# Stock valuation Question

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

Is it B?

yeah

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 super-growth 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

I remember doing this Q. What a pain.