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63 All of the capital ratios that govern banks are stated in terms of book value of equity, though equity is
defined broadly to include preferred stock.

pricing model, where the cost of equity is determined by the sensitivity to multiple
unspecified economic factors or a multiple factor model, where sensitivity to macro-
economic variables is used to measure risk.
In both these models, the key inputs are the riskfree rate, the risk premiums

and the beta (in the CAPM) or betas (in the APM). The last of these inputs is
usually estimated using historical data on prices; in the case of private firms,
they might have to be estimated using comparable publicly traded firms.
While the betas are estimated using historical data, they are determined by the

fundamental decisions that a firm makes on its business mix, its operating and
financial leverage.
The cost of capital is a weighted average of the costs of the different components of

financing, with the weights based on the market values of each component. The cost
of debt is the market rate at which the firm can borrow, adjusted for any tax
advantages of borrowing. The cost of preferred stock, on the other hand, is the
preferred dividend.
The cost of capital is the minimum acceptable hurdle rate that will be used to

determine whether to invest in a project.

Live Case Study
Risk and Return: Analysis for the Firm
Objective: To develop a risk profile for your company, estimate its risk parameters and
use these parameters to estimate costs of equity and capital for the firm.

Key Questions:
What is the risk profile of your company? (How much overall risk is there in this

firm? Where is this risk coming from (market, firm, industry or currency)? How
is the risk profile changing?)
What is the performance profile of an investment in this company? What return

would you have earned investing in this company™s stock? Would you have under
or out performed the market? How much of the performance can be attributed to
How risky is this company™s equity? Why? What is its cost of equity?

How risky is this company™s debt? What is its cost of debt?

What is this company™s current cost of capital?

Framework for Analysis:
1. Estimating Historical Risk Parameters (Top Down Betas)
Run a regression of returns on your firm™s stock against returns on a market
index, preferably using monthly data and 5 years of observations (or)
If you have access to Bloomberg, go into the beta calculation page and print of the page
(after setting return intervals to monthly and using 5 years of data)
What is the intercept of the regression? What does it tell you about the

performance of this company™s stock during the period of the regression?
What is the slope of the regression?

What does it tell you about the risk of the stock?

How precise is this estimate of risk? (Provide a range for the estimate.)

What portion of this firm™s risk can be attributed to market factors? What

portion to firm-specific factors? Why is this important?
How much of the “risk” for this firm is due to business factors? How much of

it is due to financial leverage?

2. Comparing to Sector Betas (Bottom up Betas)
Break down your firm by business components, and estimate a business beta

for each component
Attach reasonable weights to each component and estimate a unlevered beta

for the business.
Using the current leverage of the company, estimate a levered beta for each

3. Choosing Between Betas
Which of the betas that you have estimated for the firm (top down or bottom

up) would you view as more reliable? Why?
Using the beta that you have chosen, estimate the expected return on an equity

investment in this company to
a short term investor

a long term investor

As a manager in this firm, how would you use this expected return?

4. Estimating Default Risk and Cost of Debt
If your company is rated,

What is the most recent rating for the firm?

What is the default spread and interest rate associated with this rating?

If your company has bonds outstanding, estimate the yield to maturity

on a long term bond? Why might this be different from the rate
estimated in the last step?
What is the company™s marginal tax rate?

If your company is not rated,

Does it have any recent borrowings? If yes, what interest rate did the

company pay on these borrowing?
Can you estimate a “synthetic” rating? If yes, what interest rate would

correspond to this rating?)
5. Estimating Cost of Capital
Weights for Debt and Equity

What is the market value of equity?


Estimate a market value for debt. (To do this you might have to collect

information on the average maturity of the debt, the interest expenses
in the most recent period and the book value of the debt)
What are the weights of debt and equity?

Cost of Capital

What is the cost of capital for the firm?

Getting Information on Risk and Return
If you want to run a regression of stock returns against a market index to estimate
a beta, you will need to estimate past returns for both the stock and index. Several
services including Bloomberg and S&P provide access to the data. If you want a beta
estimate for your firm, you can find it online or look it up in Value Line. If you want to
estimate bottom-up betas, based upon comparable firms, you will first have to identify
the businesses that your firm operates in (which should be available in the firm™s 10-K),
find comparable firms in each business and then estimate the average beta and debt to
equity ratio for these firms.
You can find the rating for your company from the S&P and Moody publications
that list all traded bonds and their ratings. Alternatively, you can estimate an interest
coverage ratio and a synthetic rating.
Online sources of information:

Problems and Questions

1. In December 1995, Boise Cascade™s stock had a beta of 0.95. The treasury bill rate at the time
was 5.8%, and the treasury bond rate was 6.4%. The firm had debt outstanding of $ 1.7 billion
and a market value of equity of $ 1.5 billion; the corporate marginal tax rate was 36%.
a. Estimate the expected return on the stock for a short term investor in the company.
b. Estimate the expected return on the stock for a long term investor in the company.
c. Estimate the cost of equity for the company.

2. Boise Cascade also had debt outstanding of $ 1.7 billion and a market value of equity of $ 1.5
billion; the corporate marginal tax rate was 36%.
a. Assuming that the current beta of 0.95 for the stock is a reasonable one, estimate the unlevered
beta for the company.
b. How much of the risk in the company can be attributed to business risk and how much to
financial leverage risk?

