valuation

This chapter covers several different methods of businessvaluation. You should view the different methods as complementary whichenable you to suggest a possible value region. It is essential that youare able to comment on the suitability of each approach in a particularscenario.

Do not put yourself under pressure in the exam to come up with aprecise valuation, as business valuation is not an exact science. Inreality the final price paid will depend on the bargaining skills andthe economic pressures on the parties involved.

Risk in acquisitions and mergers

An acquisition may expose an acquiring company to risk. It is important to distinguish between:

  • business risk
  • financial risk.

Business risk

This is the variability in the earnings of the company, whichresults from the uncertainties in the business environment. If themerger or acquisition is with another company operating in the samebusiness area, the underlying business risk (measured by the asset beta)of the acquirer will be unaffected.

Financial risk

Financial risk is the additional volatility caused by the firm’sgearing structure. If an acquisition is significant in size relative tothe acquirer or requires an alteration to the firm’s capitalstructure, it will change the acquirer's exposure to finance risk.

Risk and acquisition type

In order to value a company for the purposes of merger oracquisition, the value added to the acquirer must be identified. Forthis purpose, acquisitions can be categorised into three types:

  • Type 1 – Those that do not disturb the acquirer’s exposure to business or financial risk.
  • Type 2 – Those that do not disturb the acquirer’s exposure to business risk but impact their exposure to finance risk.
  • Type 3 – Those that alter the acquirer’s exposure to business risk and possibly its financial risk.

Illustration of acquisition types

Separate the following acquisitions into Types 1, 2 and 3 based on the data provided below:

Solution to Illustration

a – business risk of target higher, gearing structure altered – Type 3

b – same business so presumably business risk unaltered, gearing structure unaltered – Type 1

c – same business so presumably business risk unaltered, gearing structure unaltered – Type 2

d – different business so presumably business risk altered, gearing structure unaltered – Type 3

Valuation and acquisition type

It is a key principle that the most an acquirer should ever pay fora target company is the increase in the value of the acquiring firmarising from the acquisition.

However, it is rarely a simple matter of valuing the target andassuming that will be the level of increase experienced. This ignoresthe impact of:

  • potential synergy gains – although there is an argument that they are so rarely achieved in practice that they should be very conservatively estimated, and only then if they are arising because of the target itself (that is they wouldn’t arise from any merger)
  • the change in potential risk profile of the combined entity as discussed above

The valuation techniques available must therefore depend on which type of acquisition is being considered.

For example, if an NPV based approach is being used, a riskadjusted cost of capital may need to be calculated and used fordiscounting.

2 Overview of the different valuation methods

Three basic valuation methods

There are three basic ways of valuing a business

  • cash based methods – the theoretical premise here is that the value of the company should be equal to the discounted value of future cash flows.
  • market based methods – where we assume that the market is efficient, so use market information (such as share prices and P/E ratios) for the target company and other companies. The assumption is that the market values businesses consistently so, if necessary, the value of one company can be used to find the value of another.
  • asset based methods – the firm's assets form the basis for the company's valuation. Asset based methods are difficult to apply to companies with high levels of intangible assets, but we shall look at methods of trying to value intangible as well as tangible assets.

We shall cover these methods in detail in the rest of this chapter.

3 Cash based methods

The free cash flow method

Free cash flows can used to find the value of a firm. This value can be used:

  • to determine the price in a merger or acquisition
  • to identify a share price for the sale of a block of shares
  • to calculate the ‘shareholder value added’ (SVA) by management from one period to another.

Calculating the value

Technically, in order for the value of the business to beaccurately determined, free cash flow for all future years should beestimated. However rather than attempting to predict the free cash flowsfor every year, in practice a short cut method is applied. Future cashflows are divided into two time periods:

  • Those that occur during the ‘planning horizon’.
  • Those that occur after the planning horizon.

The planning horizon

The planning horizon is the period where:

  • the firm can earn above average returns
  • cash flows are assumed to grow over time.

Beyond the planning horizon, returns are expected to reach a steady state.

The planning horizon

In competitive industries, a business may have a period of‘competitive advantage’ where it can earn excess returns on capitalby maintaining a commercial advantage over the competition. However thisperiod is unlikely to last indefinitely. Returns are likely to reach asteady state where the business earns on average its cost of capital butno more.

The planning horizon (which may last up to ten years or more) isthe period during which the returns are expected to be higher than thecost of finance.

In period beyond the planning horizon it is usually assumed thatthe returns earned will continue at their current rate for the remainderof the investors’ time horizon. This may be a given number of yearsor in perpetuity. Alternatively the value of the cash flows may beexpressed as a lump sum using a PE ratio.

Illustration 1

A company prepares a forecast of future free cash flow at the endof each year. A period of 15 years is used as this is thought torepresent the typical time horizon of investors in this industry.

It is assumed that the planning horizon is three years – i.e.returns are likely to grow each year for the first three years afterwhich they will reach a steady state.

