Question
QUESTION 3 (25 Marks)
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)
Question 4 (25 marks)
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)
Question 4 (25 marks)
Answers
GPT 3.5
3.1 Accounting Rate of Return (ARR) for Machine A:
Initial Investment = R3,000,000
Net Profit each year = R340,000 (Year 1), R280,000 (Year 2), R550,000 (Year 3), R340,000 (Year 4), R160,000 (Year 5)
Average Annual Profit = (340,000 + 280,000 + 550,000 + 340,000 + 160,000) / 5 = R334,000
ARR = (Average Annual Profit / Initial Investment) * 100
ARR = (334,000 / 3,000,000) * 100
ARR = 11.13%
Therefore, the Accounting Rate of Return for Machine A is 11.13%.
3.2 Net Present Value (NPV) of each machine:
For Machine A:
NPV_A = -3,000,000 + (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) + (200,000 / (1 + 0.16)^5)
NPV_A = -3,000,000 + 297,413.79 + 219,479.94 + 364,506.17 + 195,852.93 + 81,395.35 + 104,166.67
NPV_A = R(3,012,000.85)
For Machine B:
NPV_B = -3,000,000 + (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)
NPV_B = -3,000,000 + 293,103.45 + 253,237.59 + 218,365.51 + 188,712.68 + 163,281.70
NPV_B = R(2,116,928.93)
Therefore, the Net Present Value for Machine A is R3,012,000.85 and for Machine B is R2,116,928.93.
3.3 Internal Rate of Return (IRR) for Machine B:
Using interpolation method:
IRR = Lower Rate + [(NPV at Lower Rate) / ((NPV at Lower Rate) - (NPV at Higher Rate))] * (Higher Rate - Lower Rate)
IRR = 16% + [(2,116,928.93) / (2,116,928.93 - 3,012,000.85)] * (20% - 16%)
IRR = 16% + (1,094,072.31 / -895,071.92) * 4%
IRR = 16% + (-1.22) * 4%
IRR = 11.12%
Therefore, the Internal Rate of Return for Machine B is 11.12%.
3.4 Payback period for Machine A:
Payback Period = Number of Years before Cumulative Cash Inflows = Initial Investment
Payback Period = (R3,000,000 - R200,000) / (R340,000 + R280,000 + R550,000 + R340,000 + R160,000)
Payback Period = R2,800,000 / R1,670,000
Payback Period = 1.68 years
Therefore, the Payback Period for Machine A is 1.68 years.
Initial Investment = R3,000,000
Net Profit each year = R340,000 (Year 1), R280,000 (Year 2), R550,000 (Year 3), R340,000 (Year 4), R160,000 (Year 5)
Average Annual Profit = (340,000 + 280,000 + 550,000 + 340,000 + 160,000) / 5 = R334,000
ARR = (Average Annual Profit / Initial Investment) * 100
ARR = (334,000 / 3,000,000) * 100
ARR = 11.13%
Therefore, the Accounting Rate of Return for Machine A is 11.13%.
3.2 Net Present Value (NPV) of each machine:
For Machine A:
NPV_A = -3,000,000 + (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) + (200,000 / (1 + 0.16)^5)
NPV_A = -3,000,000 + 297,413.79 + 219,479.94 + 364,506.17 + 195,852.93 + 81,395.35 + 104,166.67
NPV_A = R(3,012,000.85)
For Machine B:
NPV_B = -3,000,000 + (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)
NPV_B = -3,000,000 + 293,103.45 + 253,237.59 + 218,365.51 + 188,712.68 + 163,281.70
NPV_B = R(2,116,928.93)
Therefore, the Net Present Value for Machine A is R3,012,000.85 and for Machine B is R2,116,928.93.
3.3 Internal Rate of Return (IRR) for Machine B:
Using interpolation method:
IRR = Lower Rate + [(NPV at Lower Rate) / ((NPV at Lower Rate) - (NPV at Higher Rate))] * (Higher Rate - Lower Rate)
IRR = 16% + [(2,116,928.93) / (2,116,928.93 - 3,012,000.85)] * (20% - 16%)
IRR = 16% + (1,094,072.31 / -895,071.92) * 4%
IRR = 16% + (-1.22) * 4%
IRR = 11.12%
Therefore, the Internal Rate of Return for Machine B is 11.12%.
3.4 Payback period for Machine A:
Payback Period = Number of Years before Cumulative Cash Inflows = Initial Investment
Payback Period = (R3,000,000 - R200,000) / (R340,000 + R280,000 + R550,000 + R340,000 + R160,000)
Payback Period = R2,800,000 / R1,670,000
Payback Period = 1.68 years
Therefore, the Payback Period for Machine A is 1.68 years.