Let's break down the dividend growth into stages and use the **Dividend Discount Model (DDM)** for each stage: ### **Given** - \( D_0 = \$1.36 \) (dividend just paid) - **Stage 1:** Years 1-2, growth = 12.00% - **Stage 2:** Years 3-5, growth = 8.81% - **Stage 3:** Year 6+, growth = 5.00% (perpetuity) - Required return (\( r \)) = 13.00% --- ## **Step 1: Calculate Dividends for Each Year** ### **Years 1-2 (12% growth):** - \( D_1 = D_0 \times (1 + g_1) = 1.36 \times 1.12 = \$1.5232 \) - \( D_2 = D_1 \times 1.12 = 1.5232 \times 1.12 = \$1.706 \) (rounded to 3 decimals) ### **Years 3-5 (8.81% growth):** - \( D_3 = D_2 \times 1.0881 = 1.706 \times 1.0881 = \$1.857 \) - \( D_4 = D_3 \times 1.0881 = 1.857 \times 1.0881 = \$2.022 \) - \( D_5 = D_4 \times 1.0881 = 2.022 \times 1.0881 = \$2.200 \) --- ## **Step 2: Calculate Terminal Value at End of Year 5** At year 5, dividends grow at 5% forever: \[ P_5 = \frac{D_6}{r - g_3} \] Where: - \( D_6 = D_5 \times 1.05 = 2.200 \times 1.05 = \$2.310 \) - \( r = 13\% \) - \( g_3 = 5\% \) \[ P_5 = \frac{2.310}{0.13 - 0.05} = \frac{2.310}{0.08} = \$28.88 \] --- ## **Step 3: Discount All Cash Flows to Present Value** Discount each dividend and the terminal value to present: \[ PV = \frac{D_1}{(1+r)^1} + \frac{D_2}{(1+r)^2} + \frac{D_3}{(1+r)^3} + \frac{D_4}{(1+r)^4} + \frac{D_5}{(1+r)^5} + \frac{P_5}{(1+r)^5} \] Where \( r = 0.13 \): ### **Calculating Present Values:** - \( (1.13)^1 = 1.13 \) - \( (1.13)^2 = 1.2769 \) - \( (1.13)^3 = 1.442897 \) - \( (1.13)^4 = 1.629474 \) - \( (1.13)^5 = 1.840306 \) #### **PV of Dividends:** \[ PV_1 = \frac{1.5232}{1.13} = 1.348 \] \[ PV_2 = \frac{1.706}{1.2769} = 1.337 \] \[ PV_3 = \frac{1.857}{1.442897} = 1.287 \] \[ PV_4 = \frac{2.022}{1.629474} = 1.241 \] \[ PV_5 = \frac{2.200}{1.840306} = 1.195 \] #### **PV of Terminal Value:** \[ PV_{P_5} = \frac{28.88}{1.840306} = 15.695 \] --- ## **Step 4: Sum Present Values** \[ \text{Intrinsic Value} = PV_1 + PV_2 + PV_3 + PV_4 + PV_5 + PV_{P_5} \] \[ = 1.348 + 1.337 + 1.287 + 1.241 + 1.195 + 15.695 \] \[ = 22.10 \] --- ## **Final Answer** \[ \boxed{\$22.10} \] --- ### **Explanation** - Calculate each year’s dividend based on the specified growth rates. - Find the terminal value at the end of the last stage before perpetuity. - Discount all dividends and the terminal value back to the present using the required return. - Sum all present values for the intrinsic value.