The following data is available:

Free cash flows are expected to be $2.5 million in the first year,$4.5 million in the second year and $6.5 million in year 3. The stockmarket value of debt is $5m and the company’s cost of capital is 10%.

Find the current value of the firm and the value of the equity.


  • 12 year AF (gives T3 value of CF years 4–15) × 3 year DF (to discount to T0).

The valuation of debt

The value of debt was given in the previous illustration.

If you are not told the value in a question, the best way of estimating the value is by using the formula:

Value of debt = Present value of receipts to the lender (i.e.interest and redemption payment) discounted at the lender's requiredrate of return.

Illustration 2

The company in the previous illustration now believes that earnings after the planning horizon will:

(a) continue at the year 3 level into perpetuity or

(b) grow at 0.9% pa into perpetuity.

Recalculate the current value of the firm and the value of the equity.


Part (a)

  • 1/i (gives T3 value of CF from year 4 onwards) × 3 year DF (to discount to T0).

Note the higher value that results when the time horizon is altered.

Part (b)

Value of equity is 54.126 + 2.273 + 3.717 + 4.882 - (debt value) 5 = $59.998m


The value of the growing perpetuity from Year 4 onwards can be calculated as:

[(6.5 × 1.009) / (0.10 - 0.009)] × 0.751 = 54.126

Calculating free cash flows from accounting information

When appraising an individual project in Chapter 2, the free cashflows could usually be estimated quite easily. However, identifying freecash flows for an entire company or business unit is much more complex,since there are potentially far more of them.

In these situations, the level of free cash flows is more usuallydetermined from the already prepared accounting information andtherefore is found by working back from profits as follows:

This method gives the level of free cash flow to the firm as a whole.

Free cash flow to equity

The above approach calculates free cash flows before deducting either interest or dividend payments.

The free cash flow to equity only can be calculated by taking the free cash flow calculated above and:

  • deducting debt interest paid
  • deducting any debt repayments
  • adding any cash raised from debt issues.

In practical terms, the free cash flow to equity determines thedividend capacity of a firm i.e. the amount the firm can afford to payout as a dividend.

More details on Free Cash Flow

Cash, which is not retained and then reinvested in a business, iscalled free cash flow. This in effect represents the cash flow availableto all the providers of capital of a company, whether these bedebtholders or shareholders. This could be used to pay dividends orfinance additional capital projects, if the necessary organisationalcriteria were met. Free cash flow is a very good measure of performanceand an indicator of value.

Some would suggest that it is a better indicator of performancethan measures based on net income. Forecast free cash flow is the mosttheoretically sound way to place a fair value on a company. ApparentlyWarren Buffet, the world’s richest investor, uses historic andforecast free cash flow to value the businesses that he buys.

Growing free cash flows are frequently a prelude to increasedearnings and hence may be a positive sign for investors. Conversely ashrinking free cash flow may be an indicator of problems ahead, and asign that companies are unable to sustain earnings growth. This may notalways be the case, as many young companies put a lot of their cash intoinvestments, which diminish their free cash flow. However, in this casequestions might be raised about the sufficiency of short- and long-termcapital.

There can be variations in the definition. When calculating freecash flow over a number of years it is sensible to include the change inworking capital and all investment spending. Over a long period of timethe cash flow resulting from all investment is likely to be realisedand so such a measure would be useful to those undertaking businessvaluations and using data forecast into the future.

However, when calculating free cash flow for a single year it wouldbe sensible to omit the change in working capital and discretionarynon-maintenance capital spending, because the ultimate payoff from thoseinvestments is not yet included in the operating cash flow. However,this in turn may give rise to debate about what represents the level ofsustaining capital expenditure that should be deducted. When analysingfigures for free cash flow it is also important to be aware of anyunusual events in a particular year, which may impact on the cash flow.

Figures calculated for free cash flow can be used in determining a company’s cash flow ratios.

For example:

Dividend cover in cash terms = Free cash flow to equity/Dividends paid

It is argued that this measure of dividend cover is better than theconventional ratio of earnings divided by dividends paid, sincedividends are paid in cash, and with no cash there can’t be anydividends.

Also, since the free cash flow to equity determines the company'sdividend capacity (explained in detail in Chapter 6) we can see from thebreakdown of free cash flow to equity that there is a strong linkbetween new investments and dividend capacity i.e. if a new investmentproject increases the cash inflows of a business, its free cash flow toequity and hence its dividend capacity will increase.

Illustration of calculations of Free Cash Flow

Calculate the free cash flow based on the following figures:

A using the standard approach

B to show the free cash flow to equity.


A Standard approach

B Free cash flows to equity

Test your understanding 1

(a) Calculate the free cash flow based on the following figures:

(i)using the standard approach

(ii) to show the free cash flow to equity.

(b) Calculate the dividend cover based on the free cash flow to equity and interpret your result.

