Question

Consider the situation with the following initial values. The risk-free rate of return is 3 percent, and the expected return on the market is 8.7 percent. Stock A has a beta coefficient of 1.4, a dividend growth rate of 5 percent, and a current dividend of $2.60 per share. The value of the stock is $45.65 currently.

A) If the expected return on the market rises to 10 percent and the other variables remain at their initial values, what will be the value of the stock (new value is $35). Explain why the value of the stock changes from the original value of $46.65.

B) If the risk-free return rises to 4.5 percent and the return on the market rises to 10.2 percent, but all other variables remain at their initial values, what will be the value of the stock (value is $36.50). Explain why the value of the stock changes from the original value of $46.65.

C) If the beta coefficient falls to 1.1 and the other variables remain at their initial values, what will be the value of the stock (value is $63.93). Explain why the value of the stock changes from the original value of $46.65.

Answer 1

Stock price (P0) = Next-period dividend (D1) / (r - g), where

D1: Next-period dividend = D0 x (1 + g) [D0: Current period dividend = $2.6] = $2.6 x (1.05) = $2.73

r: Expected return on stock = Rf + Beta x (Rm - Rf) [where Rf; Risk free rate and Rm: Market return] and

g: Dividend growth rate = 5%

(A) Rm = 10%

r = 3% + 1.4 x (10 - 3)% = 3% + 1.4 x 7% = 3% + 9.8% = 12.8%

P0 ($) = 2.73 / (0.128 - 0.05) = 2.73 / 0.078 = 35

Since expected return on market portfolio increases, expected return on the stock in question increases. Since stock price is inversely related to expected return, higher expected return leads to a decrease in stock price.

(B) Rf = 4.5%, Rm = 10.2%

r = 4.5% + 1.4 x (10.2 - 4.5)% = 4.5% + 1.4 x 5.7% = 4.5% + 7.98% = 12.48%

P0 ($) = 2.73 / (0.1248 - 0.05) = 2.73 / 0.0748 = 36.5

Since expected return on market portfolio increases by less than the increase in risk-free rate, expected return on the stock in question increases. Since stock price is inversely related to expected return, higher expected return leads to a decrease in stock price.

(C) Beta = 1.1

r = 3% + 1.1 x (8.7 - 3)% = 3% + 1.1 x 5.7% = 3% + 6.27% = 9.27%

P0 ($) = 2.73 / (0.0927 - 0.05) = 2.73 / 0.0427 = 63.93

Since expected return on market portfolio decreases, expected return on the stock in question decreases. Since stock price is inversely related to expected return, lower expected return leads to an increase in stock price.