Project-Based Cost of CapitalProject-Based Cost of Capital

What if the project changes either the What if the project changes either the leverage of the firm or its risk or both?leverage of the firm or its risk or both?

We cannot anymore use the firm’s cost of We cannot anymore use the firm’s cost of capital (or beta) to evaluate the project.capital (or beta) to evaluate the project.

Problems with using the firm’s cost Problems with using the firm’s cost of capitalof capital

Proj

ect

IRR

Firm’s risk (beta)

SML

RF

β FIRM

Rfirm )( FMFIRMF RRβR −+

Wrongly rejected projects

Wrongly accepted projects

Taking into account the project-Taking into account the project-specific risk specific risk

We need to computeWe need to compute

Assume rAssume rDD is known. Then we need to compute r is known. Then we need to compute rEE Assuming constant D/E policy:Assuming constant D/E policy:

But how to compute rBut how to compute rUU??

““Pure-play technique”. Find firms in the market Pure-play technique”. Find firms in the market (comparables) whose whole business is similar to your (comparables) whose whole business is similar to your project, and take their rproject, and take their rUU

These firms may be levered, then you have These firms may be levered, then you have to find their rto find their rUU first. Assuming they follow a first. Assuming they follow a

constant D/E policy:constant D/E policy:

Example:Example: Comparable 1: rComparable 1: rEE=12%, r=12%, rDD=6%, D/(E+D)=40% =6%, D/(E+D)=40% ⇒⇒

rrUU=9.6%=9.6%

Comparable 2: rComparable 2: rEE=10.7%, r=10.7%, rDD=5.5%, D/=5.5%, D/

(E+D)=25% (E+D)=25% ⇒⇒ r rUU=9.4%=9.4%

Average rAverage rUU=9.5%=9.5%

Assume D/E of the firm before the project was 1, and its Assume D/E of the firm before the project was 1, and its cost of debt was = 6% (see last lecture). If we assume cost of debt was = 6% (see last lecture). If we assume that both things stay the same, we obtainthat both things stay the same, we obtain

Instead we could directly useInstead we could directly use(from the two formulas above)(from the two formulas above)where d is D/(E+D) – the where d is D/(E+D) – the project’sproject’s debt-to-value ratio debt-to-value ratio

%0.13%)6%5.9(1%5.9)( =−×+=−+= DUUE rrE

Drr

%3.8)4.01%(65.0%135.0)1( =−×+×=−+

++

= cDEwacc rDE

Dr

DE

Er τ

Note: if you don’t know rNote: if you don’t know rEE and r and rDD of the comparable firms, of the comparable firms, but know their but know their ββEE and and ββDD , then you simply use CAPM to , then you simply use CAPM to find rfind rEE and r and rDD, or you can directly compute, or you can directly compute

And then use CAPM to determine rAnd then use CAPM to determine rUU..

Note: the above formula holds only for constant D/E Note: the above formula holds only for constant D/E policypolicy

In general, your project may have D/(E+D) different from In general, your project may have D/(E+D) different from the rest of your firm. Then in the formulas in the previous the rest of your firm. Then in the formulas in the previous slide you need to use the slide you need to use the project’sproject’s D/(E+D). See D/(E+D). See example (next two slides)example (next two slides)

DEU DE

D

DE

E βββ+

++

=

Determining a project’s D/(D+E) Determining a project’s D/(D+E) (incremental leverage of a project)(incremental leverage of a project)Let dLet dpp=D=Dpp/(D/(Dpp+E+Epp) is the debt-to-value ratio you want for your ) is the debt-to-value ratio you want for your projectprojectCompute the project’s PV using WACC (assuming you know Compute the project’s PV using WACC (assuming you know the project’s risk, i.e. rthe project’s risk, i.e. rUU, and r, and rDD, you can always find its r, you can always find its rEE))

EEpp = PV = PVpp – D – Dpp and d and dpp=D=Dpp/PV/PVpp ⇒⇒ DDpp such that you achieve such that you achieve your desired dyour desired dpp

If you need to achieve certain target D/(D+E) for your firm, If you need to achieve certain target D/(D+E) for your firm, then you need to solve simultaneously:then you need to solve simultaneously: (D(Doldold +D+Dpp)/(D)/(Doldold +D+Dpp+E+Eoldold +E+Epp) = D/(D+E)) = D/(D+E) DDpp+E+Epp ≡≡ PV PVpp = discounted FCF using WACC = discounted FCF using WACC WACC is determined by dWACC is determined by dpp=D=Dpp/(D/(Dpp+E+Epp))

Valuing BusinessValuing Business

Methods of valuationMethods of valuation DCF valuation (“income” approach)DCF valuation (“income” approach) Relative valuation (“market” approach)Relative valuation (“market” approach) Cost-based valuationCost-based valuation

Relative valuation (valuation using Relative valuation (valuation using comparables)comparables)