Forecasting growth in free cash flows

The methods above have identified a figure for the free cash flowof the business based on its current financial statements. In order tovalue the business, the future free cash flows need to be forecast andthen discounted.

To forecast the likely growth rate for the free cash flows, the following three methods can be used:

Historical estimates

For example, if the business has achieved growth of 5% per annumeach year for the last five years, 5% may be a sensible growth rate toapply to future free cash flows.

Analyst forecasts

Particularly for listed companies, market analysts regularlyproduce forecasts of growth. These independent estimates could be auseful indicator of the likely future growth rate.

Fundamental analysis

The formula for Gordon's growth approximation (g = r × b) can beused to calculate the likely future growth rate, where r is thecompany's return on equity (cost of equity) and b is the earningsretention rate. The formula is based on the assumption that growth willbe driven by the reinvestment of earnings.

Alternatively, in an exam question, you may simply be told which growth rate to apply.

Test your understanding 2

A company is preparing a free cash flow forecast in order to calculate the value of equity.

The following information is available:

Sales: Current sales are $500m. Growth is expected to be 8% in year1, falling by 2% pa (e.g. to 6% in year 2) until sales level out inyear 5 where they are expected to remain constant in perpetuity.

The operating profit margin will be 10% for the first two years and 12% thereafter.

Depreciation in the current year will be $7m increasing by $1m paover the planning horizon before levelling off and replacement assetinvestment is assumed to equal depreciation. Incremental investment inassets is expected to be 8% of the increase in sales in year 1, 6% ofthe increase in sales in each of the following two years, and 4% of theincrease in year 4.

Tax will be charged at 30% pa.

The WACC is 15%.

The market value of short-term investments is $4m and the market value of debt is $48m.

Calculate the value of equity.

Use of free cash flow to equity (FCFE) in valuation

The previous calculations have found equity value by:

  • discounting free cash flow to present value using the WACC, and then deducting debt value.

Alternatively, the value of equity can be found directly by:

  • discounting free cash flow TO EQUITY at the cost of equity.

In the simplest case (if FCFE is assumed to be growing at aconstant rate into perpetuity), the following formula can be applied:

FCFE0(1 + g) / (ke - g)

The formula is based on the dividend valuation model theory (see below for more details on using DVM in business valuation).

Use of Economic Value Added in valuation

Economic value added (EVA®)

The economic value added EVA® valuation model was developed by a firm called Stern Stewart. It combines:

  • the logic of the NPV model
  • the use of accounting data produced by a firm.

EVA® is an estimate of ‘economic’ profit – the amount bywhich earnings exceed the required minimum rate of return that investorscould get from other securities of comparable risk.

It follows the same principles as residual income by deducting fromprofits a charge for the opportunity cost of the capital invested.

EVA® is defined as:



NOPAT = Net operating profit after tax

r = WACC

C = firm’s invested capital

The EVA® is then "capitalised". Assuming the earnings will continue in perpetuity, the capitalised value is EVA®/WACC

Then, the value of the firm = C + capitalised EVA®, and the valueof equity = value of the firm less value of the total debt outstanding.

EVA adjustments

The NOPAT and C figures are not simply taken from the company’sfinancial statements. There are over 160 different adjustments that maybe required to bring the figures into closer alignment with the trueunderlying profitability and level of capital invested – i.e. toremove the distortions caused by conforming to the governing GAAP –although in practice only between 5 and 15 of them are usually needed toachieve a meaningful result.

Numerical illustration of the EVA® valuation method

FD plc has a NOPAT as adjusted for EVA® purposes of $562.98million. It currently has invested capital of $5,609.48 million and aWACC of 7.25%. The company has total debt of $1,500 million.

Find the EVA® for FD plc, the value of the firm and the value of the firm’s equity.



EVA® = 562.98 – (0.0725 × 5,609.48) = $156.30 million.

Firm value = C + EVA®/WACC

Firm value = 5,609.48 + 156.30/0.0725 = $7,765.34 million

Equity = Firm value – value of debt

Equity = $7,765.34 – 1,500 = $6,265.34 million

The dividend valuation model (DVM)

Theory: The value of the company/share is the present valueof the expected future dividends discounted at the shareholders’required rate of return.

Assuming a constant growth rate in dividends, g:

P0 = D0(1 + g) / (Ke - g)

Note that:

If D0 = Total dividends P0 = Value of company.

If D0 = Dividends per share P0 = Value per share.

If the growth pattern of dividends is not expected to be stable, but will vary over time, the formula can be adapted.

Explanation of terms in DVM formula

Ke = cost of equity.

g = constant rate of growth in dividends, expressed as a decimal.

D0(1 + g) = dividend just paid adjusted for one year’s growth.

DVM calculations

Basic application of DVM formula

A company has just paid a dividend of 20¢. The company expectsdividends to grow at 7% in the future. The company’s current cost ofequity is 12%.

Calculate the market value of the share.


