Question

The current price of a stock is $65.88. If dividends are expected to be $1 per share for the next five years, and the required return is 10%, then what should the price of the stock be in 5 years when you plan to sell it? If the dividend and required returns remained the same; and the stock price is expected to increase by $1 five years from now, does the current stock price also increase by $1? Why or why not?

I only need d) to be solved, thanks

(a) Derive the answer to price of the stock in 5 years (i.e. Find: Ps.) The question does not specify expected dividends or the required rate of return for beyond five years. Assume that following the fifth year (i.e. in the 6th year) that dividends grow at a constant rate forever and that the required rate of return remains at 10%

b) Find the growth rate of dividends that is consistent with your answer in part (a) to Ps. (Hint: use the Gordon growth model.) Now suppose instead that Ps-101.

c) What is the price of the stock today? Finally, suppose that dividends stay at S1 forever.

d）Unlike question b) above, consider a “two-stage Gordon growth model” where the growth rate of dividends is greater than required rate of return over the first five years. As before, suppose D1 =1 and ke =.1. However, now dividends grow from year 1 until year 5 at 20%, and after year 5 they stop growing. What is the price of the stock today?

Answer 1

Answer for d) as specified in the question is below:

This can be done in two stages, determining the value of dividend and stock price and then discounting them to the present value.

Determining the value of dividend using formula (Dn=D(n-1)*(1+growth rate%))

D=$1, growth rate=20%

D1=$1*(1.20)=$1.20

D2=$1.20*(1.20)=$1.44

D3=$1.44*(1.20)=$1.73

D4=$1.73*(1.20)=$2.07

D5=$2.07*(1.20)$2.49

The second stage has zero percent growth rate, hence the dividend in sixth year- D6=$2.49*(1.0)=$2.49

Value of stock using Gordon growth model P=D1/(ke-g), Here D1=D6=$2.49, Ke=10%, growth rate specified in 6th year is zero(since the case mentions that after year 5 they stop growing) g=0.

P=2.49/(0.10-0)=24.9.

Computing the present value of stock and dividends by discounting them

Tenor	Cash flow	discount rate	Present Value
1	1.2	10%	1.09
2	1.44	10%	1.19
3	1.73	10%	1.30
4	2.07	10%	1.42
5	2.49	10%	1.55
5	24.9	10%	15.45
	total		21.99

present value computation is done using the formula: PV=cash flow/((1+discount rate)^tenor)

$1.09=1.2/((1+0.10)^1)

$1.19=1.44/((1+0.10)^2)

$1.30=1.73/((1+0.10)^3)

$1.42=2.07/((1+0.10)^4)

$1.55=2.49/((1+0.10)^5)

$15.45=24.9/((1+0.10)^5)

Stock value =$1.09+$1.19+$1.30+$1.42+$1.55+$15.45=$21.99.

Hence stock price today as per two-stage Gordon growth model in terms mentioned in option d) is $21.99.