CHAPTER 10 Stock Valuation 327 Mini-Case You have finally saved $10,000 and are
ID: 2797394 • Letter: C
Question
CHAPTER 10 Stock Valuation 327 Mini-Case You have finally saved $10,000 and are ready to make your first Your required rates of return for these investments are inestment. You have the three following alternatives for invest- 6 percent for the bond, 7 percent for the preferred stock, and g that money: Capital Cities ABC, Inc. bonds with a par value of $1,000 swer and a coupon interest rate of 8.75 percent, are selling for a. Calculate the value of each investment based on your re- 15 percent for the common stock. Using this information, an- $1,314 and mature in 12 years. quired rate of return. Southwest Bancorp preferred stock is paying a dividend of b. Which investment would you select? Why? $2.50 and selling for $25.50. c. Assume Emerson Electric's managers expect an earnings ng for $36.75. The downturn and a resulting decrease in growth of 3 percent. How does this affect your answers to parts a and b? stock recently paid a $1.32 dividend and the firm's earnings er share has increased from $1.49 to $3.06 in the past five d. What required rates of return would make you indifferent to years. The firm expects to grow at the same rate for the all three options? foreseeable future.Explanation / Answer
Solution for part (a) & (b)
Value of Bond
Required rate of return on bonds = 6% p.a
Assuming coupon is paid semiannually, coupon = 1000*8.75%/2 = 43.75
Value of bond = cdf(3%,24) x coupon + df(3%,24) x Par Value
= 16.9355 x 43.75 + 0.4919 x 1000
Value of bond = 1232.83
Prevailing market price of bond = 1314
Therefore, it is not worth investing in bond
Value of Preferred Stock
Required Rate of return on preferred stock = 7%
Value of preferred stock = 2.5 / 7% = 35.71
Prevailing market price of Preferred stock = 25.50
Therefore, it is worth investing in Preferred stock.
Value of Common Stock:
Required rate of return = 15%
Compounded annual growth rate = {(3.06/1.49)^(1/5)-1} = 15.48%
(Hi buddy there is some error in question as growth rate cannot exceed required rate of return. In case it exceeds it is not possible to calculate value of common stock. According to me, it should be increased from 1.49 to 2.06, in which case growth rate will be = 6.70%)
Assuming, question is correct, it not possible to calculate value of common stock.
Part (c): decrease in growth rate by 3%
Growth Rate = 15.48%-3% = 12.48%
Therefore value of equity = D0 (1+g) / (ke-g)
= 1.32 (1.1248) / (0.15-0.1248) = 58.92
Therefore it is worth investing in Common Stock.
(d) Required rates of return that would make us indifferent.
Required return on bond
Value of bond = cdf(3%,24) x coupon + df(3%,24) x Par Value
1314 = cdf(x%,24) x 43.75 + df(x%,24) x 1000
Solving for x,
therefore required return on bond = 2.60 per half annum = 5.20 % p.a.
Required return on preferred stock = 2.50/25.50 = 9.80%
It wont be possible to solve for common stock, as there is some error in question.