Question

Portman Industries just paid a dividend of $2.40 per share. The company expects the coming year to be very profitable, and its dividend is expected to grow by 20.00% over the next year. After the next year, though, Portman’s dividend is expected to grow at a constant rate of 4.00% per year. The risk free rate is 3%, the market risk premium is 3.6% and Portman's beta is 1.9.

Required:
a. What are Portman's Dividends Year One, Year Two, and Year Three from now?
b. If you want to buy Portman's stock today, how much will you be willing to pay?
c. If you buy Portman's stock today, how much will you be able to sell it at the end of year 4?

Answer 1

Find my detailed explanations and answers below

Step-by-step explanation:

a.

The dividend in the future is the current dividend multiplied by dividend growth factor as shown thus:

Year 1 dividend=$2.40*(1+20.00%)=$2.88

Note that the growth rate after year 1 is 4.00%

Year 2 dividend=$2.88*(1+4.00%)=$3.00

Year 3 dividend=$3.00*(1+4.00%)=$3.12

b.

The stock price today is the present value of dividend in year 1 and the present value of the terminal value of dividend beyond year 1

Year 1 dividend=$2.88

terminal value=year 1 dividend*(1+terminal growth rate)/(cost of equity-terminal growth rate)

terminal growth rate=4.00%

cost of equity=risk-free rate+(beta*market risk premium)

cost of equity=3%+(1.9*3.6%)=9.84%

terminal value=$2.88*(1+4.00%)/(9.84%-4.00%)

terminal value=$51.29

stock price today=$2.88/(1+9.84%)^1+$51.29/(1+9.84%)^1

stock price today=$49.32

c.

Year 1 dividend=$2.88

Year 2 dividend=$3.00

Year 3 dividend=$3.12

Year 4 dividend=$3.12*(1+4.00%)=$3.24

Terminal value beyond year 4 is the price after year 4(let us assume it is X)

$49.32=$2.88/(1+9.84%)^1+$3.00/(1+9.84%)^2+$3.12/(1+9.84%)^3+$3.24/(1+9.84%)^4+X/(1+9.84%)^4

$49.32=$9.69+X/(1+9.84%)^4

$49.32-$9.69=X/(1+9.84%)^4

$39.63=X/(1+9.84%)^4

X=$39.63*(1+9.84%)^4

X=$57.69

Alternative approach:

terminal value beyond year 4=$3.24*(1+4.00%)/(9.84%-4.00%)

terminal value beyond year 4=$57.70(difference of $0.01 due to rounding error)