Question

The risk-free rate is 3.99% and the market risk premium is 5.45%. A stock with a β of 1.66 just paid a dividend of $1.69. The dividend is expected to grow at 22.79% for three years and then grow at 4.25% forever. What is the value of the stock? round to 2 decimals

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) ]

Required rate of return is computed as shown below:

= risk free rate + beta x market risk premium

= 0.0399 + 1.66 x 0.0545

= 13.037% or 0.13037

So, the value of the stock is computed as follows:

= ($ 1.69 x 1.2279) / 1.13037 + ($ 1.69 x 1.2279²) / 1.13037² + ($ 1.69 x 1.2279³) / 1.13037³ + 1 / 1.13037³ [ ($ 1.69 x 1.2279³ x 1.0425) / ( 0.13037 - 0.0425) ]

= $ 2.075151 / 1.13037 + $ 2.548077913 / 1.13037² + $ 3.128784869 / 1.13037³ + 1 / 1.13037³ [ ($ 37.12027115) ]

= $ 2.075151 / 1.13037 + $ 2.548077913 / 1.13037² + $ 40.24905602 / 1.13037³

= $ 31.70 Approximately

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