Question

14. An issue of common stock currently sells for $52.00 per share, has an expected annual dividend to be paid at the end of the year of $0.90 per share, and has an expected growth rate to infinity of 5.00% per year. The expected rate of return on this security is A) 62.78% B) 62.86% C) 61.36% D) 6.82% E) 6.73%

Answer 1

Solution:

As per the Gordon growth model the price of a stock can be calculated using the following formula:

P₀ = D₁ / ( K_e – g )

Where,

P₀ = Current Price of the stock ; D₁ = Expected dividend to be paid at the end of the year

K_e = Expected rate of Return ; g = Expected growth rate

As per the information given in the question we have

P₀ = $ 52.00     ;   D₁ = $ 0.90    ;    g = 5.00 % = 0.05   ; K_e = to find

Applying the above values in the formula we have

52.00 = 0.90 / (K_e – 0.05 )

(K_e – 0.05 ) = 0.90 / 52.00

(K_e – 0.05 ) = 0.017308

K_e = 0.05 + 0.017308

K_e = 0.067308

K_e = 6.7308 %

K_e = 6.73 % ( when rounded off to two decimal places )

Thus K_e = 6.73 %

Thus the expected rate of return on this security is = 6.73 %

The solution is Option E) 6.73 %