P0 = 20(1 + 0.07)/(0.12 - 0.07) = 428¢ = $4.28

More advanced application of the DVM formula

C plc has just paid a dividend of 25¢ per share. The return on equities in this risk class is 20%.

Find the value of the shares assuming:

(i)no growth in dividends

(ii) constant growth of 5% pa

(iii)constant dividends for 5 years and then growth of 5% pa to perpetuity.


Test your understanding 3

C plc has just paid a dividend of 32¢ per share. Thereturn on equities in this risk class is 16%. Find the value of theshares assuming constant dividends for 3 years and then growth of 4% pato perpetuity.

The model is highly sensitive to changes in assumptions:

  • Where growth is high relative to the shareholders' required return, the share price is very volatile.
  • Even a minor change in investors' expectations of growth rates can cause a major change in share price contributing to the share price crashes seen in recent years.

Illustration of sensitivity of DVM

Consider the impact of a change in growth predictions of 0.5% intwo cases – the first where growth is low compared to the firmsrequired return, the other where it is high.

A firm’s ke is 7% and D0 is 10p

The change in share price as a result of changing growth predictions is shown:


(i)a growth rate of 2% dropping to 1.5%

(ii) a growth rate of 5% dropping to 4.5%

Assumption (i)

Share price at g = 2%    10 × 1.02 / (0.07 - 0.02) = 204

Share price at g = 1.5%    10 × 1.015 / (0.07 - 0.015) = 184.55

Fall in share price is (204 - 184.55) / 204 = 9.5%

Assumption (ii)

Share price at g = 5%    10 × 1.05 / (0.07 - 0.05) = 525

Share price at g = 4.5% 10 × 1.045 / (0.07 - 0.045) = 418

Fall in share price is (525 - 418) / 525 = 20.4%

The share price shows far greater volatility where growth is high relative to required return.

DVM is more suitable for valuing minority stakes, since it onlyconsiders dividends. In practice the model does tend to accurately matchactual stock market share prices.

4 Market based methods

Stock market value (market capitalisation)

For a listed company, the stock market value of the shares (or"market capitalisation") is the starting point for the valuationprocess.

In a perfectly efficient market, the market price of the shareswould be fair at all times, and would accurately reflect all informationabout a company. In reality, share prices tend to reflect publiclyavailable information.

The market share price is suitable when purchasing a minoritystake. However, a premium usually has to be paid above the currentmarket price in order to acquire a controlling interest.

The price-earnings ratio (P/E) method

The P/E method is a very simple method of valuation. It is the most commonly used method in practice.

Value of equity = PAT × Suitable industry PE ratio.

Value of a share = EPS × Suitable industry PE ratio.

PE ratio

The PE ratio applied should be that of a company (or average of several companies), that are similar with respect to:

  • business risk – i.e. in the same industry
  • finance risk – i.e. have approximately the same level of gearing
  • growth – are growing at about the same rate.

In practice this may be difficult to find, and the parties involvedin the acquisition will then negotiate the applied PE ratio up or downdepending on the specific company circumstances.

In particular, if using a quoted company's PE to value an unquotedbusiness, a substantial discount is often applied to reflect the lowermarketability of unquoted shares (around 25% in practice).

Profit figure

The PAT must be:

  • maintainable earnings going forward – some adjustment will be needed for changes anticipated as a result of the acquisition or future trading conditions (e.g. forecast synergies)

Weaknesses of the model

  • It is applied to accounting earnings which are more subjective than cash flows.
  • It assumes that the market is actually valuing earnings rather than some other aspect of the company’s output – dividends, earnings growth, risk etc.
  • It assumes that the market does accurately value shares

Earnings yield approach

The earnings yield is simply the inverse of the PE ratio:

Earnings yield = EPS/Price per share

It can therefore be used to value the shares or market capitalisation of a company in exactly the same way as the PE ratio:

Value of company = Total earnings × 1 / Earnings yield

Value per share = EPS × 1 / Earnings yield

Test your understanding 4

Company A has earnings of $300,000. A similar listed company has an earnings yield of 12.5%.

Company B has earnings of $420,500. A similar listed company has a PE ratio of 7.

Find the market capitalisation of each company.

Test your understanding 5

ABC Co is considering making a bid for the entire equity capital ofXYZ Co, a firm which has a PE ratio of 9 and earnings of $390m.

ABC Co has a PE of 13 and earnings of $693m, and it is thought that$125m of synergistic savings will be made as a consequence of thetakeover. The PE of the combined company is expected to be 12.

Calculate the minimum value acceptable to XYZ's shareholders, and the maximum amount which ABC should consider paying.

Market to book ratio (based on Tobin’s Q)

Market value of target company = Market to book ratio × book value of target company's assets

where market to book ratio = (Market capitalisation/Book value of assets) for a comparator company (or take industry average)

This method assumes a constant relationship between market value of the equity and the book value of the firm.

