a. Ganado’s cost of equity
b. Ganado’s cost of debt
c. Ganado’s weighted average cost of capital Domestic International
Assumptions CAPM ICAPM
Ganado’s beta, β1.05 0.85
a) Ganado’s cost of equity 9.270% 7.340%
ke = krf + ( km – krf ) β
Problem 13.1 Ganado’s Cost of Capital
Market conditions have changed. Maria Gonzalez now estimates the risk-free rate to be 3.60%, the company‘s
credit risk premium is 4.40%, the domestic beta is estimated at 1.05, the international beta at .85, and the
company‘s capital structure is now 30% debt. All other values remain the same. For both the domestic CAPM
and ICAPM, calculate:
a. 8.00% c. 5.00%
b. 7.00% d. 4.00%
Domestic International
Assumptions CAPM ICAPM
Ganado’s beta, β1.05 0.85
Risk-free rate of interest, krf 4.00% 4.00%
a) Ganado’s cost of equity 12.400% 10.800%
ke = krf + ( km – krf ) β
Differing Equity Risk Premiums CAPM ICAPM
b. 7.00% 9.583% 8.603%
d. 4.00% 7.378% 6.818%
Problem 13.2 Ganado and Equity Risk Premiums
Using the original cost of capital data for Ganado used in the chapter, calculate both the CAPM and ICAPM
costs of capital for the following equity risk premium estimates.
Answer for part a
a. If Thunderhorse beta is estimated at 1.1, what is its weighted average cost of capital?
Assumptions a) Values b) Values
Thunderhorse’s beta 1.10 0.80
Cost of debt, before tax 7.000% 7.000%
Calculation of the WACC
Cost of debt, after-tax 5.250% 5.250%
kd x ( 1 – t )
Problem 13.3 Thunderhose Oil
b. If Thunderhorse’s beta is estimated at 0.8, significantly lower because of the continuing profit
prospects in the global energy sector, what is the company’s weighted average cost of capital?
Thunderhorse Oil is a U.S. oil company. Its current cost of debt is 7%, and the 10-year U.S. Treasury
yield, the proxy for the risk-free rate of interest, is 3%. The expected return on the market portfolio is
8%. The company‘s effective tax rate is 39%. Its optimal capital structure is 60% debt and 40% equity.
a. What is Nestle’s cost of equity based on the domestic portfolio of a Swiss investor?
b. What is Nestle’s cost of equity based on a global portfolio for a Swiss investor?
Assumptions Domestic Portfolio Global Portfolio
Swiss bond index yield, the risk-free rate 0.520% 0.520%
Problem 13.4 Nestle of Switzerland Revisited
Nestle of Switzerland is revisiting its cost of equity analysis in 2014. As a result of extraordinary actions
by the Swiss Central Bank, the Swiss bond index yield (10-year maturity) has dropped to a record low of
0.520%. The Swiss equity markets have been averaging 8.400% returns, while the Financial Times
global equity market returns, indexed back to Swiss francs, is at 8.820%. Nestle’s corporate treasury staff
has estimated the company’s domestic beta at 0.825, but its global beta (against the larger global equity
market portfolio) at .515.
a. If Corcovado’s beta is estimated at 1.1, what is its weighted average cost of capital?
Assumptions a. Values b. Values
Corcovado’s beta 1.10 0.80
Cost of debt, before tax 7.000% 7.000%
Calculation of the WACC
Cost of debt, after-tax 5.250% 5.250%
kd x ( 1 – t )
Problem 13.5 Corcovado Pharmaceuticals
Corcovado Pharmaceutical’s cost of debt is 7%. The risk-free rate of interest is 3%. The expected return
on the market portfolio is 8%. After effective taxes, Corcovado’s effective tax rate is 25%. Its optimal
capital structure is 60% debt and 40% equity.
b. If Corcovado’s beta is estimated at 0.8, significantly lower because of the continuing profit prospects
in the global energy sector, what is its weighted average cost of capital?
