Question

Synovec Co. is growing quickly. Dividends are expected to grow at a rate of 30 percent for the next three years, with the growth rate falling off to a constant 4 percent thereafter. If the required return is 11 percent, and the company just paid a dividend of $2.45, what is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The current share price will be equal to the total present value of the expected (future) dividends of the firm, discounted at the required rate of return of 11 %.

Current Dividend = D0 = $ 2.45

Dividends grow at 30 % per annum for 3 years (i.e D1, D2 and D3) followed by a stable growth of 4 % to perpetuity.

D1 = 2.45 x 1.3 = $ 3.185, D2 = 3.185 x 1.3 = $ 4.1405 and D3 = 4.1405 x 1.3 = $ 5.38265

D4 = 5.38265 x 1.04 = $ 5.597956

Present Value of supernormally growing (growth rate of 30%) dividends = 3.185 / 1.11 + 4.1405 / (1.11)^(2) + 5.38265 / (1.11)^(3) = P1 = $ 10.166

Terminal Value of Perpetually Growing Dividends (at the end of year 3) = D4 / (0.11 - 0.04) = 5.597956 / (0.11 - 0.04) = $ 79.9708

Present Value of Terminal Value of Perpetually Growing Dividend = P2 = 79.9708 / (1.11)^(3) = $ 58.474

Current Share Price = P1 + P2 = 10.166 + 58.474 = $ 68,64 approximately.