Investment Appraisal Questions: Method, Traps and Worked Approach

Investment appraisal questions have a recognisable shape. A business is considering a project, a page of data is supplied in narrative form, and the requirement asks for a calculation, a recommendation and a short discussion. Almost all the marks are lost in the same places, and almost all of them are recoverable by working in a fixed order.

This page sets out that order, the traps that sit at each stage, and what the discussion element is actually asking for.

Read the requirement before the data

The requirement determines which figures matter. A question asking for net present value and payback needs a cash flow table by year; a question asking for the internal rate of return needs two discount rates; a question asking whether to accept a contract at a stated price needs relevant costing instead of discounting at all.

Reading the data first produces an attempt to use everything in it, and appraisal questions routinely include figures that are deliberately irrelevant. Identifying what is not needed is part of the test.

Build the cash flow table first

Set up a table with a column for each year and a row for each item before calculating anything. Year 0 is the point of the initial outlay; the first year of operation is year 1.

Working in a table and not in prose has three effects. Every item lands in a specific year, so timing errors become visible. Each line can be marked independently, so an error in one does not cascade. And the discounting becomes a single mechanical step at the end, which is where it belongs.

The order that keeps it clean

1. Initial investment. The purchase cost and any directly attributable set-up cost, in year 0. Add the opportunity cost of any existing asset the project will use.

2. Operating cash flows. Incremental revenue less incremental cash operating costs, year by year. Not profit: add back any depreciation included in a profit figure the question supplies.

3. Working capital. The initial requirement as an outflow in year 0, increases as outflows in the year they occur, and recovery of the cumulative balance in the final year unless the question says otherwise. Where working capital is stated as a percentage of sales, it is required at the start of the year to which the sales relate, not at the end.

4. Tax on operating flows. Apply the rate to the operating flow, then check the timing. Where tax is payable one year in arrears, the year 1 operating flow produces a year 2 tax payment, and the final year's tax falls in a year after the project ends. That extra column is frequently forgotten.

5. Capital allowances. Compute the allowance, then the tax saved on it, and place the saving in the correct year with the same lag. Remember the balancing allowance or charge in the final year, calculated on the difference between written down value and disposal proceeds.

6. Scrap or residual value. In the final year, as a cash inflow, with any tax consequence handled through the balancing figure, not separately.

7. Discount. Only now, and only with the discount factors consistent with the inflation basis chosen.

The eight traps

Sunk costs. Market research already commissioned, feasibility work already done, a consultant's fee already paid. None of it is incremental, and a question that mentions it is testing whether it is excluded.

Depreciation. Not a cash flow. It appears only through capital allowances, and any profit figure supplied has to be converted back to cash by adding it.

Interest and loan repayments. Excluded from the cash flows entirely. The cost of finance is in the discount rate; including both double counts.

Opportunity cost. An asset the business already owns is not free. The relevant cost is the best alternative use foregone — rent receivable, sale proceeds, or the contribution from the product it would otherwise make.

Fixed overhead apportionment. An allocation of existing fixed cost is not incremental. Only genuinely additional fixed cost belongs in the table.

Working capital recovery. The cumulative amount comes back at the end. Omitting it understates the result, and it is a large number in a working capital intensive project.

Mixed inflation bases. Money cash flows are discounted at a money rate, real cash flows at a real rate. Where a question supplies current price cash flows, a specific inflation rate per item and a money cost of capital, the intended route is to inflate each flow to money terms and discount at the money rate. Converting the rate instead only works where every flow inflates at the same rate.

Tax timing. One year in arrears is the usual convention and it must be applied consistently to both the tax on operating flows and the relief on allowances.

The Fisher relationship

The link between the three rates is worth committing to memory, because a question that supplies two of them expects the third.

One plus the money rate equals one plus the real rate multiplied by one plus the inflation rate. The approximation that the money rate is the real rate plus inflation is close enough at low rates and visibly wrong at high ones, and questions are often set at rates where the difference shows.

Doing the calculation for internal rate of return

Compute the net present value at two discount rates, ideally one giving a positive result and one negative, and interpolate linearly between them.

Two points about presentation. State the rates used, because the interpolated answer depends on them and a marker cannot follow the arithmetic otherwise. And say that the relationship is not linear, so the interpolated figure is an approximation that is most accurate when the two rates are close together.

Recommend, and say what it depends on

A calculation without a recommendation loses marks that cost nothing to secure.

State the decision, the figure supporting it, and the basis. Then name the two or three assumptions the decision is most sensitive to, which for most projects are the sales volume, the selling price and the discount rate.

Where the requirement asks for sensitivity, the calculation is the net present value divided by the present value of the item being varied, expressed as a percentage. That figure is the amount by which the item can deteriorate before the project's value reaches zero, and it is stated as a percentage of that item and not of the project.

The discussion element

The written part usually carries a quarter to a third of the marks and is answered generically far too often.

If asked to compare methods, compare them on this project. Net present value is preferred here because the flows change sign, or because the projects are of different scale and the percentage measure would mislead. That is an answer; a paragraph on the theoretical superiority of discounted measures is a memorised passage.

If asked about limitations, point at the specific estimates. The volume forecast runs six years into a market the question describes as competitive; the residual value is eight per cent of the total present value and rests on an assumption about a specialised asset; the discount rate is the company's existing cost of capital applied to a project of different risk. Each of those is a real limitation of this appraisal.

If asked about non-financial factors, name factors the numbers genuinely exclude and connect them to a decision: the effect on existing product lines, whether the workforce can operate the new asset, a regulatory or environmental obligation, what the flexibility to abandon the project after two years would be worth.

Where the question supplies more than one project

Mutually exclusive projects introduce two complications that a single-project question never raises.

Where the projects have different lives, comparing their net present values directly is not valid, because the shorter project releases the asset for replacement earlier. The equivalent annual cost or annual equivalent value converts each to a per-year figure on a comparable basis, and that is what the comparison should use.

Where the projects differ in scale, the internal rate of return will frequently favour the smaller one, because a high percentage on a small outlay can beat a lower percentage on a large one while adding less value. Say so explicitly and rank on net present value.

Relevant costing, which uses the same discipline

Some questions ask whether to accept an order, make or buy, or continue a product, and ask for a minimum price rather than a present value. The discounting disappears and the relevance tests do not.

A cost is relevant if it is future, incremental and cash. Material already held is valued at replacement cost if it is in regular use, and at the higher of scrap proceeds and the saving from its alternative use if it is not. Labour already employed and not otherwise occupied costs nothing extra; labour that must be diverted from other work costs its pay plus the contribution foregone.

The discipline is the same as in an appraisal question, which is why the two are usually set together: decide what would change if the decision went the other way, and count only that.

How the marks are allocated

In a typical question the arithmetic carries around half, the recommendation and its basis a further sixth, and the discussion the remainder.

That allocation explains the most efficient approach. A clean table with correct timing and a stated inflation basis secures the calculation marks even where an individual figure is wrong, because the method is visible. A recommendation with a named sensitivity secures the next block in three sentences. And a discussion that refers to the numbers just calculated secures the rest, while a discussion that could have been written before seeing the question does not.