Assumptions Values
Combined federal and state tax rate 40%
Desired capital structure:
Incremental
a. To raise $120,000,000 Debt Market Debt Cost Equity Market Equity Cost WACC
First $40,000,000 European 6.00% Domestic 12.00% 7.80%
Incremental
b. To raise $60,000,000 Debt Market Debt Cost Equity Market Equity Cost WACC
Assumptions Symbol Goldman Sachs Bank of New York
Components of beta: β
Estimate of correlation between security and market
ρjm 0.90 0.85
Estimate of standard deviation of Kashmiri’s returns σj 24.0% 30.0%
Estimating Costs of Capital
Estimated beta
β = ( ρjm x σj ) / ( σm ) β1.20 1.16
Problem 13.7 Kashmiri’s Cost of Capital
Kashmiri is the largest and most successful specialty goods company based in Bangalore, India. It has not entered the North
American marketplace yet, but is considering establishing both manufacturing and distribution facilities in the United States
through a wholly owned subsidiary. It has approached two different investment banking advisors, Goldman Sachs and Bank
of New York, for estimates of what its costs of capital would be several years into the future when it planned to list its
American subsidiary on a U.S. stock exchange. Using the following assumptions by the two different advisors, calculate the
prospective costs of debt, equity, and the WACC for Kashmiri (U.S.),
Assumptions Symbol Company A Company B Cargill
Total sales Sales $10.5 billion $45 billion $113 billion
Company‘s beta β0.83 0.68 0.90
Company credit rating S&P AA AAA
Estimating Costs of Capital Symbol Company A Company B Cargill
Cost of equity
ke = krf + (km – krf) βke 9.065% 8.240% 9.450%
Once the data is organized, the absence of a beta for Cargill is the obvious data deficiency.
A series of observations is then helpful:
1. Note that beta and credit ratings do not necessarily parallel one another
2. Credit rating and cost of debt do follow expected norms; lower the rating, the higher the cost
Problem 13.8 Cargill’s Cost of Capital
Comparables
Cargill is generally considered to be the largest privately held company in the world. Headquartered in Minneapolis, Minnesota,
the company has been averaging sales of over $113 billion per year over the past 5 year period. Although the company does not
have publicly traded shares, it is still extremely important for it to calculate its weighted average cost of capital properly in order
to make rational decisions on new investment proposals.
Assuming a risk-free rate of 4.50%, an effective tax rate of 48%, and a market risk premium of 5.50%, estimate the weighted
average cost of capital first for companies A and B, and then make a ‘guestimate’ of what you believe a comparable WACC
would be for Cargill.
Brazilian Economic Performance 1995 1996 1997 1998 1999 Mean
Inflation rate (IPC) 23.20% 10.00% 4.80% 1.00% 10.50% 9.90%
All three are on the right track. It is mostly a matter of finding the linkages beween their individual arguments.
1. Theoretically, Curly is correct in that CAPM assumes that all equity returns are over and above risk-free rates. These are of course,
expected returns, and are the investor’s expectations or requirements going INTO the investment.
3. Larry also is on the right track arguing that actual market returns will often result in less than various interest or debt instruments. One of
the more helpful arguments here is that equity returns and interest returns arise from very different economic and financial processes. Most
Problem 13.9 The Tombs
At this point both Larry and Mo simply stared at Curly, paused, and both ordered another beer. Using the Brazilian data presented, comment on this week’s
Moe – interrupts: “But you’re missing the point. The cost of capital is what the investor requires in compensation for the risk taken going into the investment.
If he doesn’t end up getting it, and that was happening here, then he pulls his capital out and walks.”
Larry argues that “its all about expected versus delivered. You can talk about what equity investors expect, but they often find that what is delivered for years
at a time is so small – even sometimes negative – that in effect the cost of equity is cheaper than the cost of debt.”