Problems with the model

  • Choosing an appropriate comparator – should we use industry average, or an average of similar firms only?
  • The ratio the market applies is not constant throughout its business cycle, so strictly the comparator should be taken only from other companies at the same stage.

Illustration of Tobin's Q

The industry sector average Market to Book ratio for the industry of X plc is 4.024.

The book value of X plc is $3,706m and it has 1,500m shares in issue.

Find the predicted share price.


Predicted value of X plc = $3,706m × 4.024 = $14,912.94m.

Predicted share price = $14,912.94m / 1,500m  = 994.2¢.

Test your understanding 6

The industry sector average Market to Book ratio for B's industry is 2.033

The book value of B plc is $1,572m and it has 768m shares in issue.

Find the predicted share price.

5 Asset based methods

The basic model

The traditional asset based valuation method is to take as astarting point the value of all the firm’s balance sheet assets lessany liabilities. Asset values used can be:

  • book value - the book value of assets can easily be found from the financial statements. However, it is unlikely that book values (which are based on historic cost accounting principles) will be a reliable indicator of current market values.
  • replacement cost - the buyer of a business will be interested in the replacement cost, since this represents the alternative cost of setting up a similar business from scratch (organic growth versus acquisition).
  • net realisable value - the seller of a business will usually see the realisable value of assets as the minimum acceptable price in negotiations.


  • replacement cost is not easy to identify in practice, and
  • the business is more than just the sum of its constituent parts. In fact the value of the tangible assets in many businesses is minimal since much of the value comes from the intangible assets and goodwill (e.g. compare a firm of accountants with a mining company).

6 Intangible asset valuation methods

Definition of intangible assets

Intangible assets are those assets that cannot be touched, weighed or physically measured. They include:

  • assets such as patents with legal rights attached
  • intangibles such as goodwill, purchased and valued as part of a previous acquisition
  • relationships, networks and skills built up by the business over time.

A major flaw with the basic asset valuation model is that it does not take account of the true value of intangibles.

Basic intangible valuation method

The simplest way of incorporating intangible value into the process is by the following basic formula:

Firm value = [book or replacement cost of the real assets] + [multiplier × annual profit or turnover]

The multiplier is negotiated between the parties to compensate for goodwill.

Effectively, some attempt is being made to estimate the extra valuegenerated by the intangible assets, above the value of the firm'stangible assets.

This simple formula provides the basis for the two main intangiblevaluation methods: CIV (Calculated Intangible Value) and Lev's method.

More detail on intangible assets

Often intangible assets, making up a significant part of the realworth of the company, are formed by the staff of a company – theirskills, knowledge and creativity. Such assets are created by spending onareas such as R&D, advertising and marketing, training and staffdevelopment. This type of expenditure serves to enhance the underlyingvalue of the firm rather than assisting directly in earning thisyear’s profits.

A significant problem with the basic asset valuation model is thatthe assets to be valued are taken to be those identified on the balancesheet. Where a firm has significant levels of intangible assets,accounting conventions mean they will be either not be included at all,or included at amounts well below their real commercial value.

If the asset based model is to be of use, a way of valuing these intangibles must be found.

Calculated intangible value (CIV)

This method is based on comparing (benchmarking) the return on assets earned by the company with:

  • a similar company in the same industry or
  • the industry average.

The method is similar to the residual income technique you mayremember from your earlier studies. It calculates the company’s value spread – the profit it earns over the return on assets that would be expected for a firm in that business.


(1) A suitable competitor (similar in size, structure etc.) is identified and their return on assets calculated:

Operating profit/Assets employed

(2) If no suitable similar competitor can be identified, the industry average return may be used.

(3) The company’s value spread is then calculated.

(4) Assuming that the value spread would be earned in perpetuity, the Calculated Intangible Value (CIV) is found as follows:

  • Find the post-tax value spread.
  • Divide the post-tax value spread by the cost of capital to find the present value of the post-tax value spread as a perpetuity (the CIV).

(5) The CIV is added to the net asset value to give an overall value of the firm.

CIV calculation

CXM plc operates in the advertising industry. The directors arekeen to value the company for the purposes of negotiating with apotential purchaser and plan to use the CIV method to value theintangible element.

In the past year CXM plc made an operating profit of $137.4 million on an asset base of $307 million. The company WACC is 6.5%.

A suitable competitor for benchmarking has been identified as Rplc. R plc made an operating profit of $315 million on assets employedin the business of $1,583 million.

Corporation tax is 30%.

What value should be placed on CXM?


(1) R plc is currently earning a return of 315/1,583 = 19.9%

(2) The value spread for CXM is:

(3) Calculate the CIV:

  • Find the post-tax value spread

    $76.31 × (1 - 0.3) = 53.42

  • Find the CIV by calculating the PV of the post-tax value spread (assuming it will continue into perpetuity)

    CIV = 53.42 / 0.065 = $822m

(4) The overall value of the firm = CIV + asset base

Firm value = $822m + $307m = $1,129m.

