Test 2 solution sketches

Winter 2014, Version A

Note for multiple-choice questions: Choose the closest

answer

Growing Dividends Thunder Chargers Printers is expected

to pay out dividends as follows: A $C dividend will be paid today. Each subsequent dividend will be paid yearly, and grow by 4% per year. The final dividend will be paid 30 years from today. After the final dividend is paid, the company will go out of business and never pay anything to stock holders again. Find C if the effective annual discount rate is 8% and the current stock value is $45 per share.

Growing Dividends

45 = C + C * 26 * [1 – (0.962963)30]

C = 45/18.6197 C = $2.42

Geometric Average In the hypothetical country of

Egonischle, the annual rate of return for long-term government bonds for the last 6 years was 20%, 15%, –50%, 25%, 30%, and 10%. What is the geometric average rate of return during this period?

Geometric Average RG = [1.2*1.15*.5*1.25*1.3*1.1]1/6

– 1 RG = [1.233375] 1/6 – 1 RG = 0.03558 = 3.56%

Portfolio Standard Deviation Two stocks, X and Y, have a

covariance of zero. Suppose that you invest in a portfolio of 70% of your money in stock X and 30% of your money in stock Y. what is the standard deviation of this portfolio if the standard deviation of stock X’s return is 15% and the standard deviation of stock Y’s return is 25%?

Portfolio Standard Deviation Portfolio Variance = (.7)2(.15)2 +

2*(.7)(.3)(0) + (.3)2(.25)2

Portfolio Variance = 0.1665 Portfolio s.d. = 12.90%

Bond PV Joe owns a bond. The bond has

three remaining coupon payments of $600 per year, starting later today. It also has a face value payment of $1000 on the date of the last coupon payment. If the stated annual discount rate is 8%, compounded monthly, what is the present value of this bond?

Bond PV EAR = (1 + .08/12)12 – 1 = 0.0830 PV = 600 + 600/1.0830 +

600/1.08302 + 1000/1.08302 PV = 1154.02 + 1364.15 PV = $2,518.17

CAPM Use the following information to

answer the next two questions: Assume that the risk-free return in

the market is currently 5%, and a stock with beta (ß) of 4 has an expected return of 17%.

CAPM What is the expected return on the

market portfolio (as defined in lecture)? .17 = .05 + 4 * (RM – .05) .12 = 4RM – .2 RM = .08

What is the risk premium? RM – RF = .08 – .05 RM – RF = .03

Growing Dividends Yakima Yak Food, Inc. will start

paying out dividends 10 years from today. The first dividend 10 years from today will be $8. Each subsequent dividend will be 12% higher than the previous dividend. The effective annual discount rate for this stock is 17%. What is the present value of this stock?

Growing Dividends Yakima Yak Food, Inc. will start

paying out dividends 10 years from today. The first dividend 10 years from today will be $8. Each subsequent dividend will be 12% higher than the previous dividend. The effective annual discount rate for this stock is 17%. What is the present value of this stock?

Growing Dividends PV = 8/(.17-.12) * 1/(1.17)9

PV = 160 * (1/4.10840) PV = $38.94

Confidence Interval From Jan. 1, 1910, to Jan. 1, 1991,

the historical average annual rate of return in the hypothetical county of Ipaly was 14%. The annual standard deviation of the rate of return was 27%. What is the lower bound of the 95.4% confidence interval for the annual rate of return based on this information?

Confidence Interval Hint: You need to be within 2

standard errors of the average to find the upper and lower bounds of the 95.4% confidence interval. S.E. = std. dev./(n1/2) = .27/(81)1/2

= .03 C.I. = R ± 2 * S.E. C.I. = .14 ± 2 * (.03) = [.08, .20] C.I. lower bound = 8%

Random Walk Use the following information to

answer the next two questions: Charlie Quack Soda stock exhibits price changes that are a random walk. In a given day, the value of the stock goes up by $3 with probability 0.2 and down by $1 with probability 0.8. The stock’s current value is $70.

Random Walk What is the probability that the

value of the stock will be more than $76 three days from today? Only way to have a price>$76 is up,

up, up Pr (up, up, up) = (.2)3 = 0.008

Random Walk What is the probability that the

value of the stock will be the same three days from today? No combination will give a price of

exactly $70 in three days Probability = 0

Cash Cow & Retained Earnings Phoenix currently owns a share of stock

in Mel’s Kitchen Supplies, Inc. Without any re-investment of their earnings, the company will earn $40 per share every year forever. The effective annual discount rate for the company is 14%. Assume that the next dividend payment will be made in 1 year. Suppose that Mel’s Kitchen Supplies could retain all of its earnings 5 years from today, and earn 25% on these earnings the following year.

Cash Cow & Retained Earnings (In other words, no dividend would

be paid 5 years from today if Mel’s Kitchen Supplies retains all of its earnings that year, and would continue to act as a cash cow in the other years.)

(a) What is the PV of this stock if it continues to act as a cash cow? PV = 40/.14 = $285.71

Cash Cow & Retained Earnings (b) Should Mel’s Kitchen Supplies

retain its earnings 5 years from today? Why/why not?

Yes, because the rate of return (25%) is higher than the discount rate (14%). Alternative answer: show that PV of

stock increases

Cash Cow & Retained Earnings (c) How much does the present

value of Mel’s Kitchen Supplies change if the company retains its earnings 5 years from today? NPV of retaining earnings

= -40/1.145 + 40(1.25)/1.146

= $2.0046

Bond Face Value A bond with face value of $X pays

a $70 coupon twice, 4 months from today and 10 months from today. The bond matures 10 months from today, and the bond currently sells for $650. If the effective annual interest rate for this bond is 11%, then what is X?

Bond Face Value 650 = 70/(1.11)4/12 + 70/(1.11)10/12

+ X/(1.11)10/12

650 = 67.61 + 64.17 + X / 1.09086

518 = X / 1.09086 X = $565.31