Question

wants to get rid of her stock. She offers to sell it to her friend. The stock will not pay dividend for the next 5 years.  After year 5, the stock will pay a dividend of $3, and dividend is expected to grow at 30% in year 6, 30% in year 7, and thereafter, the stock will grow at 5%.  If the risk free is 7%, the market risk premium is 8% and a beta of 1.25.  What is the current stock price?  

Answer 1

Current Stock price
= Present Value of Future Dividends + Present Value of Stock price at the end of Year 7
Calculation of Cost of Equity
Cost of Equity (r)
= Expected Return by investor
= Risk Free Rate + Beta * Market Risk Premium
= 7% + 1.25*8%
= 7% + 10%
= 17%
Dividend at the end of Year 5 (D5) = $3
Dividend at the end of Year 6 (D6)
= Dividend of Year 5 * (1+ Growth Rate)
= $3 * (1+30%)
= $3 * (1.30)
= $3.90
Dividend at the end of Year 7 (D7)
= Dividend of Year 7 * (1+ Growth Rate)
= $3.90 * (1+30%)
= $3.90 * (1.30)
= $5.07
Price at the end of Year 7 (P7)
= Dividend of Year 8 / (Cost of Equity - Perpetual Growth Rate)
= [Dividend of Year 7 * (1+Growth Rate)] / (Cost of Equity - Perpetual Growth Rate)
= [$5.07*(1+5%)] / (17% - 5%)
= [$5.07*(1.05)] / 12%
= $5.3235 / 12%
= $44.3625
So,
Current Stock price
= Present Value of Future Dividends + Present Value of Stock price at the end of Year 7
= Dividend of nth Year / (1+Cost of Equity)^n + Price at the end of Year 7 / (1+Cost of Equity)^7
Where, n= No of Years
= D5/(1+r)^5 + D6/(1+r)^6 + D7/(1+r)^7 + P7/(1+r)^7
= $3/(1+17%)^5 + $3.90/(1+17%)^6 + $5.07/(1+17%)^7 + $44.3625/(1+17%)^7
= $3/(1.17)^5 + $3.90/(1.17)^6 + $5.07/(1.17)^7 + $44.3625/(1.17)^7
= $3/2.1924480357 + $3.90/2.56516420176 + $5.07/3.00124211605 + $44.3625/3.00124211605
= $1.36 + $1.52 +$1.69 + $14.78
= $19.35