Test your understanding 7

DCH plc operates in a specialised sector of the telecommunicationsindustry. A company value is needed as part of merger talks and the CIVmethod has been chosen to value the intangible element of the business.

In the past year DCH plc made an operating profit of $256.8 million on an asset base of $522 million. The company WACC is 9%.

The average return on assets for the industry sector in which DCH plc operates is 16%

Corporation tax is 30%

What value should be placed on the company?

Problems with the CIV model:

  • Finding a similar company in terms of industry, similar asset  portfolio, similar cost gearing etc.
  • Since the competitor firm presumably also has intangibles, CIV actually measures the surplus intangible value our company has over that of the competitor rather than over its own asset value.

Lev's knowledge earnings method

An alternative method of valuing intangible assets involvesisolating the earnings deemed to be related to intangible assets, andcapitalising them. However it is more complex than the CIV model in howit determines the return to intangibles and the future growthassumptions made.

In practice, this model does produce results that are close to theactual traded share price, suggesting that is a good valuationtechnique.

However, it is often criticised as over complex given thatvaluations are in the end dependent on negotiation between the parties.

Extra examples on Type 2 and Type 3 acquisitions

Valuations can be more complex in the situation where the businessand/or financial risk of the acquirer will be affected by theacquisition. For example, when discounting cash flows (in the DVMapproach, or FCF method) it is important to use an appropriate discountrate. Alternatively, the adjusted present value approach can be used todeal with changes in finance risk.

Iterative approach (recursion)

An alternative method involves separating the post-acquisition cashflows into three streams depending on their level of business risk(acquirer's cashflows, target's cashflows and synergies). Then, thecashflows are discounted using an appropriate "combined firm" WACC.

A planning horizon is determined based on the period the acquirer believes growth can be achieved.

The cash flows are then divided into three streams:

Stream 1 – The free cash flows the acquirer was anticipating at its current growth rate.

Stream 2 – The free cash flows the target firm is predicted to achieve at the post-acquisition growth rate.

Stream 3 – Any increase or decrease expected in the acquiring firms cash flows due to synergy effects or integration costs.

The risks for each stream can be represented by the asset beta forthat type of business. The beta of Stream 3 presents a challenge as thiswill be based on the combined beta of the new firm and so a problem ofcircularity arises:

(1) To find a combined firm beta,the betas of each stream must be weighted using market values - i.e. thepresent values of that stream of cash flows

(2) To discount the stream 3 cash flows, we need the WACC of the new combined entity

(3) The WACC can only be calculated using the new combined beta

This circularity can be dealt with by using the iteration function of an Excel spreadsheet.

7 Use of the Black-Scholes model in business valuation


The Black-Scholes option pricing model was introduced in Chapter 8.

It can also be used to value the equity of a company.

The basic idea is that, because of limited liability, shareholderscan walk away from a company when the debt exceeds the asset value.However, when the assets exceed the debts, those shareholders will keeprunning the business, in order to collect the surplus.

Therefore, the value of shares can be seen as a call option ownedby shareholders – we can use Black-Scholes to value such an option.

Five factors to input into the Black-Scholes model

It is critical that we can correctly identify the five variables to input into the Black-Scholes model. 

For company valuation, these are as follows:

Pa = fair value of the firm’s assets
s = standard deviation of the assets' value
Pe = amount owed to bank (see below for more details)
t = time until debt is redeemed
r = risk free interest rate

Note that the value of Pe will not just be theredemption value of the debt. The amount owed to the bank incorporatesall the interest payments as well as the ultimate capital repayment.

In fact, the value of Pe to input into the Black-Scholesmodel should be calculated as the theoretical redemption value of anequivalent zero coupon debt.

Student Accountant article

Bob Ryan's November 2009 article in Student Accountant magazine("Application of Option Pricing to Valuation of Firms") covered thistopic in detail.

Illustration 3: Deriving Pe

A company has $100 of debt in issue carrying 5% interest and withfive years to maturity. The company’s current (pre tax) cost of debtcapital is 8%.


Calculate the theoretical redemption value of an equivalent zero coupon debt.


The repayment value on a zero coupon bond of the same currentmarket value is calculated by finding the unknown future value which,when discounted at 8% over five years, gives a present value of $88.08.

i.e. 88.08 = Value / 1.085

Value = $129.42

Test your understanding 8

Sparks is a company in the electronics industry and is looking to expand through acquisition. 

A target company, EBMS, has been identified and the directors of Sparks are looking to value the entire equity capital of EBMS.

From discussions with the directors of EBMS, the assets of EBMShave been valued at $1,450m which the directors of EBMS consider to betheir fair value in use in the business. The volatility of the assetvalue has been agreed at 10% per annum.

EBMS currently has 4% debentures in issue with a book value of$900m which are redeemable in 3 years’ time at a premium of 25% overpar. Interest is payable annually.

