How much should you pay for a share of stock that offers a constant growth rate of 13%, requires a 18% rate of return, and is expected to sell for $50 one year from now?

$44.25

Explanation:

procedure 1:

we can determine the present value of the stock using the following formula:

present value = future value / (1 + constant growth rate)ⁿ

present value = $50 / (1 + 13%) = $50 / 1.13 = $44.25

procedure 2 (optional):

future value = future dividend / (required rate of return - constant growth rate)

$50 = future dividend / (18% - 13%)

future dividend = $50 x 5% = $2.50

now we must determine the dividend for the current year:

current dividend = future dividend / (1 + constant growth rate)

current dividend = $2.50 / (1 + 13%) = $2.50 / 1.13 = $2.21

now we apply the Gordon growth model:

present value = dividend / (required rate of return - constant growth rate)

present value = $2.21 / (18% - 13%) = $2.21 / 5% = $44.25