Question

Comfort Ice Cream has plans to pay decreasing annual dividends of $1.75, $1.60, and $1.45 over the next three years, respectively. After that, the firm will increase the dividend by 4 percent each year. What is the value of this stock today at a discount rate of 12 percent?

Answer 1

$15.85

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 = $1.75 x ( 1 + 12% )^-1 = $1.56

2nd year

PV of Dividend = $1.60 x ( 1 + 12% )^-2 = $1.28

3rd year

PV of Dividend = $1.45 x ( 1 + 12% )^-3 = $ 1.03

After three years the dividend will grow at a constant rate of 4%, so we will use the following formula to calculate the present value

PV of Dividend = [ $1.45 x ( 1 + 4% ) / ( 12% - 4% ) ] x [ ( 1 + 12% )^-4 ]

PV of Dividend = $11.98

Value of Stock = $1.56 + $1.28 + $1.03 + $11.98 = $15.85

Answer 2

The value of this stock today at a discount rate of 12 percent is $17.24

Step-by-step explanation:

According to the given data we would have to calculate first the followng:

Year 4 dividend = 1.45 * 1.04 = 1.508

Value at year 3 = D4 / required rate - growth rate

Value at year 3 = 1.508 / 0.12 - 0.040

Value at year 3 = 18.85

Therefore, Value of stock today = 1.72 / ( 1 + 0.12)∧1 + 1.60 / ( 1 + 0.12)∧2 + 1.45 / ( 1 + 0.12)∧3 + 18.85 / ( 1 + 0.12)3

=1.53+1.27+1.03+13.41

Value of stock today = $17.24

The value of this stock today at a discount rate of 12 percent is $17.24