Let's solve the problem **step by step** using the **Free Cash Flow to Equity (FCFE) approach**. --- ### **Step 1: Calculate FCFE for each year** The formula for FCFE: \[ \text{FCFE} = \text{Net Income} + \text{Depreciation} - \text{Change in Net Operating Capital} - \text{Principal Debt Repayment} + \text{New Debt Issued} \] But since depreciation and new debt issued are not given, and debt increases to maintain constant capital structure, we use: \[ \text{FCFE} = \text{Net Income} - (\text{Change in Net Operating Capital} - \text{Change in Debt}) \] **Net Income calculation:** \[ \text{Net Income} = (\text{EBIT} - \text{Interest}) \times (1 - \text{Tax Rate}) \] Tax rate = 30% #### **Year 1:** - EBIT = $11.0M - Interest = $3.0M - Debt = $34.1M - Net Operating Capital = $105.1M \[ \text{Net Income}_1 = (11.0 - 3.0) \times (1 - 0.3) = 8.0 \times 0.7 = \$5.6M \] #### **Year 2:** - EBIT = $13.2M - Interest = $3.3M - Debt = $40.3M - Net Operating Capital = $107.1M \[ \text{Net Income}_2 = (13.2 - 3.3) \times (1 - 0.3) = 9.9 \times 0.7 = \$6.93M \] #### **Year 3:** - EBIT = $16.5M - Interest = $3.6M - Debt = $43.4M - Net Operating Capital = $109.1M \[ \text{Net Income}_3 = (16.5 - 3.6) \times (1 - 0.3) = 12.9 \times 0.7 = \$9.03M \] --- Now, **calculate change in Net Operating Capital** and **Change in Debt**: - Change in Net Operating Capital = Current Year - Previous Year - Change in Debt = Current Year - Previous Year #### **Year 1:** - No change (starting year): Both 0 #### **Year 2:** - Change in Net Operating Capital: \(107.1 - 105.1 = \$2.0M\) - Change in Debt: \(40.3 - 34.1 = \$6.2M\) #### **Year 3:** - Change in Net Operating Capital: \(109.1 - 107.1 = \$2.0M\) - Change in Debt: \(43.4 - 40.3 = \$3.1M\) --- ### **Calculate FCFE for Each Year** #### **Year 1:** \[ \text{FCFE}_1 = 5.6 - (0 - 0) = \$5.6M \] #### **Year 2:** \[ \text{FCFE}_2 = 6.93 - (2.0 - 6.2) = 6.93 - (-4.2) = 6.93 + 4.2 = \$11.13M \] #### **Year 3:** \[ \text{FCFE}_3 = 9.03 - (2.0 - 3.1) = 9.03 - (-1.1) = 9.03 + 1.1 = \$10.13M \] --- ### **Step 2: Calculate the Horizon (Terminal) Value** After year 3, FCFE grows at 4% per year: \[ \text{Horizon Value at end of Year 3} = \frac{\text{FCFE}_4}{r - g} \] Where: - \(r = 16.36\%\) (cost of equity) - \(g = 4\%\) - \(\text{FCFE}_4 = \text{FCFE}_3 \times (1 + g) = 10.13 \times 1.04 = 10.53\) \[ \text{Horizon Value} = \frac{10.53}{0.1636 - 0.04} = \frac{10.53}{0.1236} = \$85.23M \] --- ### **Step 3: Calculate the **Value of FCFE (Present Value of FCFE + Horizon Value)** Discount all FCFE and horizon value to present using \(r = 16.36\%\): \[ \text{PV} = \frac{\text{FCFE}_1}{(1+r)^1} + \frac{\text{FCFE}_2}{(1+r)^2} + \frac{\text{FCFE}_3 + \text{Horizon Value}}{(1+r)^3} \] \[ \text{PV}_1 = \frac{5.6}{1.1636} = 4.81 \] \[ \text{PV}_2 = \frac{11.13}{(1.1636)^2} = \frac{11.13}{1.354} = 8.22 \] \[ \text{PV}_3 = \frac{10.13 + 85.23}{(1.1636)^3} = \frac{95.36}{1.575} = 60.59 \] \[ \text{Total Value of FCFE} = 4.81 + 8.22 + 60.59 = \$73.62M \] --- ## **Answers for the Fill in the Blanks and True/False** ### 1. **FCFE horizon value:** **\$85.23M** ### 2. **Value of FCFE:** **\$73.62M** ### 3. **The estimated value of Purple Turtle's operations after the merger is more/less than the market value of Purple Turtle's equity?** - Value from FCFE (\$73.62M) is **more** than the market equity value (\$12M). ### 4. **Wealth of shareholders will increase/decrease if merged?** - **Increase** (since the value is higher after merger). ### 5. **True/False Statement (Horizon value in FCFE vs APV):** - The horizon value in the FCFE approach is for equity, while in APV it's for total value of operations. - **True** --- ## **Summary Table for Answers** | Value | Answer | |------------------------------|-------------| | FCFE horizon value | $85.23M | | Value of FCFE | $73.62M | | Estimated value is | more | | Wealth of shareholders will | increase | | True/False (horizon value) | True | --- **If you need calculations for a specific part in more detail, let me know!**