Practice questions
Original questions written by HomiLabs in the style of the exam, with answers and mark schemes. They are not
Cambridge past paper questions and have not been reviewed by Cambridge. Try each one before opening the answer.
Q1Investment decision and sensitivity · Core · Paper 4 style · 4 marksA rice mill in Larkana is thinking of replacing an old husking machine.
- (a) State two non-financial factors a business should consider before replacing a machine. [2]
- (b) Explain one advantage of net present value over the payback method. [2]
Show answer
- (a) Any two: effect on employees (training, job losses, morale); quality of output; environmental impact; reliability and after-sales service of the supplier; flexibility of the new machine.
1 mark each.
- (b) NPV considers all cash flows over the project's life and the time value of money, whereas payback ignores cash flows after the payback point.
1 mark advantage; 1 mark explanation.
The manager of a cinema in Karachi has been told that a new projector has a positive net present value.
- (a) Explain what is meant by a positive net present value. [2]
- (b) State two limitations of the net present value method. [2]
Show answer
- (a) The present value of the future net cash inflows is greater than the initial cost; the project earns more than the cost of capital and increases the value of the business.
1 mark PV of inflows > cost; 1 mark return above cost of capital.
- (b) Any two: cash flows are hard to forecast; choosing the right discount rate is difficult; ignores non-financial factors; harder to understand than payback; assumes the cost of capital stays the same.
1 mark each.
The finance director of a cement company is appraising a new kiln.
- (a) Explain why a business uses its cost of capital as the discount rate. [2]
- (b) Explain what is meant by sensitivity analysis. [2]
- (c) State one limitation of sensitivity analysis. [1]
Show answer
- (a) It is the return the business must pay to its providers of finance; a project must earn at least this return to add value.
1 mark cost of finance; 1 mark minimum required return.
- (b) Testing how much one estimate (e.g. sales volume, cost, discount rate) can change before the NPV becomes zero, to show which estimates the decision depends on most.
1 mark change one variable; 1 mark effect on NPV/decision.
- (c) Changes one variable at a time, whereas in reality several change together / gives no probability of the change happening.
1 mark.
Khan Engineering can afford only one of two projects. Its cost of capital is 10%. Results: Project Canal Project BridgeNet present value $24,000 $19,500Payback period 3.2 years 2.1 yearsAccounting rate of return 18% 22%Internal rate of return 15% 17%The company has a large bank overdraft.
- (a) Advise the directors which project they should choose. Justify your answer. [7]
Show answer
- (a) Either project may be recommended with justification; a strong answer recommends Project Canal on NPV (it adds the most value) unless liquidity is a priority.
Canal (max 3): higher NPV ($24,000 v $19,500) so adds more to shareholder value; NPV is the most reliable method; both IRRs exceed the 10% cost of capital. Bridge (max 3): faster payback (2.1 v 3.2 years), less risk and better for cash flow; higher ARR and IRR; later cash flows of Canal are harder to forecast. Other points: non-financial factors such as staff, customers, environment; forecasts are estimates. Clear decision (1).
A project costing $100,000 is expected to give net cash inflows of $32,000 a year for five years. The cost of capital is 12% and the sum of the discount factors for years 1–5 at 12% is 3.605.
- (a) Calculate the net present value. [2]
- (b) Calculate the percentage by which the annual cash inflow could fall before the project became unprofitable, correct to two decimal places. [2]
- (c) Explain what your answer to (b) shows. [1]
Show answer
- (a) 32,000 × 3.605 = 115,360; NPV = 115,360 − 100,000 = $15,360
M1; A1.
- (b) 15,360 ÷ 115,360 × 100 = 13.31%
M1 NPV ÷ PV of the inflows; A1.
- (c) If annual inflows fall by more than 13.31% (below about $27,739), the NPV becomes negative; a small margin means the project is risky.
1 mark.
