1. FIN449 Valuation
Michael Dimond

2. Cost of Capital Ke Kd
WACC

3. Estimating Inputs: Discount Rates
Critical ingredient in discounted cashflow valuation. Errors in estimating the discount rate or mismatching cashflows and discount rates can lead to serious errors in valuation.
At an intuitive level, the discount rate used should be consistent with both the riskiness and the type of cashflow being discounted.
Equity versus Firm: If the cash flows being discounted are cash flows to equity, the appropriate discount rate is a cost of equity. If the cash flows are cash flows to the firm, the appropriate discount rate is the cost of capital.
Currency: The currency in which the cash flows are estimated should also be the currency in which the discount rate is estimated.
Nominal versus Real: If the cash flows being discounted are nominal cash flows (i.e., reflect expected inflation), the discount rate should be nominal
While discount rates are a critical ingredient in discounted cashflow valuation, I think we spend far too much time on discount rates and far too little on cashflows. The most significant errors in valuation are often the result of failures to estimate cash flows correctly….
As companies increasingly become global, and multiple listings abound (Royal Dutch has six equity listings in different markets) the consistently principle becomes very important. The currency used in estimating cash flows should also be the currency in which you estimate discount rates - Euro discount rates for Euro cashflows and peso discount rates for peso cash flows.
Recently, I came across a valuation of a Mexican company, where the cashflows were in nominal pesos but the discount rate used was the dollar cost of capital of a U.S. acquirer…. As a result, the value was inflated by more than 300%….

4. Cost of Equity
The cost of equity should be higher for riskier investments and lower for safer investments
While risk is usually defined in terms of the variance of actual returns around an expected return, risk and return models in finance assume that the risk that should be rewarded (and thus built into the discount rate) in valuation should be the risk perceived by the marginal investor in the investment
Most risk and return models in finance also assume that the marginal investor is well diversified, and that the only risk that he or she perceives in an investment is risk that cannot be diversified away (i.e, market or non-diversifiable risk)
Re-emphasizes a key assumption that we make in risk and return models in finance. It is not risk that matters, but non-diversifiable risk and the cost of equity will increase as the non-diversifiable risk in an investment increases.
This view of the world may pose a problem for us when valuing private companies or closely held, small publicly traded firms, where the marginal investor (owner, venture capitalist….) may not be diversified.

5. The CAPM: Cost of Equity
Consider the standard approach to estimating cost of equity:
Cost of Equity = Rf + Equity Beta * (E(Rm) - Rf)
where,
Rf = Riskfree rate
E(Rm) = Expected Return on the Market Index (Diversified Portfolio)
In practice,
Short term government security rates are used as risk free rates
Historical risk premiums are used for the risk premium
Betas might be estimated by regressing stock returns against market returns
While this equation is set up in terms of the capital asset pricing model, the issues raised with the CAPM apply to the more complex models as well -the APM and the multi-factor model

6. Short term Governments are not riskfree
On a riskfree asset, the actual return is equal to the expected return. Therefore, there is no variance around the expected return.
For an investment to be riskfree, then, it has to have
No default risk
No reinvestment risk
Thus, the riskfree rates in valuation will depend upon when the cash flow is expected to occur and will vary across time
A simpler approach is to match the duration of the analysis (generally long term) to the duration of the riskfree rate (also long term)
In emerging markets, there are two problems:
The government might not be viewed as riskfree (Brazil, Indonesia)
There might be no market-based long term government rate (China)
Treasury bills may be default free but there is reinvestment risk when they are used as riskless rates for longer-term cashflows. A 6-month T.Bill is not riskless when looking at a 5-year cashflow.
Would a 5-year treasury be riskfree? Not really. The coupons would still expose you to reinvestment risk. Only a 5-year zero-coupon treasury would be riskfree for a 5-year cash flow.
If you were a purist, you would need different riskfree rates for different cashflows. A pragmatic solution would be to estimate the duration of the cashflows in a valuation and use a treasury of similar duration. (Since the duration is the weighted average of when the cashflows come in, this should be fairly long, especially when you count in the fact that the terminal value is the present value of cashflows forever).

