Investment Appraisal, Part I: Payback Periods, ARR, NPV and IRR

Companies invest in projects all the time, whether they be short-term or long-term, but what defines a project to each company depends on the length of time capital is invested in a project relative to the company’s other investments. Some companies’ main function is to invest in long-term projects, whilst others – particularly manufacturing companies – tend to invest in day-to-day capital items. Therefore, it is necessary to understand the difference between different forms of expenditure: revenue, working capital, and capital.


Revenue Expenditure: for day-to-day items that are consumed quickly i.e. within one accounting period.

Working Capital Expenditure: for investment in short-term net assets.

Capital Expenditure: for investments that will bring long term benefits i.e. it increases the value of the company. Examples of capital expenditure include, but are not limited to:

  • Takeovers
  • Setting up a new subsidiary
  • Buying a new machine
  • Developing a new product
  • Spending on advertising/sponsorship

Capital expenditure often involves large amounts funding on irregular projects. As long-term projects are not as common as short-term projects, it is vital that a company fully assesses each potential project and makes the correct decision as to which project to take, as making an incorrect decision could have catastrophic consequences for the company. To do so, companies should have a robust investment appraisal system which carries out these analytical functions in order to provide management with useful information which will help their decision-making process regarding which project(s) to take.

Capital investment is crucial to the success of the company – it is what creates the additional wealth for shareholders on top of the wealth generated from its every day operations. Capital investment creates profitability at such a level that the company could not reach simply through its own operations.

Firms usually have a formal capital budgeting process, such as the following structure which I have generated into a schematic diagram:

Investment Appraisal Process

Types of Cash Flows

Money Cash Flows

These cash flows are expressed as the amount of money actually expected to be received/paid. They are the rates that are quoted in the newspapers, by banks etc. and include and element of inflation.

Money rates example:

If the rate was 10%, part of that would cover inflation and the rest would be the return which would be compensation for the risk involved and for time preference.

Real Cash Flows

These cash flows are expressed in terms of today’s purchasing power (i.e. the amount required to compensate for risk and time preference and exclude the inflation element, thus they are smaller money rates.

The relationship between real and money returns was shown by Fisher 1930.

(1 + money) = (1 + real)(1 + inflation)

Rates example:

If the money rate is 12% and inflation 3%, calculate the real rate:

Equation rearranged  = (1 + real) = (1 + money) / (1 + inflation)

Substitute in figures        = 1.12 / 1.03 = 1.0874     = (1.0874 – 1) x 100 = 8.74%


Prices usually rise over time due to inflation, and therefore if a project is going to take place over several years, the effect of inflation on the cash flows needs to be considered during the investment analysis.

Types of inflation:

  • Specific inflation: inflation on a specific product.
  • General inflation: the rate of inflation on a ‘basket’ of goods and is usually referred to as the general price index.


Investment Appraisal

At stages 3 and 4 in the appraisal process, companies must decide which projects will meet their objectives (which may be a prescribed set of criteria), and thus which projects should taken, and which should be rejected.

Although various advantages and disadvantages to all, there are a number of techniques available to do this and they are known as Investment Appraisal Techniques (IATs). For the purposes of this article, we will look at the four most common IATs:

  • Payback Period (including DPP)
  • Accounting Rate of Return
  • Net Present Value
  • Internal Rate of Return

Payback Period (including DPP)

The payback period is the length of time it takes for a project to pay back its initial capital investment. It may be shown in either years or months e.g. 2.5 years or 2 year 6 months. The decision rule for this technique is:

✓ Accept if it meets a predetermined figure.

✓ Choose the project that pays back the fastest.


  • It is simple to use and understand.
  • It favours the project with the quickest return, which minimizes risk and maximizes liquidity.


  • It ignores the time value of money.
  • It ignores the timing of cash flows.
  • It ignores the cash flows after the payback period, so it ignores profitability.

Payback period example:

Payback Period

Discounted Payback Period

The basic payback period calculation ignores the time value of money. The discounted payback period calculates the payback period using discounted cash flows. Therefore, this payback period will be longer than basic payback, however, all the criticisms (less ignoring time value of money) for the basic payback period apply to this calculation as well.

Discounted payback period example:

Discounted Payback Period

Accounting Rate of Return

The accounting rate of return is a return on capital employed (ROCE) ratio and there are several ways of calculating it:


*Average annual accounting profit is after depreciation but before interest and tax.

NOTE: the second method is normally used.

The decision rule for this technique is:

✓ Accept if ARR is greater than a target figure.

✓ Choose the project with the highest ARR.


  • The outcome is a percentage which is simple and comparable.


  • It is based on profits which are affected by accounting policies (e.g. depreciation), and can be manipulated.
  • It ignores the time value of money.
  • It ignores the timing of cash flows.

