Question

Harold’s 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 $3.00. It expected zero growth in one year. In years two and three, 2% growth is expected, and in year 4, 6% growth. In year 5 and thereafter, growth should be a constant 4% per year. What is the maximum price per share that an investor who requires a return of 12% should pay for Harold’s Hotel’s common stock?

Answer 1

The price is computed as shown below:

= 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) ]

= ($ 3 x 1.02) / 1.12² + ($ 3 x 1.02²) / 1.12³ + ($ 3 x 1.02² x 1.06) / 1.12⁴ + 1 / 1.12⁴ x [ ($ 3 x 1.02² x 1.06 x 1.04) / (0.12 - 0.04) ]

= $ 3.06 / 1.12² + $ 3.1212 / 1.12³ + $ 3.308472 / 1.12⁴ + 1 / 1.12⁴ x [ $ 43.0101136 ]

= $ 3.06 / 1.12² + $ 3.1212 / 1.12³ + $ 46.318608 / 1.12⁴

= $ 34.10 Approximately

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