7. 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
Period T.Bills T.Bonds T.Bills T.Bonds
% 6.84% 6.21% 5.17%
% 4.68% 4.74% 3.90%
% 6.90% 9.44% 6.17%
While everyone uses historical risk premiums, the actual premium in use can vary depending upon
How far back you go in time
Whether you T.Bills or T.Bonds
Whether you use arithmetic or geometric averages
This table was developed using data that is publicly accessible on the S&P 500, treasury bills and 10-year treasury bonds on the Federal Reserve of St. Louis web site.
Dataset: histretSP.xls

8. If you choose to use historical premiums….
Go back as far as you can. A risk premium comes with a standard error. Given the annual standard deviation in stock prices is about 25%, the standard error in a historical premium estimated over 25 years is roughly:
Standard Error in Premium = 25%/√25 = 25%/5 = 5%
Be consistent in your use of the riskfree rate. Since we argued for long term bond rates, the premium should be the one over T.Bonds
Use the geometric risk premium. It is closer to how investors think about risk premiums over long periods.
The noise in stock prices is such that you need years of data to arrive at reasonably small standard errors. It is pointless estimating risk premiums with years of data.
Consistent with our argument of using a treasury bond rate as a riskfree rate, we would estimate the premium over the treasury bond rate.
If you wanted a risk premium for the next year, you would use the arithmetic average - it is the single best estimate of next year’s premium. If you want a risk premium to use in a cost of equity which will be compounded over time, you should use a geometric average.

9. Implied Equity Premiums
If we use a basic discounted cash flow model, we can estimate the implied risk premium from the current level of stock prices.
For instance, if stock prices are determined by a variation of the simple Gordon Growth Model:
Value = Expected Dividends next year/ (Required Returns on Stocks - Expected Growth Rate)
Dividends can be extended to included expected stock buybacks and a high growth period.
Plugging in the current level of the index, the dividends on the index and expected growth rate will yield a “implied” expected return on stocks. Subtracting out the riskfree rate will yield the implied premium.
This model can be extended to allow for two stages of growth - an initial period where the entire market will have earnings growth greater than that of the economy, and then a stable growth period.
The simplest analogy is to a bond. If you know the price of a bond, you can compute the yield to maturity as the discount rate that makes the present value of the expected cashflows on the bond equal to the price of the bond. Similarly, if you know the current market value of equities in the aggregate (or of an equity index), you can compute the discount rate that makes the present value of the expected cashflows on the index equal to the price of the index today.
There are two practical problems:
Unlike a bond, the cashflows on stocks are not promised but expected - you need an expected growth rate.
Unlike a bond, stocks have infinite lives. You have to consider cashflows forever.

10. Estimating Implied Premium
for U.S. Market: Jan 1, 2002
Level of the index = 1148
Treasury bond rate = 5.05%
Expected Growth rate in earnings (next 5 years) = 10.3% (Consensus estimate for S&P 500)
Expected growth rate after year 5 = 5.05%
Dividends + stock buybacks = 2.74% of index (Current year)
Year 1 Year 2 Year 3 Year 4 Year 5
Expected Dividends = $34.72 $38.30 $42.24 $46.59 $51.39
+ Stock Buybacks
Expected dividends + buybacks in year 6 = (1.0505) = $ 54.73
1148 = 34.72/(1+r) /(1+r) /(1+r) /(1+r)4 + (51.39+(54.73/(r-.0505))/(1+r)5
Solving for r, r = 8.67%. (Only way to do this is trial and error)
Implied risk premium = 8.67% % = 3.62%
Example of equity risk premium calculation as of January 1, I am assuming that the growth rate after 5 years will converge on the growth rate of the economy. (I used a growth rate of 5.5% for the economy, but it might be safer to set it equal to the treasury bond rate of 5.1%.
For the inputs, I used:
The 10- year bond rate for the T.Bond rate
The consensus estimate of growth in earnings for the S&P 500 from Zacks
I used only net stock buybacks (stock buybacks - new stock issues) in addition to dividends as a percent of the index.
Excel spreadsheet: implprem.xls

11. Traces the ebb and flow of implied premiums over time
Traces the ebb and flow of implied premiums over time. Note that as the implied premium rises, stock prices are falling.
The implied premium reached a historical high of 6.5% in 1978 and a historical low of 2% in December 1999.
Would you buy equities if you were told that you could expect to make a premium of 2% over the riskless rate?
If the answer is no, you think equities are over priced.

12. 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.
The standard approach for estimating betas- regressions - leads to flawed and backward looking estimates of risk.

