Last Study Topics

• Discount Rates for International Projects• International Risk• Asset Beta• Risk, DCF and CEQ

Today’s Study Topics

• Numerical• Cases• Statement

Numerical

• Example: “The cost of capital always depends on the risk of the project being evaluated. Therefore the company cost of capital is useless.” Do you agree?– It is true that the cost of capital depends on the

risk of the project being evaluated. However, if the risk of the project is similar to the risk of the other assets of the company, then the appropriate rate of return is that company’s cost of capital.

Case: British Stocks

• The following table shows estimates of the risk of two well-known British stocks during the five years ending July 2001:

Standard Deviation

R2 Beta Standard Error of Beta

British Petroleum (BP)

25 .25 .90 .17

British Airways

38 .25 1.37 .22

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• a. What proportion of each stock’s risk was market risk, and what proportion was unique risk?

• Solution: a. Both British Petroleum and British Airways had R2 values of 0.25, which means that, for both stocks 25% of total risk comes from movements in the market (i.e., market risk). – Therefore, 75% of total risk is unique risk.

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• b. What is the variance of BP? What is the unique variance?

• Solution: b. The variance of British Petroleum is: – (25)2 = 625

• Unique variance for British Petroleum is: – (0.75 × 625) = 468.75

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• c. What is the confidence level on British Airways beta?

• c. The t-statistic for βBA is: – (0.90/0.17) = 5.29

– This is significant at the 1% level, so that the confidence level is 99%.

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• d. If the CAPM is correct, what is the expect-ed return on British Airways? – Assume a risk-free interest rate of 5 % and an

expected market return of 12 %.

• Solution: – rBP = rf + βBP ×(rm - rf)

– = 0.05 + (1.37)×(0.12 – 0.05) – = 0.1459 – = 14.59%

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• e. Suppose that next year the market provides a zero return. What return would you expect from British Airways?

• Solution: – rBP = rf + βBP ×(rm - rf) – = 0.05 + (1.37)×(0 – 0.05) – = -0.0185– = -1.85%

Project’s Beta?

• What would be your best estimated beta value for a specific project incase project’s beta is not available at the first place?

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• Solution:

– If we don’t know a project’s β, we should use our best estimate. If β’s are uncertain, the required return depends on the expected β. If we know nothing about a project’s risk, our best estimate of β is 1.0, but we usually have some information on the project that allows us to modify this prior belief and make a better estimate.

Case: Lorelei Co.

• You are given the following information for Lorelei Motorwerke;

Long-term debt outstanding: Euro 300,000

Current yield to maturity (rdebt): 8%

No. of Shares of Common Stock: 10,000

Price per share: Euro 50

Book value per share: Euro 25

Expected rate of return on the stock (requity) 15%

Solution

• a. Calculate Lorelei’s company cost of capital. Ignore taxes.

• Solution: – a. The total market value of outstanding debt is

300,000 euros. – The cost of debt capital is 8%. For the common

stock, the outstanding market value is: (50 euros × 10,000) = 500,000 euros.

– The cost of equity capital is 15%.

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• Thus, Lorelei’s weighted-average cost of capital is:

– Rassets = 0.124

– = 12.4%

equitydebtassets rV

Er

V

DR

Continue• b. How would requity and the cost of capital

change if Lorelei’s stock price fell to 25 due to declining profits? Business risk Is unchanged.

• Solution: – Because business risk is unchanged, the

company’s weighted-average cost of capital will not change.

– The financial structure, however, has changed. Common stock is now worth 250,000 euros.

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• Assuming that the market value of debt and the cost of debt capital are unchanged,

• use the same equation as in Part (a) to calculate the new equity cost of capital, :

• requity= 0.177 = 17.7%

equitydebtassets rV

Er

V

DR

Case: Burlington Northern

• a. Calculate Burlington’s cost of equity from the CAPM using its own beta estimate and the industry beta estimate. How different are your answers? Assume a riskfree rate of 3.5% and a market risk premium of 8%.

