Let's analyze the problem step-by-step. --- # **Given Data:** | Solution | Initial Cost | Annual Cost | Life | |------------|-------------------------------|--------------| Build | R2,000,000 | R100,000 | Infinite | Rent | R400,000 |300,000 |8 years - Cost of: 14 per year Need to determine which solution is better for Tumelo --- # **Part 1: Which solution should Tumelo select?** ### **Step 1: Calculate the Present Value (PV) of the Build solution** Since the Build solution has an *infinite* project life, its PV is calculated as the **perpetuity**: \[ PV_{Build} = \frac{\text{Annual Cost}}{\text{Cost of Capital}} = \frac{R100,000}{.14} \approx R714,285.71 \] *(Note: The initial cost is ignored for PV of costs because it's a sunk cost; however, in capital budgeting, initial cost is relevant for decision-making. But here, since we are comparing ongoing costs, the PV of costs is most relevant.)* ### **Step 2: Calculate the PV of the Rent solution** The Rent solution has a finite life of 8 years: - Initial Cost: R400,000 - Annual Cost: R300,000 - Life: 8 years - Discount rate: 14% The PV of costs for Rent includes: - Present value of annual costs over 8 years - Initial cost --- ### **Step 3: Calculate PV of annual costs for Rent** This is an annuity: \[ PV_{Annual\ Costs} = R300,000 \times \frac{1 - (1 + r)^{-n}}{r} \] Where: - \( r = .14 \) - \( n = 8 \) Calculate: \[ PV_{Annual\ Costs} = R300,000 \times \frac{1 - (1 + .14)^{-8}}{.14} \] Calculate \((1 + .14)^{-8}\): \[ (1 + .14)^8 \approx 2.937 \] \[ (1 + .14)^{-8} = \frac{1}{2.937} \approx .340 \] Plug into the formula: \[ PV_{Annual\ Costs} = R300,000 \times \frac{1 - .340}{.14} = R300,000 \times \frac{.66}{.14} \approx R300,000 \times 4.714 \approx R1,414,286 \] ### **Step 4: Total PV of Rent solution** Include the initial cost: \[ PV_{Rent} = R400,000 + R1,414,286 = R1,814,286 \] --- # **Step 5: Compare PVs** - Build: R714,285.71 - Rent: R1,814,286 **Conclusion:** Since the PV of costs for *Build* is significantly lower than for *Rent*, **Tumelo should select the Build solution**. --- # **Part 2: Weakness of the Method Used** **The method used in Part 1 is the present value comparison of costs over time, which is a common technique in capital budgeting.** **Weakness:** - *Assumption of constant costs*: This method assumes costs remain constant over time, ignoring potential changes in costs, inflation, or other economic factors. For instance, annual costs could rise, making the PV estimate inaccurate. - *Ignores qualitative factors*: Factors such as flexibility, scalability, or strategic fit are not considered. --- # **Final Answers:** ### **1. Which solution should Tumelo select?** **Answer:** **Build** is the preferable option because its present value of costs (R714,285.71) is significantly lower than Rent (R1,814,286). ### **2. Weakness of the method:** **Answer:** The method assumes constant costs and discount rates over time, which may not reflect real-world fluctuations, potentially leading to inaccurate comparisons.

# Step-by-Step Solution with Explanation ## Given Data: | Solution | Initial Cost | Annual Cost | Life | |----------|--------------|--------------|----------| | Build | R2,000,000 | R100,000 | Infinite | | Rent | R400,000 | R300,000 | 8 years | | Cost of Capital | - | - | 14% | ## Part 1: Which Solution Should Tumelo Select? ### Step 1: Calculate the Present Value (PV) of the Build Solution The Build solution has an infinite project life, so its costs are treated as a **perpetuity**. The formula for calculating the present value of a perpetuity is: \[ PV_{Build} = \frac{\text{Annual Cost}}{\text{Cost of Capital}} \] Substituting the values: \[ PV_{Build} = \frac{R100,000}{0.14} \approx R714,285.71 \] **Theory Explanation:** The present value of a perpetuity calculates the value of a series of cash flows (annual costs) that continue indefinitely. The discount rate reflects the opportunity cost of capital. ### Step 2: Calculate the PV of the Rent Solution The Rent solution has a finite project life of 8 years. The total present value of costs will include the initial cost and the present value of annual costs over 8 years. #### Step 2.1: Calculate PV of Annual Costs for Rent Using the formula for the present value of an annuity: \[ PV_{Annual\ Costs} = R300,000 \times \frac{1 - (1 + r)^{-n}}{r} \] Where: - \( r = 0.14 \) - \( n = 8 \) **Substituting the values:** 1. Calculate \((1 + r)^{-n}\): \[ (1 + 0.14)^{-8} \approx 0.340 \] 2. Substitute into the annuity formula: \[ PV_{Annual\ Costs} = R300,000 \times \frac{1 - 0.340}{0.14} = R300,000 \times \frac{0.66}{0.14} \approx R300,000 \times 4.714 \approx R1,414,286 \] **Theory Explanation:** The present value of an annuity calculates the value of a series of cash flows (annual costs) that occur for a limited number of periods (8 years). It factors in the time value of money, reflecting how the worth of future cash flows diminishes over time. ### Step 3: Total PV of Rent Solution Combine the initial cost with the PV of annual costs: \[ PV_{Rent} = R400,000 + R1,414,286 = R1,814,286 \] **Theory Explanation:** The total present value for the Rent solution includes both the upfront cost and the present value of ongoing costs, providing a complete picture of the financial commitment. ### Step 4: Compare PVs - **Build:** R714,285.71 - **Rent:** R1,814,286 **Conclusion:** Since the present value of costs for the Build solution (R714,285.71) is significantly lower than that for the Rent solution (R1,814,286), Tumelo should select the **Build solution**. --- ## Part 2: Weakness of the Method Used **Weakness:** 1. **Assumption of Constant Costs:** - The method assumes that costs (both initial and annual) will remain constant over time. In reality, costs could increase due to inflation, maintenance, or operational changes, leading to an inaccurate assessment of the present value. 2. **Ignores Qualitative Factors:** - The analysis focuses solely on quantitative financial metrics and does not consider qualitative factors such as flexibility, scalability, and alignment with the company's long-term strategy, which can have significant implications on the choice of storage solution. **Theory Explanation:** While present value analysis is a widely used technique in capital budgeting, it relies on certain assumptions that may not hold true in practice. Understanding these limitations is crucial for making informed financial decisions. --- ### Final Answers: ### 1. Which Solution Should Tumelo Select? **Answer:** Tumelo should select the **Build** solution, as its present value of costs is significantly lower (R714,285.71) compared to the Rent solution (R1,814,286). ### 2. Weakness of the Method: **Answer:** The method assumes constant costs and discount rates, which may not be realistic, potentially leading to inaccurate financial comparisons. Additionally, it neglects qualitative factors that could influence the decision.