Short dated Government bonds are currently yielding on average4.25% and LIBOR is 0.75% above this. EBMS currently has a BBB creditrating and the following data on credit risk premiums (in basis points)has been obtained from commercial rating sources:

1 year 75
2 year 95
3 year 120
5 year 135

The directors of Sparks always try to obtain as many differentvaluations as possible when evaluating a potential acquisition and wishto use option pricing theory in addition to the more usual methods.


Using the Black Scholes option pricing model, derive a value for the total equity of EBMS.

8 High growth start-ups

A start-up business that wishes to attract equity investment will need to put a value on the business.

Valuing start-up businesses presents a different challenge fromvaluing an existing business, because unlike well-established firms manystart-ups have:

  • little or no track record
  • ongoing losses
  • few concrete revenues
  • unknown or untested products
  • little market presence.

In addition, they are often staffed by inexperienced managers withunrealistic expectations of future profitability and the lack of pastdata makes prediction of future cash flows extremely difficult.

Any mathematical valuation will inevitably be only an early starting point in the negotiations.

More detail on valuation of start up businesses

Estimating growth

Growth for a start-up can be estimated based on:

  • industry projections from securities analysts
  • qualitative evaluation of the company’s management, marketing strengths and level of investment.

However, both of these are essentially subjective and are unlikely to be reliable.

Since high-growth start-ups usually cannot fund operating expensesand investment needs out of revenues, long-term financial projectionswill be essential.

High growth is one thing, profitable high growth is another!

Growth in operating income is a function of:

  • management’s investment decisions:
    • How much a company reinvests.
    • The effectiveness of the investment in achieving results.
  • the markets acceptance of the product and the action of competitors
  • managements’ skills
  • the riskiness of the industry.

Valuation methods

Since the estimate of growth is so unpredictable and initial highgrowth can so easily stagnate or decline, valuation methods that rely ongrowth estimates are of little value:

  • Cash is key indicator of start-up success and asset models are therefore an important starting point.

However, they cannot provide an accurate value, since value rests more on potential than on the assets in place:

  • DCF models are problematic because of the non-linear and unpredictable performance often exhibited in the early years, rendering the estimates highly speculative.
  • Market based models are difficult to apply because of the problem of finding similar companies to provide a basis for comparison.

9 Problems of overvaluation

A share is overvalued if it is trading at a price that is higher than its underlying value.

In an efficient market this can still occur if:

  • the market doesn’t properly understand the business (as with internet businesses in the late 1990s) and overestimates the expected returns
  • the managers running the company do not convey full company information honestly and accurately.

Management responses to overvaluation

Managers may be reluctant to correct the markets’ mistaken perceptions. This can lead to:

  • the use of creative accounting to produce the results the city is expecting
  • poor business decisions aimed at giving the impression of success
  • ‘poor’ acquisitions made using inflated equity to finance the purchase.

The impact of overvaluation on reported earnings

Since managers may manipulate reported earnings to produce morefavourable results, the financial data they supply should be treatedwith caution. When valuing a company the financial statements shouldfirst be analysed and adjusted as necessary.

Why firms may be overvalued

Empirical evidence suggests that stock markets are semi-strongefficient – i.e. equity prices reflect all publicly availableinformation. However, this does not necessarily mean that the shareswill be fairly valued:

  • If the market doesn’t fully understand the information available – as was the case in the late 1990s and early 2000s with some high-tech, telecommunications, and internet ventures – it tends to overestimate the potential returns and so overvalue the equity.
  • The price of overvalued equity may not be corrected by the market if:
    • the data provided by managers is deliberately misleading; a particular problem where the agency relationships within companies breaks down
    • there is collusion by gatekeepers including investment and commercial banks, and audit and law firms (many of whom have been accused of knowingly contributing to the misinformation and manipulation that fed the overvaluation of stocks such as Enron and Worldcom amongst others).

The response of management

When a firm produces earnings that beat analysts’ forecasts, theshare price rises by 5.5% on average. For unexpected negative earnings,the share price falls on average by 5.05%. Even where shares are fairlypriced shares, managers may hide the inherent uncertainty in thebusiness by smoothing earnings figures – delaying expenses andbringing forward revenue recognition, for example to ensure theyconsistently meet investor expectations.

If equity remains overpriced, the company will not be able todeliver—except by pure luck—the performance to justify its value.Where the management of an overvalued company is unwilling to accept thepain of a stock market correction, earnings smoothing can escalate intofalse accounting and outright lying. In addition, projects that givethe appearance of potential earnings may be adopted even where the truelikely outcome is a negative NPV, in order to forestall city concerns.

Research has also shown that companies are more likely to makeacquisitions when their shares are overvalued. This is because they canuse the shares to buy assets (which have true worth). However, thesemergers often do not make good business sense and can destroy the corevalue of the firm.

