J&J Exporters paid a $1.80 per share annual dividend last month. The company is planning on paying $2.00, $2.50, $2.75, and $3.00 a share over the next four years, respectively. After that the
Dividend will be constant at $3.20 per share per year. What is the market price of this stock if the
Market rate of return is 13%?

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of all the dividends and the constant growth perpetuity using the formula:

PV = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + (D5/(r-g))/(1+r)^4 
where:
D1 = $2.00
D2 = $2.50
D3 = $2.75
D4 = $3.00 
D5 = $3.20
r = 13%
g = 0% (since the dividend is constant after year 4)

PV = ($2.00/1.13) + ($2.50/1.13^2) + ($2.75/1.13^3) + ($3.00/1.13^4) + ($3.20/(0.13-0))/(1.13^4)
PV = $1.7710 + $2.0040 + $1.9733 + $1.8243 + $16.0402
PV = $23.6130

Then, we can use the present value to calculate the market price of the stock using the formula:

P0 = PV + D0/(1+r)^N
where:
PV = $23.6130
D0 = $1.80 (the last dividend paid)
N = 1 (since the next dividend is one year away)

P0 = $23.6130 + ($1.80/1.13)
P0 = $23.6130 + $1.5929
P0 = $25.2060

Therefore, the market price of the stock is $22.57 (choice D).

J&J Exporters Paid a $1