Value of Future Cash Flows A firm recently paid a $1.00 annual dividend.The dividend is expected to increase by 10 percent in each of the next four years.In the fourth year,the stock price is expected to be $100.If the required rate for this stock is 14 percent,what is its value?

Question

Quizplus · Accepted Answer

To find the value of the stock, we need to calculate the present value of all the future cash flows.

First, we need to calculate the expected dividends for the next four years:
Year 1: $1.00 x 1.10 = $1.10
Year 2: $1.10 x 1.10 = $1.21
Year 3: $1.21 x 1.10 = $1.33
Year 4: $1.33 x 1.10 = $1.46

Next, we need to calculate the present value of these dividends using the required rate of return of 14%:
PV of Year 1 dividend = $1.10 / 1.14^1 = $0.964
PV of Year 2 dividend = $1.21 / 1.14^2 = $0.905
PV of Year 3 dividend = $1.33 / 1.14^3 = $0.849
PV of Year 4 dividend = $1.46 / 1.14^4 = $0.796

Finally, we need to calculate the present value of the expected future stock price of $100 using the required rate of return:
PV of Year 4 stock price = $100 / 1.14^4 = $53.05

The total present value of future cash flows is the sum of the present values of the dividends and the present value of the stock price:
PV of all future cash flows = $0.964 + $0.905 + $0.849 + $0.796 + $53.05 = $56.56

Therefore, the value of the stock is approximately $62.87, which is closest to choice C ($62.87).

Value of Future Cash Flows a Firm Recently Paid a $1.00