Answers to Practice Questions

1.                  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 the company cost of capital.

2.                  Internet exercise; answers will vary.

3.                  Internet exercise; answers will vary.

4.         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.

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

Unique variance for British Petroleum is:  (0.75 ´ 625) = 468.75

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

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

d.         rBP = rf + bBP ´(rm - rf) = 0.05 + (1.37)´(0.12 – 0.05) = 0.1459 = 14.59%

e.         rBP = rf + bBP ´(rm - rf) = 0.05 + (1.37)´(0 – 0.05) = -0.0185 = -1.85%

5.         Internet exercise; answers will vary.

6.                  If we don’t know a project’s b, we should use our best estimate.  If b’s are uncertain, the required return depends on the expected b.  If we know nothing about a project’s risk, our best estimate of b 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.

7.         a.         The total market value of outstanding debt is 300,000 euros.  The cost of debt capital is 8 percent.  For the common stock, the outstanding market value is: (50 euros ´ 10,000) = 500,000 euros.  The cost of equity capital is 15 percent.  Thus, Lorelei’s weighted-average cost of capital is:

rassets = 0.124 = 12.4%

b.                  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.  Assuming that the market value of debt and the cost of debt capital are unchanged, we can use the same equation as in Part (a) to calculate the new equity cost of capital, requity:

requity = 0.177 = 17.7%

8.         a.         rBN = rf + bBN ´(rm - rf) = 0.035 + (0.64 ´ 0.08) = 0.0862 = 8.62%

rIND = rf + bIND ´(rm - rf) = 0.035 + (0.50 ´ 0.08) = 0.075 = 7.50%

b.                  No, we can not be confident that Burlington’s true beta is not the industry average.  The difference between bBN and bIND (0.14) is less than one standard error (0.20), so we cannot reject the hypothesis that bBN = bIND.

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.  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.

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%

9.         a.         With risk-free debt:  bassets = E/V ´ bequity

Therefore:

 bfood = 0.7 ´ 0.8 = 0.56 belec = 0.8 ´ 1.6 = 1.28 bchem= 0.6 ´ 1.2 = 0.72

b.         bassets = (0.5 ´ 0.56) + (0.3 ´ 1.28) + (0.2 ´ 0.72) = 0.81

Still assuming risk-free debt:

bassets = (E/V) ´ (bequity)

0.81 = (0.6) ´ (bequity)

bequity = 1.35

c.         Use the Security Market Line:

 rassets = rf  + bassets ´ (rm - rf)

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%

d.         With risky debt:

 bfood = (0.3 ´ 0.2) + (0.7 ´ 0.8) = 0.62 Þ rfood = 12.0% belec = (0.2 ´ 0.2) + (0.8 ´ 1.6) = 1.32 Þ relec = 17.6% bchem = (0.4 ´ 0.2) + (0.6 ´ 1.2) = 0.80 Þ rchem = 13.4%

10.

 Ratio of s’s Correlation Beta Egypt 3.11 0.5 1.56 Poland 1.93 0.5 0.97 Thailand 2.91 0.5 1.46 Venezuela 2.58 0.5 1.29

The betas increase compared to those reported in Table 9.2 because the returns for these markets are now more highly correlated with the U.S. market.  Thus, the contribution to overall market risk becomes greater.

11.             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.

12.             The information could be helpful to a U.S. company considering international capital investment projects.  By examining the beta estimates, such companies can evaluate the contribution to risk of the potential cash flows.

A German company would not find this information useful.  The relevant risk depends on the beta of the country relative to the portfolio held by investors.  German investors do not invest exclusively, or even primarily, in U.S. company stocks.  They invest the major portion of their portfolios in German company stocks.

13.       a.         The threat of a coup d’état means that the expected cash flow is less than \$250,000.  The threat could also increase the discount rate, but only if it increases market risk.

b.                  The expected cash flow is: [(0.25 ´ 0) + (0.75 ´ 250,000)] = \$187,500

Assuming that the cash flow is about as risky as the rest of the company’s business:

PV = \$187,500/1.12 = \$167,411

14.       a.         Expected daily production =

(0.2 ´ 0) + (0.8) ´[(0.4 x 1,000) + (0.6 x 5,000)] = 2,720 barrels

Expected annual cash revenues = 2,720 x 365 x \$15 = \$14,892,000

b.                  The possibility of a dry hole is a diversifiable risk and should not affect the discount rate.  This possibility should affect forecasted cash flows, however.  See Part (a).

