21.
How can investment opportunities be compared?

21.1 Introduction

Every organisation, whatever its objectives, is almost invariably constrained as to what it can do by a shortage of available money.

Organisations can raise money by:

• making profits
• receiving grants or donations
• raising new capital
• borrowing.

Having done so, they can then fund additional revenue expenditure (for example, by hiring more staff), or they can buy new equipment, which by definition will be used in their operations for more than a year. That capital expenditure will, as a result, be expensed in the first instance on its statement of financial position, with its progressive wearing out as a consequence of either use or the passage of time being recorded in the income statement via either a depreciation, or possibly an amortisation, charge.

Capital expenditure comes in an enormous variety of forms, from buying such essential things as desks and chairs, to the sums expended on complex infrastructure projects like building new energy transmission systems. It can also represent the purchase of what are called intangible assets, such as the copyright of previously published materials or software, and the goodwill associated with a business. In this unit it does not matter what such expenditure might be expended upon. Instead, what we assume is that there will be more capital expenditure projects on which money might be expended than there are funds available to pay for them all. The management of an organisation will, in that case, have to decide which projects it wishes to choose between. It is the task of the management accountant to provide them with information to assist in this process.

This unit also assumes, as many businesses do, that it is appropriate that a systematic approach towards deciding which projects should be prioritised for capital expenditure should be adopted. Most organisations like to be seen to use a rational and analytical process to support decisions of this sort. The various approaches used to support this methodology are called capex techniques. They are the focus of this unit. 

21.2 The importance of capex techniques

Some students think that capex techniques are among the more complicated issues about which they have to learn when studying accounting and finance. They are, however, in the syllabus for good reasons:

• Many organisations do use at least some of the methodologies noted in this unit, and so any student of accounting needs to be aware of them.
• The types of methodology discussed are commonly referred to by those who wish to represent themselves as using rational and even objective decision-making processes.

It is important to know which capex tool to use in the appropriate situation.

21.3 The limitations to capex techniques

All the above being noted, an important caveat has to be added before any capex techniques are discussed.

Capex techniques have been created to provide rational, systematised bases for decision-making. It should, however, be appreciated that the managers with ultimate responsibility for making decisions are human beings, and however they might like to present themselves, they are rarely as rational as they would like to suggest that they and their systems are. In other words, when final decisions are taken, they may bring their personal preferences into account. This is because the methodologies noted in this unit are based upon estimates of the value of future profits or cash flows, and therefore hypothetical situations.

Even then, those same senior managers might decide that there are entirely rational but non-quantifiable factors to take into account when making decisions on capital expenditure that mean that the outcome of any capex forecast be ignored. For example, some decisions that might seem economically rational might at the same time also compromise an organisation’s social licence to operate (see Unit 13).

Alternatively, it may be decided that the costs arising from some activities are themselves unquantified, or unquantifiable, but are significant nonetheless. For example, the cost to staff morale of changing work patterns to permit a particular item of capital expenditure to proceed may be too detrimental to incur, even though that cost might in monetary terms be unknown.

When considering the capex techniques discussed in this unit it is essential that these factors be borne in mind. Capex techniques are useful, which is why they exist. However, they are rarely able to entirely answer whether a particular project should be supported or not. Professional judgements are the ultimate arbiter on that, and capex calculations can only contribute to the formation of that judgement, rather than determine it.

21.4 Assumptions underpinning capex calculations

Before considering different types of capex calculation it is important to know the assumptions that underpin them all. Broadly speaking, these are as follows:

• The amount to be spent on a capital expenditure project can be determined in advance, and the timing of that expenditure is known.
• Potential additional income that the capital expenditure project might give rise to can be ascertained in advance for all future periods when it is likely to arise, and this data can then be used for the purposes of decision-making.
• The same can be said of the expenditure that the project is likely to give rise to.
• The cost of capital expenditure can be reliably predicted over its life.
• The anticipated life of a capital expenditure project can be reliably predicted, as can any disposal proceeds at the end of that period if they are a factor in the decision-making process.

21.5 Capex techniques

In this unit we explore four of the most commonly used capex appraisal techniques. They split into two groups:

1. the accounting rate of return (ARR) method, sometimes called the return on investment (ROI), which is a profit-based approach

2. three cash-based techniques:

   • payback
   • net present value (NPV)
   • internal rate of return (IRR).

All of these are used in practice and are important.

21.5.1 Accounting rate of return

The accounting rate of return (ARR) method of capex appraisal measures the projected profitability of a project in a way designed to reflect the rationale of the financial accounting ratio, return on capital employed (ROCE). As a result, this measures the project’s return in terms of the operating profit relative to the amount of money invested in the project.