13. Regressing Beta

14. Regressing Beta

15. 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 and a low R-squared
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.
The standard approach for estimating betas- regressions - leads to flawed and backward looking estimates of risk. 15

16. Beta Estimation: The Noise Problem
Note the standard error problem. Amazon has a beta estimate of 2.23, but the standard error of 0.50 results in a considerable range around this estimate.

17. Beta Estimation: The Index Effect
This beta looks much better (in terms of standard error) but it is misleading. Nokia dominates the Helisinki index (it was 70% of the index at the time of this regression).
The reason it is misleading is because Nokia’s largest single investor was Barclays, which manages one of the worlds’ largest global index funds. Barclays would not view the beta of this regression as a good measure of risk. (They would probably prefer a beta estimate against a global equity index like the Morgan Stanley Capital Index).

18. Fundamental Drivers of Beta
Product or Service: The beta value for a firm depends upon the sensitivity of the demand for its products and services and of its costs to macroeconomic factors that affect the overall market.
Cyclical companies have higher betas than non-cyclical firms
Firms which sell more discretionary products will have higher betas than firms that sell less discretionary products
Operating Leverage: The greater the proportion of fixed costs in the cost structure of a business, the higher the beta will be of that business. This is because higher fixed costs increase your exposure to all risk, including market risk.
Financial Leverage: The more debt a firm takes on, the higher the beta will be of the equity in that business. Debt creates a fixed cost, interest expenses, that increases exposure to market risk.
These are the three fundamentals that drive betas.
Firms that produce luxury goods (such as Gucci and Tiffanys) should have higher betas than firms that cater to more basic needs (Walmart). These firms tend to have revenues that are much more sensitive to changes in economic conditions.
Firms in businesses with high fixed cost structures (like airlines) should have higher betas than firms with more flexible cost structures.
Firms that borrow more money will have higher equity betas than otherwise similar firms that do not borrow money.

19. Solutions to the Regression Beta Problem
Modify the regression beta by
changing the index used to estimate the beta
adjusting the regression beta estimate, by bringing in information about the fundamentals of the company
Estimate the beta for the firm using
the standard deviation in stock prices instead of a regression against an index.
accounting earnings or revenues, which are less noisy than market prices.
Estimate the beta for the firm from the bottom up without employing the regression technique. This will require
understanding the business mix of the firm
estimating the financial leverage of the firm
Use an alternative measure of market risk that does not need a regression.
Changing the regression parameters, which is what we do in the first approach, will yield such a large range of betas (with large standard errors) that it will leave you more confused about the true beta of a firm rather than less confused.
While you can use standard deviations to compute a relative standard deviation, you are assuming that market risk and total risk are perfectly correlated. With accounting earnings, the biggest limitation is that you will have relatively few observations in your regression.
We prefer bottom-up betas….

20. Equity Betas and Leverage
The beta of equity alone can be written as a function of the unlevered beta and the debt-equity ratio
L = u (1+ ((1-t)D/E))
where
L = Levered or Equity Beta
u = Unlevered Beta (Asset Beta)
t = Corporate marginal tax rate
D = Market Value of Debt
E = Market Value of Equity
While this beta is estimated on the assumption that debt carries no market risk (and has a beta of zero), you can have a modified version:
L = u (1+ ((1-t)D/E)) - debt (1-t) (D/E)
In some books, the unlevered beta is referred to as the asset beta. To derive this equation, set up a balance sheet with the tax benefit from debt shown as an additional asset:
Assets Value Liabilities Value
Operating Assets A ( =u) Debt D (=0)
Tax Asset tD (=0) Equity E ( =lev)
You can set the weighted averages of the two sides equal: u (A/(A+tD) = lev (E/(D+E))
Substituting in A = D+E -tD, you get the first equation. If you set the beta of debt be d instead of zero, you will get the second equation.
The first equation assumes that debt carries no market risk and works reasonably well for investment grade firms. For firms with junk bonds (which tend to behave like equity and carry market risk), the second approach works better. You will need to estimate a beta for debt - I use betas that are a function of the rating of the firm, with debt betas increasing as the rating falls.

