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give answer in 2 step with explanation at the end of each step and final answer at the end:QUESTION 4 (20 Marks) Using the information provided below, answer the following questions. INFORMATION TerraLux Africa Ltd (TLA) is a manufacturer of luxury tiles located in Johannesburg, South Africa. Due to increase in sales both locally and across the African Continental Free Trade Area (AfCFTA ), the company wishes to acquire their own manufacturing plant. The plant has an estimated five - year useful life. TLA is currently evaluating whether to purchase outright or lease the plant. The following conditions apply to the purchase and lease options: The purchase option: 1. The plant will be purchased for cash at an installed cost price of R1,500,000. 2. The annual service costs will amount to R80, 000 per annum for the first 2 years and R100, 000 for the remaining 3 years. 3. Software licensing costs will amount to R 70,000 in the first year and it is envisaged that it will increase by 5% each year thereafter. 4. The plant due to its high usage will be sold as scrap at the end of the five - year term for 20% of the purchase price. 5. TLA uses the straight - line depreciation method to systematically allocate the cost of its tangible assets over their useful lives. The lease option: If the plant is leased, the following will apply: 1. A deposit of 30% of the purchase price is payable immediately. 10% of this amount will be refunded at the end of the lease period. 2. To compensate for expected inflationary effects, the lessor requires an initial annual lease payment of R 500,000 in the first year, with subsequent payments escalating by 4% each year thereafter. Additional Information: - The after - tax cost of debt is 10% . - Assume a tax rate of 30% REQUIRED: 4.1. Determine the present value of cash flows associated with the purchase and lease alternatives (show all calculations and round off figures to the nearest Rand). (16 Marks ) 4.2. Based on the results obtained in 4.1, provide recommendation to the management of TLA on the best option. (4 Marks

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give answer in 2 step with explanation at the end of each step and final answer at the end:Uploaded ImageQUESTION 4 (20 Marks) Using the information provided below, answer the following questions. INFORMATION TerraLux Africa Ltd (TLA) is a manufacturer of luxury tiles located in Johannesburg, South Africa. Due to increase in sales both locally and across the African Continental Free Trade Area (AfCFTA ), the company wishes to acquire their own manufacturing plant. The plant has an estimated five - year useful life. TLA is currently evaluating whether to purchase outright or lease the plant. The following conditions apply to the purchase and lease options: The purchase option: 1. The plant will be purchased for cash at an installed cost price of R1,500,000. 2. The annual service costs will amount to R80, 000 per annum for the first 2 years and R100, 000 for the remaining 3 years. 3. Software licensing costs will amount to R 70,000 in the first year and it is envisaged that it will increase by 5% each year thereafter. 4. The plant due to its high usage will be sold as scrap at the end of the five - year term for 20% of the purchase price. 5. TLA uses the straight - line depreciation method to systematically allocate the cost of its tangible assets over their useful lives. The lease option: If the plant is leased, the following will apply: 1. A deposit of 30% of the purchase price is payable immediately. 10% of this amount will be refunded at the end of the lease period. 2. To compensate for expected inflationary effects, the lessor requires an initial annual lease payment of R 500,000 in the first year, with subsequent payments escalating by 4% each year thereafter. Additional Information: - The after - tax cost of debt is 10% . - Assume a tax rate of 30% REQUIRED: 4.1. Determine the present value of cash flows associated with the purchase and lease alternatives (show all calculations and round off figures to the nearest Rand). (16 Marks ) 4.2. Based on the results obtained in 4.1, provide recommendation to the management of TLA on the best option. (4 Marks

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Asked by: Firdos
Created at: 2025-11-10 20:08:46