15.             The opportunity cost of capital is given by:

r = rf + b(rm - rf) = 0.05 + (1.2)´(0.06) = 0.122 = 12.2%

Therefore:

 CEQ1 = 150(1.05/1.122) = 140.37 CEQ2 = 150(1.05/1.122)2 = 131.37 CEQ3 = 150(1.05/1.122)3 = 122.94 CEQ4 = 150(1.05/1.122)4 = 115.05 CEQ5 = 150(1.05/1.122)5 = 107.67

 a1 = 140.37/150 = 0.9358 a2 = 131.37/150 = 0.8758 a3 = 122.94/150 = 0.8196 a4 = 115.05/150 = 0.767 a5 = 107.67/150 = 0.7178

From this, we can see that the a t values decline by a constant proportion each year:

 a2/a1 = 0.8758/0.9358 = 0.9358 a3/a2 = 0.8196/0.8758 = 0.9358 a4/a3 = 0.7670/0.8196 = 0.9358 a5/a4 = 0.7178/0.7670 = 0.9358

16.       a.         Using the Security Market Line, we find the cost of capital:

r = 0.07 + 1.5´(0.16 - 0.07) = 0.205 = 20.5%

Therefore:

b.

 CEQ1 = 40´(1.07/1.205) = 35.52 CEQ2 = 60´(1.07/1.205)2 = 47.31 CEQ3 = 50´(1.07)/1.205)3 = 35.01

c.

 a1 = 35.52/40 = 0.888 a2 = 47.31/60 = 0.7885 a3 = 35.01/50 = 0.7001

d.         Using a constant risk-adjusted discount rate is equivalent to assuming that at decreases at a constant compounded rate.

17.        At t = 2, there are two possible values for the project’s NPV:

Therefore, at t = 0:

Challenge Questions

1.                  It is correct that, for a high beta project, you should discount all cash flows at a high rate.  Thus, the higher the risk of the cash outflows, the less you should worry about them because, the higher the discount rate, the closer the present value of these cash flows is to zero.  This result does make sense.  It is better to have a series of payments that are high when the market is booming and low when it is slumping (i.e., a high beta) than the reverse.

The beta of an investment is independent of the sign of the cash flows.  If an investment has a high beta for anyone paying out the cash flows, it must have a high beta for anyone receiving them.  If the sign of the cash flows affected the discount rate, each asset would have one value for the buyer and one for the seller, which is clearly an impossible situation.

2.                  a.         The real issue is the degree of risk relative to the investor’s portfolio.  If German investors hold a stock portfolio comprised largely of German equities, then they are likely to find that U.S. pharmaceutical stocks are less highly correlated with their portfolios than they are with U.S. stocks, and will therefore have lower betas.  This suggests that German investors might require a lower return for investing in U.S. pharmaceutical companies than U.S. investors require.  That does not necessarily imply that they should move their R&D and production facilities to the U.S. however.  First, there might be extra costs involved in managing the business in a foreign country.  Also, R&D that simply serves a German parent company may be more highly correlated with the German market.

b.         The answer here depends on the reason that German investors keep much of their money at home.  If there are high costs for shareholders to invest overseas, then the German company may well provide its shareholders with a service by providing them with cheap international diversification.

c.                  Not necessarily.  The German company needs to be remunerated only for the risk it is taking relative to its German portfolio.  If the German company holds a portfolio comprised primarily of U.S. holdings, then 13% is the appropriate rate.

3.         a.         Since the risk of a dry hole is unlikely to be market-related, we can use the same discount rate as for producing wells.  Thus, using the Security Market Line:

rnominal = 0.06 + (0.9)´(.08) = 0.132 = 13.2%

We know that:

(1 + rnominal) = (1 + rreal) ´ (1 + rinflation)

Therefore:

b.

d.                  Expected income from Well 1: [(0.2 ´ 0) + (0.8 ´ 3 million)] = \$2.4 million

Expected income from Well 2: [(0.2 ´ 0) + (0.8 ´ 2 million)] = \$1.6 million

Discounting at 8.85 percent gives.

e.                  For Well 1, one can certainly find a discount rate (and hence a “fudge factor”) that, when applied to cash flows of \$3 million per year for 10 years, will yield the correct NPV of \$5,504,600.  Similarly, for Well 2, one can find the appropriate discount rate.  However, these two “fudge factors” will be different.  Specifically, Well 2 will have a smaller “fudge factor” because its cash flows are more distant.  With more distant cash flows, a smaller addition to the discount rate has a larger impact on present value.

4.                  Internet exercise; answers will vary.