Project appraisal, flexing the numbers and sensitivity analysis

Project appraisal is where well-prepared candidates most often go wrong, because they know too much. They rush to build their own net present value from invented assumptions, when the case already gave the data and the requirement asked for something specific. This topic shows how to appraise within the information given, how to choose a technique, and how to flex the numbers and test sensitivity.

Appraisal in the Case Study

Many cases need some form of project appraisal as part or all of a financial data requirement. There are many well-known techniques, but you must use the information presented and the requirement as written. Often the request is plain: analyse a project with a simple tool such as payback. If no tool is named, the information given will usually allow only one sensible tool.

Project appraisal is an area where candidates have a lot of prior knowledge and wrongly rush to add their own assumptions. They produce a fully worked net present value from invented figures, with no supporting information in the case and no such calculation requested.

Questioning assumptions is a key skill, but creating a new set of assumptions and criteria, such as discount rates, to permit a favoured calculation is not that skill. It shows only that the candidate is answering a question they prepared in advance. Such work will almost certainly earn no reward, however accurate the arithmetic.

The opposite failure also costs marks. In the Sadeco case the examiner reported that most candidates did not answer the appraisal requirement, apparently because they did not know how to find the net contribution used in the net present value. The data was in the case. Your task is to build the calculation from what is given.

The detailed calculations are assumed from earlier subjects. Use the tool that is requested or suggested by the information.

Sensitivity analysis

Every decision has variables that affect the outcome, and each is uncertain. Sensitivity analysis tests how the expected outcome changes when the values of key decision variables change. For example, a budget can be tested for changes in sales volume, inflation, materials cost or minimum wages.

It can be used to find how far an item of cost or revenue must differ from its estimate before the decision changes. It can also answer a what-if question, such as what happens if sales are 5% below expectation. If a manager thinks sales volume might be wrong by up to 20%, the analysis shows the profit or loss at that level.

The steps are:

1. Set the original plan or estimate, such as expected profit or NPV.
2. Identify the key variables, such as price, volume, material cost, labour cost or completion time. Change each by a percentage that is a reasonable estimate of its possible variation and recalculate.
3. Measure how sensitive the decision is to each change.

Applied to each variable in turn, the method shows which ones are most critical, where an error would have the largest effect. Management can then decide whether it has enough confidence in the estimates to go ahead, or whether the uncertainty makes the project too risky.

Flexing the numbers

After you assess the assumptions given, you must be able to flex the numbers given or calculated and comment on the adjusted effect. In the Case Study this may mean correcting a series of erroneous transactions or proposed adjustments, flexing a forecast for changed assumptions or circumstances, or changing assumptions in a calculation such as breakeven or a tender price.

Sometimes errors in the information make the need obvious. Often you must decide whether flexing is worthwhile. You are not expected to produce endless similar speculative calculations, so identify your critical factors with care. If you find numbers that should be flexed but have no time to do every calculation, you must still comment on the likely direction and size of the change.

Whatever the time pressure, you earn no marks for recommending that sensitivity analysis should be performed or that all figures should be checked and flexed. That only shows that you have not done what the task needed.

Worked example: the Sadeco food processing project

The Sadeco case asked for an appraisal of a proposed food processing project using net present value, in Appendix 2 of the report. The solution table used these cash flows and factors, which correspond to a discount rate of 18%. Figures are in naira.

The NPV is about ₦199.8 million, and the solution concluded that the project meets the foreign partner’s expectation. Now flex the result.

1. Annual cash flow. The five annual factors add up to 3.1272. The present value of the annual flows is about ₦1,218.7 million. Without the ₦300 million final item, NPV would still be about ₦68.7 million.
2. How far can cash flow fall?
   For NPV to be zero, the present value of annual flows must be 1,150.0 − 131.1 = ₦1,018.9 million.
   That is an annual flow of about ₦325.8 million, a fall of about 16% from ₦389.7 million.
3. Judgement. The project is attractive, but a fall of around one-sixth in annual net contribution would remove the whole gain. The contribution depends on demand, prices and input costs, so management should test those before it commits.

Common mistakes

• Building a new NPV with invented discount rates when the requirement asked for another tool.
• Failing to find the contribution or cash flow from data that the case supplied.
• Writing that sensitivity analysis should be done, instead of doing it.
• Flexing many variables with no explanation and no view on which matters most.
• Presenting the result with no decision, or a decision that ignores the sensitivity result.

Quick revision

• Use the data and the tool the requirement gives. Do not invent assumptions or rates.
• Payback and ARR are not discounted. NPV, IRR and PI are discounted.
• Sensitivity: original estimate, change key variables, measure effect, find the critical ones.
• Flex even if you cannot do every calculation, and comment on direction and size.
• Never write that sensitivity analysis should be done. Do it.

Practice questions

These are original questions in the style of the Institute of Chartered Accountants of Nigeria exam. Try each one before you open the answer.

Model answer

The next topic covers risk and uncertainty in decision making.

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