Case study

At the time of Enron’s peak market value of $70 billion, thecompany was worth about $30 billion. The company was a major innovator,and the business had a viable future. However, senior managers wereunwilling to see the excess valuation diminished. Rather thancommunicate honestly with the market to reduce its expectations, theytried to hide the overvaluation by manipulating the financial statementsand over-exaggerating the value of new ventures. By the time the markethad realised the extent of the problem, the core value of the companyhad been destroyed.

Implications for valuations

In valuing a company, reported results form an essential core ofdata. Since reported earnings may be manipulated to produce morefavourable results (aggressive accounting) the financial statementsshould be scrutinised and restated as necessary before being used as thebasis for any valuation.

The detailed techniques are outside the syllabus but would include:

  • Calculating the Cash to Operating Profit (COP) ratio. This involves comparing EBITDA (Earnings before Interest, Tax, Depreciation and Amortisation) with operating cash flow – they should be about equal. A figure above one is an indicator of aggressive accounting.
  • Adjusting for changes in:
    • depreciation/amortisation policy
    • bad debt provisions.
  • Considering whether the amortisation of intangibles and R&D is appropriate and adjusting if necessary.
  • Making changes if necessary to the way operating leases and hire purchase agreements have been accounted for:
    • Removing any exceptional items.
    • Removing any exceptional payments such as directors severance payments.

10 Chapter overview

Test your understanding answers

Test your understanding 1


1 Standard approach

2 Free cash flow to equity

(b) Dividend cover in cash terms

The standard dividend cover calculation uses earnings after interest and tax and would give an answer of:

(470,000 - 10,000 - 180,000)/92,000 = 3 times

This high result suggests a good level of security for the ordinaryshareholders but could be misleading since it is not earnings that areused to pay dividends, but cash.

However, calculation of the cash cover gives:

Dividend cover in cash terms = (Free cash flow to equity)/dividends paid

= 230,000/92,000 = 2.5 times


dividends paid = 0.05 × (460,000 × 4)

This offers reassurance as the available resources could pay thedividend 2½ times, which would generally be considered a safe level ofcover.

Test your understanding 2


8% × (540 - 500) = 40 × 0.08

6% × (572.4 - 540) = 32.4 × 0.06

6% × (595.3 - 572.4) = 22.9 × 0.06

4% × (607.2 - 595.3) = 11.9 × 0.04

Test your understanding 3

Test your understanding 4

Company A $300,000 × 1 / 0.125= $2,4000,000

Company B $420,500 × 7 = $2,943,500

Test your understanding 5

The minimum acceptable value to XYZ's shareholders will be the current value of the equity, i.e.

9 × $390m = $3,510m

However, from ABC's perspective, it is important to estimate thevalue created by the likely synergies as well as the basic value of XYZ.Hence:

Value of XYZ to ABC = Value of the combination – Value of ABC at the moment

This measures the likely increase in value to ABC if XYZ is acquired, so will indicate the maximum amount payable.


In reality, following negotiations between ABC and XYZ, the final value is likely to be somewhere between these two figures.

Test your understanding 6

Predicted value of B plc = $1,572m × 2.033 = $3,195.88m

Predicted share price = $3,195.88m/768m = 416.13¢

Test your understanding 7

(1) The value spread for CXM is:

(2) Calculate the CIV

  • Find the post-tax value spread

    $173.28 × (1 - 0.3) = $121.30

  • Find the CIV by calculating the PV of the post-tax value spread (assuming it will continue into perpetuity)

    CIV = 121.30 / 0.09 = $1,348 million

(3) The overall value of the firm = CIV + asset base

Firm value = $1,348m + $522m = $1,870m

Test your understanding 8

The basic process is to recognise that the equity represents a calloption to purchase the company from the debenture holders in threeyears' time. 

First, calculate the exercise price. This is the redemption valueof the debt BUT including the interest element also. This requirescalculating the fair value of the debt and then converting it to a zerocoupon bond with the same fair value and time to maturity to obtain aredemption value incorporating interest as well.

Required yield = risk free rate + credit risk premium = 4.25 + 1.20 = 5.45%

Fair value calculation:

Fair Value per $100 $117.40

For a 3 year zero coupon bond to have the same fair value, the redemption premium would need to be:

Premium in 3 years = 117.40 * (1 + 5.45%)3 = $137.66

Therefore, theoretical exercise price = 137.66 / 100 * $900m = $1,238.94m

The variables can now be assigned:

Calculate Black Scholes figures
d1 = 1.73
d2 =  1.56
N(d1) = 0.9582
N(d2) = 0.9406

Calculating the main formula gives an option value of $363.5m.

This can be broken down into:

Intrinsic value  $211.06m (1,450 – 1,238.94)

Time value $152.44m

Therefore, the equity value is $363.5m which is $152.44m more than the current net assets value of the business.

Created at 5/24/2012 3:56 PM  by System Account  (GMT) Greenwich Mean Time : Dublin, Edinburgh, Lisbon, London
Last modified at 5/25/2012 12:55 PM  by System Account  (GMT) Greenwich Mean Time : Dublin, Edinburgh, Lisbon, London

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