A company that just paid a $1.60 annual dividend is currently priced at $40. You estimate the company will grow at 10% per year for the next 4 years and then grow at 6% per year for the next 2 years before leveling off to an estimated terminal growth rateof 4%. Assume stock’s beta is 1.2, the risk-free rate is 3% and the return on the market portfolio is 9%. Based on your assumptions, is this stock undervalued or overvalued? By how much?

The stock stock's fair value is $34.02 and it is over valued in the market by $5.98

Explanation:

The required rate of return on the stock can be calculated using the SML approach. The required rate using SML will be,

r = rRF + Beta  * (rM - rRF)

r = 3% + 1.2 * (9% - 3%)

r = 10.20%

Using the dividend discount model, we can calculate the fair price of the stock today. DDM bases the value of a stock on the present value of the expected future dividends from the stock. The price today under DDM is,

P0 = 1.6 * (1+0.1) / (1+0.102)  +  1.6 * (1+0.1)^2 / (1+0.102)^2  +  

1.6 * (1+0.1)^3 / (1+0.102)^3  +  1.6 * (1+0.1)^4 / (1+0.102)^4 +

1.6 * (1+0.1)^4 * (1+0.06) / (1+0.102)^5 + 1.6 * (1+0.1)^4 * (1+0.06)^2 / (1+0.102)^6

+  [ (1.6 * (1+0.1)^4 * (1+0.06)^2 * (1+0.04) / (0.102 - 0.04))  /  (1+0.102)^6 ]

P0 = $34.02

Difference = 40 - 34.02 = $5.98

The stock's fair value is less than the market value which means that the stock is overvalued in the market by $5.98.

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