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 %

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