The ARR method takes the projected average annual accounting operating profit across the intended operational life of the proposed project expressed as a percentage of the proposed financial investment.

For example, if the average annual operating profit projected to be made over the life of a four-year project is £20,000 and the investment is £80,000, the ARR is £20,000/£80,000 = 25%.

This appears straightforward, but there are complications in determining the average annual operating profit figure and the investment figure to be used.

ARR: A first example

Consider a proposed four-year project with a financial profile as detailed in Figure 21.1, based on investment in equipment costing £80,000 with zero residual value at the end of its useful life of four years, using straight-line depreciation.

The total annual operating profit across the four years is £80,000. To obtain the average annual operating profit we divide this by four, which gives a total of £20,000. We then express the average annual operating profit of £20,000 as a percentage of the time-zero (meaning the moment when the investment takes place) investment – of £80,000 – generating an ARR of 25%.

ARR: Using (simple) average investment

The approach noted in the previous paragraph assumed a single upfront investment in the project. In practise, few investments work in that way. Investments often take place over a period of time. A simple average investment approach seeks to address this issue.

This could be applied to the example above. The average investment in that project was not the £80,000 initial cost, but was instead that sum plus the residual value of the equipment at the end of the project life, divided by two. In other words, it is:

\[(£80,000 + £0)/2 = £40,000\]

Using the average annual operating profit of £20,000 divided by the simple average investment of £40,000 produces an ARR of 50%.

This is, however, simplistic. Residual values of zero are, for example, unlikely. Suppose that a residual value of £20,000 might be assumed for the equipment that was to be purchased. This residual value would reduce the depreciation charge over the life of the project by £20,000, because only £60,000 of depreciation would need to be provided over the four years (that is, £80,000 − 20,000 = £60,000). Operating profits in the example noted previously would rise to £25,000 per annum as a result because depreciation would reduce to £15,000 each year (£60,000/4 = £15,000). The average value of the investment would also fall. This would now be £30,000 ((£80,000 − 20,000)/2), meaning that the simple average investment rate of return would now be £25,000/30,000, or 83.3%.

Either approach – time-zero investment or average investment – may be used as long as it is used consistently.

Where ARR is used, it is usual for a management team to determine what is a minimum acceptable ARR percentage, and chosen investments must meet or, preferably, exceed that return.

ARR: Evaluating investment performance

For more detail on ROCE, refer to Unit 16.

ARR is a metric based on profit rather than cash. Its advantage is that it is based on the widely used ROCE financial accounting ratio. When using ARR, projects are chosen that achieve a minimum target ARR. This target could be based on previous investments’ actual ROCEs or an industry-average ROCE.

Given that private sector businesses seek to increase owners’ wealth, ARR may be viewed as a logical way to appraise investment opportunities.

ARR results are also expressed as percentages, meaning that they provide a relative measure rather than a static profit figure. Many see this as an advantage.

However, there are perceived problems with using ARR as an evaluation tool. ARR uses accounting profit, specifically operating profit. Profit measurement involves a degree of subjectivity due to the application of varying accounting policies (for example, depreciation charges, inventory valuation, and provisions). Making an investment decision solely on an ARR calculation based on what some consider to be a subjective operating profit figure may be unwise. This is why cash-based methods of appraisal are often used instead.

Appraisal of cash consequences: Relevant costs

If cash flows are to be used as the basis for capex appraisal, the relevant cash costs to use have to be identified.

Some are obvious, such as cash receipts and cash outlays that are clearly and directly linked to proceeding with the proposed project.

However, there may be other cash consequences, including those which are not actual physical cash receipts and cash outlays, that need to be considered when capex appraisal based on cash flows is undertaken. These include sunk costs, opportunity costs, unchanged costs, costs already committed to being paid, and costs saved. When added to the obvious cash flows, these can be used to determine the ‘relevant costs’ for making the decisions, which have to be based on the incremental cash flows the project creates. A statement of relevant costs (the incremental cash flows) should be set out for the investment at time zero and for each year of the project.

As an example of issues that need consideration when deciding what these relevant incremental costs might be, suppose a project requires two staff members with annual salaries of £50,000 each. One is an existing staff member. One is new. In profit terms this is a £100,000 salary expense. However, only the new employee’s salary is a relevant cash flow for inclusion in an investment appraisal because the other salary would have been incurred anyway.

Another example might relate to overhead costs. A company might like to make an internal charge of 10% of project sales to a project when estimating its profitability, this being considered a contribution to overhead costs. However, unless the project actually changes overhead costs incurred, this is not relevant for capex decision-making purposes as only the incremental change in costs should be considered for that purpose. The overhead recharge is not an incremental charge. It is just a cost allocation and should be ignored.

