Which is the amount that should be paid for a stock that will pay a dividend of $2.38 in one year and $6.93 in two years? After that, the stock price will grow at a constant 5% per year forever. The appropriate discount rate is 12%. Show your answer to the nearest $.01. Do not use the $ sign in your answer.
D1 = 2.38, D2 = 6.93
After this, the stock price will grow at a constant 5% per year forever. g = 5%, D3 = 6.93*1.05 = 7.2765
Discount rate = r = 12%
The present value of future dividends:
PV of D1 = 2.38/(1.12)1 = 2.125
PV of D2 = 6.93/(1.12)2 = 5.524554
Value of future dividends at year 2 starting from year 3 and growing at 5% = D3/(r-g) = 7.2765/(12%-5%) = 103.95
Value of future dividends at t = 0 starting from year 3 and growing at 5% = 103.95/(1.12)2 = 82.868303571
Therefore, present value of the stock = PV of D1 + PV of D2 + PV of future dividends starting from year 3 and growing at 5% = 2.125+5.524554+82.868303571 = 90.517857143
Answer -> 90.52
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