Saba Textiles may install a dyeing plant costing $180,000. Net cash inflows are forecast at $55,000, $65,000, $70,000 and $45,000 in years 1–4. The cost of capital is 10%.Discount factors at 10%: year 1 0.909; year 2 0.826; year 3 0.751; year 4 0.683
- (a) Calculate the net present value. [3]
- (b) Calculate the percentage increase in the initial cost that would make the NPV zero, correct to two decimal places. [2]
- (c) Comment on your answer to (b). [1]
Show answer
- (a) Year Cash flow $ Factor Present value $0 (180,000) 1.000 (180,000)1 55,000 0.909 49,9952 65,000 0.826 53,6903 70,000 0.751 52,5704 45,000 0.683 30,735NPV 6,990
M1 discounting; M1 less cost; A1.
- (b) 6,990 ÷ 180,000 × 100 = 3.88%
M1; A1 OF.
- (c) The project is very sensitive to the initial cost: an overspend of under 4% would make it unprofitable, so cost control/fixed-price quotes are important.
1 mark.
Zainab runs a packaging factory in Lahore. Her old machine breaks down often and three customers complained about late orders last month. A new machine would cost $95,000, financed by a bank loan at 9% interest. Its NPV at the 10% cost of capital is $8,400 and its payback period is 3.8 years over a 5-year life. It uses 15% less electricity. Staff would need two weeks of training, during which output would fall.
- (a) Advise Zainab whether she should buy the new machine. Justify your answer. [7]
Show answer
- (a) A justified recommendation, e.g. buy: positive NPV, solves the reliability problem and saves energy, but she should plan the training and loan carefully.
For (max 4): NPV positive ($8,400) at the 10% cost of capital; breakdowns of the old machine have caused late orders and lost customers; 15% energy saving and lower emissions; better quality may win new contracts. Against (max 4): payback of 3.8 years in a 5-year life leaves little margin; NPV small compared with $95,000 cost so sensitive to forecasts; staff need two weeks of training and output will fall; loan increases gearing and interest at 9%. Decision (1).
A company may launch a water pump. It needs a machine costing $110,000 with a four-year life and no residual value. It expects to sell 5,000 pumps a year at a contribution of $12 each. Extra fixed cash costs are $20,000 a year. The cost of capital is 10%; the sum of the discount factors for years 1–4 is 3.169.
- (a) Calculate the net present value. [2]
- (b) Calculate the percentage by which sales volume could fall before the NPV becomes zero, correct to two decimal places. [3]
- (c) Calculate the minimum annual sales volume needed, in whole units. [1]
Show answer
- (a) Annual cash flow 5,000 × 12 − 20,000 = 40,000; 40,000 × 3.169 − 110,000 = $16,760
M1; A1.
- (b) PV of contribution = 60,000 × 3.169 = 190,140; 16,760 ÷ 190,140 × 100 = 8.81%
M1 only contribution varies with volume; M1 NPV ÷ PV of contribution; A1.
- (c) (110,000 ÷ 3.169 + 20,000) ÷ 12 = 4,559.3 → 4,560 units
1 mark.
Hassan Foods has $300,000 to invest and a cost of capital of 12%. It is considering two projects: Project Tulip Project LotusInitial cost $300,000 $150,000Life 6 years 4 yearsNet present value $42,000 $31,000Internal rate of return 18% 21%Payback period 3.5 years 2.4 yearsFall in annual inflows that makes NPV zero 7% 16%
- (a) Advise the directors which project, if either, they should invest in. Justify your answer. [7]
Show answer
- (a) Either may be chosen with justification; e.g. Lotus: lower risk, faster payback and higher IRR, and leaves $150,000 for other uses, although Tulip has the higher NPV.
Tulip (max 3): higher NPV $42,000 adds most value; uses all available funds productively; longer life gives returns for six years. Lotus (max 3): higher IRR 21% v 18%; payback 2.4 v 3.5 years; NPV only falls to zero if inflows drop 16% (Tulip only 7%) so far less risky; half the investment, leaving $150,000 for another project, which could make total NPV higher. Other: forecasts over six years less reliable; non-financial factors. Decision (1).