Figure 21.2 summarises some of these issues relating to incremental costs.

21.5.2 Understanding payback and its calculation

The payback method of capex appraisal has a clear objective. It seeks to determine how long it takes for a project to recover the cash invested in that project. The logic is straightforward. It assumes that the sooner cash is recovered, the lower the risk implicit in a project and the more likely it is to succeed as a result. The payback method of capex has an implicit appraisal of uncertainty inherent within it. It assumes that the longer it takes to recover the cash invested in a project, the more uncertain that return will be.

To illustrate, suppose a three-year project requires a time-zero (upfront) investment of £180,000. The projected net cash flows at the end of each year are:

Year	Net cash flow, £’000	Net cumulative cash flow, £’000
0	(180,000)	(180,000)
1	80,000	(100,000)
2	100,000	0
3	120,000	120,000

This project has a payback period of two years. Things are not always this neat: sometimes the payback period will not be precise numbers of years. It can then be expressed as a decimal, or if a company wishes, in years and months, or even years and days.

Important aspects of the payback calculation

Many organisations set a maximum allowable payback period for proposed projects. If the organisation’s maximum payback period is two years and nine months (2.75 years), the project in the illustration above meets the criterion. However, if the maximum allowable payback period is one year and six months (1.5 years), the project falls short.

When comparing multiple projects, assuming all fall within the allowable payback period, the key is to choose the one with the shortest payback period. However, the trade-off between risk and return should also be considered. Imagine two four-year projects, A and B, with an organisational target maximum payback period of two years. Assume project A has a payback period of one year, while project B’s payback period is one year and six months (1.5 years). Although project A pays back more quickly, project B may bring in more cash over a longer period. Management teams must weigh waiting for greater cash returns against minimising risk by opting for the shorter payback period of project A, even if it means less cash initially. Depending on the risk attitudes of management teams and judgements about the economic landscapes, some organisations may opt for less risk and less cash returns, while others will make the alternate decision. All capex appraisal involves subjective judgement.

Payback: Evaluating investment performance

The advantage of payback period capex appraisal is that it is simple and straightforward to calculate and interpret. If an organisation seeks to generate cash quickly to reinvest and grow the organisation, the identification of a short payback period may be beneficial, with cash being generated more quickly for such reinvestment purposes. Where a range of appraisal techniques are being used to assess several similar projects and the results are similar or contrasting, the payback period help an organisation to choose.

Payback period methodology does, however, have some disadvantages. One is that it does not provide a comprehensive view of the profile of the investment opportunity. This is because it focuses solely on recouping the initial investment with no consideration of longer-term risk–return trade-offs. In that context, it ignores important matters such as operational lives of competing projects, cash flows beyond the payback period, and, importantly, the expectations of funders. This latter aspect is particularly important and is considered in detail when the idea of cost of capital is explored.

Understanding cost of capital: Rationale and nature

The payback method of capex appraisal does not consider funders’ expectations, particularly their required rates of return. The next two methods of capex appraisal take into account the interest rates required to keep funders satisfied and make the organisation an attractive investment.

The first problem to note is that shareholders, who are often the primary funding source for capital investment projects, are not homogenous. Their expected rates of return will vary, as will their risk appetites. In addition, shareholders do not make decisions on individual projects within companies; they decide whether to invest in the company as a whole. As such their required rate of return may be different from that which the company requires on individual projects because diverse projects in the company can mitigate risk. Companies do, therefore, have to estimate what return their shareholders require based very largely on past performance and market averages, but still need to judge what rates to use for their internal capex appraisals.

Project funding might also come from borrowing, in which case the interest rate payable might provide an indication of the required return for capex purposes. Since interest expenses are tax-deductible, a 10% loan interest when combined with a 20% tax rate has an effective cost of debt to 8%.

When funding comes from both shareholders and debt providers, the overall cost of capital is calculated as an average. If the funding is split equally, a simple average is used; otherwise, a weighted average cost of capital (WACC) is applied, considering the relative weights of each funding source.

Incorporating risk premiums

After determining the WACC, organisations might adjust it further to account for the risk associated with specific projects. Riskier projects often warrant a higher expected return. Accordingly, an adjusted WACC helps ensure that the projected returns sufficiently compensate for the perceived risk, thereby aligning investment decisions with the organisation’s risk management strategy.

In summary, the cost of capital reflects the required return that funders expect, and it is crucial to estimate it as accurately as possible by considering both the funding sources and their respective weights. Adjustments for tax benefits and project-specific risks further refine the evaluation.

