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 equity if the market rate of return is 15%?

Question

Quizplus · Accepted Answer

Step 1: Calculate the present value of the dividends for the next four years using the formula:

PV = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4

PV = (€3.00/1.15) + (€5.00/1.15^2) + (€7.50/1.15^3) + (€10.00/1.15^4)
PV = €2.61 + €3.87 + €5.24 + €6.47
PV = €18.19

Step 2: Calculate the present value of the constant dividend of €2.50 using the formula:

PV = D/r

PV = €2.50/0.15
PV = €16.67

Step 3: Calculate the total present value of dividends using the formula:

Total PV of dividends = PV of dividends for next four years + PV of constant dividend

Total PV of dividends = €18.19 + €16.67
Total PV of dividends = €34.86

Step 4: Calculate the market price of the equity using the formula:

Market price of equity = Total PV of dividends + PV of expected stock price

Expected stock price = constant dividend/r
Expected stock price = €2.50/0.15
Expected stock price = €16.67

PV of expected stock price = €16.67/1.15^4
PV of expected stock price = €9.77

Market price of equity = €34.86 + €9.77
Market price of equity = €44.63

The closest answer is C) €26.57. However, the correct answer should be calculated as follows:

Since the constant dividend of €2.50 per share per year will begin in year 5, the present value of the expected stock price (in year 4) should be calculated as:
PV of expected stock price = expected stock price / (1+r)^4
PV of expected stock price = €10.00 / (1+0.15)^4
PV of expected stock price = €4.53

Total PV of dividends = PV of dividends for next four years + PV of constant dividend
Total PV of dividends = €18.19 + (€2.50/(0.15 - 0.07)) + (€2.50/(1.15^2 - 0.15)) + (€2.50/(1.15^3 - 0.15)) + (€2.50/(1.15^4 - 0.15)) (using the formula for the present value of perpetuities)
Total PV of dividends = €18.19 + €35.71
Total PV of dividends = €53.90

Market price of equity = Total PV of dividends + PV of expected stock price
Market price of equity = €53.90 + €4.53
Market price of equity = €58.43

Therefore, the correct answer is not given, but the closest one is C) €26.57.