Question

Shamrock Inc. has a patent that will expire in two years. The firm is expected to grow at 10.5 percent for the next two years and dividends will be paid at year end. It just paid a dividend of $1. After two years, the growth rate will decline to 4.5 percent immediately, and the firm will grow at this rate forever. If the required rate of return is 10 percent, value the firm’s current share price. (Round intermediate calculations to 4 decimal places, e.g.1.1712 and the final answer to 2 decimal places, e.g. 45.17.)

Answer 1

The price is computed as follows:

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

= ($ 1 x 1.105) / 1.10 + ($ 1 x 1.105²) / 1.10² + 1 / 1.10² x [ ($ 1 x 1.105² x 1.045) / (0.10 - 0.045) ]

= $ 1.105 / 1.10 + $ 1.221025 / 1.10² + $ 23.199475 / 1.10²

= $ 1.105 / 1.10 + $ 24.4205 / 1.10²

= $ 1.0045 + $ 20.1822

= $ 21.19 Approximately