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Elsies Limited is a nationally recognised supplier of catering equipment. It offers safe and secure shopping via its online store and its state-of-the-art premises in each of the provinces of South Africa. The company offers a wide selection of catering equipment and supplies at competitive prices. The target market includes restaurants, hotels, hostels and spaza shops. Their products carry an industry-leading warranty that is backed by good after-sales service and availability of spares. The company was established in 2015 with an authorised share capital of 1 500 000 ordinary shares of which 900 000 were issued at R2 each at the initial public offering in 2015. The financial manager and her team were in the process of forecasting the financial performance for 2024 and financial position of the company as of 31 December 2024. The starting point was the following figures that were obtained from the financial statements for the year ended 31 December 2023: The sales amounted to R9 600 000, and the cost price of the goods sold was R7 200 000. Operating expenses totaled R1 200 000 whilst the company tax amounted to R336 000. The carrying value of the fixed assets was R4 200 000 whilst the inventories, trade debtors and cash reflected values of R1 200 000, R1 800 000 and R600 000 respectively. The ordinary share capital balance remained unchanged since the establishment of the company in 2015 whilst the undistributed profits of the company accumulated to R2 100 000. An amount of R2 400 000 was owed to Jip Bank for a long-term loan. The amount owed to trade creditors was R1 467 000 and the company tax payable to SARS was R33 000. The following predictions were made for the financial year ended 31 December 2024: Sales are expected to increase by 25%. Seventy-five percent (75%) of the total sales is estimated to be on credit. Company tax will be calculated at 27% of the pre-tax profit and 10% of this amount is expected to be unpaid on 31 December 2024. A final dividend of R400 000 is expected to be declared on 31 December 2024, and is payable during 2025. The unsold shares are expected to be issued on 31 March 2024 at R3 each. The amount owed by trade debtors will be based on a collection period of 54.75 days. The company’s closing inventory and the amount owed to trade creditors are expected to change directly with the change in sales in 2024. A new machine with a cost price of R700 000 will be purchased during January 2024. Depreciation for 2024 (included in the operating expenses) is expected to amount to R300 000. R760 000 will be paid to Jip Bank during 2024 and this amount includes R360 000 for interest. The cash balance must be calculated (balancing figure). Elsies Limited is considering the purchase of a machine to manufacture some of the spare parts for the catering equipment during 2025. The company desires a minimum required rate of return of 12%. The machine will cost R2 000 000 plus R400 000 for installation and is predicted to have a useful life of five years. A salvage value of R100 000 is estimated. The machine is expected to generate cash inflows of R800 000 per year but will require the employment of two new machine operators at R100 000 per year for each operator, and it will require maintenance and repairs averaging R40 000 per year. Depreciation will be calculated using the straight-line method. Refer to the investment opportunity for 2025 and calculate the following. (Ignore taxes.) Where discount factors are required, use the four decimals present value tables that appear in the module guide. 2.1 Accounting Rate of Return on average investment (expressed to two decimal places). (3) 2.2 Benefit Cost Ratio (expressed to two decimal places). (4) 2.3 Internal Rate of Return (expressed to two decimal places). Your answer must reflect two NPV calculations (using consecutive rates/percentages) and interpolation.

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Answer to a math question Elsies Limited is a nationally recognised supplier of catering equipment. It offers safe and secure shopping via its online store and its state-of-the-art premises in each of the provinces of South Africa. The company offers a wide selection of catering equipment and supplies at competitive prices. The target market includes restaurants, hotels, hostels and spaza shops. Their products carry an industry-leading warranty that is backed by good after-sales service and availability of spares. The company was established in 2015 with an authorised share capital of 1 500 000 ordinary shares of which 900 000 were issued at R2 each at the initial public offering in 2015. The financial manager and her team were in the process of forecasting the financial performance for 2024 and financial position of the company as of 31 December 2024. The starting point was the following figures that were obtained from the financial statements for the year ended 31 December 2023: The sales amounted to R9 600 000, and the cost price of the goods sold was R7 200 000. Operating expenses totaled R1 200 000 whilst the company tax amounted to R336 000. The carrying value of the fixed assets was R4 200 000 whilst the inventories, trade debtors and cash reflected values of R1 200 000, R1 800 000 and R600 000 respectively. The ordinary share capital balance remained unchanged since the establishment of the company in 2015 whilst the undistributed profits of the company accumulated to R2 100 000. An amount of R2 400 000 was owed to Jip Bank for a long-term loan. The amount owed to trade creditors was R1 467 000 and the company tax payable to SARS was R33 000. The following predictions were made for the financial year ended 31 December 2024: Sales are expected to increase by 25%. Seventy-five percent (75%) of the total sales is estimated to be on credit. Company tax will be calculated at 27% of the pre-tax profit and 10% of this amount is expected to be unpaid on 31 December 2024. A final dividend of R400 000 is expected to be declared on 31 December 2024, and is payable during 2025. The unsold shares are expected to be issued on 31 March 2024 at R3 each. The amount owed by trade debtors will be based on a collection period of 54.75 days. The company’s closing inventory and the amount owed to trade creditors are expected to change directly with the change in sales in 2024. A new machine with a cost price of R700 000 will be purchased during January 2024. Depreciation for 2024 (included in the operating expenses) is expected to amount to R300 000. R760 000 will be paid to Jip Bank during 2024 and this amount includes R360 000 for interest. The cash balance must be calculated (balancing figure). Elsies Limited is considering the purchase of a machine to manufacture some of the spare parts for the catering equipment during 2025. The company desires a minimum required rate of return of 12%. The machine will cost R2 000 000 plus R400 000 for installation and is predicted to have a useful life of five years. A salvage value of R100 000 is estimated. The machine is expected to generate cash inflows of R800 000 per year but will require the employment of two new machine operators at R100 000 per year for each operator, and it will require maintenance and repairs averaging R40 000 per year. Depreciation will be calculated using the straight-line method. Refer to the investment opportunity for 2025 and calculate the following. (Ignore taxes.) Where discount factors are required, use the four decimals present value tables that appear in the module guide. 2.1 Accounting Rate of Return on average investment (expressed to two decimal places). (3) 2.2 Benefit Cost Ratio (expressed to two decimal places). (4) 2.3 Internal Rate of Return (expressed to two decimal places). Your answer must reflect two NPV calculations (using consecutive rates/percentages) and interpolation.

