Sure! Let’s structure the solution step by step for clarity. We’ll **compare the two options** using **Net Present Value (NPV)**, which is the most appropriate method for investment appraisal. --- ### **1. DATA EXTRACTION** #### **Option 1: Set up New Division at Home (South Africa)** | Item | Amount (Rand) | |------------------------------|-----------------| | Cost of setting up premises | 3,500,000 | | Cost of machinery | 1,800,000 | | Annual sales | 4,500,000 | | Annual variable cost | 1,300,000 | | Head office expenses | 600,000* | | Depreciation (machinery) | 10% p.a. | > *Note: Head office expense includes existing expense of R150,000.* #### **Option 2: Acquire Dutch Subsidiary (Purple Guard)** | Item | Amount (Euros) | |------------------------------|-----------------| | Acquire shares | 1,500,000 | | Redundancy costs | 600,000 | | Annual sales | 3,200,000 | | Annual variable costs | 1,600,000 | | Annual fixed costs | 600,000 | | Consultants fees (Year 0) | 50,000 | #### **Additional Data** - Project duration: **10 years** - Cost of capital: **13%** - Dutch inflation < SA inflation by **2%** per year - **Spot rate**: R20/€ - Depreciation (machinery): **10% per year** --- ### **2. CALCULATE CASH FLOWS** #### **A. Set up New Division at Home** ##### **Year 0 Investment** - Premises: R3,500,000 - Machinery: R1,800,000 - **Total Initial Outlay = R5,300,000** ##### **Annual Cash Flows (Years 1–10)** 1. **Sales**: R4,500,000 2. **Less: Variable Costs**: R1,300,000 3. **Less: Head Office Expenses**: R600,000 - *But only R450,000 is incremental (R600,000 - existing R150,000)* 4. **Depreciation**: R180,000 (10% of R1,800,000) 5. **Operating Profit (EBIT):** - = 4,500,000 - 1,300,000 - 600,000 - 180,000 = **R2,420,000** 6. **Tax**: Not mentioned, so assume pre-tax cash flows. 7. **Add back depreciation (non-cash):** +R180,000 **Net Annual Cash Flow** = EBIT + Depreciation = R2,420,000 + R180,000 = **R2,600,000** But since only **R450,000** of head office expense is incremental, Annual cash flow (adjusted): = R2,600,000 + R150,000 = **R2,750,000** But since depreciation is non-cash, actual cash outflow is: - Sales: R4,500,000 - Less: Variable costs: R1,300,000 - Less: Head office expense (incremental): R450,000 Operating cash flow before depreciation = R4,500,000 - R1,300,000 - R450,000 = R2,750,000 --- #### **B. Acquire Dutch Subsidiary** ##### **Year 0 Investment** - Acquisition: €1,500,000 × R20 = R30,000,000 - Redundancy: €600,000 × R20 = R12,000,000 - Consultant: €50,000 × R20 = R1,000,000 **Total Initial Outlay = R43,000,000** ##### **Annual Cash Flows (Years 1–10)** All figures in Euros, convert to Rand using R20/€ (for year 1 cash flows, adjust for inflation/exchange for later years). - Sales: €3,200,000 - Less: Variable cost: €1,600,000 - Less: Fixed cost: €600,000 **Operating cash flow = €3,200,000 - €1,600,000 - €600,000 = €1,000,000 per year** In Rand: 1,000,000 × 20 = **R20,000,000 per year** (Year 1) **Adjust for Inflation & Exchange Rate:** Dutch inflation is 2% below SA. If we assume no inflation in Euros, the Rand will depreciate by 2% per year (i.e., you get more Rand per Euro each year). Year 1: R20 per € Year 2: R20 × 1.02 = R20.40 per € Year 3: R20 × (1.02)^2 = R20.80 per € ... and so on. So, annual Rand cash flows will **increase by 2% per year**. --- ### **3. NPV CALCULATION** #### **A. Set up New Division at Home** - **Initial outlay:** R5,300,000 - **Annual cash flows:** R2,750,000 for 10 years - **Discount rate:** 13% **PV of Annuity Formula:** PV = C × [(1 - (1 + r)^-n) / r] Where: C = R2,750,000 r = 0.13 n = 10 PV = 2,750,000 × [(1 - (1 + 0.13)^-10) / 0.13] PV = 2,750,000 × [1 - (1/3.395) / 0.13] (1 + 0.13)^10 = 3.395 1/3.395 = 0.2945 1 - 0.2945 = 0.7055 0.7055 / 0.13 = 5.427 PV = 2,750,000 × 5.427 = **R14,924,250** **NPV = PV - Initial Outlay = R14,924,250 - R5,300,000 = R9,624,250** --- #### **B. Acquire Dutch Subsidiary** - **Initial outlay:** R43,000,000 - **Year 1 cash flow:** R20,000,000, growing at 2% per year for 10 years - **Discount rate:** 13% **PV of Growing Annuity Formula:** PV = C × [(1 - ((1 + g)/(1 + r))^n) / (r - g)] Where: C = R20,000,000 g = 0.02 r = 0.13 n = 10 First, calculate (1 + g)/(1 + r): (1.02/1.13) = 0.9027 (0.9027)^10 = 0.350 1 - 0.350 = 0.650 0.650 / (0.13 - 0.02) = 0.650 / 0.11 = 5.909 PV = 20,000,000 × 5.909 = **R118,180,000** **NPV = R118,180,000 - R43,000,000 = R75,180,000** --- ## **4. RECOMMENDATION** - **Set up New Division at Home:** NPV = **R9,624,250** - **Acquire Dutch Subsidiary:** NPV = **R75,180,000** **Conclusion:** Apple Limited should acquire the Dutch subsidiary **Purple Guard**, as it offers a much higher NPV (R75.18 million) compared to setting up a new division at home (R9.62 million). This means the Dutch investment generates significantly more value for Apple Limited’s shareholders. --- ### **Summary Table** | Option | NPV (Rand) | |--------------------------|-----------------| | New Division at Home | 9,624,250 | | Acquire Dutch Subsidiary | 75,180,000 | **Advise:** **Acquire Purple Guard in the Netherlands.** --- ### **Workings Summary** - All calculations assume pre-tax cash flows (since tax is not mentioned). - Exchange rate changes reflect inflation differentials. - Depreciation is treated as a non-cash expense for cash flow calculation. - Only incremental head office expenses are included. - Consultant and redundancy fees are assumed to be paid at the start (Year 0). - If tax and working capital are relevant, adjust accordingly. --- **If you need a more detailed breakdown (e.g., year-by-year cash flows), let me know!**