ValuationThe Big Picture Aswath Damodaran http://www.damodaran.com
DCF Choices: Equity Valuation versus Firm Valuation Firm Valuation: Value the entire business Equity valuation: Value just the equity claim in the business
The Cost of Capital is central to both corporate finance and valuation • In corporate finance, the cost of capital is important because • It operates as the hurdle rate when considering new investments • It is the metric that allows firms to choose their optimal capital structure • In valuation, it is the discount rate that we use to value the operating assets of the firm.
A Simple Test • You are valuing Ambev in U.S. dollars and are attempting to estimate a risk free rate to use in the analysis. The risk free rate that you should use is • The interest rate on a nominal real denominated Brazilian government bond • The interest rate on an inflation-indexed Brazilian government bond • The interest rate on a dollar denominated Brazilian government bond (11.20%) • The interest rate on a U.S. treasury bond (4.70%)
Everyone uses historical premiums, but.. • The historical premium is the premium that stocks have historically earned over riskless securities. • Practitioners never seem to agree on the premium; it is sensitive to • How far back you go in history… • Whether you use T.bill rates or T.Bond rates • Whether you use geometric or arithmetic averages. • For instance, looking at the US: Arithmetic average Geometric Average Stocks - Stocks - Stocks - Stocks - Historical Period T.Bills T.Bonds T.Bills T.Bonds 1928-2004 7.92% 6.53% 6.02% 4.84% 1964-2004 5.82% 4.34% 4.59% 3.47% 1994-2004 8.60% 5.82% 6.85% 4.51%
Two Ways of Estimating Country Risk Premiums… September 2003 • Default spread on Country Bond: In this approach, the country risk premium is based upon the default spread of the bond issued by the country (but only if it is denominated in a currency where a default free entity exists. • Brazil was rated B2 by Moody’s and the default spread on the Brazilian dollar denominated C.Bond at the end of September 2003 was 6.01%. (10.18%-4.17%) • Relative Equity Market approach: The country risk premium is based upon the volatility of the market in question relative to U.S market. Country risk premium = Risk PremiumUS* Country Equity / US Equity Using a 4.53% premium for the US, this approach would yield: Total risk premium for Brazil = 4.53% (33.37%/18.59%) = 8.13% Country risk premium for Brazil = 8.13% - 4.53% = 3.60% (The standard deviation in weekly returns from 2001 to 2003 for the Bovespa was 33.37% whereas the standard deviation in the S&P 500 was 18.59%)
And a third approach • Country ratings measure default risk. While default risk premiums and equity risk premiums are highly correlated, one would expect equity spreads to be higher than debt spreads. • Another is to multiply the bond default spread by the relative volatility of stock and bond prices in that market. In this approach: • Country risk premium = Default spread on country bond* Country Equity / Country Bond • Standard Deviation in Bovespa (Equity) = 33.37% • Standard Deviation in Brazil C-Bond = 26.15% • Default spread on C-Bond = 6.01% • Country Risk Premium for Brazil = 6.01% (33.37%/26.15%) = 7.67%
Can country risk premiums change? Updating Brazil in January 2005 • Brazil’s financial standing and country rating improved dramatically towards the end of 2004. Its rating improved to B1. In January 2005, the interest rate on the Brazilian C-Bond dropped to 7.73%. The US treasury bond rate that day was 4.22%, yielding a default spread of 3.51% for Brazil. • Standard Deviation in Bovespa (Equity) = 25.09% • Standard Deviation in Brazil C-Bond = 15.12% • Default spread on C-Bond = 3.51% • Country Risk Premium for Brazil = 3.51% (25.09%/15.12%) = 5.82%
From Country Spreads to Corporate Risk premiums • Approach 1: Assume that every company in the country is equally exposed to country risk. In this case, E(Return) = Riskfree Rate + Country Spread + Beta (US premium) Implicitly, this is what you are assuming when you use the local Government’s dollar borrowing rate as your riskfree rate. • Approach 2: Assume that a company’s exposure to country risk is similar to its exposure to other market risk. E(Return) = Riskfree Rate + Beta (US premium + Country Spread) • Approach 3: Treat country risk as a separate risk factor and allow firms to have different exposures to country risk (perhaps based upon the proportion of their revenues come from non-domestic sales) E(Return)=Riskfree Rate+ b (US premium) + l (Country Spread)
Estimating Company Exposure to Country Risk: Determinants • Source of revenues: Other things remaining equal, a company should be more exposed to risk in a country if it generates more of its revenues from that country. A Brazilian firm that generates the bulk of its revenues in Brazil should be more exposed to country risk than one that generates a smaller percent of its business within Brazil. • Manufacturing facilities: Other things remaining equal, a firm that has all of its production facilities in Brazil should be more exposed to country risk than one which has production facilities spread over multiple countries. The problem will be accented for companies that cannot move their production facilities (mining and petroleum companies, for instance). • Use of risk management products: Companies can use both options/futures markets and insurance to hedge some or a significant portion of country risk.
