Question

The risk-free rate is 2.05% and the market risk premium is 7.75%. A stock with a β of 1.03 just paid a dividend of $2.11. The dividend is expected to grow at 20.48% for three years and then grow at 3.23% forever. What is the value of the stock? Round to 2 decimal places

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) ]

The required rate of return is computed as follows:

= Risk free rate + beta x market risk premium

= 0.0205 + 1.03 x 0.0775

= 10.0325% or 0.100325

So, the value of the stock will be as follows:

= ( $ 2.11 x 1.2048¹ ) / 1.100325 + ( $ 2.11 x 1.2048² ) / 1.100325² + ( $ 2.11 x 1.2048³ ) / 1.100325³ + 1 / 1.100325³ [ ($ 2.11 x 1.2048³ x 1.0323 ) / ( 0.100325 - 0.0323 ) ]

= $ 2.542128 / 1.100325 + $ 3.062755814 / 1.100325² + $ 3.690008205 / 1.100325³ + $ 55.99699331 / 1.100325³

= $ 49.64 Approximately

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