An engineering firm in Sialkot appraised a project costing $160,000 with net cash inflows of $45,000 a year for five years and no residual value. The finance manager now believes the inflows will be 10% lower, but the equipment could be sold for $12,000 at the end of year 5. The cost of capital is 10%.Discount factors at 10%: year 1 0.909; year 2 0.826; year 3 0.751; year 4 0.683; year 5 0.621
- (a) Calculate the original net present value. [2]
- (b) Calculate the revised net present value. [3]
- (c) Comment on what the revision shows about the project. [1]
Show answer
- (a) Sum of factors = 3.790; 45,000 × 3.790 − 160,000 = $10,550
M1; A1.
- (b) 40,500 × 3.790 = 153,495; residual 12,000 × 0.621 = 7,452; NPV = $947
M1 inflows reduced by 10%; M1 residual at year 5; A1.
- (c) The NPV falls to only $947: the project is still just acceptable but is very sensitive to the sales forecast.
1 mark.
A school in Abbottabad may install solar panels costing $85,000. Electricity savings are expected to be $23,500 a year for five years, with no residual value. The cost of capital is 8%.Discount factors at 8%: year 1 0.926; year 2 0.857; year 3 0.794; year 4 0.735; year 5 0.681
- (a) Calculate the sum of the discount factors for years 1 to 5. [1]
- (b) Calculate the minimum annual net cash inflow needed for the project to be worthwhile, to the nearest dollar. [3]
- (c) Calculate the percentage by which the expected inflow of $23,500 could fall before the project is rejected, correct to two decimal places. [2]
Show answer
- (a) 3.993
1 mark.
- (b) 85,000 ÷ 3.993 = $21,287
M1 NPV = 0; M1 cost ÷ annuity factor; A1.
- (c) (23,500 − 21,287) ÷ 23,500 × 100 = 9.42%
M1; A1 OF.
A dairy in Okara is considering a new bottling machine costing $80,000. It would give net cash inflows of $26,000 at the end of each of the next four years. The cost of capital is 10%.Discount factors at 10%: year 1 0.909; year 2 0.826; year 3 0.751; year 4 0.683
- (a) Calculate the net present value of the machine. [3]
- (b) State whether the machine should be bought, based on your answer to (a). [1]
Show answer
- (a) Year Cash flow $ Factor Present value $0 (80,000) 1.000 (80,000)1 26,000 0.909 23,6342 26,000 0.826 21,4763 26,000 0.751 19,5264 26,000 0.683 17,758NPV 2,394
M1 present values of inflows; M1 less cost; A1.
- (b) Yes: the NPV of $2,394 is positive.
1 mark OF.
A private school in Islamabad plans to build a science laboratory costing $150,000. Extra fee income less extra running costs is expected to be $40,000, $55,000, $60,000 and $35,000 in years 1 to 4. The cost of capital is 12%.Discount factors at 12%: year 1 0.893; year 2 0.797; year 3 0.712; year 4 0.636
- (a) Calculate the net present value of the project. [4]
- (b) Explain what your answer to (a) shows. [1]
Show answer
- (a) Year Cash flow $ Factor Present value $0 (150,000) 1.000 (150,000)1 40,000 0.893 35,7202 55,000 0.797 43,8353 60,000 0.712 42,7204 35,000 0.636 22,260NPV (5,465)
M1 each year discounted; M1 total present value; M1 less cost; A1.
- (b) The NPV is negative (−$5,465): the project does not earn the 12% cost of capital, so on financial grounds it should not go ahead.
1 mark OF.
A courier firm in Peshawar may buy an electric van for $36,000. Fuel and repair savings are expected to be $11,000, $12,000, $12,000 and $9,000 in years 1 to 4, and the van will be sold for $4,000 at the end of year 4. The cost of capital is 14%.Discount factors at 14%: year 1 0.877; year 2 0.769; year 3 0.675; year 4 0.592
- (a) Calculate the net present value of buying the van. [4]
- (b) State, with a reason, whether the van should be bought on financial grounds. [1]
Show answer
- (a) Year Cash flow $ Factor Present value $0 (36,000) 1.000 (36,000)1 11,000 0.877 9,6472 12,000 0.769 9,2283 12,000 0.675 8,1004 13,000 0.592 7,696NPV (1,329)
M1 cash flow for year 4 includes sale proceeds; M1 discounting; M1 total; A1.
