Question

Common stock value—Variable growth  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 ​$4.50. It expects zero growth in the next year. In years 2 and​ 3, 5​% growth is​ expected, and in year​ 4, 21​% growth. In year 5 and​ thereafter, growth should be a constant 12​% per year. What is the maximum price per share that an investor who requires a return of 18​% should pay for Home Place Hotels common​ stock?

The maximum price per share that an investor who requires a return of 18​% should pay for Home Place Hotels common stock is ​$

Answer 1

The price is computed as follows:

= Dividend in year 2 / (1 + required rate of return)² + Dividend in year 3 / (1 + required rate of return)³ + Dividend in year 4/ (1 + required rate of return)⁴ + 1 / (1 + required rate of return)⁴[ ( Dividend in year 4 (1 + growth rate) / ( required rate of return - growth rate) ]

= ($ 4.50 x 1.05) / 1.18² + ($ 4.50 x 1.05²) / 1.18³ + ($ 4.50 x 1.05² x 1.21) / 1.18⁴ + 1 / 1.18⁴ x [ (($ 4.50 x 1.05² x 1.21 x 1.12) / (0.18 - 0.12) ]

= $ 4.725 / 1.18² + $ 4.96125 / 1.18³ + $ 6.0031125 / 1.18⁴ + $ 112.0581 / 1.18⁴

= $ 4.725 / 1.18² + $ 4.96125 / 1.18³ + $ 118.0612125 / 1.18⁴

= $ 67.31 Approximately