Estimating Lambdas: The Revenue Approach • The easiest and most accessible data is on revenues. Most companies break their revenues down by region. One simplistic solution would be to do the following: l = % of revenues domesticallyfirm/ % of revenues domesticallyavg firm • Consider, for instance, Embraer and Embratel, both of which are incorporated and traded in Brazil. Embraer gets 3% of its revenues from Brazil whereas Embratel gets almost all of its revenues in Brazil. The average Brazilian company gets about 77% of its revenues in Brazil: • LambdaEmbraer = 3%/ 77% = .04 • LambdaEmbratel = 100%/77% = 1.30 • There are two implications • A company’s risk exposure is determined by where it does business and not by where it is located • Firms might be able to actively manage their country risk exposures
Estimating Lambdas: Stock Returns versus C-Bond Returns ReturnEmbraer = 0.0195 + 0.2681 ReturnC Bond ReturnEmbratel = -0.0308 + 2.0030 ReturnC Bond ReturnAmbev = 0.0290+ 0.4136 ReturnC Bond ReturnPetrobras= -0.0308 + 0.6600 ReturnC Bond ReturnVale = 0.02169 + 0.3760.ReturnC Bond
Estimating a US Dollar Cost of Equity for Embraer - September 2003 • Assume that the beta for Embraer is 1.07, and that the riskfree rate used is 4.17%. The historical risk premium from 1928-2002 for the US is 4.53% and the country risk premium for Brazil is 7.67%. • Approach 1: Assume that every company in the country is equally exposed to country risk. In this case, E(Return) = 4.17% + 1.07 (4.53%) + 7.67% = 16.69% • Approach 2: Assume that a company’s exposure to country risk is similar to its exposure to other market risk. E(Return) = 4.17 % + 1.07 (4.53%+ 7.67%) = 17.22% • Approach 3: Treat country risk as a separate risk factor and allow firms to have different exposures to country risk (perhaps based upon the proportion of their revenues come from non-domestic sales) E(Return)= 4.17% + 1.07(4.53%) + 0.27 (7.67%) = 11.09%
Implied Equity Premiums • We can use the information in stock prices to back out how risk averse the market is and how much of a risk premium it is demanding. • If you pay the current level of the index, you can expect to make a return of 7.87% on stocks (which is obtained by solving for r in the following equation) • Implied Equity risk premium = Expected return on stocks - Treasury bond rate = 7.87% - 4.22% = 3.65%
An Intermediate Solution • The historical risk premium of 4.84% for the United States is too high a premium to use in valuation. It is much higher than the actual implied equity risk premium in the market • The current implied equity risk premium requires us to assume that the market is correctly priced today. (If I were required to be market neutral, this is the premium I would use) • The average implied equity risk premium between 1960-2004 in the United States is about 4%. We will use this as the premium for a mature equity market.
Implied Premium for Brazil: June 2005 • Level of the Index = 26196 • Dividends on the Index = 6.19% of 16889 • Other parameters (all in US dollars) • Riskfree Rate = 4.08% • Expected Growth (in dollars) • Next 5 years = 8% (Used expected growth rate in Earnings) • After year 5 = 4.08% • Solving for the expected return: • Expected return on Equity = 11.66% • Implied Equity premium = 11.66% - 4.08% = 7.58% • Implied Equity premium for US on same day = 3.70% • Implied country premium for Brazil = 7.58% - 3.70% = 3.88%
Estimating Beta • The standard procedure for estimating betas is to regress stock returns (Rj) against market returns (Rm) - Rj = a + b Rm • where a is the intercept and b is the slope of the regression. • The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock. • This beta has three problems: • It has high standard error • It reflects the firm’s business mix over the period of the regression, not the current mix • It reflects the firm’s average financial leverage over the period rather than the current leverage.