Expert avatar
Cristian
4.7
118 Answers
Let's tackle each of the required calculations step by step:

### Part 2.1: Accounting Rate of Return (ARR) on Average Investment

**Solution By Steps**

*Step 1: Calculate the Total Annual Net Cash Inflow*
- Annual Cash Inflows: R800,000
- Annual Expenses:
- Machine Operators: 2 \times R100,000 = R200,000
- Maintenance and Repairs: R40,000
- Net Annual Cash Inflows: R800,000 - R200,000 - R40,000 = R560,000

*Step 2: Calculate Annual Depreciation Expense*
- Cost of Machine: R2,000,000 + R400,000 = R2,400,000
- Salvage Value: R100,000
- Useful Life: 5 years
- Annual Depreciation: \frac{R2,400,000 - R100,000}{5} = R460,000

*Step 3: Calculate Annual Accounting Profit*
- Annual Accounting Profit: R560,000 - R460,000 = R100,000

*Step 4: Calculate Average Investment*
- Initial Investment: R2,400,000
- Average Investment: \frac{R2,400,000 + R100,000}{2} = R1,250,000

*Step 5: Calculate ARR*
- ARR: \frac{R100,000}{R1,250,000} \times 100 = 8.00\%

**Final Answer**
The Accounting Rate of Return (ARR) on average investment is 8.00%.

### Part 2.2: Benefit-Cost Ratio (BCR)

**Solution By Steps**

*Step 1: Calculate the Total Present Value (PV) of Cash Inflows*
- Annual Cash Inflows: R560,000
- Present Value Factor (for 12%, 5 years): 3.6048 (from PV tables)
- Total PV of Cash Inflows: R560,000 \times 3.6048 = R2,018,688

*Step 2: Calculate the Initial Investment*
- Initial Investment: R2,400,000

*Step 3: Calculate BCR*
- BCR: \frac{Total PV of Cash Inflows}{Initial Investment} = \frac{R2,018,688}{R2,400,000} = 0.84

**Final Answer**
The Benefit-Cost Ratio (BCR) is 0.84.

### Part 2.3: Internal Rate of Return (IRR)

**Solution By Steps**

*Step 1: Calculate NPV at a Lower Discount Rate (10%)*
- PV Factor (10%, 5 years): 3.7908
- Total PV of Cash Inflows: R560,000 \times 3.7908 = R2,123,848
- NPV at 10%: R2,123,848 - R2,400,000 = -R276,152

*Step 2: Calculate NPV at a Higher Discount Rate (14%)*
- PV Factor (14%, 5 years): 3.4331
- Total PV of Cash Inflows: R560,000 \times 3.4331 = R1,922,536
- NPV at 14%: R1,922,536 - R2,400,000 = -R477,464

*Step 3: Interpolate to find IRR*
- Using the formula: IRR = R_1 + \frac{NPV_1 \times (R_2 - R_1)}{(NPV_1 - NPV_2)}
- R_1 = 10\% , R_2 = 14\%
- IRR = 10 + \frac{(-R276,152) \times (14 - 10)}{(-R276,152 - -R477,464)}
- IRR = 10 + \frac{-R276,152 \times 4}{R201,312}
- IRR = 10 + \frac{-1,104,608}{201,312}
- IRR = 10 + (-5.48)
- IRR = 4.52\%

**Final Answer**
The Internal Rate of Return (IRR) is 4.52%.

### Key Concept

**Key Concept**
Investment evaluation methods such as ARR, BCR, and IRR are critical for determining the viability and profitability of capital investments. They provide insights into the expected returns and help compare different investment opportunities.

**Key Concept Explanation**
- **ARR**: Measures the average annual profit of an investment as a percentage of the initial investment, useful for evaluating the profitability in accounting terms.
- **BCR**: Compares the present value of cash inflows to the initial investment cost, helping to assess the overall value generated by the investment.
- **IRR**: The discount rate at which the net present value of cash flows from an investment is zero, indicating the expected annualized return and aiding in comparing the profitability of multiple investments.

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