Stock valuation Question valuation, increase, required, company, annual

siavosh

9.Assume a company has earnings per share of $5 and this year paid out 40% in dividends. The earnings and dividend growth rate for the next 3 years will be 20%. At the end of the third year the company will start paying out 100% of earnings in dividends and earnings will increase at an annual rate of 5% thereafter. If a 12% rate of return is required, the value of the company is approximately:
A) $92.92.
B) $102.80.
C) $55.69.
D) $104.80.
I’ll tell you the answer in a bit,
I didn’t like it!
Thamnks

bpdulog

First year’s dividend: 5*1.2*0.4=2.4
Second year’s dividend: 5*1.2*1.2*0.4=2.88
Third year’s dividend, is the first year when 100% of earnings is given in dividends:5*1.2*1.2*1.2=8.64
At the same 3rd year we can use DDM to calculate the value of stock, given that 100% of earnings continue being given out in dividends, and the company has constant growth of 5%: 5*1.2^3*1.05/(.12.05)=9.072/.07=129.6. The cash flow at this year 3 would be not only the last supergrowth dividend but the value of the stock too.
CF0=0
CF1=2.4, F1=1
CF2=2.88, F2=1
CF3=8.64+129.6=138.24
Hit NPV, with I=12, NPV (hence CF0) would be 102.83528~102.80

former

I remember doing this Q. What a pain.