Question

A share of stock is now selling for $115. It will pay a dividend of $9 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 5% and the expected rate of return on the market is 14%. (Round your answer to 2 decimal places.)
Expected selling price $

Answer 1

Answer:

The expected price of the stock is $122.03

Explanation:

To calculate the expected price of the stock at the end of the year or at Year 1, we first need to determine the required rate of return on the stock. We will use the CAPM equation to calculate the required rate of return.

The required rate of return is calculated as,

r = rRF + Beta * (rM - rRF)

Where,

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

r = 0.05 + 1 * (0.14 - 0.05)

r = 0.14

We already have the price of the stock today, the D1 and the required rate of return. Using the constant dividend growth model of DDM, we calculate the growth rate in dividends to be,

P0 = D1 / (r - g)

115 = 9 / (0.14 - g)

115 * (0.14 - g)  =  9

16.1 - 115g  =  9

16.1 - 9 = 115g

7.1 / 115 = g

g = 0.0617 or 6.17%

Using the same formula and replacing D1 with D2, we can calculate the price of the stock at the end of the year or at start of Year 1.

P1 = 9 * (1+0.0617)  /  (0.14 - 0.0617)

P1 = $122.03