Based on comparison with similar firms on the marketBased on comparison with similar firms on the market Uses ratios (multiples) of similar firms to estimate the share price Uses ratios (multiples) of similar firms to estimate the share price

or EV of a given firmor EV of a given firm

Most commonly used multiples:Most commonly used multiples: Earnings multiplesEarnings multiples

P/E – price to earnings ratio (share price / earnings per share P/E – price to earnings ratio (share price / earnings per share ≡≡ Market Cap / Net Income)Market Cap / Net Income)EV/EBITDAEV/EBITDA

Revenue multiplesRevenue multiplesP/S – price to sales ratioP/S – price to sales ratioEV/S – enterprise value to sales ratioEV/S – enterprise value to sales ratio

Book (or replacement) Value multiplesBook (or replacement) Value multiplesP/BV – price to book value ratioP/BV – price to book value ratioEV/BVEV/BV

Theoretical rationale for using Theoretical rationale for using multiplesmultiples

If cash flows grow at constant rate If cash flows grow at constant rate gg::

PV PV = = CFCF11/(/(rr--gg) = ) = cash flow multiplecash flow multiple ×× CFCF11

Net Income or EBITDA are not cash flows, Net Income or EBITDA are not cash flows, but the implicit assumption is that they are but the implicit assumption is that they are either close or roughly proportional to CF either close or roughly proportional to CF (the same logic of “proportionality” applies (the same logic of “proportionality” applies to using sales multiples or customer to using sales multiples or customer multiples)multiples)

Example. Valuing Ideko Corporation (BDM, ch. 19)Example. Valuing Ideko Corporation (BDM, ch. 19)

Line of business: designing and manufacturing sports Line of business: designing and manufacturing sports eyeweareyewear

Estimated 2005 Income Statement and Balance Sheet:Estimated 2005 Income Statement and Balance Sheet:

Sales = 75,000Sales = 75,000EBITDA = 16,250EBITDA = 16,250Net Income = 6,939Net Income = 6,939Debt = 4,500Debt = 4,500

Imagine you are considering acquiring this company at a Imagine you are considering acquiring this company at a price of $150 mln. Is it a fair price?price of $150 mln. Is it a fair price?At this price:At this price: P/E = 21.6P/E = 21.6 EV = E + D – cash. Assume you estimate that Ideko holds $6.5 EV = E + D – cash. Assume you estimate that Ideko holds $6.5

mln in cash in excess of its working capital needs (i.e. invested mln in cash in excess of its working capital needs (i.e. invested at a market rate of return)at a market rate of return)EV = 150 + 4.5 – 6.5 = $148 mlnEV = 150 + 4.5 – 6.5 = $148 mln

EV/Sales = 2EV/Sales = 2 EV/EBITDA = 9.1EV/EBITDA = 9.1

Ideko Financial Ratios ComparisonIdeko Financial Ratios Comparison

Prices based on multiples averaged across the three Prices based on multiples averaged across the three comparable firms:comparable firms: P/E = 23.7 P/E = 23.7 ⇒⇒ P = 164.2 P = 164.2 EV/Sales = 2.07 EV/Sales = 2.07 ⇒⇒ EV = 155 EV = 155 ⇒⇒ P = EV – D + excess cash = 157 P = EV – D + excess cash = 157 EV/EBITDA = 11.8 EV/EBITDA = 11.8 ⇒⇒ EV = 191 EV = 191 ⇒⇒ P = 193 P = 193

Hence, 150 looks like a good price, though the Hence, 150 looks like a good price, though the conclusion is not clear-cut if we look at the industry conclusion is not clear-cut if we look at the industry multiples. multiples.

We can get a further idea by looking at the We can get a further idea by looking at the range of prices implied by the range of range of prices implied by the range of multiples for comparable firms:multiples for comparable firms: Price range implied by P/E: 126.3 to 194.3Price range implied by P/E: 126.3 to 194.3 Price range implied by EV/Sales: 107 to 204.5Price range implied by EV/Sales: 107 to 204.5 Price range implied by EV/EBITDA: 153.1 to Price range implied by EV/EBITDA: 153.1 to

236236

Problems with relative valuationProblems with relative valuation

Difficult to find truly good matches (even if they do the Difficult to find truly good matches (even if they do the same business, your firm may be at a different stage of same business, your firm may be at a different stage of development, have different growth prospects, development, have different growth prospects, different business risk, different capital structure, etc.)different business risk, different capital structure, etc.)