- (b) No: the NPV is negative (−$1,329), so the savings do not cover the cost at a 14% cost of capital.
1 mark OF.
A food processor in Multan is considering a new production line costing $200,000. It needs extra working capital of $25,000 at the start, which will be released at the end of year 5. Net operating cash inflows will be $52,000 a year for five years and the line will be sold for $30,000 at the end of year 5. The cost of capital is 8%.Discount factors at 8%: year 1 0.926; year 2 0.857; year 3 0.794; year 4 0.735; year 5 0.681
- (a) Calculate the net cash flow for year 0 and for year 5. [2]
- (b) Calculate the net present value of the project. [3]
- (c) Explain why the working capital is shown as an inflow in year 5. [1]
Show answer
- (a) Year 0: 200,000 + 25,000 = ($225,000). Year 5: 52,000 + 30,000 + 25,000 = $107,000.
1 mark each.
- (b) Year Cash flow $ Factor Present value $0 (225,000) 1.000 (225,000)1 52,000 0.926 48,1522 52,000 0.857 44,5643 52,000 0.794 41,2884 52,000 0.735 38,2205 107,000 0.681 72,867NPV 20,091
M1 years 1–4 discounted; M1 year 5 discounted; A1.
- (c) The extra inventory and receivables are no longer needed when the project ends, so the cash tied up is released.
1 mark.
A transport company in Karachi may buy a bus for $120,000. It will be used for four years and then sold for $20,000. Depreciation is straight-line. Forecast profits after depreciation are: year 1 $18,000; year 2 $22,000; year 3 $27,000; year 4 $15,000. The cost of capital is 10%.Discount factors at 10%: year 1 0.909; year 2 0.826; year 3 0.751; year 4 0.683
- (a) Calculate the net cash flow for each of years 1 to 4. [2]
- (b) Calculate the net present value. [3]
- (c) State whether the project should be accepted. [1]
Show answer
- (a) Depreciation = (120,000 − 20,000) ÷ 4 = 25,000. Cash flows: 43,000, 47,000, 52,000, 40,000 + 20,000 residual = 60,000.
M1 add back depreciation; A1 including residual value.
- (b) Year Cash flow $ Factor Present value $0 (120,000) 1.000 (120,000)1 43,000 0.909 39,0872 47,000 0.826 38,8223 52,000 0.751 39,0524 60,000 0.683 40,980NPV 37,941
M1 discounting; M1 less cost; A1 OF.
- (c) Accept: NPV is positive.
1 mark OF.
A company in Hyderabad can afford only one of two projects, each costing $60,000 now. Net cash inflows:Year Project Indus $ Project Ravi $1 25,000 10,0002 25,000 20,0003 20,000 30,0004 10,000 35,000The cost of capital is 10%.Discount factors at 10%: year 1 0.909; year 2 0.826; year 3 0.751; year 4 0.683
- (a) Calculate the net present value of each project. [5]
- (b) State which project should be chosen on financial grounds and give one reason why the result may be less certain for the other project. [1]
Show answer
- (a) Project IndusYear Cash flow $ Factor Present value $0 (60,000) 1.000 (60,000)1 25,000 0.909 22,7252 25,000 0.826 20,6503 20,000 0.751 15,0204 10,000 0.683 6,830NPV 5,225Project RaviYear Cash flow $ Factor Present value $0 (60,000) 1.000 (60,000)1 10,000 0.909 9,0902 20,000 0.826 16,5203 30,000 0.751 22,5304 35,000 0.683 23,905NPV 12,045
M1 discounting A; A1; M1 discounting B; A1; 1 mark presentation.
- (b) Project Ravi (higher NPV). Ravi's cash flows come later, so they are harder to forecast and riskier.
1 mark for both points.