21. Bottom-up Betas The bottom up beta can be estimated by :
Taking a weighted (by sales or operating income) average of the unlevered betas of the different businesses a firm is in.
(The unlevered beta of a business can be estimated by looking at other firms in the same business)
Lever up using the firm’s debt/equity ratio
The bottom up beta will give you a better estimate of the true beta when
It has lower standard error (SEaverage = SEfirm / √n (n = number of firms)
It reflects the firm’s current business mix and financial leverage
It can be estimated for divisions and private firms.
While we still use regression betas to compute bottom-up betas, the law of large numbers works in your favor. The average of a large number of imprecise betas is more precise than any one regression beta. The reason we unlever and relever is because different firms may have different debt ratios. Three measurement issues come up:
How broadly or narrowly do we define comparable firms?
We would argue for a broader rather than a narrow definition, because the savings in standard error increase with the number of firms.
How do we deal with differences in operating leverage and business mix that may persist across these firms?
Assume that there are no differences in operating leverage and business mix or that the differences average out.
Adjust for the differences quantitatively. For instance, you could decompose the unlevered beta further into a business beta and the operating leverage effect:
Unlevered beta = Business beta (1 + (Fixed Cost/Variable costs))
How do we compute an average - simple or weighted?
I prefer simple averages. Otherwise, your betas reflect those of the largest and most stable firms in the business.

22. Comparable Firms
For investment purposes, is one stream of cash flows much like another?
Size
Growth Expectations
Cash Flows
Volatility
Exposure to economic inputs

23. Bottom-up Beta: Firm in Multiple Businesses Boeing in 1998
Segment Estimated Value Unlevered Beta Segment Weight
Commercial Aircraft 30, %
Defense 12, %
Estimated Value = Revenues of division * Enterprise Value/SalesBusiness
Unlevered Beta of firm = 0.91 (.7039) (.2961) = 0.88
Levered Beta Calculation
Market Value of Equity = $ 33,401
Market Value of Debt = $8,143
Market Debt/Equity Ratio = 24.38%
Tax Rate = 35%
Levered Beta for Boeing = 0.88 (1 + ( ) (.2438)) = 1.02
The information on business breakdown is usually available in the 10K… However, you can usually get only revenues and operating income by division. To estimate the value, I used the average enterprise value/sales multiple in each business:
Business Revenues EV/Sales Enterprise Value
Aircraft $26.9 billion 1.12 $30.16 billion
Defense $18.1 billion 0.7 $12.69 billion
You can use other multiples such as value to book and value to EBIT as well.

24. A little about country risk…

25. Country Risk Premiums
Historical risk premiums are almost impossible to estimate with any precision in markets with limited history - this is true not just of emerging markets but also of many Western European markets.
For such markets, we can estimate a modified historical premium beginning with the U.S. premium as the base:
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
Country Bond approach: In this approach, the country risk premium is based upon the default spread of the bond issued by the country.
Country risk premium = Risk PremiumUS+ Country bond default spread
Combined approach: In this approach, the country risk premium incorporates both the country bond spread and equity market volatility.
Relative Equity Market approach:
Assume, for the moment, that you are using a mature market premium for the United States of 5.51% and that the annual standard deviation of U.S. stocks is 20%. If the annual standard deviation of Indonesian stocks is 35%, the estimate of a total risk premium for Indonesia would be as follows.
Risk Premium for Indonesia = 5.51% (35/20) = 9.64%
Problem with approach: Some very risky markets have low standard deviations because of non-trading.
Country Bond Approach Brazil has dollar-denominated C-Bonds which trade at a spread of 4.83% over and above the treasury bond rate. You could treat this default spread as the country risk premium.
Problem with approach: Equity is riskier than bonds. The country spread should be larger.

26. Estimating Firm Exposure to Country Risk
Different companies should be exposed to different degrees to country risk. For instance, a Brazilian firm that generates the bulk of its revenues in the United States should be less exposed to country risk in Brazil than one that generates all its business within Brazil.
The factor “l” measures the relative exposure of a firm to country risk. One simplistic solution would be to do the following:
l = % of revenues domesticallyfirm/ % of revenues domesticallyavg firm
For instance, if a firm gets 35% of its revenues domestically while the average firm in that market gets 70% of its revenues domestically
l = 35%/ 70 % = 0.5
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
This approach, based only on revenues, is simplistic, but may be the only realistic choice given information constraints. In fact, it would be useful to know where a company’s factories are located, what currency its contracts are denominated and how much it uses derivatives.
An alternative approach worth exploring is to regress the returns on a company’s stock against the country bond and using the slope on this regression as the lambda.
Note, though, that a company could potentially then have multiple country risk exposures and that this exposure is independent of where the company is incorporated and traded. Thus, Nestle and Coca Cola should have emerging market risk premiums reflected in their costs of equity - you could look at the proportion of the revenues that each company derives from emerging markets and adjust the cost of equity accordingly.

