IB DP Business Management: Investment appraisal – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – the IB holds copyright in its own papers. Use these alongside the official past papers available through your school or the IB store.

These questions cover section 3.8, Investment appraisal, of the IB Business management guide (first assessment 2024). Payback period and ARR are SL and HL. Questions on NPV are marked (HL only). All sums are in dollars. Before you start, revise with the study guide and the revision notes. Wider Unit 3 practice is in the Unit 3 practice questions. Course hub: IB DP Business Management. Printable list: checklist.

Questions

1. Define the term payback period. [2]

2. Wilderby Gym buys fitness equipment for 135,000. It expects extra net returns of 30,000 each year. Work out the payback period, giving your answer in years and months. [2]

3. Windrow Greenhouses plans to build a new glasshouse costing 240,000. Forecast net returns over five years are 50,000, 70,000, 80,000, 90,000 and 60,000.

(a) Calculate the payback period, in years to two decimal places. [3] (b) Calculate the average rate of return (ARR), to one decimal place. [3]

4. Cobalt Quay Couriers is considering a van costing 48,000. It expects net returns of 14,000, 16,000, 16,000 and 12,000 over four years. The owners want an ARR of at least 6%. Calculate the ARR and state whether the van meets the target. [4]

5. Explain one limitation of using payback period to appraise an investment. [3]

6. (HL only) Explain why NPV uses a discount rate. [3]

7. (HL only) Lumen Arc Studios plans to buy lighting equipment costing 90,000. It forecasts net returns of 30,000, 35,000 and 40,000 in years 1 to 3. Use the 10% factors of 0.9091 (year 1), 0.8264 (year 2) and 0.7513 (year 3) to find the net present value (NPV). [4]

8. Bluefin Kayak Hire can fund one of two options, each costing 60,000 and lasting four years.

Year	Option P returns	Option Q returns
1	20,000	10,000
2	25,000	15,000
3	25,000	30,000
4	10,000	45,000

(a) Find the payback period of each option, in years to one decimal place. [3] (b) Calculate the ARR of each option, to one decimal place. [3] (c) Evaluate the two options and recommend one. [5]

9. (HL only) Caldervale Foods is appraising a 55,000 project with net returns of 15,000, 20,000, 25,000 and 15,000 in years 1 to 4. Discount factors at 4% are 0.9615, 0.9246, 0.8890 and 0.8548. At 20% they are 0.8333, 0.6944, 0.5787 and 0.4823.

(a) Calculate the NPV at 4%. [3] (b) Calculate the NPV at 20%. [3] (c) Comment on what the two results suggest about the project. [2]

10. Analyse two non-financial factors that a business might consider when deciding whether to invest in new equipment. [4]

11. Garnet Mill is considering rooftop solar panels costing 180,000. They are expected to save 36,000 a year for eight years. The mill’s policy is to accept projects with a payback of four years or less. Its bank charges 6% a year on borrowing.

(a) Calculate the payback period. [2] (b) Calculate the ARR. [3] (c) Justify whether Garnet Mill should invest. [7]

Answers

1. The length of time [1] it takes for the returns (cash inflows) from an investment to repay its capital cost [1]. [2] Examiner insight: Strong definitions refer to both the returns and the capital cost; “how long a project takes” on its own is vague.

2. 135,000 ÷ 30,000 = 4.5 [1] = 4 years 6 months [1]. [2] Examiner insight: When the question asks for years and months, converting the decimal (0.5 × 12) completes the task; leaving 4.5 is incomplete.

3. (a) Cumulative returns: 50,000; 120,000; 200,000 [1]. Still 40,000 needed in year 4, and 40,000 ÷ 90,000 = 0.444 [1]. Payback = 3.44 years [1]. [3] (b) Total returns = 350,000 and net gain = 110,000; 110,000 ÷ 5 = 22,000 [1]. 22,000 ÷ 240,000 [1] × 100 = 9.2% [1]. [3] Examiner insight: Show the cumulative line and each ARR stage; an error is far simpler to locate when the working can be seen.

4. Total returns = 58,000 [1]. Net gain 10,000, so 2,500 a year [1]. 2,500 ÷ 48,000 × 100 = 5.2% [1]. This is below 6%, so the van does not meet the target [1]. [4] Examiner insight: A calculation followed by a comparison with the stated target is what “state whether” asks for; the number alone is not the answer.

5. Payback ignores returns after the cost has been recovered [1]. A project with modest early returns but a long profitable life may look weak [1]. The business could reject a project that would add more to profits than the one it chooses [1]. [3] Examiner insight: “Explain” answers usually need the limitation, a reason and a consequence; naming the weakness alone is only the first step.

6. A dollar due next year is worth less than a dollar held now [1], because it could be used or invested now and future receipts are uncertain [1]. Discounting converts each return to a present value so the total can be compared with the original cost [1]. [3] Examiner insight: Linking the discount rate to the time value of money and to the comparison with today’s cost shows understanding; “it adjusts for inflation” alone is incomplete.