Current earnings and sales may not accurately reflect Current earnings and sales may not accurately reflect the firm’s prospectsthe firm’s prospects

What if the market is inefficient and incorrectly values What if the market is inefficient and incorrectly values your matches? (i.e. the whole industry can be your matches? (i.e. the whole industry can be overpriced)overpriced)

Correcting for Growth RateCorrecting for Growth Rate

Assume firms similar to yours have different earnings per Assume firms similar to yours have different earnings per share (or Net Income) growth rates.share (or Net Income) growth rates.Two firms with the same current earnings but different Two firms with the same current earnings but different expected growth rates should have different prices (a expected growth rates should have different prices (a firm with a higher growth rate should be priced higher)firm with a higher growth rate should be priced higher)You should use growth-adjusted P/E ratio to value your You should use growth-adjusted P/E ratio to value your firm: PEG=(P/E)/g, where g is the expected growth in firm: PEG=(P/E)/g, where g is the expected growth in EPSEPSNote: PEG does not have a strong theoretical rationale:Note: PEG does not have a strong theoretical rationale: P P = = CFCF11/(/(rr--gg). Assuming CF ~ NI and dividing by g, we obtain:). Assuming CF ~ NI and dividing by g, we obtain: (P/E)/(P/E)/gg = 1/(( = 1/((r-gr-g))gg). RHS ). RHS dependsdepends on g! on g! But it’s true that, at least for g<r, 1/((But it’s true that, at least for g<r, 1/((r-gr-g))gg) is less sensitive to g ) is less sensitive to g

than 1/(than 1/(r-gr-g). In particular, at g=r/2 its derivative w.r.t. g equals 0.). In particular, at g=r/2 its derivative w.r.t. g equals 0.

Imagine a firm in the IT industry, InfoSoft, with Net Income = $977,300Imagine a firm in the IT industry, InfoSoft, with Net Income = $977,300

Based on Average PE its equity value (MCap) should be 977,300*28.41 = $27.765 mln

But imagine InfoSoft’s Net Income expected growth rate is 27.03%.

Then a more correct estimate of its equity value = 977,300*1.40*27.03 = $ 36.983 mln

Transaction vs. Trading MultiplesTransaction vs. Trading Multiples

Trading multiples: based on stock prices of publicly Trading multiples: based on stock prices of publicly traded comparable firmstraded comparable firmsTransaction multiples: based on acquisition prices of Transaction multiples: based on acquisition prices of comparable firmscomparable firmsAre transaction multiples normally higher or lower than Are transaction multiples normally higher or lower than trading multiples?trading multiples?Usually higher. Why?Usually higher. Why? Control premiumControl premium SynergiesSynergies Operational improvementsOperational improvements

At the same time: discount for illiquidity can lower At the same time: discount for illiquidity can lower transaction multipletransaction multiple

Example. Radio One Inc.Example. Radio One Inc.

US company. Largest radio group US company. Largest radio group targeting Afro-Americans.targeting Afro-Americans.

In 2000 Radio One got a chance to In 2000 Radio One got a chance to acquire 12 urban radio stationsacquire 12 urban radio stations

That would double Radio One’s size and That would double Radio One’s size and help build its national platformhelp build its national platform

What should the price be?What should the price be?

Valuation using trading multiplesValuation using trading multiples

Source: HBS case 9-201-025BCF = OI before depreciation, amortization and corporate expenses.

Rationale for using Radio One multiples:Rationale for using Radio One multiples: new stations are similar to Radio One’s existing stationsnew stations are similar to Radio One’s existing stations even if not very similar initially, after acquisition they will be even if not very similar initially, after acquisition they will be

operated by Radio One’s managementoperated by Radio One’s management

Problems with using Radio One multiples:Problems with using Radio One multiples: Current multiples may reflect the expectation of acquisitionCurrent multiples may reflect the expectation of acquisition

Valuation using transaction Valuation using transaction multiplesmultiples

Shortly before, Infinity Broadcasting acquired 18 stations Shortly before, Infinity Broadcasting acquired 18 stations from the same company that Radio One is going to from the same company that Radio One is going to acquire stations from.acquire stations from.The price was 21.5The price was 21.5×× 2000 BCF. 2000 BCF.If we use this multiple and BCF forecast for 2001, we get If we use this multiple and BCF forecast for 2001, we get 21.5*76,436 = 1.64 billion.21.5*76,436 = 1.64 billion.If we use actual 2000 BCF, we get 21.5*65,041 = 1.4 If we use actual 2000 BCF, we get 21.5*65,041 = 1.4 billion.billion.

Note: DCF analyses yielded 1.2-1.5 billion.Note: DCF analyses yielded 1.2-1.5 billion.What happened: the actual acquisition price was 1.4 What happened: the actual acquisition price was 1.4 billion billion

Why we need relative valuation? Why we need relative valuation? Why not always use DCF? Why not always use DCF?

You may need to get a quick estimateYou may need to get a quick estimateYou may not have enough data to build a financial You may not have enough data to build a financial model of the firmmodel of the firm Information is undisclosedInformation is undisclosed The company is too young (start-up) to have a history of The company is too young (start-up) to have a history of

operationsoperations

It may be impossible to do accurate predictions of It may be impossible to do accurate predictions of FCF for a long termFCF for a long term Multiples are often used to estimate a terminal valueMultiples are often used to estimate a terminal value

Useful to verify an estimate obtained by DCFUseful to verify an estimate obtained by DCF