Question

A stock does not currently pay a dividend because the firm needs to plow back its earnings to fuel growth. However, it is expected to pay a dividend of $2.00 five years from today. This dividend is then expected to grow at a rate of 8% for the following 5 years. It will then level off and grow at a rate of 5% indefinitely. For the next 5 years, R = 10%. R = 8% for the following 4 years and then R = 6% indefinitely.

What is the expected stock price today?  

Answer 1

Calculation of stock price(Gorden Growth Model):-

STEP:-1Price for the first 5 years (Zero Growth In Future Dividned for First 5 years):-

P= Dividend/r

So,Price today=$2/10%

=$20

STEP:-2 Price for the Second Period-6th year to 9th year.(Growth Rate=8%,Required rate of return=8%)

As there is growth rate for dividend:-

Year(A)	Dividend(B)	PV @8%(C)	Present Value(B)*(C)
6	20*1.08=21.6	0.925	19.98
7	21.6*1.08=23.33	0.857	19.999
8	23.33*1.08=25.19	0.793	19.975
9	25.19*1.08=27.21	0.735	19.999
		Total	79.953

This 79.953 is stands at the end of 5th year.We have to pull back at present with the help of rate of return for first five years i.e.@10%

=$79.953*0.6209

   =$49.643

   ***(0.6209 is the present value of 1 pulled 5 years back)

STEP 3:-Price after 10th year for indefinately period(Growth rate=5%.Rate of Return=6%)

Dividend for 10th year=Dividend for 9th year+5%Growth

=27.14+5%

=28.49

Since,Growth rate and Rate of return is for indefinate period.So Formula is (P=Dividend/r-g)

Price at end of 9th year=28.49/0.06-0.05

=28.49/0.01

=2849

Price Stands Today=2849*0.4563

=$1300

Therefore,Price Stands Today=STEP 1+STEP 2+STEP 3

   =$20+49.643+$1300

   =1369.64