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

To find the market price of the equity, we need to use the formula for the present value of a growing perpetuity:

PV = D / (r - g)

Where PV is the present value, D is the dividend, r is the required rate of return, and g is the growth rate. In this case, the dividend is expected to grow at different rates for the next four years before settling into a constant growth rate of 2.5%. So we'll need to find the present value of each of the expected dividends as follows:

PV1 = 3.00 / (1 + 0.15)^1 = 2.6087
PV2 = 5.00 / (1 + 0.15)^2 = 3.9864
PV3 = 7.50 / (1 + 0.15)^3 = 4.9829
PV4 = 10.00 / (1 + 0.15)^4 = 6.1213

Then we need to find the present value of the expected future dividends starting in year 5:

PV5 = 2.50 / (0.15 - 0.025) = 19.7674

Adding up all the present values of the dividends, we get:

PV = 2.6087 + 3.9864 + 4.9829 + 6.1213 + 19.7674 = 37.4667

Therefore, the market price of the equity would be:

Market price = PV = €26.57

Therefore, the best choice is C.