Question

Ten years ago, Pac Pac Toys began manufacturing and selling retro arcade games for sports bars. Dividends are currently $2.60 per share, having grown at a 13.00 percent compound annual rate over the past 5 years. That growth rate is expected to be maintained for the next 2 years, after which dividends are expected to grow at half that rate for 3 years. Beyond that time, Pac Pac Toys’s dividends are expected to grow at 3.00 percent per year. What is the current value of a share of Pac Pac Toys common stock if your required return is 25.00 percent?

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) ]

= ($ 2.60 x 1.13) / 1.25 + ($ 2.60 x 1.13²) / 1.25² + ($ 2.60 x 1.13² x 1.065) / 1.25³ + ($ 2.60 x 1.13² x 1.065²) / 1.25⁴ + ($ 2.60 x 1.13² x 1.065³) / 1.25⁵ + 1 / 1.25⁵ x [ ($ 2.60 x 1.13² x 1.065³ x 1.03) / (0.25 - 0.03) ]

= $ 2.938 / 1.25 + $ 3.31994 / 1.25² + $ 3.5357361 / 1.25³ + $ 3.765558947 / 1.25⁴ + $ 4.010320278 / 1.25⁵ + $ 18.77559039 / 1.25⁵

= $ 2.938 / 1.25 + $ 3.31994 / 1.25² + $ 3.5357361 / 1.25³ + $ 3.765558947 / 1.25⁴ + $ 22.78591067 / 1.25⁵

= $ 15.29 Approximately

Do ask in case of any doubts.