Sharif Ltd may make a new juicer. A machine costing $190,000 and a launch campaign costing $15,000 would both be paid now. The juicer would sell 6,000 units a year for five years at $45 each, with a variable cost of $27 per unit. Extra fixed cash costs would be $48,000 a year. The machine would be scrapped for $10,000 at the end of year 5. The cost of capital is 12%.Discount factors at 12%: year 1 0.893; year 2 0.797; year 3 0.712; year 4 0.636; year 5 0.567
- (a) Calculate the annual net cash flow from operating the machine. [2]
- (b) Calculate the net present value of the project. [4]
- (c) State one reason why the net present value may not be reliable. [1]
Show answer
- (a) 6,000 × (45 − 27) − 48,000 = $60,000
M1 contribution less fixed cash costs; A1.
- (b) Year Cash flow $ Factor Present value $0 (205,000) 1.000 (205,000)1 60,000 0.893 53,5802 60,000 0.797 47,8203 60,000 0.712 42,7204 60,000 0.636 38,1605 70,000 0.567 39,690NPV 16,970
Year 0 includes launch costs: 190,000 + 15,000 (1); scrap in year 5 (1); discounting (1); A1.
- (c) Any one: sales volume, price or costs are estimates; the cost of capital may change; the machine's life or scrap value may differ.
1 mark.
A private hospital in Lahore may buy a scanner costing $250,000. It would bring net cash inflows of $70,000 a year for six years. A major overhaul costing $40,000 would be needed at the end of year 3, and the scanner could be sold for $15,000 at the end of year 6. The cost of capital is 10%.Discount factors at 10%: year 1 0.909; year 2 0.826; year 3 0.751; year 4 0.683; year 5 0.621; year 6 0.564
- (a) Calculate the present value of the annual cash inflows, using the sum of the discount factors. [2]
- (b) Calculate the net present value of the project. [4]
- (c) State one non-financial factor the hospital board should consider. [1]
Show answer
- (a) Sum of factors years 1–6 = 4.354; 70,000 × 4.354 = $304,780
M1; A1.
- (b) PV inflows 304,780 − overhaul 40,000 × 0.751 = 30,040 + residual 15,000 × 0.564 = 8,460 − cost 250,000 = $33,200
M1 overhaul discounted at year 3; M1 residual at year 6; M1 less cost; A1.
- (c) Any one: patient waiting times/quality of care; staff training; reliability of the supplier; space needed.
1 mark.
A printing firm in Faisalabad forecasts for a new press:Year Revenue $ Total costs $1 90,000 67,0002 105,000 73,0003 120,000 81,000Total costs include depreciation of $15,000 a year on the press.
- (a) Calculate the net cash flow for each year. [3]
- (b) Explain why depreciation is not included in the net cash flows. [1]
Show answer
- (a) Year 1: 90,000 − (67,000 − 15,000) = $38,000; Year 2: 105,000 − (73,000 − 15,000) = $47,000; Year 3: 120,000 − (81,000 − 15,000) = $54,000
M1 depreciation removed from costs; A1 A1 (all three for 2 marks).
- (b) Depreciation is not a payment of cash; the cash outflow is the purchase cost at the start.
1 mark.
Fatima Foods is considering a new snack line for four years. Information:1 Market research already paid: $8,0002 New machine, paid now: $70,000 (no residual value)3 Extra supervisor: $14,000 a year4 Share of head office costs charged to the line: $6,000 a year5 Contribution from sales: $40,000 a year
- (a) For each of the items 1 to 5, state whether it is a relevant cash flow for the decision and give a reason for items 1 and 4. [3]
- (b) Calculate the net cash flow for year 0 and for each of years 1 to 4. [2]
Show answer
- (a) 1 not relevant: market research is a sunk cost (already paid). 2 relevant. 3 relevant. 4 not relevant: apportioned head office cost will be paid whether or not the project goes ahead. 5 relevant.
1 mark for all five classifications; 1 mark each reason.
- (b) Year 0: ($70,000). Years 1–4: 40,000 − 14,000 = $26,000 each year.
