Question

An investor demands an annual return of 14 percent on her stock investments. She is considering the purchase of a stock that just paid a dividend (today) of $3.50 per share. Requirement 1: What is the current price of the stock if the investor expects the firm's dividends to grow at a constant rate of 4 percent per year indefinitely? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Current Stock Price Requirement 2: If the expected growth rate in dividends for the stock is zero, what is the current price of the stock to the investor? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Current Stock Price Requirement 3: What is the current price of the stock if the investor expects dividends to grow at a rate of 10 percent per year for 2 years, and then grow at a more normal rate of 4 percent per year for every year thereafter? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Current Stock Price

Answer 1

1.
Current stock price = (D0 * (1+g)) / (r - g)
= ($3.50 * (1+4%)) / (14% - 4%)
= $3.64 / 10%
= $36.40

Current stock price = $36.40

2.
growth rate = 0

Thus, current stock price = D0 / r
= $3.50 / 14%
= $25.00

Current stock price = $25.00

3.
D1 = $3.50 * (1+10%) = $3.85
D2 = $3.85 * (1+10%) = $4.235
D3 = $4.235 * (1+4%) = $4.4044

P2 = D3 / (r - g)
= $4.4044 / (0.14 - 0.04)
= $4.4044 / 0.10
= $44.044

P0 = ($3.85 / 1.14) + ($4.235 / 1.14^2) + ($44.044 / 1.14^2)
= $3.3772 + $3.2587 + $33.8904
= $40.53

Current stock price = $40.53