Question

Investors require an after-tax rate of return of 13% on their stock investments. Assume that the tax rate on dividends is 30% while capital gains escape taxation. A firm will pay a $3 per share dividend 1 year from now, after which the firm's stock is expected to sell at a price of $22.

a. Find the current price of the stock. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. Find the expected before-tax rate of return for a 1-year holding period. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

c. Now suppose that the dividend will be $5 per share. If the expected after-tax rate of return is still 13% and investors still expect the stock to sell at $22 in 1 year, at what price must the stock now sell? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

d. What is the before-tax rate of return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

(a) Required After-Tax Rate of Return = 13 %, Tax Rate on Dividends = 30 %, Tax Rate on Capital Gains = 0% and Expected Dividends Next year = D = $ 3.

Expected Price in one year = P1 = $ 22 and let the current price be $P0

Therefore, [22+(1-0.3) x 3 - P0] / P0 = 0.13

22 + 2.1 - P0 = 0.13P0

24.1 = P0 + 0.13P0 = 1.13P0

P0 = 24.1 / 1.13 = $ 21.327 ~ $ 21.33

(b) Before-Tax Rate of Return = [22 + 3 - 21.33] / 21.33 = 0.172058 or 17.2058 % ~ 17.21 %

(c) Let the initial stock price be $P0 and new dividend = $ 5

Therefore, 0.13 = [22 + 5 x (1-0.3) - P0] / P0

22 + 3.5 - P0 = 0.13P0

25.5 = 1.13P0

P0 = 25.5 / 1.13 = $ 22.56637 ~ $ 22.57

(d) Before-Tax Rate of Return = [22 + 5 - 22.57] / 22.57 = 0.196278 or 19.6278 % ~ 19.63 %