Question

Questions 22-26 are based on the following information. CAPM and stock valuation. Your aunt, Beth, plans to invest in the common stock of Smart-investment Corporation. Knowing that you are studying finance, she asks for your suggestion. Your calculation shows that yield on Treasury securities is 6%. You know that the S&P 500 Index’s expected annual return is 14%. Your econometric model tells you that beta of this company’s stock is 1.25. Aunt Beth tells you that this company just paid an annual dividend of $2. After collecting as much information about this firm as possible, you expect the firm’s dividend will grow at an annual rate of 7% forever. The stock is currently being sold for $25 per share.

The firm’s dividend of next year is expected to be _______. a. $1.75 b. $2.00 c. $2.14 d. $2.44 23. The market risk free rate is _____. a. 6% b. 7% c. 14%

The expected return of the market portfolio is _____. a. 6% b. 7% c. 14%

The valuation of the stock is _____. a. $12.5 b. $13.375 c. $22.22 d. $23.78

Your suggestion to Aunt Beth is _____. a. buy this stock because it is underpriced b. do not buy this stock because it is overpriced

If shareholders are granted a preemptive right they will: a. be given the choice of receiving dividends either in cash or in additional shares of stock. b. be paid dividends prior to the preferred shareholders during the preemptive period. c. be entitled to two votes per share of stock. d. have priority in the purchase of any newly issued shares.

What market yield is implied by a share of common stock currently selling for $44 whose dividend just paid this year was $2.00 and is expected to grow at an annual rate of 10% forever? a. 6% b. 9% c. 14.5% d. 15%

Answer 1

Soln : Firm's dividend this year = $2, dividend will grow at , g = 7% annually i.e. Dividend next year D = 2*1.07 = $2.14

Option c is correct

Treasury security rate is given as 6%, which is considered risk free rate, hence option a is correct

S&P expected return is 14% annually, which is equivalent to expected return of market portfolio

Option c is correct.

Let P be the price of stock, using DDM we can calculate the same along with CAPM, beta of stock given as 1.25

Let r be the expected return , as per CAPM, r = risk free rate + beta*(market return - risk free rate) = 6 +1.25*(14-6)

r = 16%

Using DDM we can say , P = D/(r-g) = 2.14/(16%-7%) = 2.14/0.09 = 23.78

Option d is correct, valuation of stock = $23.78

Suggestion to Aunt Beth not to buy this stock as it is overpriced, (market price is $25> valuation)

If shareholders are granted a preemptive right they will have the priority in purchasing the newly issued shares over any other market investor. option d is correct.

Let R be the market yield to calculate:

Using DDM, we can say 44 = 2*1.1/(R-0.1)

or R-0.1 = 2.2/44 = 0.05

R = 15%, hence option d is the correct ans.