.17.50PortfolioIndustry

.21.40PacificUnion

.26.52SouthernNorfolk

.24.46tionTransporta CSX

.20.64Northern Burlington

Error Standard.Beta

Solution

• rBN = rf + βBN ×(rm - rf) – = 0.035 + (0.64 × 0.08) – = 0.0862 = 8.62%

• rIND = rf + βIND ×(rm - rf) – = 0.035 + (0.50 × 0.08) – = 0.075 = 7.50%

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• b. Can you be confident that Burlington’s true beta is not the industry average?

• Solution: – b. No, we can not be confident that Burlington’s

true beta is not the industry average. – The difference between βBN and βIND (0.14) is less

than one standard error (0.20), so we cannot reject the hypothesis that βBN = βIND.

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• c. Under what circumstances might you advise Burlington to calculate its cost of equity based on its own beta estimate?

• Solution:• c. Burlington’s beta might be different from

the industry beta for a variety of reasons. – For example, Burlington’s business might be more

cyclical than is the case for the typical firm in the industry.

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– Or Burlington might have more fixed operating costs, so that operating leverage is higher.

• Another possibility is that;– Burlington has more debt than is typical for the

industry so that it has higher financial leverage.

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• d. Burlington’s cost of debt was 6 percent and its debt-to-value ratio, D/V, was .40. What was Burlington’s company cost of capital? Use the industry average beta.

• Solution: – d. Company cost of capital = (D/V)(rdebt) + (E/V)(requity)

– Company cost of capital – = (0.4 × 0.06) + (0.6 × 0.075) – = 0.069 = 6.9%

Explain

• 11. “Investors’ home country bias is diminishing rapidly. Sooner or later most investors will hold the world market portfolio, or a close approximation to it.”

– Suppose that statement is correct. What are the implications for evaluating foreign capital investment projects?

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• Solution:• Foreign capital investment projects will be

evaluated on the basis of the amount of market risk the project brings to the portfolio.

• Further, the decrease in diversifiable country bias may result in higher overall correlations.

Case: Amalgamated ProductsDivision % of Firm Value

Food 50

Electronics 30

Chemicals 20

To estimate the cost of capital for each division, Amalgamated has identified the following three principal competitors:

Estimated Equity Beta Debt/(Debt + Equity)

United Foods .8 .3

General Electronics 1.6 .2

Associated Chemicals 1.2 .4

Requirements

• a. Assuming that the debt of these firms is risk-free, estimate the asset beta for each of Amalgamated’s divisions.

• a. With risk-free debt: βassets = E/V × βequity

– Therefore:– βfood = 0.7 × 0.8 = 0.56

– βelec = 0.8 × 1.6 = 1.28

– βchem= 0.6 × 1.2 = 0.72

Continue• b. Amalgamated’s ratio of debt to debt plus

equity is .4. If your estimates of divisional betas are right, what is Amalgamated’s equity beta?

• b. βassets = (0.5 × 0.56) + (0.3 × 1.28) + (0.2 × 0.72) = 0.81– Still assuming risk-free debt:– βassets = (E/V) × (βequity)

– 0.81 = (0.6) × (βequity)

– βequity = 1.35

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• c. Assume that the risk-free interest rate is 7 percent and that the expected return on the market index is 15%. Estimate the cost of capital for each of Amalgamated’s divisions.

• Solution: • Use the Security Market Line:– rassets = rf + βassets × (rm - rf)

Continue• We have:• rfood = 0.07 + (0.56)×(0.15 - 0.07) – =0.115 = 11.5%

• relec = 0.07 + (1.28)×(0.15 - 0.07) – =0.172 = 17.2%

• rchem = 0.07 + (0.72)×(0.15 - 0.07) – =0.128 = 12.8%

Continue• d. How much would your estimates of each

division’s cost of capital change if you assumed that debt has a beta of .2?

• Solution: With risky debt:– βfood = (0.3 × 0.2) + (0.7 × 0.8) = 0.62

– ⇒ rfood = 12.0%

– βelec = (0.2 × 0.2) + (0.8 × 1.6) = 1.32

– ⇒ relec = 17.6%

– βchem = (0.4 × 0.2) + (0.6 × 1.2) = 0.80

– ⇒ rchem =13.4%

Summary

• Numerical• Cases• Statement