27. Estimating a Riskfree Rate
Estimate a range for the riskfree rate in local terms:
Approach 1: Subtract default spread from local government bond rate:
Government bond rate in local currency terms - Default spread for Government in local currency
Approach 2: Use forward rates and the riskless rate in an index currency (say Euros or dollars) to estimate the riskless rate in the local currency.
Do the analysis in real terms (rather than nominal terms) using a real riskfree rate, which can be obtained in one of two ways –
from an inflation-indexed government bond, if one exists
set equal, approximately, to the long term real growth rate of the economy in which the valuation is being done.
Do the analysis in another more stable currency, say US dollars.
Approach 1: Assume that the Indian government bond rate is 12% and that the rating assigned to the Indian government is A. If the default spread for A rated bonds is 2%, the riskless Indian rupee rate would be 10%.
Riskless Rupee rate = Indian Government Bond rate – Default Spread
= 12% - 2% = 10%
Approach 2: If the current spot rate is Thai Baht per US dollar, the ten-year forward rate is Baht per dollar and the current ten-year US treasury bond rate is 5%, the ten-year Thai risk free rate (in nominal Baht) can be estimated as follows
In general, while many practitioners use the last approach (working with a different, more stable currency) to avoid having to deal with inflation in the local currency, they shift the problem of making these estimates to the cashflows from the discount rates. 27

28. A Simple Test
You are valuing Ambev, a Brazilian company, in U.S. dollars and are attempting to estimate a riskfree rate to use in the analysis. The riskfree rate that you should use is
The interest rate on a Brazilian Real denominated long term Government bond
The interest rate on a US $ denominated Brazilian long term bond (C-Bond)
The interest rate on a US $ denominated Brazilian Brady bond (which is partially backed by the US Government)
The interest rate on a US treasury bond
The correct riskfree rate is the treasury bond rate. The C-Bond has a default spread component -the additional country risk can be built into the equity risk premium.. 28

29. The Cost of Equity: A Recap
Cost of Equity = Risk Free Rate β x (Market Risk Premium)
The best approach is usually a bottom-up beta based on other firms in the business and the firm’s own capital structure
Rf must be in the same economy & currency as the cash flows being discounted, and defined in the same inflationary terms (real or nominal)
MRP can be the Historical Premium or the Implied Premium. The Historical Premium in the U.S. is the mature equity market premium earned by stocks over TBonds (between 4.5% & 5.5%).
Big Picture of Cost of Equity

30. Cost of Debt

31. Estimating the Cost of Debt
The cost of debt is the rate at which you can borrow at currently, It will reflect not only your default risk but also the level of interest rates in the market.
The cost of debt is not the rate at which you borrowed money historically. That is why you cannot use the book cost of debt in the cost of capital calculation.
The two most widely used approaches to estimating cost of debt are:
Looking up the yield to maturity on a straight bond outstanding from the firm. The limitation of this approach is that very few firms have long term straight bonds that are liquid and widely traded
Looking up the rating for the firm and estimating a default spread based upon the rating. While this approach is more robust, different bonds from the same firm can have different ratings. You have to use a median rating for the firm

32. Estimating the Cost of Debt
While ratings seem like useful tools for coming up with the cost of debt, there can be problems:
A firm may have no publicly traded debt.
A firm can have multiple ratings. You need a rating across all of a firm’s debt, not just its safest.
While many companies have bonds outstanding, corporate bonds often have special features attached to them and are not liquid, making it difficult to use the yield to maturity as the cost of debt.
A firm’s bonds can be structured in such a way that they can be safer than the rest of the firm’s debt - they can be more senior or secured than the other debt of the firm.
The alternative is to estimate a synthetic rating for your firm and determine the cost of debt based upon that rating.

