Let's break this down step-by-step. **Given:** - D₀ (current dividend) = $5.00 - Dividends grow at 9% for 3 years, then 6% forever after that - Required return (r) = 16% We need to find the intrinsic value (price to pay) today, \(P_0\). --- ### Step 1: Calculate the first 3 dividends - **Year 1:** \( D_1 = D_0 \times (1+0.09) = 5.00 \times 1.09 = \$5.45 \) - **Year 2:** \( D_2 = D_1 \times 1.09 = 5.45 \times 1.09 = \$5.9405 \) - **Year 3:** \( D_3 = D_2 \times 1.09 = 5.9405 \times 1.09 = \$6.474145 \) --- ### Step 2: Find the terminal value (as a growing perpetuity starting Year 4) - **Year 4 Dividend:** \( D_4 = D_3 \times 1.06 = 6.474145 \times 1.06 = \$6.8625947 \) - **Terminal Value at end of Year 3:** \[ \text{TV}_3 = \frac{D_4}{r-g} = \frac{6.8625947}{0.16 - 0.06} = \frac{6.8625947}{0.10} = \$68.625947 \] --- ### Step 3: Discount all cash flows back to present value \[ P_0 = \frac{D_1}{(1+r)^1} + \frac{D_2}{(1+r)^2} + \frac{D_3}{(1+r)^3} + \frac{\text{TV}_3}{(1+r)^3} \] Plug in the numbers: - \( (1.16)^1 = 1.16 \) - \( (1.16)^2 = 1.3456 \) - \( (1.16)^3 = 1.560896 \) \[ P_0 = \frac{5.45}{1.16} + \frac{5.9405}{1.3456} + \frac{6.474145}{1.560896} + \frac{68.625947}{1.560896} \] Calculate each term: - \( 5.45 / 1.16 = 4.698 \) - \( 5.9405 / 1.3456 = 4.416 \) - \( 6.474145 / 1.560896 = 4.147 \) - \( 68.625947 / 1.560896 = 43.953 \) Sum them up: \[ P_0 = 4.698 + 4.416 + 4.147 + 43.953 = \boxed{ \$57.21 } \] --- ## **Final Answer** **You would pay approximately $57.21 for a share in this company.**

The value of a stock is determined by the present worth of all its expected future dividends. As dividends grow at different rates over time, the stock price reflects these changes discounted back to today.