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## Step 1: Calculate Present Value (PV) of Cash Flows for **Purchase Option** ### **Given Data:** - **Purchase Price:** R1,500,000 (Year ) - **Annual Service Costs:** R80,000 (Year 1-2), R100,000 (Year 3-5) - **Software Licensing (Year 1):** R70,000, increases by 5% p.a. - **Scrap Value (end of Year 5):** 20% of R1,500,000 = R300,000 - **Depreciation:** Straight-line, R1,500,000 / 5 = R300,000/year - **Tax Rate:** 30% - **Discount Rate (after-tax):** 10% ### **Cash Flows:** #### **Year :** - Outflow: R1,500,000 #### **Year 1:** - Service: R80,000 - Software: R70,000 - Depreciation: R300,000 (non-cash, for tax shield) - Tax Shield: 30% × R300,000 = R90,000 - Net Outflow (before tax): R80,000 + R70,000 = R150,000 - Tax savings: R90,000 - After-tax outflow: R150,000 - R90,000 = R60,000 #### **Year 2:** - Service: R80,000 - Software: R70,000 × 1.05 = R73,500 - Net Outflow (before tax): R80,000 + R73,500 = R153,500 - After-tax outflow: R153,500 - R90,000 = R63,500 #### **Year 3:** - Service: R100,000 - Software: R73,500 × 1.05 = R77,175 - Net Outflow (before tax): R100,000 + R77,175 = R177,175 - After-tax outflow: R177,175 - R90,000 = R87,175 #### **Year 4:** - Service: R100,000 - Software: R77,175 × 1.05 = R81,034 - Net Outflow (before tax): R100,000 + R81,034 = R181,034 - After-tax outflow: R181,034 - R90,000 = R91,034 #### **Year 5:** - Service: R100,000 - Software: R81,034 × 1.05 = R85,086 - Net Outflow (before tax): R100,000 + R85,086 = R185,086 - After-tax outflow: R185,086 - R90,000 = R95,086 - Scrap Value (inflow): R300,000 (taxable gain, but fully depreciated, so taxed: 30% × R300,000 = R90,000 tax) - After-tax inflow: R300,000 - R90,000 = R210,000 ### **Present Value Calculation:** \[ PV = \sum \frac{CF_t}{(1 + r)^t} \] Where \( r = 10\% \) - Year : \( -1,500,000 \) - Year 1: \( -60,000/(1.1)^1 \) - Year 2: \( -63,500/(1.1)^2 \) - Year 3: \( -87,175/(1.1)^3 \) - Year 4: \( -91,034/(1.1)^4 \) - Year 5: \( (-95,086 + 210,000)/(1.1)^5 \) #### **Calculations:** - Year 1: \( -60,000/1.1 = -54,545 \) - Year 2: \( -63,500/1.21 = -52,479 \) - Year 3: \( -87,175/1.331 = -65,503 \) - Year 4: \( -91,034/1.4641 = -62,179 \) - Year 5: \( (210,000 - 95,086) = 114,914/1.61051 = 71,400 \) **Sum:** \[ PV = -1,500,000 - 54,545 - 52,479 - 65,503 - 62,179 + 71,400 = -1,663,306 \] --- **Explanation:** We calculated the after-tax cash outflows and tax shields for each year, discounted them to present value, and summed them. --- ## Step 2: Calculate Present Value (PV) of Cash Flows for **Lease Option** ### **Given Data:** - **Deposit:** 30% × R1,500,000 = R450,000 (Year ), with 10% refunded at end (R45,000 at Year 5) - **Lease Payment Year 1:** R500,000, increases by 4% p.a. - **Tax Rate:** 30% - **Discount Rate:** 10% ### **Lease Payments (after-tax):** - Year 1: R500,000 × (1 - .3) = R350,000 - Year 2: R500,000 × 1.04 × .7 = R364,000 - Year 3: R500,000 × 1.0816 × .7 = R378,560 - Year 4: R500,000 × 1.124864 × .7 = R393,702 - Year 5: R500,000 × 1.169858 × .7 = R409,451 ### **Present Value Calculation:** - Year : \(-450,000\) - Year 1: \(-350,000/1.1 = -318,182\) - Year 2: \(-364,000/1.21 = -300,826\) - Year 3: \(-378,560/1.331 = -284,565\) - Year 4: \(-393,702/1.4641 = -268,958\) - Year 5: \((-409,451 + 45,000)/1.61051 = -226,099\) **Sum:** \[ PV = -450,000 - 318,182 - 300,826 - 284,565 - 268,958 - 226,099 = -1,848,630 \] --- **Explanation:** We calculated the after-tax lease payments, discounted them, and included the deposit and its partial refund. --- ## **Final Answer** ### **Present Values:** - **Purchase Option PV:** **-R1,663,306** - **Lease Option PV:** **-R1,848,630** ### **Recommendation:** Since the **Purchase Option** has a higher (less negative) present value, **TLA should purchase the plant outright** as it is financially preferable to leasing. --- **Summary Table:** | Option | PV of Cash Flows (R) | |-----------|----------------------| | Purchase | -1,663,306 | | Lease | -1,848,630 | --- **Best Option:** **Purchase the plant outright**.

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