Gross Debt versus Net Debt Approaches: Embraer in September 2003 • Net Debt Ratio for Embraer = (Debt - Cash)/ Market value of Equity = (1953-2320)/ 11,042 = -3.32% • Levered Beta for Embraer = 0.95 (1 + (1-.34) (-.0332)) = 0.93 • The cost of Equity using net debt levered beta for Embraer will be much lower than with the gross debt approach. The cost of capital for Embraer, though, will even out since the debt ratio used in the cost of capital equation will now be a net debt ratio rather than a gross debt ratio.
Estimating Synthetic Ratings • The rating for a firm can be estimated using the financial characteristics of the firm. In its simplest form, the rating can be estimated from the interest coverage ratio Interest Coverage Ratio = EBIT / Interest Expenses • For Embraer’s interest coverage ratio, we used the interest expenses and EBIT from 2002. Interest Coverage Ratio = 2166/ 222 = 9.74 • For Ambev’s interest coverage ratio, we used the interest expenses and EBIT from 2003. Interest Coverage Ratio = 2213/ 570 = 3.88 • For Vale’s interest coverage ratio, we used the interest expenses and EBIT from 2003 also Interest Coverage Ratio = 6371/1989 = 3.20
Interest Coverage Ratios, Ratings and Default Spreads If Interest Coverage Ratio is Estimated Bond Rating Default Spread(2003) Default Spread(2004) > 8.50 (>12.50) AAA 0.75% 0.35% 6.50 - 8.50 (9.5-12.5) AA 1.00% 0.50% 5.50 - 6.50 (7.5-9.5) A+ 1.50% 0.70% 4.25 - 5.50 (6-7.5) A 1.80% 0.85% 3.00 - 4.25 (4.5-6) A– 2.00% 1.00% 2.50 - 3.00 (4-4.5) BBB 2.25% 1.50% 2.25- 2.50 (3.5-4) BB+ 2.75% 2.00% 2.00 - 2.25 ((3-3.5) BB 3.50% 2.50% 1.75 - 2.00 (2.5-3) B+ 4.75% 3.25% 1.50 - 1.75 (2-2.5) B 6.50% 4.00% 1.25 - 1.50 (1.5-2) B – 8.00% 6.00% 0.80 - 1.25 (1.25-1.5) CCC 10.00% 8.00% 0.65 - 0.80 (0.8-1.25) CC 11.50% 10.00% 0.20 - 0.65 (0.5-0.8) C 12.70% 12.00% < 0.20 (<0.5) D 15.00% 20.00% The first number under interest coverage ratios is for larger market cap companies and the second in brackets is for smaller market cap companies. For Embraer and Ambev , I used the interest coverage ratio table for smaller/riskier firms (the numbers in brackets) which yields a lower rating for the same interest coverage ratio.
Estimating the cost of debt Company EBIT Interest Interest Rating Company Country Cost of Expense Coverage Spread Spread Debt($) Embraer (2003) 2166 222 9.76 AA 1.00% 4% 9.17% Ambev 2213 570 3.88 BB+ 2.00% 4% 10.70% Vale 6371 1989 3.20 BB 2.50% 4% 11.20% Petrobras 14974 3195 4.69 A- 1% 4% 9.70% Riskfree Rate = 4.17% for Embraer in 2003, 4.70% for all other firms Cost of debt ($) = Riskfree Rate + Company Spread + Country Spread (I have assumed that all of these companies will have to bear only a portion of the total country default spread of Brazil which is 4.50%)
Weights for the Cost of Capital Computation • The weights used to compute the cost of capital should be the market value weights for debt and equity. • There is an element of circularity that is introduced into every valuation by doing this, since the values that we attach to the firm and equity at the end of the analysis are different from the values we gave them at the beginning. • As a general rule, the debt that you should subtract from firm value to arrive at the value of equity should be the same debt that you used to compute the cost of capital.
