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 1.20^{2}) /
1.12^{2} + ($ 2.5 x 1.20^{3}) / 1.12^{3} +
1 / 1.12^{3} x [ (($ 2.5 x 1.20^{3} x 1.05) / (0.12
- 0.05) ]

= $ 3 / 1.12 + $ 3.6 / 1.12^{2} + $ 4.32 /
1.12^{3} + 1 / 1.12^{3} x [ $ 64.8 ]

= $ 3 / 1.12 + $ 3.6 / 1.12^{2} + $ 69.12 /
1.12^{3}

**= $ 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**

Feel free to ask in case of any query relating to this question

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