Question

What is the multi-stage DDM applied price of a stock which is expected to begin paying a $3 dividend 6 years from now. The firm is expected to grow dividends by 15% per year for the next four years after that, followed by a constant growth rate of 4% thereafter forever. Assume that investors require a rate of return of 16% for this firm’s common shares.

$25.75

$16.36

$11.23

$18.75

Answer 1

Answer is $16.36

Dividend in Year 6, D6 = $3.00

Growth rate for next 4 years is 15% and a constant growth rate (g) of 4% thereafter

D7 = $3.0000 * 1.15 = $3.4500
D8 = $3.4500 * 1.15 = $3.9675
D9 = $3.9675 * 1.15 = $4.5626
D10 = $4.5626 * 1.15 = $5.2470
D11 = $5.2470 * 1.04 = $5.4569

Required Return, rs = 16%

P10 = D11 / (rs - g)
P10 = $5.4569 / (0.16 - 0.04)
P10 = $5.4569 / 0.12
P10 = $45.4742

P0 = $3.00/1.16^6 + $3.45/1.16^7 + $3.9675/1.16^8 + $4.5626/1.16^9 + $5.2470/1.16^10 + $45.4742/1.16^10
P0 = $16.36

Therefore, price of a stock is $16.36