33. 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
Cov.Ratio Est. Bond Rating
> 8.50 AAA AA A+ A A–
BBB BB B+ B
B –
CCC CC C
< 0.20 D
This is a simplistic approach but it uses the ratio that explains the largest proportion of the differences between ratings at non-financial service U.S. companies - I tried the 8 ratios that S&P said it depends upon the most to rate companies (which are available on its web site) and correlated them with bond ratings in 1999.
You could expand this approach to incorporate other ratios and create a score - similar to the Altman Z score - but you have to decide on whether the trade off is worth it - more complexity for less transparency.

34. Estimating Synthetic Ratings
Interest Coverage Ratio = EBIT / Interest Expenses
Consider two firms, Company Y and Company Z
For Company Y
EBIT = $161MM
Interest Expense = $48MM
Interest Coverage Ratio =
For Company Z
EBIT = $55,467MM
Interest Expense = $4,028MM
This is a simplistic approach but it uses the ratio that explains the largest proportion of the differences between ratings at non-financial service U.S. companies - I tried the 8 ratios that S&P said it depends upon the most to rate companies (which are available on its web site) and correlated them with bond ratings in 1999.
You could expand this approach to incorporate other ratios and create a score - similar to the Altman Z score - but you have to decide on whether the trade off is worth it - more complexity for less transparency.

35. Estimating Synthetic Ratings
Interest Coverage Ratio = EBIT / Interest Expenses
Consider two firms, Company Y and Company Z
For Company Y
EBIT = $161MM
Interest Expense = $48MM
Interest Coverage Ratio = 161/48 = 3.33
For Company Z
EBIT = $55,467MM
Interest Expense = $4,028MM
Interest Coverage Ratio = 55,467/ 4028= 13.77
This is a simplistic approach but it uses the ratio that explains the largest proportion of the differences between ratings at non-financial service U.S. companies - I tried the 8 ratios that S&P said it depends upon the most to rate companies (which are available on its web site) and correlated them with bond ratings in 1999.
You could expand this approach to incorporate other ratios and create a score - similar to the Altman Z score - but you have to decide on whether the trade off is worth it - more complexity for less transparency.

36. 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
Cov.Ratio Est. Bond Rating
> 8.50 AAA AA A+ A A–
BBB BB B+ B
B –
CCC CC C
< 0.20 D
Company Z
Company Y
This is a simplistic approach but it uses the ratio that explains the largest proportion of the differences between ratings at non-financial service U.S. companies - I tried the 8 ratios that S&P said it depends upon the most to rate companies (which are available on its web site) and correlated them with bond ratings in 1999.
You could expand this approach to incorporate other ratios and create a score - similar to the Altman Z score - but you have to decide on whether the trade off is worth it - more complexity for less transparency.

37. 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
Cov.Ratio Est. Bond Rating Spread
> 8.50 AAA 0.50%
AA 0.65%
A+ 0.85%
A 1.00%
A– 1.10%
BBB 1.60%
BB 3.35%
B+ 3.75%
B 5.00%
B – 5.25%
CCC 8.00%
CC 10.00%
C 12.00%
< 0.20 D 15.00%
Company Z
Company Y
This is a simplistic approach but it uses the ratio that explains the largest proportion of the differences between ratings at non-financial service U.S. companies - I tried the 8 ratios that S&P said it depends upon the most to rate companies (which are available on its web site) and correlated them with bond ratings in 1999.
You could expand this approach to incorporate other ratios and create a score - similar to the Altman Z score - but you have to decide on whether the trade off is worth it - more complexity for less transparency.

38. Estimating Synthetic Ratings
Assuming the appropriate Risk Free Rate is 4.71%...
Company Y’s Cost of Debt is 5.81% (4.71% %)
Company Z’s Cost of Debt is 5.21% (4.71% %)
Cov.Ratio Est. Bond Rating Spread
> 8.50 AAA 0.50%
AA 0.65%
A+ 0.85%
A 1.00%
A– 1.10%
BBB 1.60%
BB 3.35%
B+ 3.75%
B 5.00%
B – 5.25%
CCC 8.00%
CC 10.00%
C 12.00%
< 0.20 D 15.00%
Company Z
Company Y
This is a simplistic approach but it uses the ratio that explains the largest proportion of the differences between ratings at non-financial service U.S. companies - I tried the 8 ratios that S&P said it depends upon the most to rate companies (which are available on its web site) and correlated them with bond ratings in 1999.
You could expand this approach to incorporate other ratios and create a score - similar to the Altman Z score - but you have to decide on whether the trade off is worth it - more complexity for less transparency.

