Tutorial 8 On Economics And Statistics With Provided Solutions PDF

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1. WACC A company is 40% financed by risk-free debt. The interest rate is 10%, the expected market risk premium is 8%, and the beta of the company's common stock is .5. What is the company cost of capital? What is the after-tax WACC, assuming that the company pays tax at a 35% rate?

Company cost of capital = 10 x .4 + (10 + .5 x 8) x .6 = 12.4% After-tax WACC = (1 - .35) x 10 x .4 + (10 + .5 x 8) x .6 = 11.0%

2. Asset Betas EZCUBE Corp. is 50% financed with long-term bonds and 50% with common equity. The debt securities have a beta of .15. The company's equity beta is 1.25. What is EZCUBE's asset beta? Beta of assets = .5 × .15 + .5 × 1.25 = .7

3.

Certainty Equivalents A project has a forecasted cash flow of $110 in year 1 and $121 in year 2. The interest rate is 5%, the estimated risk premium on the market is 10%, and the project has a beta of .5. If you use a constant riskadjusted discount rate, what is The PV of the project? The certainty-equivalent cash flow in year 1 and year 2? The ratio of the certainty-equivalent cash flows to the expected cash flows in years 1 and 2?

a.

PV =

121 110 + 1+r f + β ( r m−r f ) [ 1+ r f + β ( r m+ r f )]2

110 121 =$ 200 + 2 = 1 . 10 1. 10

b.

CEQ1/1.05 = 110/1.10, CEQ1 = $105; CEQ2 /1.052 = 121/1.102, CEQ2 = $110.25.

c.

Ratio1 = 105/110 = .95; Ratio2 = 110.25/121 = .91.

4. Cost of Capital The total market value of the common stock of the Okefenokee Real Estate Company is $6 million, and the total value of its debt is $4 million. The treasurer estimates that the beta of the stock is currently 1.5 and that the expected risk premium on the market is 6%. The Treasury bill rate is 4%. Assume for simplicity that Okefenokee debt is risk-free and the company does not pay tax. 1. 2. 3. 4.

What is the required return on Okefenokee stock? Estimate the company cost of capital. What is the discount rate for an expansion of the company's present business? Suppose the company wants to diversify into the manufacture of rose-colored spectacles. The beta of unleveraged optical manufacturers is 1.2. Estimate the required return on Okefenokee's new venture.

a. requity = rf +   (rm – rf) = 0.04 + (1.5  0.06) = 0.13 = 13%

b.

r assets =

(

)(

E D r debt + r equity= $4million ×0. 04 + $6million ×0 . 13 V $10million $10million V

)

rassets = 0.094 = 9.4% c. The cost of capital depends on the risk of the project being evaluated. 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. Here, the appropriate discount rate is 9.4%. d. requity = rf +   (rm – rf) = 0.04 + (1.2  0.06) = 0.112 = 11.2%

r assets =

(

rassets = 0.0832 = 8.32%

5.

)(

D $4million $6million E ×0. 04 + ×0 . 112 r debt + r equity= V $10million $10million V

Cost of Capital Nero Violins has the following capital structure:

)

What is the firm's asset beta? (Hint: What is the beta of a portfolio of all the firm's securities?) Assume that the CAPM is correct. What discount rate should Nero set for investments that expand the scale of its operations without changing its asset beta? Assume a risk-free interest rate of 5% and a market risk premium of 6%.

a.

(

)( )(

)(

)

D P C + β preferred × + βcommon × = V V V $100million $40million $299million + 0 .20× × 1. 20× =0 . 836 0× $439million $439million $439million βassets = βdebt ×

( b.

6.

)(

)

r = rf +   (rm – rf) = 0.05 + (0.836 0.06) = 0.10016 = 10.016%

Measuring Risk

The following table shows estimates of the risk of two well-known Canadian stocks:

1. 2.

What proportion of each stock's risk was market risk, and what proportion was specific risk? What is the variance of Toronto Dominion? What is the specific variance? 3. What is the confidence interval on Loblaw's beta? (See page 227 for a definition of “confidence interval.”) 4. If the CAPM is correct, what is the expected return on Toronto Dominion? Assume a risk-free interest rate of 5% and an expected market return of 12%. 5. Suppose that next year the market provides a zero return. Knowing this, what return would you expect from Toronto Dominion?

a.

The R2 value for Toronto Dominion was 0.25, which means that 25% of total risk comes from movements in the market (i.e., market risk). Therefore, 75% of total risk is unique risk. The R2 value for Canadian Pacific was 0.30, which means that 30% of total risk comes from movements in the market (i.e., market risk). Therefore, 70% of total risk is unique risk.

b.

