Question

Among Homer Simpson’s many experiences as an entrepreneur is the time that he started a firm to recycle used grease. The current dividend on this stock is $0.55, and Homer expects that the dividend growth rate will be 7% for each of the next two years, and then will remain steady at 9% thereafter. Given the risky nature of purifying grease, prospective investors require a 15% rate of return if they are to invest in the stock of this enterprise. How much is this stock worth today? Based on the above information, how much should you expect the stock to cost in two years?

Answer 1

Solution:-

The value of stock is the sum of present values of dividends for the next 2 years and the terminal value at the end of second year (since perpetuyal growth rate kicks in 3rd year onwards).

Dividend (Year 1)= $0.55*107%= $0.5885

Dividend (Year 2)= $0.5885*107%= $0.6297

Dividend (Year 3)= $0.6297*109%= $0.6864

Terminal value at the end of year 2= $0.6864/(cost of equity-perpetual growth rate)= $0.6864/(15%-9%)= $11.44

Value of share today= $0.5885*(1/1.15) + $0.6297*(1/1.15)² + $11.44*(1/1.15)²

Value of share today= $0.5885*870 + $0.6297*0.756 + $11.44*0.756 = $9.64

Value of stock two years from now= Expected dividend Year 3/(Cost of equity-growth rate)= $0.6864/(15%-9%)= $11.44