1 mark each.
Amir runs a car-wash in Sukkur. New equipment would cost $66,000, last three years and be sold for $6,000. Forecast profits after straight-line depreciation are $14,000, $19,000 and $11,000.
- (a) Explain why profit is not used directly in net present value calculations. [2]
- (b) Calculate the net cash flow for each of years 1 to 3. [3]
Show answer
- (a) Profit includes non-cash items such as depreciation and is based on accruals; NPV discounts the timing of actual cash receipts and payments.
1 mark non-cash/accruals; 1 mark timing of cash.
- (b) Depreciation = (66,000 − 6,000) ÷ 3 = 20,000. Year 1 34,000; year 2 39,000; year 3 31,000 + 6,000 = $37,000
M1 depreciation; M1 added back; A1 including residual.
A laundry in Dubai plans to buy machinery for $120,000, to be used for four years and then sold for $12,000. Extra working capital of $18,000 is needed at the start and will be recovered at the end of year 4. Revenue is forecast at $100,000, $110,000, $95,000 and $80,000 in years 1–4. Variable costs are 40% of revenue. Fixed cash costs are $22,000 a year, and depreciation will be $27,000 a year.
- (a) Calculate the net cash flow for year 0. [1]
- (b) Calculate the net cash flow for each of years 1 to 4. [5]
Show answer
- (a) Machine 120,000 + working capital 18,000 = ($138,000)
1 mark.
- (b) Year 1: 100,000 × 60% − 22,000 = 38,000; Year 2: 110,000 × 60% − 22,000 = 44,000; Year 3: 95,000 × 60% − 22,000 = 35,000; Year 4: 80,000 × 60% − 22,000 = 26,000; year 4 total including working capital 18,000 and residual 12,000 = $56,000
M1 contribution = 60% of revenue; M1 fixed cash costs deducted; M1 depreciation (27,000) not deducted; M1 working capital released year 4; A1 residual value year 4.
A solar-panel project has an NPV of $4,500 at 8% and −$3,000 at 12%.
- (a) Explain what is meant by the internal rate of return. [2]
- (b) Calculate the internal rate of return. [2]
- (c) State why the answer to (b) is only an estimate. [1]
Show answer
- (a) The discount rate at which the net present value of a project is zero; the project should be accepted if it is higher than the cost of capital.
1 mark NPV = 0; 1 mark decision rule.
- (b) 8 + 4 × 4,500 ÷ (4,500 + 3,000) = 10.4%
M1; A1.
- (c) Interpolation assumes NPV changes in a straight line between the two rates, but the real relationship is curved.
1 mark.
A project has a net present value of $18,400 at a discount rate of 10% and −$6,200 at 18%. The company's cost of capital is 14%.
- (a) Calculate the internal rate of return, correct to two decimal places. [3]
- (b) State whether the project should be accepted. [1]
Show answer
- (a) 10 + 8 × 18,400 ÷ (18,400 + 6,200) = 15.98%
M1 interpolation formula; M1 correct substitution; A1.
- (b) Accept: the IRR of 15.98% is above the 14% cost of capital.
1 mark OF.
A clinic in Karachi may buy dental equipment for $90,000. Net cash inflows are expected to be $25,000, $35,000, $40,000 and $30,000 in years 1–4.Discount factors at 10%: year 1 0.909; year 2 0.826; year 3 0.751; year 4 0.683Discount factors at 16%: year 1 0.862; year 2 0.743; year 3 0.641; year 4 0.552
- (a) Calculate the net present value at 10%. [2]
- (b) Calculate the net present value at 16%. [2]
- (c) Calculate the internal rate of return, correct to two decimal places. [2]
- (d) The cost of capital is 12%. State whether the project should go ahead and give one advantage of the IRR method. [2]
Show answer
- (a) Year Cash flow $ Factor Present value $0 (90,000) 1.000 (90,000)1 25,000 0.909 22,7252 35,000 0.826 28,9103 40,000 0.751 30,0404 30,000 0.683 20,490NPV 12,165
M1; A1.