3. Biogen Inc., as biotechnology firm, had a beta of 1.70 in 1995. It had no debt outstanding at
the end of that year.
a. Estimate the cost of equity for Biogen, if the treasury bond rate is 6.4%.
b. What effect will an increase in long term bond rates to 7.5% have on Biogen™s cost of equity?
c. How much of Biogen™s risk can be attributed to business risk?

4. Genting Berhad is a Malaysian conglomerate, with holding in plantations and tourist resorts.
The beta estimated for the firm, relative to the Malaysian stock exchange, is 1.15, and the long
term government borrowing rate in Malaysia is 11.5%.
a. Estimate the expected return on the stock.
b. If you were an international investor, what concerns, if any, would you have about using the
beta estimated relative to the Malaysian Index? If you do, how would you modify the beta?

5. You have just done a regression of monthly stock returns of HeavyTech Inc., a manufacturer
of heavy machinery, on monthly market returns over the last five years and come up with the
following regression:
RHeavyTech = 0.5% + 1.2 RM

The variance of the stock is 50% and the variance of the market is 20%. The current T.Bill rate is
3% (It was 5% one year ago). The stock is currently selling for $50, down $4 over the last year,
and has paid a dividend of $2 during the last year and expects to pay a dividend of $2.50 over the
next year. The NYSE composite has gone down 8% over the last year, with a dividend yield of
3%. HeavyTech Inc. has a tax rate of 40%.
a. What is the expected return on HeavyTech over the next year?
b. What would you expect HeavyTech's price to be one year from today?
c. What would you have expected HeavyTech's stock returns to be over the last year?
d. What were the actual returns on HeavyTech over the last year?
e. HeavyTech has $100 million in equity and $ 5 million in debt. It plans to issue $50 million
in new equity and retire $50 million in debt. Estimate the new beta.

6. Safecorp, which owns and operates grocery stores across the United States, currently has $50
million in debt and $100 million in equity outstanding. Its stock has a beta of 1.2. It is planning a
leveraged buyout , where it will increase its debt/equity ratio of 8. If the tax rate is 40%, what
will the beta of the equity in the firm be after the LBO?

7. Novell, which had a market value of equity of $2 billion and a beta of 1.50, announced that it
was acquiring WordPerfect, which had a market value of equity of $ 1 billion, and a beta of 1.30.
Neither firm had any debt in its financial structure at the time of the acquisition, and the
corporate tax rate was 40%.
a. Estimate the beta for Novell after the acquisition, assuming that the entire acquisition was
financed with equity.
b. Assume that Novell had to borrow the $ 1 billion to acquire WordPerfect. Estimate the beta
after the acquisition.

8. You are analyzing the beta for Hewlett Packard and have broken down the company into four
broad business groups, with market values and betas for each group.
Business Group Market Value of Equity Beta
Mainframes $ 2.0 billion 1.10
Personal Computers $ 2.0 billion 1.50
Software $ 1.0 billion 2.00
Printers $ 3.0 billion 1.00

a. Estimate the beta for Hewlett Packard as a company. Is this beta going to be equal to the beta
estimated by regressing past returns on HP stock against a market index. Why or Why not?
b. If the treasury bond rate is 7.5%, estimate the cost of equity for Hewlett Packard. Estimate the
cost of equity for each division. Which cost of equity would you use to value the printer
c. Assume that HP divests itself of the mainframe business and pays the cash out as a dividend.
Estimate the beta for HP after the divestiture. (HP had $ 1 billion in debt outstanding.)

9. The following table summarizes the percentage changes in operating income, percentage
changes in revenue and betas for four pharmaceutical firms.
Firm % Change in Revenue % Change in Operating Income Beta
PharmaCorp 27% 25% 1.00
SynerCorp 25% 32% 1.15
BioMed 23% 36% 1.30
Safemed 21% 40% 1.40
a. Calculate the degree of operating leverage for each of these firms.
b. Use the operating leverage to explain why these firms have different betas.

10. A prominent beta estimation service reports the beta of Comcast Corporation, a major cable
TV operator, to be 1.45. The service claims to use weekly returns on the stock over the prior five
years and the NYSE composite as the market index to estimate betas. You replicate the
regression using weekly returns over the same period and arrive at a beta estimate of 1.60. How
would you reconcile the two estimates?

11. Battle Mountain is a mining company, which mines gold, silver and copper in mines in South
America, Africa and Australia. The beta for the stock is estimated to be 0.30. Given the volatility
in commodity prices, how would you explain the low beta?
12. You have collected returns on AnaDone Corporation (AD Corp.), a large diversified
manufacturing firm, and the NYSE index for five years:
Year AD Corp NYSE
1981 10% 5%
1982 5% 15%

1983 -5% 8%
1984 20% 12%
1985 -5% -5%
a. Estimate the intercept (alpha) and slope (beta) of the regression.
b. If you bought stock in AD Corp. today how much would you expect to make as a
return over the next year? [The six-month T.Bill rate is 6%]
c. Looking back over the last five years, how would you evaluate AD's performance


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