Question

In practice, a common way to value a share of stock when a company pays dividends is to value the dividends over the next five years or so, then find the “terminal” stock price using a benchmark PE ratio. Suppose a company just paid a dividend of $1.25. The dividends are expected to grow at 20 percent over the next five years. The company has a payout ratio of 40 percent and a benchmark PE of 20. The required return is 12 percent. a. What is the target stock price in five years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the stock price today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a. The target stock price will be as follows:

= [ Dividend just paid x (1 + growth rate)ⁿ ] / payout ratio ] x PE ratio

= [ [ $ 1.25 x 1.20⁵ ] / 0.40 ] x 20

= [ $ 3.1104 / 0.40 ] x 20

= $ 155.52

b. The current 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 + 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 + Target price in year 5 / (1 + required rate of return)⁵

= ($ 1.25 x 1.20) / 1.12¹ +  ($ 1.25 x 1.20²) / 1.12² +  ($ 1.25 x 1.20³) / 1.12³ +  ($ 1.25 x 1.20⁴) / 1.12⁴ +  ($ 1.25 x 1.20⁵) / 1.12⁵ + $ 155.52 / 1.12⁵

= $ 1.5 / 1.12¹ + $ 1.8 / 1.12² + $ 2.16 / 1.12³ + $ 2.592 / 1.12⁴ + $ 3.1104 / 1.12⁵ + $ 155.52 / 1.12⁵

= $ 1.5 / 1.12¹ + $ 1.8 / 1.12² + $ 2.16 / 1.12³ + $ 2.592 / 1.12⁴ + $ 158.6304 / 1.12⁵

= $ 95.97 Approximately

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