You have joined your friends at the local watering hole, The Tombs, for your weekly debate on international finance. The topic this week is whether the cost
of equity can ever be cheaper than the cost of debt. The group has chosen Brazil in the mid-1990s as the subject of the debate. One of the group members has
torn the following table of data out of a book, which is then the subject of the analysis.
Before After
Assumptions Symbol Diversification Diversification
Correlation between G-H and the market
ρjm 0.88 0.76
Standard deviation of G-H’s returns σj
28.0% 26.0%
Standard deviation of market’s returns
σm18.0% 18.0%
Estimating Costs of Capital
Estimated beta
β = ( ρjm x σj ) / ( σm ) β1.37 1.10
Estimated cost of equity
Estimated cost of equity with additional risk premium
Problem 13.10 Genedak-Hogan Cost of Equity
Use the following information to answer questions 10 through 12. Genedak-Hogan is an American conglomerate which is actively
debating the impacts of international diversification of its operations on its capital structure and cost of capital. The firm is planning
on reducing consolidated debt after diversification.
Senior management at Genedak-Hogan is actively debating the implications of diversification on its cost of equity. Although both
parties agree that the company’s returns will be less correlated with the reference market return in the future, the financial advisors
believe that the market will assess an additional 3.0% risk premium for ‘going international’ to the basic CAPM cost of equity.
Calculate Genedak-Hogan’s cost of equity before and after international diversification of its operations, with and without the
hypothetical additional risk premium, and comment on the discussion.
35.0% 35.0%
Calculate the weighted average cost of capital for Genedak-Hogan for before and after international diversification.
Before After
Assumptions Symbol Diversification Diversification
Correlation between G-H and the market
ρjm 0.88 0.76
Standard deviation of G-H’s returns σj
28.0% 26.0%
Before After
Estimating Costs of Capital Diversification Diversification
Estimated beta
β = ( ρjm x σj ) / ( σm ) β1.37 1.10
Estimated cost of equity
ke = krf + (km – krf) βke 10.529% 9.038%
Estimated cost of equity with additional risk premium
ke* = krf + (km – krf) β + RPM ke + RPM 10.529% 12.038%
Cost of debt, after-tax kd (1-t)
Weighted average cost of capital WACC
Weighted average cost of capital with RPM WACC*
There are a number of different factors at work here. First, as a result of international diversification, their access to debt
has improved, resulting in a lower cost of debt capital. This is not fully appreciated, however, as the firm has chosen to
reduce its overall use of debt post-diversification (common among MNEs).
Problem 13.11 Genedak-Hogan’s WACC
a. Did the reduction in debt costs reduce the firm’s weighted average cost of capital? How would you describe the impact of
international diversification on its costs of capital?
b. Adding the hypothetical risk premium to the cost of equity introduced in problem 10 (an added 3.0% to the cost of equity
because of international diversification), what is the firm’s WACC?
35.0% 35.0%
Before After
Assumptions Symbol Diversification Diversification
Correlation between G-H and the market
ρjm 0.88 0.76
Standard deviation of G-H’s returns σj
28.0% 26.0%
Before After
Estimating Costs of Capital Diversification Diversification
Estimated beta
β = ( ρjm x σj ) / ( σm ) β1.37 1.10
Estimated cost of equity
ke = krf + (km – krf) βke 10.529% 9.038%
Estimated cost of equity with additional risk premium
ke* = krf + (km – krf) β + RPM ke + RPM 10.529% 12.038%
Cost of debt, after-tax kd (1-t)
Weighted average cost of capital WACC
Weighted average cost of capital with RPM WACC*
Problem 13.12 Genedak-Hogan’s WACC and Effective Tax Rate
Many MNEs have greater ability to control and reduce their effective tax rates when expanding international operations. If Genedak-
Hogan was able to reduce its consolidated effective tax rate from 35% to 32%, what would be the impact on its WACC?
35.0% 32.0%