7. Present values: 30,000 × 0.9091 = 27,273 [1]; 35,000 × 0.8264 = 28,924; 40,000 × 0.7513 = 30,052 [1]. Total = 86,249 [1]. NPV = 86,249 − 90,000 = −3,751 [1]. [4] Examiner insight: Two easy steps to skip are deducting the original cost and keeping the minus sign on a negative NPV; the sign changes the decision.

8. (a) Option P: cumulative 20,000; 45,000; 70,000, so 15,000 ÷ 25,000 = 0.6 in year 3, giving 2.6 years [1]. Option Q: cumulative 10,000; 25,000; 55,000; 100,000, so 5,000 ÷ 45,000 = 0.11 in year 4, giving 3.1 years [1]. Cumulative working shown [1]. [3] (b) P: total returns 80,000, net gain 20,000, 5,000 a year, 5,000 ÷ 60,000 × 100 = 8.3% [1]. Q: total returns 100,000, net gain 40,000, 10,000 a year, 10,000 ÷ 60,000 × 100 = 16.7% [1]. Method shown [1]. [3] (c) P pays back faster (2.6 against 3.1 years), so cash returns sooner and risk is lower [1]. Q’s ARR is double P’s (16.7% against 8.3%) because it earns more in total [1]. Q’s biggest returns come in year 4, so they depend on forecasts furthest ahead [1]. Neither method accounts for when returns arrive, so more information on the cost of finance would help [1]. Judgement: Q is better if the forecasts are reliable and the business can wait; otherwise P [1]. [5] Examiner insight: An “evaluate” answer is stronger when both options are weighed with figures and the recommendation states what it depends on.

9. (a) Present values: 14,422.5; 18,492; 22,225; 12,822 [1]. Total = 67,961.5 [1]. NPV = 12,961.5 [1]. [3] (b) Present values: 12,499.5; 13,888; 14,467.5; 7,234.5 [1]. Total = 48,089.5 [1]. NPV = −6,910.5 [1]. [3] (c) The NPV is positive at 4% but negative at 20% [1], so the decision depends on the discount rate; the business needs a rate that reflects its real cost of finance [1]. [2] Examiner insight: A comment should say what changes the decision, not only that the figures differ.

10. Any two developed factors, for example: employee impact, such as new skills or job losses [1], which may affect morale and productivity [1]; environmental impact, such as lower or higher emissions [1], which may affect reputation and how customers see the business [1]. [4] Examiner insight: Each factor needs a consequence for the business; a list of factors without development gains little.

11. (a) 180,000 ÷ 36,000 [1] = 5 years [1]. [2] (b) Total returns = 288,000, net gain = 108,000 [1]. 108,000 ÷ 8 = 13,500 [1]. 13,500 ÷ 180,000 × 100 = 7.5% [1]. [3] (c) Payback of 5 years is longer than the 4-year policy, so the project fails the policy [1]. ARR of 7.5% exceeds the 6% borrowing rate [1], but ARR ignores when savings arrive, so the comparison is only a rough guide [1]. Savings rely on energy prices and panel performance staying as forecast for eight years [1]. Savings after year 5 are never counted by payback [1]. Non-financial benefits, such as a lower environmental impact and a better image with stakeholders [1]. Judgement: a case to invest can be made if the policy is flexible, since the returns exceed borrowing costs and last beyond payback, but the mill should test the forecast first [1]. [7] Examiner insight: A justified decision refers to the case figures and to both sides, then commits to a position and states its conditions.

Where marks are usually lost

• Leaving payback as a decimal when years and months are asked for.
• Forgetting the part-year step in uneven payback, or using the wrong year’s return.
• Dividing ARR by total returns instead of capital cost, or omitting the division by years.
• Giving total present value instead of NPV, so the original cost is not deducted.
• Using the wrong year’s discount factor.
• Writing a limitation without a consequence, or one that does not apply to that method.
• Giving a recommendation with no counter-point, or one that ignores the figures in the case.
• Missing units, such as years, percentage or dollars.

Next steps

• Re-read the revision notes and the study guide.
• Course hub: IB DP Business Management and the checklist.
• Try all free 10-minute diagnostics.
• Book a free trial class: /trial/.

Frequently asked questions

What are common mistakes on investment appraisal calculations? Frequent errors include leaving payback as a decimal when years and months are asked for, dividing ARR by total returns instead of the capital cost, giving total present value instead of NPV, and using the wrong year’s discount factor. Missing units such as years, percentages or dollars also loses marks.

Is NPV on the SL syllabus for IB Business Management? No. In section 3.8 of the IB Business management guide, payback period and average rate of return are studied at SL and HL, while net present value is HL only.

Will I be given the investment appraisal formulas in the exam? The guide says a copy of its formulae will be provided for the examination, and HL candidates are given a discount table for NPV. You still need to know the steps for each method and show your working.

How should you write a recommendation on an investment? Use the figures you have calculated, compare them with any benchmark in the case, and include a counter-point such as the reliability of forecasts. A recommendation based on one number with no counter-argument is a common way to lose marks.

Official syllabus

Source: Business management guide, first assessment 2024, International Baccalaureate Organization. Section 3.8, Investment appraisal; formulae and discount table as printed in the guide.