# Expected growth rate, required rate of return, current price

Please show work you can use either calculator.

Other things being equal, an increase in a firm's expected growth rate would cause its required rate of return to

a. fluctuate more than before.

b. fluctuate less than before.

c. decrease.

d. increase.

e. possibly increase, possibly decrease, or possibly remain constant.

Stocks A and B have the same price and are in equilibrium, but Stock A has the higher required rate of return. Which of the following statements is CORRECT?

a. Stock A must have both a higher dividend yield and a higher capital gains yield than Stock B.

b. If Stock A has a lower dividend yield than Stock B, its expected capital gains yield must be higher than Stock B's.

c. Stock B must have a higher dividend yield than Stock A.

d. Stock A must have a higher dividend yield than Stock B.

e. If Stock A has a higher dividend yield than Stock B, its expected capital gains yield must be lower than Stock B's.

Which of the following statements is CORRECT, assuming stocks are in equilibrium?

a. Assume that the required return on a given stock is 15%. If the stock's dividend is growing at a constant rate of 4%, its expected dividend yield is 6%.

b. Other things held constant, the higher a company's beta coefficient, the lower its required rate of return.

c. A required condition for one to use the constant growth model is that the stock's expected growth rate is lower than its required rate of return.

d. A stock's dividend yield can never exceed its expected growth rate

e. All of the above statements are correct

A stock is expected to pay a dividend of $0.75 at the end of the year. The required rate of return is r = 10.5%, and the expected constant growth rate is g = 6.0%. What is the stock's current price?

a. $16.67

b. $18.50

c. $20.83

d. $15.83

e. $18.67

Gay Manufacturing is expected to pay a dividend of $1.25 per share at the end of the year. The stock sells for $21.50 per share, and its required rate of return is 10.5%. The dividend is expected to grow at some constant rate, g, forever. What is the equilibrium expected growth rate?

Molen Inc. has an outstanding issue of perpetual preferred stock with an annual dividend of $2.50 per share. If the required return on this preferred stock is 6.5%, at what price should the stock sell?

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#### Solution Summary

The solution computes Expected growth rate, required rate of return, stock equilibrium, current price.

Compute the current price of a stock in the given cases.

Problem 1

Suppose a dividend of $1.25 was paid. The stock has a required rate of return of 11.2% and investors expect the dividend to grow at a constant rate of 10%. Complete parts (a) through (e) below.

a) Compute D0, D1, D2, D3 and D7.

b) Compute the present value of the dividends for t = 3 years.

c) Compute the current market price.

d) Assume that the constant growth rate is actually 0%. What is the current market price?

e) Describe the behavior of the present value of each future dividend (i.e. the behavior as t increases).

Problem 2

Suppose a dividend that pays at $1.07 has a growth rate of 20% for the first 3 years. After the 3 years, there is a long-run growth rate of 8%. The stock has a required rate of return of 12.4%. Find the current market price of a share of common stock.

Problem 3

Assume the beta coefficient for a company's stock is b=0.2, the risk-free rate of return, rRF, is 8% and the required rate of return on the market, rM, is 14%. Assume the dividend expected during the coming year is D1 = $2.50 and the growth rate is a constant 7%. Complete parts (a) through (c) below.

a) Compute the price at which the company's stock should sell.

b) Find the new price of the stock assuming the risk-free rate of return is 5% and the required rate of return on the market is 11%.

c) What would be needed for a stock to be in equilibrium?