Question

A share of stock is now selling for $120. It will pay a dividend of $10 per share at the end of the year. Its beta is 1. What must investors expect the stock to sell for at the end of the year? Assume the risk-free rate is 6% and the expected rate of return on the market is 18%. (Round your answer to 2 decimal places.)

Answer 1

Using the dividend discount model and the capital asset pricing model, we can estimate that the stock will sell for approximately $78.58 at the end of the year.

Step-by-step explanation:

The price of a stock at the end of the year can be estimated using the dividend discount model (DDM) and the capital asset pricing model (CAPM). The DDM calculates the present value of all expected dividends, and the CAPM calculates the expected return based on the risk-free rate, the market rate of return, and the stock's beta.

Using the DDM, we can calculate the present value of the $10 dividend at the end of the year. Assuming a risk-free rate of 6%, the present value of the dividend is $10 / (1 + 0.06) = $9.43.

Using the CAPM, we can calculate the expected return based on the risk-free rate of 6%, the expected market rate of return of 18%, and the stock's beta of 1. The expected return is 6% + 1 * (18% - 6%) = 12%.

To estimate the stock price at the end of the year, we can divide the expected dividend by the expected return: $9.43 / 0.12 = $78.58. Therefore, investors can expect the stock to sell for approximately $78.58 at the end of the year.

Answer 2

P1 = 131.6566627 rounded off to $131.66

Step-by-step 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 = 0.06 + 1 * (0.18 - 0.06)

r = 0.18 or 18%

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,

120 = 10 / (0.18 - g)

120* (0.18 - g) = 10

21.6 - 120g = 10

g = (10 - 21.6) / -120

g = 0.096667 or 9.6667% rounded off to 9.67%

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

P1 = 10 * (1+0.0967) / (0.18 - 0.0967)

P1 = 131.6566627 rounded off to $131.66