Question

PC 31 is a solar power company that developed new technology that makes solar power more affordable. As a result, they are expecting a 15% annual growth rate for the next five years. By the end of 5 years, the growth rate will slow to 5% per year. Stockholders require a return of 12% on BC31’s stock. The most recent dividend, paid yesterday, was $1.75.

-What is the is the expected per share value of the stock today?

-If the current market price was $70 per share, would you buy it or short it?

-If the current market price was $45 per share, would you buy it or short it?

Answer 1

The 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 + Dividend in year 5 / (1 + required rate of return)⁵ + 1 / (1 + required rate of return)⁵ [ ( Dividend in year 5 (1 + growth rate) / ( required rate of return - growth rate) ]

= ($ 1.75 x 1.15) / 1.12 + ($ 1.75 x 1.15²) / 1.12² + ($ 1.75 x 1.15³) / 1.12³ + ($ 1.75 x 1.15⁴) / 1.12⁴ + ($ 1.75 x 1.15⁵) / 1.12⁵ + 1 / 1.12⁵ x [ ($ 1.75 x 1.15⁵ x 1.05) / (0.12 - 0.05) ]

= $ 2.0125 / 1.12 + $ 2.314375 / 1.12² + $ 2.66153125 / 1.12³ + $ 3.060760938 / 1.12⁴ + $ 3.519875078 / 1.12⁵ + 1 / 1.12⁵ x [ ($ 52.79812617) ]

= $ 2.0125 / 1.12 + $ 2.314375 / 1.12² + $ 2.66153125 / 1.12³ + $ 3.060760938 / 1.12⁴ + $ 56.31800125 / 1.12⁵

= $ 39.44

If the current market price is $ 70, we shall short it since the price is overpriced.

If the current market price is $ 45, we shall short it since the price is overpriced.