Question

A share of stock is now selling for $100. It will pay a dividend of $9 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

Answer 1

According to the dividend discount model calculation, investors can expect the stock to sell for $90 at the end of the year.

Step-by-step explanation:

The price that investors expect the stock to sell for at the end of the year can be calculated using the dividend discount model (DDM). The DDM assumes that the stock's value is equal to the present value of its future dividends. In this case, the stock is expected to pay a dividend of $9 per share at the end of the year, so investors will expect the stock to sell for the present value of that dividend. The present value can be calculated using a discount rate, which represents the investor's required rate of return. Since the beta is given as 1, we can assume a discount rate of 10%. Using these values, the expected stock price can be calculated as:

Expected Stock Price = Dividend / (Discount Rate - Growth Rate)

Substituting the values, we get:

Expected Stock Price = $9 / (0.10 - 0)

Expected Stock Price = $9 / 0.10 = $90

Answer 2

The investors must expect the stock to sell for $109 at the end of the year

How to determine this?

To determine what the stock is expected to sell for at the end of the year, we use the formula:

Stock price = d1 / (r - g)

Where:

d1 = Next dividend to be paid = $9

r = Cost of equity

g = Dividend growth rate

To determine the cost of equity using the Capital Asset Pricing Model (CAPM):

Cost of equity = Risk-free rate + Beta × (Market rate of return - Risk-free rate)

Given:

Risk-free rate = 8%

Market rate of return = 18%

Beta = 1

So, the cost of equity would be:

Cost of equity = 8% + 1 × (18% - 8%) = 18%

To find the dividend growth rate using the formula rearranged:

100 = $9 / (18% - g)

Solving for g:

g = 9%

Finally, to find the stock price:

Stock price = $9 × (1 + 0.09) / (0.18 - 0.09)

Stock price = $9.81 / 0.09 = $109

Therefore, after reworking the calculations based on the given information, investors can expect the stock to be sold at approximately $109 at the end of the year.