Question

AC Electric just paid a $2.10 per share annual dividend. The firm pledges to increase its dividend by 2.4 percent for the next 5 years and then maintain a constant 2 percent rate of dividend growth. If the required return is 15 percent, what is the current value of one share of this stock?

Answer 1

Answer:

$16.74

Explanation:

First , find the dividend per year;

D1 = 2.10(1.0.24) = 2.1504

D2 = 2.1504(1.024) = 2.2020

D3 = 2.2020(1.024) = 2.2548

D4 = 2.2548(1.024) = 2.3089

D5 = 2.3089(1.024) = 2.3643

D6 = 2.3643(1.02) = 2.4116

Next, find the present value of the dividends;

PV (of D1) = 2.1504/ 1.15 = 1.8699

PV (of D2) = 2.2020/ 1.15² = 1.6650

PV (of D3) = 2.2548/ 1.15³ = 1.4826

PV (of D4) = 2.3089/ (1.15^4) = 1.3201

PV (of D5) = 2.3643/ (1.15^5) = 1.1755

PV (of D6 onwards)$= \frac{\frac{2.4116}{0.15-0.02} }{1.15^{5} } \\ \\ =\frac{18.5508}{2.0114}$

PV (of D6 onwards) = 9.2228

Next, sum up the PVs to find the price of the stock;

= 1.8699 + 1.6650 + 1.4826 + 1.3201 + 1.1755 + 9.2228

= 16.7359

Therefore the value of one share is $16.74