Accounting rate of return example:

ARR Example

Condition 1:                scrap value of £0

Condition 2:                scrap value of £20,000

Condition 1

((20,000 + 50,000 + 60,000 + 30,000) – 100,000) / 4    =    £15,000

Initial Capital                                (15,000 / 100,000) x 100    =    15.0%

Average Capital                           (15,000 / (100,000/2)) x 100    =    7.5%

Condition 2

((20,000 + 50,000 + 60,000 + 30,000) – 80,000) / 4    =    £20,000

Initial Capital                                (20,000 / 100,000) x 100    =    20.00%

Average Capital                           (20,000 / (100,000 + 20,000/2)) x 100          =   18.18%

Net Present Value (NPV)

The NPV is the sum of the present values of all relevant cash flows discounted at the opportunity cost of capital (or WACC). This decision rule for this technique is:

✓ Accept if the net present value is positive, reject if negative.

In order to calculate the NPV, we need to know which cash flows are relevant:


  • Opportunity costs – e.g. using a building for one project means that building cant be used for another project.
  • Incidental effects – e.g. sales of the new project may affect those of the old one.
  • Project specific overheads

Don’t include:

  • Sunk costs – money has already been allocated/spent, so it doesn’t affect the decision making process.
  • Depreciation – this is not a cash flow item.
  • Interest – the cost of debt is taken into account when cash flows are discounted.
  • Allocated overheads

A net present value of zero means that the project is just earning enough to cover the costs of the funds (debt and equity). A positive NPV is therefore a surplus, as debt holders have a fixed return. The whole of this surplus accrues to the ordinary shareholders – the greater the surplus, the greater shareholder wealth is maximised. This shows that NPV therefore has a direct link to shareholder wealth.


  • It provides a direct link to shareholder wealth.
  • It considers the time value of money.
  • It uses all cash flows.


  • It is difficult to explain e.g. to managers.
  • It requires a cost of capital percentage.

NPV example:

NPV Example

Internal Rate of Return (IRR)

The internal rate of return is the discount rate that gives a net present value of 0. It is the annual rate of return earned by the project. The decision rule for this technique is:

✓ Accept if the internal rate of return is greater than the opportunity cost of capital, reject if less.

The process is to find an internal rate of return that gives a negative net present value, as the rate that gives 0% will lie between the accounting rate of return and this internal rate. This is called interpolation.


Interpolation Formula


  • Considers time value of money.
  • Uses cash flows.
  • Outcome is a percentage, which is easier to understand and compare.


  • Multiple IRR’s occur when a project has unconventional cash flows
    • Conventional cash flow:       – + + + + = inflow, – = outflow.
    • Unconventional cash flow:   – + + + –
      • Every time the sign changes, there is a new IRR.
      • It may provide an incorrect ranking for mutually exclusive projects, which may mean that shareholder wealth is not maximized.
  • Numerical example:
    • The IRR would suggest taking project B, however project A will maximize shareholder wealth. This is because NPV is an absolute figure, whereas IRR is relative to the amount invested.

IRR Example

  • It is complicated.

IRR example:

Interpolation Numbers


Risk with Investment Appraisal

The cash flows that have been used in the investment appraisal techniques above are estimates, and different cash flows are likely to actually be achieved. If cash flows change considerably, then the project may become unviable. Therefore, the company needs to test how a change in the cash flow will affect the net present value of the project. 

Sensitivity Analysis

Sensitivity analysis looks at how sensitive the net present value is to changes in cash flows. If sensitivity analysis is carried out on each component of the cash flows, then it can clearly be seen which items of the project are most sensitive. This enables managers to concentrate on these items, however it doesn’t show the likelihood of these items changing, for example, the project may be very sensitive to changes in the selling price, however if the project is on a signed contract, then this may not be as worrying a factor as it first appears.

Viewing the figures without considering the likelihood of them changing can be misleading, as it doesn’t account for other factors or situations. Sensitivity analysis views changes to the components in isolation i.e. one figure changes at a time, however, in reality this is rarely the case, for example, generally when material costs increase, selling price increases to make up for the loss in profit margin.

Unequal Lives

If two projects are mutually exclusive, only one project can be chosen. Normally, the project with the highest net present value (NPV rule) would be chosen as this maximises shareholder wealth. However, there are several techniques which can be used to make investments more comparable.

The ‘Lowest Common Multiple’ (LCM) method is used to find the lowest common multiple of the projects lives, and calculates the NPV of each project over that time, assuming each project is taken more than once.

Lowest common multiple example:

Project A has an estimated life of 2 years, yielding a positive NPV of £10,000. Alternatively, the company could take Project B which is expected to have a life of 3 years, and a NPV of £14,000.

The lowest common multiple is 6:

Take project A 3 times:    NPV = 6/2 x £10,000 = £30,000

Take project B 2 times:    NPV = 6/3 x £14,250 = £28,500

As project A is higher (£30,000 > £28,500), the company should take project A over project B.

The ‘Terminal Value‘ method involves using an explicit forecast horizon, which for mutually exclusive projects is usually taken as the short of the projects life spans. The NPV is cut off at this point in time, and calculated proportionately (for the longer project).

Terminal value example:

Using the above information, project A has the shorter life of the two projects, thus the forecasting horizon should be set at 2 years. The NPVs of the two projects should therefore be £10,000 for project A, and £9,500 ((£14,250 / 3) x 2) for project B. As the NPV of project A is greater over the same time period, the company would be advised to invest in project A.

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