Question

Common stock valuelong dashVariable growth  Personal Finance Problem   Home Place​ Hotels, Inc., is entering into a​ 3-year remodeling and expansion project. The construction will have a limiting effect on earnings during that​ time, but when it is​ complete, it should allow the company to enjoy much improved growth in earnings and dividends. Last​ year, the company paid a dividend of ​$4.40. It expects zero growth in the next year. In years 2 and​ 3, 6​% growth is​ expected, and in year​ 4, 17​% growth. In year 5 and​ thereafter, growth should be a constant 9​% per year. What is the maximum price per share that an investor who requires a return of 17​% should pay for Home Place Hotels common​ stock?

Answer 1

Firstly , let us calculate dividend amount per year;

D1 = D0(1+g ) = 4.40(1+0) = 4.40

D2 = 4.40*(1.06) =4.664

D3 = 4.664*(1.06) =4.9438

D4= 4.9438*(1.17) = 5.7843

D5 = 5.7843*(1.09) = 6.3049

Terminal value = D5/ (rate of return – growth rate) = [6.3049/ (0.17- 0.09)]

= 78.81125

Now, let us calculate Present value of each year's dividend;

PV (of D1) = 4.40/ (1.17 ) = 3.7607

PV (of D2) = 4.664/ (1.17² ) = 3.4071

PV (of D3) = 4.9438/ (1.17³ ) = 3.0868

PV (of D4) = 5.7843/ (1.17⁴ ) = 3.0868

PV (of D5 and onwards) = terminal value / 1.17⁴ = 78.81125

= 42.0576

Maximum price of stock = sum of present values

= 3.7607 + 3.4071 + 3.0868 + 3.0868 + 78.81125

= 92.15265

Maximum price per share = $92.15