Question

A share of stock just recently released a dividend for $0.67 per share, and has expected growth rate of 3.00% in the next year, 4.60% in the second year, 2.80% in the third year and 1.60% in the fourth year. Finally the firm expects the growth to become 4.20% long-term thereafter. Given that the expected discount rate on these bonds is 22.10%, what is the expected price of this stock? Could you please give a brief explanation to the steps you took to solve it. Thanks!

Answer 1

Year 1 dividend = 0.67 (1 + 3%) = 0.6901

Year 2 dividend = 0.6901 (1 + 4.6%) = 0.721845

Year 3 dividend = 0.721845 (1 + 2.8%) = 0.742056

Year 4 dividend = 0.742056 (1 + 1.6%) = 0.753929

Year 5 dividend = 0.753929 (1 + 4.2%) = 0.785594

Value at year 4 = D4 / required rate - growth rate

Value at year 4 = 0.785594 / 0.221 - 0.042

Value at year 4 = 0.785594 / 0.179

Value at year 4 = 4.388793

Expected price = Present value of cash inflows

Expected price = 0.6901 / (1 + 0.221)^1 + 0.721845 / (1 + 0.221)^2 + 0.742056 / (1 + 0.221)^3 + 0.753929 / (1 + 0.221)^4 + 4.388793 / (1 + 0.221)^4

Expected price = $3.77