Question

cape corp. will pay a dividend of $2.70 next year. the company has stated that it will maintain a constant growth rate of 4.75 percent a year forever. a. if you want a return of 16 percent, how much will you pay for the stock? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. if you want a return of 11 percent, how much will you pay for the stock? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Using the Gordon Growth Model, for a required return of 16%, you would pay $26.47 for Cape Corp. stock, and for an 11% return, you would pay $50.59.

Step-by-step explanation:

To determine the price you would pay for Cape Corp. stock given a desired rate of return, you can use the Gordon Growth Model (also known as the Dividend Discount Model). This model calculates the intrinsic value of a stock based on the next year's dividends, the constant growth rate of the dividends, and the required rate of return.

The formula for the Gordon Growth Model is P = D / (k - g), where P is the price of the stock, D is the expected dividends next year, k is the required rate of return, and g is the growth rate.

For part (a), to achieve a return of 16%, the calculations would be:

P = $2.70 / (0.16 - 0.0475) = $26.47

For part (b), to achieve a return of 11%, the calculations would be:

P = $2.70 / (0.11 - 0.0475) = $50.59

Answer 2

If you want a return of 11 percent, you will pay $43.20 for the stock.

How to solve

a. If you want a return of 16 percent, how much will you pay for the stock?

The price of the stock can be calculated using the following formula:

Price = Dividend / (Required return - Growth rate)

Plugging in the values given in the problem, we get:

Price = $2.70 / (0.16 - 0.0475) = $24.00

Therefore, if you want a return of 16 percent, you will pay $24.00 for the stock.

b. If you want a return of 11 percent, how much will you pay for the stock?

Using the same formula as before, we get:

Price = $2.70 / (0.11 - 0.0475) = $43.20

Therefore, if you want a return of 11 percent, you will pay $43.20 for the stock.