The Extreme Reaches Corp. last paid a $1.50 per share annual dividend. The company is planning on paying $3.00,$5.00,$7.50,and $10.00 a share over the next four years,respectively. After that the dividend will be a constant $2.50 per share per year. What is the market price of this stock if the market rate of return is 15%?

Question

Quizplus · Accepted Answer

Step 1: Calculate the present value of all future dividends from year 1 to year 4 using the formula:
Present value (PV) = Future value (FV) / (1 + r)n
where r = market rate of return = 15%, n = number of years from now

PV of $3.00 dividend in year 1 = $3.00 / (1 + 0.15)1 = $2.61
PV of $5.00 dividend in year 2 = $5.00 / (1 + 0.15)2 = $3.99
PV of $7.50 dividend in year 3 = $7.50 / (1 + 0.15)3 = $4.83
PV of $10.00 dividend in year 4 = $10.00 / (1 + 0.15)4 = $5.35

Step 2: Calculate the present value of the constant $2.50 dividend from year 5 onwards using the formula:
PV of perpetuity = annual dividend / required rate of return on equity
where required rate of return on equity = market rate of return = 15%

PV of perpetuity = $2.50 / 0.15 = $16.67

Step 3: Calculate the total present value of all dividends by adding up the present values from step 1 and step 2:

Total PV = $2.61 + $3.99 + $4.83 + $5.35 + $16.67 = $33.45

Step 4: Add the present value of the last dividend to the total present value of all dividends to get the present value of the stock:

PV of stock = Total PV + PV of last dividend
PV of last dividend = $2.50 / (0.15 - 0.05) = $25.00 (using the formula for present value of a growing perpetuity)

PV of stock = $33.45 + $25.00 = $58.45

Step 5: Calculate the market price of the stock by dividing the present value of the stock by the number of shares:

Market price of stock = PV of stock / number of shares
Assume there are 1,000 shares outstanding
Market price of stock = $58.45 / 1,000 = $26.57

Therefore, the answer is (C) $26.57.