# The Incremental IRR

Despite their apparent wealth maximisation defects, IRR project rankings that conflict with NPV can be brought into line by a supplementary IRR procedure whereby management:

Determine the incremental yield (IRR) from an incremental investment, which measures marginal profitability by subtracting one project's cash inflows and outflows from those of another to create a sub-project (sometimes termed a ghost or shadow project).

To prove the point, let us incrementalise the data from Section 3.1.Two projects that not only differ with respect to their cash flow patterns (size and timing) but also their investment cost.

 Project Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 IRR(%) NPV (10%) 1 less 2 (35) (30) - 20 40 50 15% 11.1

You will recall that IRR maximisation favored a higher percentage return on the smaller more liquid investment (Project1), whereas NPV maximisation focused on higher money profits overall (Project 2). Now see how the incremental IRR (15%) on the incremental investment (Project 1 minus Project 2 = £35k) exceeds the discount rate (10%) so Project 1 is accepted. Moreover, this corresponds to Equation (1) on single project acceptance. The incremental NPV is positive (£11.1k) because its discount rate r < incremental IRR.

# Capital Rationing, Project Divisibility and NPV

If finance is unconstrained, management should accept all projects with a positive NPV. But if capital is rationed and smaller projects with smaller NPVs can be replicated, or projects are divisible into fractional investments, we need to compare investments of different size by indexing their NPV per £1 invested using the following formula.

The Profitability Index (NPV^) then ranks projects, or proportions of them that maximise total NPV, relative to their cost, rather than their absolute surplus.

Activity 2

Using data from our previous Activity plotted in Figure 3.1, confirm the following (£k).

Now assume the company has only £180,000 to invest. The projects are not mutually exclusive but they are infinitely divisible. Tabulate management's optimum strategy.

The following table confirms that ranking projects by the NPV per £ method, rather than their individual NPV, maximises overall NPV and hence total corporate wealth.

 Method Ranking Capital Cost NPV NPV (£) 1 (135) 45.4 2 (45/100) (45) 15.4 Sub-optimal (180) 60.8 NPV, 2 (100) 34.3 1 (80/135) (80) 26.9 Optimal (180) 61.2

# Relevant Cash Flows and Working Capital

So far, we have taken as given the cash flows that underpin DCF analyses. However, management need to determine those that are relevant to a project's appraisal.

Relevant cash flows are based on the opportunity cost concept which defines the incremental net inflows if a project is accepted. The analysis incorporates outflows that are unavoidable, or inflows which are sacrificed elsewhere, if a project is accepted.

Thus, accounting concepts of historical cost and net book value (NBV) are irrelevant because they are sunk costs. Likewise, forecast income and expenses based on accrual accounting are irrelevant. Assets purchased five years ago for £10k with an NBV of £1k may be surplus to current requirements but with a market (opportunity) value of £9k and as a substitute for assets costing £12k they can reduce future project costs by £3k. Likewise, if the assets are used for this project, rather than another, then the project cash foregone must be included in the selected project's opportunity flows if it is the next highest valued alternative (say £9.5k).

With regard to accounting income there is a timing issue; periodic turnover rarely corresponds to cash inflow because of credit sales. Expenses too, may be accrued or prepaid. There is also depreciation to consider.

Depreciation should always be added back to net accounting profits when they are used for project selection. It is a non-cash expense, not an Incremental outflow; that part of earnings retained to recoup an investment's cost (I0)) over its useful life. Since NPV analyses already subtract I0 from project cash flows (NPV = PV - I0) the use of profit after depreciation as a proxy for net cash inflow in project appraisal obviously double counts the investment's cost.

Since our test for opportunity cost focuses upon differential costs, we must also incorporate adjustments for working capital investment designed to fuel projects when up and running.

Working capital is basically stock (inventory), debtors, plus cash, minus creditors. This net investment in current assets may differ for different project proposals, vary from year to year, or build up gradually Disinvestment may also occur beyond a project's life, for example when debtors repay, creditors are satisfied and surplus inventory is sold on.

Working capital should be regarded as a cash outflow at the outset of a project's life with adjustments in subsequent years for the net investment caused by project acceptance. At the end of a project's life, the funds still tied up will be released for use elsewhere. Therefore, we show this amount as a cash inflow in the last year or whenever it is made available. The net effect of these working capital adjustments are to charge the project with the interest foregone (opportunity cost of capital) on the funds, which are invested throughout its entire life.

Activity 3

Never under estimate the role of working capital management in project appraisal. Select a random sample of published company accounts and you will observe that current assets represent more than 50 per cent of total capital investment for a significant number.