Question

# The risk-free rate is 1.83% and the market risk premium is 7.31%. A stock with a...

The risk-free rate is 1.83% and the market risk premium is 7.31%. A stock with a β of 1.50 just paid a dividend of \$1.78. The dividend is expected to grow at 20.80% for five years and then grow at 4.03% forever. What is the value of the stock?

First we have to find the cost of equity=risk free rate+(beta*market risk premium)=1.83%+(1.5*7.31%)=12.80%

D1=D0*(1+20.8%)=\$1.78*(1.208)=\$2.15 (rounding to two digit decimals)

D2=\$2.15*(1.208)=\$2.60

D3=\$2.60*(1.208)=\$3.14

D4=43.14*(1.208)=\$3.79

D5=\$3.79*1.208=\$4.58

D6=\$4.58*1.0403=\$4.76

Terminal value at year5=D6/(cost of equity-growth rate)=\$4.76/(12.80%-4.03%)=\$54.35

Value of the stock=(D1/1+12.8%)+(D2/(1+12.8%)^2)+(D3/(1+12.8%)^3)+(D4/(1+12.8%)^4)+(D5+Terminal value at Year5)/(1+12.8%)^5

(\$2.15/1.128)+(2.60/1.128^2)+(3.14/1.128^3)+(3.79/1.128^4)+((4.58+54.35)/1.128^5)

Value of the stock=\$40.75

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