The variance of Toronto Dominion is: (25)2 = 625

Market risk for Toronto Dominion: 0.25 × 625 = 156.25 Unique risk for Alcan: 0.75 × 625 = 468.75 c.

The t-statistic for CP is: 1.04/0.20 = 5.20 This is significant at the 1% level, so that the confidence level is 99%.

d.

rTD = rf + TD  (rm – rf) = 0.05 + [0.82  (0.12 – 0.05)] = 0.1074 = 10.74% rTD = rf + TD  (rm – rf) = 0.05 + [0.82  (0 – 0.05)] = 0.0090 = 0.90%

6.

Company Cost of Capital You are given the following information for Golden Fleece Financial:

Calculate Golden Fleece's company cost of capital. Ignore taxes.

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

r assets =

500,000 × 0 .08 +( × 0. 15 (300,000 ) 300,000 + 500,000 300,000 + 500,000 )

rassets = 0.124 = 12.4%

7.

Certainty Equivalents A project has the following forecasted cash flows:

The estimated project beta is 1.5. The market return rm is 16%, and the risk-free rate rf is 7%. 1. 2. 3.

Estimate the opportunity cost of capital and the project's PV (using the same rate to discount each cash flow). What are the certainty-equivalent cash flows in each year? What is the ratio of the certainty-equivalent cash flow to the expected cash flow in each year?

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:

PV =

50 60 40 = 103. 09 + + 2 1. 205 1. 205 1 .205 3

8. Changing Risks The McGregor Whisky Company is proposing to market diet scotch. The product will first be test-marketed for two years in southern California at an initial cost of $500,000. This test launch is not expected to produce any profits but should reveal consumer preferences. There is a 60% chance that demand will be satisfactory. In this case McGregor will spend $5 million to launch the scotch nationwide and will receive an expected annual profit of $700,000 in perpetuity. If demand is not satisfactory, diet scotch will be withdrawn. Once consumer preferences are known, the product will be subject to an average degree of risk, and, therefore, McGregor requires a return of 12% on its investment. However, the initial test-market phase is viewed as much riskier, and McGregor demands a return of 20% on this initial expenditure. What is the NPV of the diet scotch project?

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

NPV 2 ( if test is not successful ) = 0

NPV 2 ( if test is successful )= −5,000,000 +

700,000 =$833,333 0 .12

Therefore, at t = 0: NPV0  500,000 

(0.40 0)  (0.60 833,333)  $244,898 1.202

9.

An oil company executive is considering investing $10 million in one or both of two wells: well 1 is expected to produce oil worth $3 million a year for 10 years; well 2 is expected to produce $2 million for 15 years. These are real (inflation-adjusted) cash flows.

The beta for producing wells is .9. The market risk premium is 8%, the nominal risk-free interest rate is 6%, and expected inflation is 4%. The two wells are intended to develop a previously discovered oil field. Unfortunately there is still a 20% chance of a dry hole in each case. A dry hole means zero cash flows and a complete loss of the $10 million investment. Ignore taxes and make further assumptions as necessary. 1. 2. 3. 4.

What is the correct real discount rate for cash flows from developed wells? The oil company executive proposes to add 20 percentage points to the real discount rate to offset the risk of a dry hole. Calculate the NPV of each well with this adjusted discount rate. What do you say the NPVs of the two wells are? Is there any single fudge factor that could be added to the discount rate for developed wells that would yield the correct NPV for both wells? Explain.

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  0.08) = 0.132 = 13.2% We know that: (1 + rnominal) = (1 + rreal)  (1 + rinflation) Therefore:

r real = b.

1. 132 − 1 = 0. 0885 = 8 .85% 1 .04 10

NPV 1 = −10 million +

∑

t=1

3million = −10 million +[ (3million )× (3. 1914 )] 1. 2885t

NPV 1 = −$425,800 15

NPV 2 = −10 million +

∑

t=1

2million = −10million +[ (2million )× (3. 3888 )] 1. 2885t

NPV 2 = −$3,222,300 c.

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: 10

NPV 1 = −10 million +

∑

t=1

2 . 4million = −10 million + [ (2. 4million )× (6 . 4602 )] 1. 0885t

NPV 1 = $5,504,600 15

NPV 2 = −10 million +

∑

t=1

1 .6million = −10million +[ (1 .6million )× ( 8 .1326 )] 1 . 0885t

NPV 2 = $3,012,100 d. 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...