Aboki Ltd is considering whether to set up a division to manufacture a new product, the Zinco. The following statement has been prepared, showing the projected profitability per unit of the new product as follows: ₦ ₦ Selling Price 2,200 Less: Direct labour (2 hours at ₦250 per hour) 500 Material (3 kg at ₦150 per kg) 450 Overheads 1,150 2,100 Net profit per unit 100 A feasibility study, recently undertaken at a cost of ₦5,000,000, suggests that a selling price of ₦2,200 per Zinco should be set. At this price, it is expected that 10,000 units of Zinco would be sold each year. Demand for Zinco is expected to cease after 5 years. Direct labour and material costs would be incurred only for the duration of the product life. Overheads per unit have been calculated as follows: N Variable overheads 250 Rent (see note 1 below) - N800,000 ÷ 10,000 units 80 Manager’s salary (see note 2 below) - N700,000 ÷ 10,000 units 70 Depreciation (see note 3 below) - N5,000,000 ÷ 10,000 units 500 Head office costs (see note 4 below) - 2 hours at ₦125 per hour 250 1,150 (1) Zinco would be manufactured in a factory rented specially for the purpose. Annual rental would be ₦800,000 payable only for as long as the factory was occupied. (2) A manager would be employed to supervise production of Zinco, at a salary of ₦700,000 per annum. The manager is at present employed by Aboki Ltd, but is due to retire in the near future on an annual pension of ₦200,000, payable by the company. If he continued to be employed, his pension would not be paid during the period of his employment. His subsequent pension rights would not be affected. (3) Manufacture of the Zinco would require a specialised machine costing ₦25,000,000. The machine would be capable of producing Zinco for an indefinite period, although due to its specialised nature it would not have any resale or scrap value when the production of Zinco ceases. It is the policy of Aboki Ltd to provide depreciation on non-current assets using the straight-line method. The annual charge of ₦5,000,000 for the new machine is based on a life of 5 years, equal to the period during which Zinco is expected to be produced. (4) Aboki Ltd allocates its head office fixed costs to all products at the rate of ₦125 per direct labour hour. Total head office fixed costs would not be affected by the introduction of the Zinco to the company’s range of products. The cost of capital of Aboki Ltd is estimated at 5% per annum, and you may assume that all costs and prices given above will remain constant. All cash flows would arise at the end of each year, with the exception of the cost of the machine which would be payable immediately. The Directors of Aboki Ltd are very confident about the accuracy of all the estimates given above with the exception of those relating to product life, annual sales volume and material cost per Zinco. Required:
Calculate the net present value based on the estimates provided, to show whether Aboki Ltd should proceed with the manufacture of Zinco.
Prepare a statement showing how sensitive the net present value of manufacturing Zinco is, to errors of estimation in each of the three factors: product life; annual sales volume and material cost per Zinco.
Assess the strengths and weaknesses of sensitivity analysis as a method of evaluating risk and uncertainty in capital project appraisal. How does simulation provide an improvement over sensitivity analysis in this regard?
Revise this question
Relevant cash flows in investment appraisal › Which costs are relevantNet present value and the case for discounted cash flow › Net present valueRisk and uncertainty in appraisal: sensitivity analysis › The method: sensitivity marginsRisk and uncertainty in appraisal: sensitivity analysis › Strengths and weaknessesSimulation, risk-adjusted discount rates and discounted payback › SimulationSuggested answer
a) Calculation of NPV (₦000) Years 0 1 - 5 Machine (25,000) - Factory rental - (800) Manager’s salary (W4) - (700) Variable production costs (W5) -___ (12,000) Total outflows (25,000) (13,300) Sales revenue -___ 22,000 NCF (25,000) 8,700 PVF at 5% 1 4.329 PV (25,000) 37,662 NPV = ₦12,667,000 The NPV of the project is positive and if all other factors are held constant, it should be accepted. Working Notes
1. Machine depreciation: is irrelevant, being a non-cash item. 2. Head office costs: These are non-incremental costs and therefore irrelevant 3. Feasibility study: The amount spent on feasibility study is a sunk cost and therefore irrelevant. 4. Only the extra salary payable to the manager is relevant. ₦000 Salary 700 Pension saved (200) Incremental salary 500
5. Variable costs The only relevant costs per unit are: ₦ Direct labour 500 Material 450 Variable overheads 250 1,200 Total per annum = 1,200 × 10,000 units = ₦12,000,000.
b) Sensitivity analysis
i) Life of project: The breakeven life of the project can be calculated using discounted payback period (DPBP). Year NCF PVF at 5% PV CUM PV ₦000 ₦000 ₦000 0 (25,000) 1 (25,000) (25,000) 1 8,700 0.952 8,282 (16,718) 2 8,700 0.909 7,729 (8,810) 3 8,700 0.864 7,517 (1,293) 4 8,700 0.823 7,160 5,867 DPBP = 3 + (1,293/7,160) = 3.18 years The sensitivity margin = (4 – 3.18)/4 = 20.5%. This means that the life of the project can be shortened by 20.5%.
