1. **Problem statement:** A firm paid a dividend of $3.00 per share this year. Dividends are expected to grow at 8% for 4 years and thereafter at 5% indefinitely. The required rate of return is 12%. Calculate the value of the share. 2. **Formula and approach:** We use the Dividend Discount Model (DDM) with two-stage growth: - For the first 4 years, dividends grow at 8%. - After year 4, dividends grow indefinitely at 5%. The value of the share is the present value of dividends during the high growth period plus the present value of the stock price at the start of the stable growth period. 3. **Calculate dividends for the first 4 years:** $$D_0 = 3.00$$ $$D_1 = D_0 \times (1 + 0.08) = 3.00 \times 1.08 = 3.24$$ $$D_2 = D_1 \times 1.08 = 3.24 \times 1.08 = 3.4992$$ $$D_3 = D_2 \times 1.08 = 3.4992 \times 1.08 = 3.7791$$ $$D_4 = D_3 \times 1.08 = 3.7791 \times 1.08 = 4.0816$$ 4. **Calculate the stock price at year 4 (start of stable growth):** Using the Gordon Growth Model: $$P_4 = \frac{D_5}{r - g}$$ where $$D_5 = D_4 \times (1 + 0.05) = 4.0816 \times 1.05 = 4.2857$$ $$r = 0.12, \quad g = 0.05$$ So, $$P_4 = \frac{4.2857}{0.12 - 0.05} = \frac{4.2857}{0.07} = 61.2243$$ 5. **Calculate the present value of dividends for years 1 to 4:** $$PV_{dividends} = \sum_{t=1}^4 \frac{D_t}{(1 + r)^t} = \frac{3.24}{1.12} + \frac{3.4992}{1.12^2} + \frac{3.7791}{1.12^3} + \frac{4.0816}{1.12^4}$$ Calculate each term: $$\frac{3.24}{1.12} = 2.8929$$ $$\frac{3.4992}{1.2544} = 2.7880$$ $$\frac{3.7791}{1.4049} = 2.6893$$ $$\frac{4.0816}{1.5735} = 2.5947$$ Sum: $$2.8929 + 2.7880 + 2.6893 + 2.5947 = 10.9649$$ 6. **Calculate the present value of $P_4$:** $$PV_{P_4} = \frac{61.2243}{1.12^4} = \frac{61.2243}{1.5735} = 38.9113$$ 7. **Calculate the total value of the share:** $$P_0 = PV_{dividends} + PV_{P_4} = 10.9649 + 38.9113 = 49.8762$$ **Final answer:** The value of the share is approximately **49.88**.