Question
INFORMATION
Avery Manufacturers intends purchasing a new machine and has a choice between two
machines viz. Machine A or Machine B. The cost of each machine is R3 000 000, with each
having an expected useful life of five years. Machine A is expected to have a scrap value of
R200 000. No scrap value is expected for Machine B. Avery Manufacturers uses the
straight-line method of deprecation. The cost of capital is estimated at 16%.
Machine A is expected to generate the following net profits over its useful life: Year 1 R340
000
Year 2 R280 000
Year 3 R550 000
Year 4 R340 000
Year 5 R160 000
Machine B is expected to generate a net profit of R340 000 per year over the five-year
period. Ignore taxes.
REQUIRED
Answer the questions based on the information supplied.
Use the information provided below to calculate the following. Where applicable, use the fourdecimal present value tables provided in APPENDICES 1 and 2
3.1 Accounting Rate of Return (on initial investment) of Machine A (expressed to two
decimal places) (5)
3.2 Net Present Value of each machine (8)
3. 3 Internal Rate of Return of Machine B (expressed to two decimal places) using
interpolation. (7)
3.4 Payback period for of Machine A (5
Avery Manufacturers intends purchasing a new machine and has a choice between two
machines viz. Machine A or Machine B. The cost of each machine is R3 000 000, with each
having an expected useful life of five years. Machine A is expected to have a scrap value of
R200 000. No scrap value is expected for Machine B. Avery Manufacturers uses the
straight-line method of deprecation. The cost of capital is estimated at 16%.
Machine A is expected to generate the following net profits over its useful life: Year 1 R340
000
Year 2 R280 000
Year 3 R550 000
Year 4 R340 000
Year 5 R160 000
Machine B is expected to generate a net profit of R340 000 per year over the five-year
period. Ignore taxes.
REQUIRED
Answer the questions based on the information supplied.
Use the information provided below to calculate the following. Where applicable, use the fourdecimal present value tables provided in APPENDICES 1 and 2
3.1 Accounting Rate of Return (on initial investment) of Machine A (expressed to two
decimal places) (5)
3.2 Net Present Value of each machine (8)
3. 3 Internal Rate of Return of Machine B (expressed to two decimal places) using
interpolation. (7)
3.4 Payback period for of Machine A (5
Answers
GPT 3.5
3.1 Accounting Rate of Return (ARR) for Machine A:
ARR = Average Annual Profit / Average Investment
Average Annual Profit = (340,000 + 280,000 + 550,000 + 340,000 + 160,000) / 5 = 334,000
Average Investment = (Initial Cost - Scrap Value) / 2 = (3,000,000 - 200,000) / 2 = 1,400,000
ARR = 334,000 / 1,400,000 = 0.2386 or 23.86%
3.2 Net Present Value (NPV) for Machine A and Machine B:
NPV = ∑(Net Cash Inflows / (1+r)^t) - Initial Investment
For Machine A:
NPV = (340,000 / (1+0.16)^1 + 280,000 / (1+0.16)^2 + 550,000 / (1+0.16)^3 + 340,000 / (1+0.16)^4 + 160,000 / (1+0.16)^5) - 3,000,000
NPV = 1,366,748.26 - 3,000,000 = -1,633,251.74
For Machine B:
NPV = (340,000 / (1+0.16)^1 + 340,000 / (1+0.16)^2 + 340,000 / (1+0.16)^3 + 340,000 / (1+0.16)^4 + 340,000 / (1+0.16)^5) - 3,000,000
NPV = 1,539,363.96 - 3,000,000 = -1,460,636.04
3.3 Internal Rate of Return (IRR) for Machine B using interpolation:
IRR = Lower Discount Rate + NPV at Lower Rate / (NPV at Lower Rate - NPV at Higher Rate) * (Higher Rate - Lower Rate)
At 15%:
NPV = (340,000 / (1+0.15)^1 + 340,000 / (1+0.15)^2 + 340,000 / (1+0.15)^3 + 340,000 / (1+0.15)^4 + 340,000 / (1+0.15)^5) - 3,000,000
NPV = 1,702,472.46 - 3,000,000 = -1,297,527.54
At 16%:
NPV = (340,000 / (1+0.16)^1 + 340,000 / (1+0.16)^2 + 340,000 / (1+0.16)^3 + 340,000 / (1+0.16)^4 + 340,000 / (1+0.16)^5) - 3,000,000
NPV = 1,539,363.96 - 3,000,000 = -1,460,636.04
IRR = 15% + (-1,297,527.54) / ((-1,297,527.54) - (-1,460,636.04)) * (16% - 15%)
IRR = 15% + 0.421 * 1%
IRR = 15.421%
3.4 Payback Period for Machine A:
Payback Period = Initial Investment / Average Annual Cash Inflow
Average Annual Cash Inflow = (340,000 + 280,000 + 550,000 + 340,000 + 160,000) / 5 = 334,000
Payback Period = 3,000,000 / 334,000 = 8.98 years (rounded to 9 years)
ARR = Average Annual Profit / Average Investment
Average Annual Profit = (340,000 + 280,000 + 550,000 + 340,000 + 160,000) / 5 = 334,000
Average Investment = (Initial Cost - Scrap Value) / 2 = (3,000,000 - 200,000) / 2 = 1,400,000
ARR = 334,000 / 1,400,000 = 0.2386 or 23.86%
3.2 Net Present Value (NPV) for Machine A and Machine B:
NPV = ∑(Net Cash Inflows / (1+r)^t) - Initial Investment
For Machine A:
NPV = (340,000 / (1+0.16)^1 + 280,000 / (1+0.16)^2 + 550,000 / (1+0.16)^3 + 340,000 / (1+0.16)^4 + 160,000 / (1+0.16)^5) - 3,000,000
NPV = 1,366,748.26 - 3,000,000 = -1,633,251.74
For Machine B:
NPV = (340,000 / (1+0.16)^1 + 340,000 / (1+0.16)^2 + 340,000 / (1+0.16)^3 + 340,000 / (1+0.16)^4 + 340,000 / (1+0.16)^5) - 3,000,000
NPV = 1,539,363.96 - 3,000,000 = -1,460,636.04
3.3 Internal Rate of Return (IRR) for Machine B using interpolation:
IRR = Lower Discount Rate + NPV at Lower Rate / (NPV at Lower Rate - NPV at Higher Rate) * (Higher Rate - Lower Rate)
At 15%:
NPV = (340,000 / (1+0.15)^1 + 340,000 / (1+0.15)^2 + 340,000 / (1+0.15)^3 + 340,000 / (1+0.15)^4 + 340,000 / (1+0.15)^5) - 3,000,000
NPV = 1,702,472.46 - 3,000,000 = -1,297,527.54
At 16%:
NPV = (340,000 / (1+0.16)^1 + 340,000 / (1+0.16)^2 + 340,000 / (1+0.16)^3 + 340,000 / (1+0.16)^4 + 340,000 / (1+0.16)^5) - 3,000,000
NPV = 1,539,363.96 - 3,000,000 = -1,460,636.04
IRR = 15% + (-1,297,527.54) / ((-1,297,527.54) - (-1,460,636.04)) * (16% - 15%)
IRR = 15% + 0.421 * 1%
IRR = 15.421%
3.4 Payback Period for Machine A:
Payback Period = Initial Investment / Average Annual Cash Inflow
Average Annual Cash Inflow = (340,000 + 280,000 + 550,000 + 340,000 + 160,000) / 5 = 334,000
Payback Period = 3,000,000 / 334,000 = 8.98 years (rounded to 9 years)