Question

The Island Hotel Company, Inc. just paid a dividend of $2.75 per share, and that dividend

is expected to grow at a constant rate of 5.50% per year in the future. The company's

beta is 2.95, the market risk premium is 6.75%, and the risk-free rate is 3.50%. Using

CAPM, at what price should the company's stock sell? Note: Enter your answer

rounded off to the nearest cent. Do not enter $ or comma in the answer box.

Answer 1

First we will calculate the required rate of return by the CAPM equation. Required / Expected return of the stock is given by:

Required return = Risk free rate + Beta * Market risk premium

Given: Risk free rate = 3.5%, Market risk premium = 6.75%, Beta = 2.95

Putting the given values in the above equation, we get,

Required return = 3.5 + (2.95 * 6.75)

Required return = 3.5 + 19.9125

Required return = 23.41%

Now, as per Gordon model, share price is given by:

Share price = D1 / k -g

where, D1 is next years' dividend, k is the required rate of return = 23.41% and g is the growth = 5.5%

We will calculate next years' dividend now. Dividend will grow at the rate of 5.5% annually. So we will calculate the D1 by future value formula as per below:

FV = P * (1 + r)ⁿ

where, FV = Future value, which is the dividend next year,  P is current years' dividend = $2.75, r is the rate of interest = 5.5% and n is 1 years

Now, putting these values in the above formula, we get,

FV = 2.75 * (1 + 5.5%)¹

FV = 2.75 * (1 + 0.055)

FV = 2.75 * 1.055

FV = 2.90125

So, value of D1 is 2.90125

Now, we will calculate the share price by putting the values in the Gordon Model formula:

Share price = 2.90125 / 23.41% - 5.5%

Share price = 2.90125 / 17.91%

Share price = 16.20