Question

The market price of XYZ Inc. stock is $60, and the company recently paid a
$2.5 cash dividend. It is expected that the dividend will grow at the rate of 20 percent for the next 3 years, and then grow forever at a constant rate of 5%, while the required rate of return on this kind of stock is 12%.

• Calculate the expected price of the stock based on non-constant dividend discount model
• Is the stock under or overpriced? Should we buy or sell the stock if we decide only based on the available information?

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 + 1 / (1 + required rate of return)³ [ ( Dividend in year 3 (1 + growth rate) / ( required rate of return - growth rate) ]

= ($ 2.5 x 1.20) / 1.12 + ($ 2.5 x 1.20²) / 1.12² + ($ 2.5 x 1.20³) / 1.12³ + 1 / 1.12³ x [ (($ 2.5 x 1.20³ x 1.05) / (0.12 - 0.05) ]

= $ 3 / 1.12 + $ 3.6 / 1.12² + $ 4.32 / 1.12³ + 1 / 1.12³ x [ $ 64.8 ]

= $ 3 / 1.12 + $ 3.6 / 1.12² + $ 69.12 / 1.12³

= $ 54.75 Approximately

Since the market price of the stock is greater than the fair value of the stock, hence the stock is overpriced.

We shall sell the stock since the stock is overpriced in the market

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