Final answer:
The multi-stage DDM applied price of the stock is approximately $18.75.
Step-by-step explanation:
To calculate the multi-stage DDM applied price of a stock, you need to calculate the present value of each future dividend and the terminal value. The present value of each dividend is calculated using the discount rate, which in this case is the investors' required rate of return of 16%. The present value of the terminal value is calculated using the constant growth rate of 4%. Then, you add up all the present values to get the total value of the stock.
Calculating the present value of dividends for the initial four years of 15% growth:
D1 = D0 * (1 + g1) = $3 * (1 + 0.15) = $3.45
D2 = D1 * (1 + g1) = $3.45 * (1 + 0.15) = $3.97
D3 = D2 * (1 + g1) = $3.97 * (1 + 0.15) = $4.57
D4 = D3 * (1 + g1) = $4.57 * (1 + 0.15) = $5.26
Calculating the present value of dividends after the fourth year with a constant growth rate of 4%:
D5 = D4 * (1 + g2) = $5.26 * (1 + 0.04) = $5.47
D6 = D5 * (1 + g2) = $5.47 * (1 + 0.04) = $5.69
Calculating the present value of all these dividends using the required rate of return of 16%:


= $2.97 + $3.10 + $3.18 + $3.17 + $2.93 + $2.73
= $18.08