Final answer:
The task is to calculate the present value of future dividends for a stock with an increasing dividend for five years and no dividends after that, using a 14 percent required rate of return. Each year's dividend is discounted back to its present value and summed to determine what an investor would pay for the stock today.
Step-by-step explanation:
The question involves finding the present value of a dividend-paying stock using the dividend discount model when the company has an unusual dividend policy. Maurer, Inc., has just paid a dividend of $4 per share and will increase the dividend by $6 per share for the next five years, then pay no more dividends. To calculate the present value of these future dividends, we discount each future dividend by the required rate of return of 14 percent. Here is the calculation:
Dividend in Year 1: $4 + $6 = $10
Dividend in Year 2: $10 + $6 = $16
Dividend in Year 3: $16 + $6 = $22
Dividend in Year 4: $22 + $6 = $28
Dividend in Year 5: $28 + $6 = $34
We present value these dividends:
PV of Year 1 Dividend = $10 / (1 + 0.14)
PV of Year 2 Dividend = $16 / (1 + 0.14)2
PV of Year 3 Dividend = $22 / (1 + 0.14)3
PV of Year 4 Dividend = $28 / (1 + 0.14)4
PV of Year 5 Dividend = $34 / (1 + 0.14)5
Adding all these present values gives the price you would be willing to pay for the stock today:
Stock Price = PV of Year 1 + PV of Year 2 + PV of Year 3 + PV of Year 4 + PV of Year 5
The investor can use a financial calculator or spreadsheet to find the sum of these present values to determine the current value of the stock.