A company pays dividends annually on Dec. 31. Yesterday's dividend was $1. Dividends are expected to grow for the next 2 years at 10% and then settle down to a longrun growth rate of 5% in perpetuity. Because of the initial riskiness of the company, investors required a 20% rate of return over the first 2 years, but only a 12% rate of return thereafter. What is the fair price for the stock today, January 1?
D0 = $ 1
D1 = D0 x (1+g) = $ 1 x (1+0.1) = $ 1 x 1.1 = $ 1.1
D2 = D1 x (1+g) = $ 1.1 x (1+0.1) = $ 1.1 x 1.1 = $ 1.21
D3 = D2 x (1+g) = $ 1.1 x (1+0.05) = $ 1.21 x 1.05 = $ 1.2705
As per Dividend Discount Model, stock price in year 2 can be computed as:
P 2 = D3/(r – g)
r = cost of capital = 12 % or 0.12
g = Constant growth rate of dividend = 5 % or 0.05
P 2 = $ 1.2705/ (0.12 – 0.05)
= $ 1.2705/ 0.07
= $ 18.15
Current stock price P0 = D1 / (1+r) + D2 / (1+r) 2 + P2 / (1+r) 2
= $ 1.1 / (1+0.2) + $ 1.21 / (1+0.2) 2 + $ 18.15/ (1+0.2) 2
= $ 1.1 / (1.2) + $ 1.21 / (1.2) 2 + $ 18.15/ (1.2) 2
= $ 1.1 /1.2 + $ 1.21 / 1.44 + $ 18.15/ 1.44
= $ 0.916666666666667 + $ 0.840277777777778 + 12.6041666666667
= $ 14.361111111111100 or $ 14.36
Current stock price of the company is $ 14.36
Get Answers For Free
Most questions answered within 1 hours.