The risk-free rate is 3.90% and the market risk premium is 6.48%. A stock with a β of 0.82 just paid a dividend of $1.61. The dividend is expected to grow at 22.99% for five years and then grow at 3.13% forever. What is the value of the stock?
Answer format: Currency: Round to: 2 decimal places.
Please show all steps (not excel) and formulas used for better understanding~ Thank You!
Given
Risk free rate (Rf) = 3.9%
Market Risk premium = 6.48%
Beta = 0.82
Dividend (D0)= $1.61
Dividend growth rate = 22.99% for first five years (g) and then at 3.13% (gt) forever
To value stock first Cost of equity needs to be derived as follows:
Cost of equity (ke) = Riskfree rate+Betax(Market Risk premium)
= 3.9%+0.82x 6.48%
= 3.9%+5.314%
=9.21%
Value of Stock = PV of Expected Dividend + Present Value of Terminal Value
= Dividend Year 1/(1+ke)+Dividend Year 2/(1+ke)^2+Dividend Year 3/ (1+ke)^3+Dividend year 4 /(1+ke)^4+Dividend Year 5/(1+ke)^5+ ((Dividend year 5(1+gt))/(ke-gt)) / (1+ke)^5)
= 1.61*(1+22.99%)/(1+9.21%)+1.61*(1+22.99%)^2/(1+9.21%)^2+1.61*(1+22.99%)^3/(1+9.21%)^3+1.61*(1+22.99%)^4/(1+9.21%)^4+1.61*(1+22.99%)^5/(1+9.21%)^5+ ((1.61*(1+22.99%)^5*(1+3.13%))/(9.21%-3.13%))/ (1+9.21%)^5
= 1.9801*0.9157+2.4354*0.8384+2.9953*0.7677+3.6839*0.7030+4.5308*0.6437+ (4.6726/(6.08%)*0.6437
=1.8131+2.0419+2.2996+2.5897+2.9165+76.8522*0.6437
=1.8131+2.0419+2.2996+2.5897+2.9165+49.4703
=61.13
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