Estimating Cost of Capital: Embraer • Equity • Cost of Equity = 4.17% + 1.07 (4%) + 0.27 (7.67%) = 10.52% • Market Value of Equity =11,042 million BR ($ 3,781 million) • Debt • Cost of debt = 4.17% + 4.00% +1.00%= 9.17% • Market Value of Debt = 2,093 million BR ($717 million) • Cost of Capital Cost of Capital = 10.52 % (.84) + 9.17% (1- .34) (0.16)) = 9.81% The book value of equity at Embraer is 3,350 million BR. The book value of debt at Embraer is 1,953 million BR; Interest expense is 222 mil; Average maturity of debt = 4 years Estimated market value of debt = 222 million (PV of annuity, 4 years, 9.17%) + $1,953 million/1.09174 = 2,093 million BR
Estimating Cost of Capital: Ambev • Equity • Cost of Equity = 4.7% + 0.87 (4%) + 0.41 (7.87%) = 11.41% • Market Value of Equity = 29,886 million BR ($ 9,508 million) • Debt • Cost of debt = 4.7% + 4.00% +2.00%= 10.70% • Market Value of Debt = 5,808 million BR ($1,848 million) • Cost of Capital Cost of Capital = 11.41 % (.837) + 10.7% (1- .34) (0.163)) = 10.70% The book value of equity at Ambev is 4,209 million BR. The book value of debt at Ambev is 5,980 million BR; Interest expense is 570 mil; Average maturity of debt = 3 years Estimated market value of debt = 570 million (PV of annuity, 3 years, 10.7%) + $5,980 million/1.1073 = 5,808 million BR
Estimating Cost of Capital: Vale • Equity • Cost of Equity = 4.7% + 1.04 (4%) + 0.37 (7.87%) = 11.77% • Market Value of Equity = 56,442 million BR ($ 17,958 million) • Debt • Cost of debt = 4.7% + 4.00% +2.50%= 11.20% • Market Value of Debt = 14,484 million BR ($ 4,612 million) • Cost of Capital Cost of Capital = 11.77 % (.796) + 11.2% (1- .34) (0.204)) = 10.88% The book value of equity at Vale is 15,937 million BR. The book value of debt at Vale is 13,709 million BR; Interest expense is 1,989 mil; Average maturity of debt = 2 years Estimated market value of debt = 1,989 million (PV of annuity, 2 years, 11.2%) + 13,709 million/1.1122 = 14,484 million BR
Estimating Cost of Capital: Petrobras • Equity • Cost of Equity = 4.70% + 0.79 (4%) + 0.66(7.87%) = 12.58% • Market Value of Equity = 85,218 million BR ($ 27,114 million) • Debt • Cost of debt = 4.7% + 4.00% + 1.00%= 9.70% • Market Value of Debt = 39,367 million BR ($ 12,537 million) • Cost of Capital Cost of Capital = 12.58 % (.684) + 9.7% (1- .34) (0.316)) = 10.63% The book value of equity at Petrobras is 50.987 million BR. The book value of debt at Petrobras is 42,248 million BR; Interest expense is 1,989 mil; Average maturity of debt = 4 years Estimated market value of debt = 3,195 million (PV of annuity, 4 years, 9.7%) + 42,248 million/1.0974 = 39,367 million BR
If you had to do it….Converting a Dollar Cost of Capital to a Nominal Real Cost of Capital - Ambev • Approach 1: Use a BR riskfree rate in all of the calculations above. For instance, if the BR riskfree rate was 12%, the cost of capital would be computed as follows: • Cost of Equity = 12% + (4%) + (7.7%) = 18.71% • Cost of Debt = 12% + 2% = 14% • (This assumes the riskfree rate has no country risk premium embedded in it.) • Approach 2: Use the differential inflation rate to estimate the cost of capital. For instance, if the inflation rate in BR is 8% and the inflation rate in the U.S. is 2% Cost of capital= = 1.107 (1.08/1.02)-1 = 17.21%
II. Valuing Control and SynergyAcquisition Valuation It is not what you buy but what you pay for it….
Issues in Acquisition Valuation • Acquisition valuations are complex, because the valuation often involved issues like synergy and control, which go beyond just valuing a target firm. It is important on the right sequence, including • When should you consider synergy? • Where does the method of payment enter the process. • Can synergy be valued, and if so, how? • What is the value of control? How can you estimate the value?
The Value of Control • Control has value because you think that you can run a firm better than the incumbent management. Value of Control = Value of firm, run optimally - Value of firm, status quo • The value of control should be inversely proportional to the perceived quality of that management and its capacity to maximize firm value. • Value of control will be much greater for a poorly managed firm that operates at below optimum capacity than it is for a well managed firm. It should be negligible or firms which are operating at or close to their optimal value
The Paths to Value Creation • Using the DCF framework, there are four basic ways in which the value of a firm can be enhanced: • The cash flows from existing assets to the firm can be increased, by either • increasing after-tax earnings from assets in place or • reducing reinvestment needs (net capital expenditures or working capital) • The expected growth rate in these cash flows can be increased by either • Increasing the rate of reinvestment in the firm • Improving the return on capital on those reinvestments • The length of the high growth period can be extended to allow for more years of high growth. • The cost of capital can be reduced by • Reducing the operating risk in investments/assets • Changing the financial mix • Changing the financing composition