Question

Common stock value—Variable 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 $4.50. It expects zero growth in the next year. In years 2 and 3, 5% growth is expected, and in year 4, 16% growth. In year 5 and thereafter, growth should be a constant 11% per year. What is the maximum price per share that an investor who requires a return of 15% should pay for Home Place Hotels common stock?

Answer 1

The current value of the stock is computed as shown below:

= Dividend in year 1 / (1 + required rate of return)¹ + 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 / 1.15 + ($ 4.50 x 1.05) / 1.15² + ($ 4.50 x 1.05²) / 1.15³ + ($ 4.50 x 1.05² x 1.16) / 1.15⁴ + 1 / 1.15⁴ x [ ($ 4.50 x 1.05² x 1.16 x 1.11) / (0.15 - 0.11) ]

= $ 4.50 / 1.15 + $ 4.725 / 1.15² + $ 4.96125 / 1.15³ + $ 5.75505 / 1.15⁴ + $ 159.7026375 / 1.15⁴

= $ 4.50 / 1.15 + $ 4.725 / 1.15² + $ 4.96125 / 1.15³ + $ 165.4576875 / 1.15⁴

= $ 105.35

Feel free to ask in case of any query relating to this question