Question

A share of stock is now selling for $110. It will pay a dividend of $8 per share at the end of the year. Its beta is 1. What do investors expect the stock to sell for at the end of the year? Assume the risk-free rate is 4% and the expected rate of return on the market is 15%. (Round your answer to 2 decimal places.)
Expected selling price $

Answer 1

Answer:

P1 = 118.5474 rounded off to $118.55

Explanation:

To calculate the price of the stock at the end of the year or P1, we first need to determine the required rate of return on the stock and the growth rate in dividends.

The required rate of return can be found using the CAPM equation. The formula for required rate of return under CAPM is,

r = rRF + Beta * (rM - rRF)

Where,

• rRF is the risk free rate
• rM is the return on market

r = 0.04 + 1 * (0.15 - 0.04)

r = 0.15 or 15%

Now we assume that the stock is a constant growth stock which means that the growth in dividends is expected to be constant throughout. The price of such a stock is found using the constant growth model of DDM. The formula for price today under the constant growth model is,

P0 = D1 / (r - g)

Where,

• P0 is price today
• D1 is expected dividend for the next period
• g is the growth rate in dividends

Plugging in the available variables, g is,

110 = 8 / (0.15 - g)

110* (0.15 - g) = 8

16.5 - 110g = 8

g = (8 - 16.5) / -110

g = 0.077272 or 7.7272% rounded off to 7.73%

So to calculate the price at the end of the year or P1, we will use D2.

P1 = 8 * (1+0.0773) / (0.15 - 0.0773)

P1 = 118.5474 rounded off to $118.55