Question

a stock just paid an annual dividend of $6. the dividend is expected to grow by 5% per year for the next 4 years. in 4 years, the p/e ratio is expected to be 12 and the payout ratio to be 60%. the required rate of return is 8%. attempt 1/3 for 5.5 pts. part 1 what is the value of the stock?

Answer 1

Answer:Part 1: Calculation of the value of the stockThe annual dividend payment made by the company is given as $6. The dividend payment is expected to grow at the rate of 5% per annum for the next four years. The required rate of return is 8%. In four years, the P/E ratio is expected to be 12 and the payout ratio is expected to be 60%.The dividend payment of a company grows at a constant rate for a finite period of time. Thus, the Gordon Growth model is used to calculate the value of the stock. The Gordon Growth model is given by,Stock price = Dividend payment next year/(Required rate of return – Dividend growth rate)After 1 year,Dividend payment = $6 × (1 + 5%) = $6.3Growth rate = 5%Required rate of return = 8%Stock price = $6.3/(8% – 5%) = $210After 2 years,Dividend payment = $6.3 × (1 + 5%) = $6.615Growth rate = 5%Required rate of return = 8%Stock price = $6.615/(8% – 5%) = $221.87After 3 years,Dividend payment = $6.615 × (1 + 5%) = $6.946Growth rate = 5%Required rate of return = 8%Stock price = $6.946/(8% – 5%) = $231.54After 4 years,Dividend payment = $6.946 × (1 + 5%) = $7.293Growth rate = 5%Required rate of return = 8%Stock price = $7.293/(8% – 5%) = $243.10Thus, the value of the stock is $243.10.