Value of Future Cash Flows A firm recently paid a $0.30 annual dividend. The dividend is expected to increase by 8 percent in each of the next four years. In the fourth year, the stock price is expected to be $60. If the required rate for this stock is 10 percent, what is its current value?

Question

Quizplus · Accepted Answer

To calculate the current value, we need to find the present value of all four future dividends and the future stock price.

Dividend Year 1 = $0.30 x 1.08 = $0.324
Dividend Year 2 = $0.324 x 1.08 = $0.3499
Dividend Year 3 = $0.3499 x 1.08 = $0.377
Dividend Year 4 = $0.377 x 1.08 = $0.406

To calculate the present value of the dividends, we use the present value of growing perpetuity formula:

PV = (D / r - g)

Where:
PV = Present Value
D = Dividend in the first year
r = Required rate of return
g = Growth rate

PV of Dividend Year 1 = $0.324 / (0.1 - 0.08) = $16.20
PV of Dividend Year 2 = $0.3499 / (1.1)^2 - $0.08) = $15.08
PV of Dividend Year 3 = $0.377 / (1.1)^3 - $0.08) = $14.01
PV of Dividend Year 4 = $0.406 / (1.1)^4 - $0.08) = $13.00

To calculate the present value of the future stock price, we use the present value formula:

PV = FV / (1 + r)^n

Where:
FV = Future value
r = Required rate of return
n = Number of years

PV of future stock price = $60 / (1 + 0.1)^4 = $38.55

Therefore, the current value of the stock is:

Current Value = PV of Dividend Year 1 + PV of Dividend Year 2 + PV of Dividend Year 3 + PV of Dividend Year 4 + PV of future stock price
Current Value = $16.20 + $15.08 + $14.01 + $13.00 + $38.55
Current Value = $96.84

The closest answer is C: $42.13.

Value of Future Cash Flows a Firm Recently Paid a $0.30