Question

You are considering the purchase of a common stock that paid a dividend of $3.00 yesterday. You expect this stock to have a growth rate of 20 percent for the next 3 years and the long-run normal growth rate after year 3 is expected to be constant at 5 percent. If you require a 14 percent rate of return, the price per share that you should you be willing to pay for this stock is closest to:

Answer 1

$50.8

Step-by-step explanation:

As per given Data

Dividend Paid = $3

Worth of the stock is the present value of all the cash flows associated with the stock. Dividend is the only cash flow that a stock holder receives against its investment in the stocks. We need to calculate the present values of all the dividend payments.

Formula for PV of dividend

PV of Dividend = Dividend x ( 1 + growth rate )^n x ( 1 + r )^-n

1st year

PV of Dividend = $3 x ( 1 + 20%)^1 x ( 1 + 14% )^-1 = $3.16

2nd year

PV of Dividend = $3 x ( 1 + 20%)^2 x ( 1 + 14% )^-2 = $3.32

3rd year

PV of Dividend = $3 x ( 1 + 20%)^3 x ( 1 + 14% )^-3 = $3.50

After three years the dividend will grow at a constant rate of 5%, so we will use the following formula to calculate the present value

PV of Dividend = [ $3 x ( 1 + 20%)^3 x ( 1 + 5%) / ( 14% - 5% ) ] x [ ( 1 + 14% )^-3 ]

PV of Dividend = $40.82

Value of Stock = $3.16 + $3.32 + $3.50 + $40.82 = $50.8