39. Historic Spreads
The Default Spread is the amount above the Risk Free Rate at the applicable time.
Ratio Est. Rating Spread(1/99) Spread(1/01)
> 8.50 AAA 0.20% 0.75%
AA 0.50% 1.00%
A+ 0.80% 1.50%
A 1.00% 1.80%
A– 1.25% 2.00%
BBB 1.50% 2.25%
BB 2.00% 3.50%
B+ 2.50% 4.75%
B 3.25% 6.50%
B – 4.25% 8.00%
CCC 5.00% 10.00%
CC 6.00% 11.50%
C 7.50% 12.70%
< 0.20 D 10.00% 15.00%
This table was last updated in 1999 (for interest coverage ratios and ratings). The default spreads get updated more frequently. Note how much the spreads increased from 2000 to 2001, reflecting the slowing of the economy.

40. Weights for 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.
The rationale for using market values is simple. You are considering how much someone who would buy the company today should be willing to pay for the company. Since he or she can buy equity and debt at today’s market value, you use those as weights. However, you could very well push the market values towards your estimated values in the process of buying the company. If this is a concern, you can iterate the weights in the cost of capital calculation to make the values used in the weights converge on the values estimated in the analysis.

41. What About International Ratings?
To develop an interest coverage ratio/ratings table, you need lots of rated firms and objective ratings agencies. This is most feasible in the United States.
The relationship between interest coverage ratios and ratings developed using US companies tends to travel well, as long as we are analyzing large manufacturing firms in markets with interest rates close to the US interest rate.
They are more problematic when looking at smaller companies in markets with higher interest rates than the US. When interest rates are high, interest coverage ratios will come under downward pressure and the premiums may need to be adjusted to reflect this.

42. Cost of Debt computations
When estimating the cost of debt for an emerging market company, you have to decide whether to add the country default spread to the company default spread when estimating the cost of debt.
Companies in countries with low bond ratings and high default risk might bear the burden of country default risk
For example, if Company Y is in such a country and the Country Default Risk is estimated as 5.25%, the rating estimated of A- yields a cost of debt as follows:
= US T.Bond rate + Country default spread + Company Default Spread
= 4.71% % % = 11.06%

43. Estimating A U.S. $ Cost of Capital for a Foreign Firm
Equity
Cost of Equity = 4.71% (4.5% %) = 15.38%
Market Value of Equity = 995 million (94.40%)
Debt
Cost of debt = 4.71% % (Country default) +1.10% (Company default) = 11.06%
Market Value of Debt = 59 Mil (5.60%)
Cost of Capital
Cost of Capital = % (.9440) % ( ) (.0560))
= % (.9440) % (.0560)
= %
Mature Market Premium
Country Risk Premium for Argentina
Same process. Much bigger impact of country risk.

44. What About Large Multinationals?
For smaller, less well known firms, it is safer to assume that firms cannot borrow at a rate lower than the countries in which they are incorporated. For larger firms, you could make the argument that firms can borrow at lower rates. In practical terms, you could ignore the country default spread or add only a fraction of that spread.

45. Dealing with Preferred Stock
When dealing with significant amounts of preferred stock, it is better to keep it as a separate component. As a rule of thumb, if the preferred stock is less than 5% of the outstanding market value of the firm, lumping it in with debt will make no significant impact on your valuation.
Preferred stock is non-tax deductible, which makes it unlike debt and unlike common equity. Here, you would make the exception and allow for a third source of capital.
The cost of preferred stock is the preferred dividend yield.

46. Dealing with Hybrids
Keep your cost of capital simple. If possible, consolidate all of your capital into either debt or equity. With convertible bonds, this is fairly simple to do.
When dealing with hybrids (convertible bonds, for instance), break the security down into debt and equity and allocate the amounts accordingly. Thus, if a firm has $ 125 million in convertible debt outstanding, break the $125 million into straight debt and conversion option components. The conversion option is equity.

47. Recapping the Cost of Capital
WACC should also include figures for Preferred Stock if it is of a significant weight. If it is insignificant, you may include it with debt, not with common equity, when valuing the equity of a firm.
Big picture of the cost of capital.