ii) Annual sales volume SM (sales volume) = NPV/PV of contribution PV of contribution = 10,000 units (₦2,200 – 1,200) × 4.329=₦43,290,000 SM = ₦12,662/43,290 = 29.25% This means that the current sales volume of 10,000 units can fall by maximum of 29.25%. Thus, the minimum sales volume is 10,000 × (100 – 29.25) % = 7075 units.
iii) Material price SM = NPV/PV of material cost PV of material cost = 10,000 × ₦450 × 4.329 = ₦19,480,500 SM = ₦12,662/₦19,480.50 = 65% This means that the material price of ₦450 per unit can increase by 65%. Thus the breakeven price per unit is ₦450 × (100 + 65) % = ₦742.50 per unit. Summary and comments The above calculations show that the manufacture of Zinco would still be worthwhile if product life fell to 3.2 years, or if annual sales fell to 7,075 units, or if material costs increased to ₦742.50 per unit of Zinco. These figures represent percentage errors of 36%, 29% and 65%, respectively on the original estimates. If the actual figures were within these percentages of the original estimates, the decision to go ahead would still be valid. These are large percentages and the NPV is therefore remarkably insensitive to errors in the three factors.
c) Introduction In capital budgeting, decisions are made under conditions of uncertainty. Future cash inflows, costs, and discount rates are often subject to change, and managers need techniques to evaluate how such uncertainty affects project viability. Sensitivity analysis and simulation are two widely used approaches. While sensitivity analysis provides a straightforward way of identifying the effect of changes in individual variables, it has important limitations. Simulation techniques, particularly Monte Carlo simulation, offer a more comprehensive approach by modelling uncertainty in a probabilistic manner. Strengths of sensitivity analysis i. Simplicity and clarity - The technique is easy to understand and implement. Managers can see directly how project outcomes (e.g., NPV, IRR) respond to changes in assumptions such as sales volume, costs, or discount rate.
ii. Identification of critical variables - Sensitivity analysis highlights which factors exert the greatest influence on project success, guiding management attention and control. iii. Communication tool - Results can be presented graphically (e.g., tornado diagrams), making it easier to convey the project’s vulnerability to stakeholders. iv. Decision support - Provides useful “what-if” scenarios that allow managers to test the robustness of a project under alternative conditions. Weaknesses of sensitivity analysis i. One-variable-at-a-time limitation - In practice, variables are interrelated. For instance, sales volume and price are likely to move together, but sensitivity analysis cannot capture such interactions. ii. No probability information - While it shows how outcomes change if assumptions vary, it does not indicate how likely such variations are. iii. Arbitrary input ranges - The percentage changes used (e.g., ±10%) are subjective and may not reflect real uncertainty. iv. Linear assumption - It often assumes a straight-line relationship between variables and outcomes, overlooking possible non-linear effects. v. Static approach - Sensitivity analysis ignores management’s ability to adapt or revise decisions over the life of a project. How simulation improves on sensitivity analysis Simulation addresses these shortcomings by allowing multiple uncertain variables to vary simultaneously according to assigned probability distributions. In particular:
i. Probabilistic outcomes - Simulation generates a distribution of possible NPVs rather than a single-point estimate, showing the probability of achieving different levels of return. ii. Interdependence of variables - Correlations between inputs (e.g., price and demand, costs and output) can be modelled. iii. Holistic risk assessment - Thousands of iterations can be run to capture the combined effect of uncertainty, providing expected values, standard deviations, and probabilities of loss. iv. Strategic insights - Managers obtain a richer understanding of risk exposure, making it possible to compare projects not only by expected NPV but also by risk profile. Limitations of Simulation must also be acknowledged: it requires large amounts of reliable data, complex modelling, and sophisticated software. Moreover, results depend heavily on the accuracy of the assumed probability distributions. Conclusion Sensitivity analysis remains a useful first step in risk assessment: it is simple, highlights critical variables, and supports communication. However, its weaknesses - especially the inability to incorporate probabilities and multiple variable interactions - limit its effectiveness as a stand-alone tool. Simulation provides a more advanced and realistic means of assessing risk by producing a full probability distribution of project outcomes. Together, both methods can complement each other: sensitivity analysis for preliminary screening, and simulation for deeper, probabilistic evaluation.
Examiner’s Report This compulsory scenario-based question tests: Calculation of Net Present Value (NPV), with emphasis on identifying relevant and irrelevant costs; Sensitivity analysis of NPV in relation to estimation errors; and Evaluation of the strengths and weaknesses of sensitivity analysis and simulation in capital project appraisal. Approximately 99% of candidates attempted this question. Performance was extremely poor. About 95% of candidates scored below average, with fewer than 5% achieving up to half of the allocated marks. Candidates’ commonest pitfalls were that most of the candidates could not identify the relevant costs nor calculate relevant ratios and NPV to evaluate the project. Candidates are advised to master the various financial management techniques and their application to scenarios.
Marking guide Question Number Question Question Requirement Total Marks Allotted Component 1 a Net Present Value of the proposed project – manufacture of Zinco. 16 marks b Sensitivity of NPV to errors of estimation of product life, annual sales volume and material cost per unit of Zinco 6 marks c Assessment of the strengths and weaknesses of sensitivity analysis as a method of evaluating risk and uncertainty in capital project appraisal. Also, how simulation provide an improvement over sensitivity analysis in this regard. 8 marks Total 30 marks