Question

The risk-free rate is 3.89% and the market risk premium is 7.55%. A stock with a β of 1.70 just paid a dividend of $2.44. The dividend is expected to grow at 24.70% for five years and then grow at 3.29% 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 + Dividend in year 4 / (1 + required rate of return)⁴ + Dividend in year 5 / (1 + required rate of return)⁵ + 1 / ( 1 + required rate of return)⁵ [ ( Dividend in year 5 (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

= 0.0389 + 1.70 x 0.0755

= 16.725% or 0.16725

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

= ( $ 2.44 x 1.2470¹ ) / 1.16725¹ + ( $ 2.44 x 1.2470² ) / 1.16725² + ( $ 2.44 x 1.2470³ ) / 1.16725³ + ( $ 2.44 x 1.2470⁴ ) / 1.16725⁴ + ( $ 2.44 x 1.2470⁵ ) / 1.16725⁵ + 1 / 1.16725⁵ [ ( $ 2.44 x 1.2470⁵ x 1.0329 ) / ( 0.16725 - 0.0329 ) ]

= $ 3.04268 / 1.16725 + $ 3.79422196 / 1.16725² + $ 4.731394784 / 1.16725³ + $ 5.900049296 / 1.16725⁴ + $ 7.357361472 / 1.16725⁵ + $ 56.56433691 / 1.16725⁵

= $ 41.05 Approximately

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