Question

A share of stock sells for $35 today. The beta of the stock is 0.9 and the expected return on the market is 12 percent. The stock is expected to pay a dividend of $0.6 in one year. If the risk-free rate is 5.9 percent, what should the share price be in one year? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

First we will calculate the expected or required rate of return of the stock as per CAPM model as per below:

Expected return = Risk free rate + Beta * (Market return - Risk free rate)

Given: Risk free rate = 5.9 Market return = 12, Beta = 0.9

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

Expected return = 5.9 + 0.9 * (12 - 5.9)

Expected return = 5.9 + (0.9 * 6.1)

Expected return = 5.9 + 5.49

Expected return = 11.39

Next, we will calculate the growth rate as per Gordon Model:

As per Gordon model, share price is given by:

Share price = D1 / k -g

where, Share price = $35, D1 is next years' dividend = $0.6, k is the required rate of return = 11.39% and g is the growth rate

Putting these values in the above formula, we get,

$35 = $0.6 / 11.39% - g

11.39% - g = $0.6 / $35

0.1139 - g = 0.0171428

g = 0.1139 - 0.0171428

g = 0.096757 or 9.6757%

Now,

Share price (after 1 year) = D2 / k -g

where, D12 is the dividend after 2 years

First we will calculate dividend after 2 years. Dividend will grow at the rate of 9.6757% annually. So we will calculate the D2 by future value formula as per below:

FV = P * (1 + r)¹⁰

where, FV = Future value, which is the dividend after 2 years,  P is next years' dividend = $0.6, r is the rate of interest = 9.6757% and n is 2 years

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

FV = $0.6 * (1 + 9.6757%)²

FV = $0.6 * (1 + 0.096757)²

FV = $0.6 * (1.096757)²

FV = $0.6 * 1.20287591705

FV = $0.7217

So, the value of D12 is $0.7217

Now, we will calculate the share price after 1 year by putting the values in the below formula:

Share price (after 1 year) = D2 / k -g

Share price (after 1 year) = $0.7217 / 11.39% - 9.6757%

Share price (after 1 year) = $0.7217 / 1.7143%

Share price (after 1 year) = $42.10