Question

Newlife Inc. announced today that it will begin paying annual dividends. The first dividend will be paid next year in the amount of $.63 a share. The following dividends will be $.68, $.83, and $1.13 a share annually for the following three years, respectively. After that, dividends are projected to increase by 4.1 percent per year. How much are you willing to pay today to buy one share of this stock if your desired rate of return is 15 percent?

Answer 1

$7.63

Step-by-step explanation:

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 + r )^-n

1st year

PV of Dividend = $0.63 x ( 1 + 15% )^-1 = $0.55

2nd year

PV of Dividend = $0.68 x ( 1 + 15% )^-2 = $0.51

3rd year

PV of Dividend = $0.83 x ( 1 + 15% )^-3 = $0.55

4th year

PV of Dividend = $1.13 x ( 1 + 15% )^-4 = $0.65

After four years the dividend will grow at a constant rate of 4.1%, so we will use the following formula to calculate the present value

PV of Dividend = [ $1.13 x ( 1 + 4.1% ) / ( 15% - 4.1% ) ] x [ ( 1 + 15% )^-5 ]

PV of Dividend = $5.37

Value of Stock = $0.55 + $0.51 + $0.55 + $0.65 + $5.37 = $7.63