- (b) Year Cash flow $ Factor Present value $0 (90,000) 1.000 (90,000)1 25,000 0.862 21,5502 35,000 0.743 26,0053 40,000 0.641 25,6404 30,000 0.552 16,560NPV (245)
M1; A1.
- (c) 10 + 6 × 12,165 ÷ (12,165 + 245) = 15.88%
M1; A1 OF.
- (d) Go ahead: IRR 15.88% exceeds 12%. Advantage: a percentage is easy to compare with the cost of capital / takes account of the time value of money.
1 mark decision; 1 mark advantage.
A furniture maker in Chiniot may buy a CNC router for $60,000. It will last five years with no residual value. Total profit after depreciation over the five years is forecast at $45,000.
- (a) Calculate the average annual profit. [1]
- (b) Calculate the accounting rate of return based on the average investment. [2]
- (c) State whether the project meets the target return of 25%. [1]
Show answer
- (a) 45,000 ÷ 5 = $9,000
1 mark.
- (b) Average investment = (60,000 + 0) ÷ 2 = 30,000; ARR = 9,000 ÷ 30,000 × 100 = 30%
M1; A1.
- (c) Yes: 30% is above 25%.
1 mark OF.
Haroon Builders may buy a crane for $140,000. It will produce net cash inflows of $50,000 a year for four years and then be sold for $20,000.
- (a) Calculate the average annual profit. [2]
- (b) Calculate the accounting rate of return on (i) the average investment and (ii) the initial investment, correct to two decimal places. [2]
- (c) State one limitation of the accounting rate of return. [1]
Show answer
- (a) Total cash inflows 200,000 − depreciation 120,000 = 80,000; ÷ 4 = $20,000
M1 depreciation deducted; A1.
- (b) (i) average investment (140,000 + 20,000) ÷ 2 = 80,000; 20,000 ÷ 80,000 = 25.00%. (ii) 20,000 ÷ 140,000 = 14.29%
1 mark each.
- (c) Any one: ignores the time value of money; uses profit not cash flow; different formulas give different answers; ignores the timing of profits.
1 mark.
A school in Lahore must choose between two projects, each costing $48,000. Project X returns $12,000 a year for six years. Project Y returns $20,000, $18,000, $15,000 and $10,000 in years 1–4. Cash flows arise evenly through each year.
- (a) Calculate the payback period for Project X. [1]
- (b) Calculate the payback period for Project Y in years and months. [3]
- (c) State one disadvantage of the payback method. [1]
Show answer
- (a) 48,000 ÷ 12,000 = 4 years
1 mark.
- (b) After 2 years 38,000 recovered; 10,000 of year 3's 15,000 needed = 0.67 of a year ≈ 8 months. Payback = 2 years 8 months.
M1 cumulative; M1 fraction; A1.
- (c) Ignores cash flows after payback / ignores the time value of money (unless discounted).
1 mark.
A bakery chain in Islamabad may open a new outlet costing $75,000. Net cash inflows are $28,000, $30,000, $26,000 and $20,000 in years 1–4, arising evenly through each year. The cost of capital is 10%.Discount factors at 10%: year 1 0.909; year 2 0.826; year 3 0.751; year 4 0.683
- (a) Calculate the simple payback period, correct to two decimal places of a year. [2]
- (b) Calculate the discounted payback period, correct to two decimal places of a year. [4]
- (c) Explain why the discounted payback period is longer than the simple payback period. [1]
Show answer
- (a) After 2 years 58,000; 17,000 ÷ 26,000 = 0.65; payback = 2.65 years
M1; A1.
- (b) Present values: 25,452, 24,780, 19,526, 13,660. Cumulative after year 3: 69,758; still to recover 5,242; 5,242 ÷ 13,660 = 0.38. Discounted payback = 3.38 years
M1 present values; M1 cumulative; M1 fraction of year 4; A1.
- (c) Discounting reduces the value of each future inflow, so it takes longer to recover the cost.
1 mark.
