Question

The risk-free rate is 1.71% and the market risk premium is 6.24%. A stock with a β of 1.34 just paid a dividend of $1.37. The dividend is expected to grow at 21.31% for three years and then grow at 4.22% forever. What is the value of the stock?

Answer 1

Required rate = Risk free rate + beta(market risk premium)

Required rate = 1.71% + 1.34(6.24%)

Required rate = 1.71% + 8.3616%

Required rate = 10.0716%

Year 1 dividend = 1.37 (1 + 21.31%) = 1.661947

Year 2 dividend = 1.661947 (1 + 21.31%) = 2.016108

Year 3 dividend = 2.016108 (1 + 21.31%) = 2.445741

Year 4 dividend = 2.445741 (1 + 4.22%) = 2.548951

Value at year 3 = D3 / required rate - growth rate

Value at year 3 = 2.548951 / 0.100716 - 0.0422

Value at year 3 = 2.548951 / 0.058516

Value at year 3 = 43.5599

Value of stock = 1.661947 / (1 + 0.100716)^1 + 2.016108 / (1 + 0.100716)^2 + 2.445741 / (1 + 0.100716)^3 + 43.5599 / (1 + 0.100716)^3

Value of stock = $37.67