21.5.3 Understanding net present value and its calculation

Net present value (NPV) is a method used for evaluating investment projects by considering the time value of money. It involves a process called discounting. This estimates the current (present) value of anticipated future cash flows, whether positive or negative, and seeks to state them in equivalent current prices, allowing them to be compared whenever they might be incurred. It does this assuming that money received or paid out in the future has a lower value than similar sums received at present, with the difference being estimated on the basis of the weighted average cost of capital, which can also be adjusted for risk.

As example, if the WACC is 10% then the net present value of a constant revenue stream of £100 per annum over a ten-year period is estimated as follows:

The cumulative discounted value is the value for the previous year multiplied by (1 − the WACC), or 0.9 in this case. So in year 2 it equals 0.9 x 0.9 or 0.81.

The implication is that at present the offer of £100 in a year’s time to a person with a WACC of 10% is worth £90. The reduced sum represents the interest effectively forgone by waiting a year for this money.

Understanding this concept is vital: it is fundamental to most concepts of financing used by accountants.

NPV reduces all expected cash inflows and outflows of a proposed project to their present values at time zero. This enables the present values of those projected future annual cash flows, or discounted cash flows to be matched – or netted off – against the cost of an investment in time zero. This then results in one final output from the calculation, which is the net present value. It is important to note:

• A positive net present value shows that the projected cash flow return is in excess of the cost of capital – and thus exceeds the expectations of the funders.
• A negative NPV shows that the projected returns do not meet the required return – and so do not meet the expectations of the funders.
• An NPV of exactly zero means that the projected returns meet exactly the cost of capital – and that is welcome in that expectations are met, but wherever possible an organisation should seek to exceed that rate.

The projected incremental cash flows, as noted previously, should be estimated for the entire lifespan of the project if the NPV is to be appropriately calculated.

The above example of a discounted income stream can be expanded. Suppose that:

1. The original investment in the project giving rise to the revenues was £500.
2. The gross revenues each year were £250.
3. Costs were £150 per annum.
4. The equipment invested in had an estimated value of £100 at the end of the project’s life.

The NPV calculation is shown in Figure 21.4.

The NPV is positive: it pays the investor to undertake this project assuming the assumptions made hold true in the future.

Using NPV as a means of investment appraisal

There are several advantages of using NPV. These include:

• It is cash-based (based on incremental cash flows) and not profit-based and thus avoids the challenges presented by using profit figures which may be somewhat subjective, having been distorted by the impact of a range of accounting policies.
• By undertaking a project with a positive NPV, it is hoped that the value of funders’ wealth – particularly shareholders’ – is increased by the value of that NPV.
• When used in ‘real-world’ scenarios with a range of complexities, the NPV calculation can be adapted to take account of challenges presented to decision-makers by the effects of inflation and taxation.
• Risk and uncertainty can be incorporated into NPV calculations through techniques such as adding an extra percentage of expected return for greater risk, sensitivity analysis, and assignment of probabilities of differing cash flow outcomes.

There are also some challenges associated with using NPV as an evaluation tool. These include:

• The value resulting from an NPV calculation is the consequence of two sets of assumptions. One is the discount rate applied. The other is the projected cash flows.

  • Sometimes the WACC may be difficult to calculate, and an inappropriate (or wrong) discount factor can be used as a consequence. If the discount factor is understated, the NPV will be overstated. Where the discount factor is overstated, the NPV will be understated.

  • If the cash flows are understated or overstated, there will also be a consequential impact on the NPV calculated.

• Additionally, the basis of the NPV calculation assumes cash flows always arise at the end of each year. However, this is very likely to be the case.
• The calculation ignores more qualitative, non-financial factors. These may be which may be equally or more important than the core financial factors.

It is also important to note that that NPV calculations risk appearing to be definitive. In particular, it is all too easy for assumptions on future cash flows to be manipulated so that the result that the person undertaking the calculation wants to be shown can be delivered by the process. This can be very hard to detect.

21.5.4 Understanding internal rate of return and its calculation

Internal rate of return (IRR) calculations are a variant on NPV calculations. The IRR is the rate of return that when applied to a forecast cash flow delivers an NPV of zero. It is therefore the actual rate of return that the project might deliver if all the assumptions made to prepare the calculation on what is otherwise an NPV basis hold true.

It follows from this observation that IRR methodology is, like NPV, a discounted cash flow technique. It therefore shares the advantages and disadvantages of that methodology.

Another advantage of an IRR calculation is that it demonstrates by how much the return on a proposed project exceeds the required rate of return of the organisation making an investment decision.

For example, suppose an organisation has a weighted cost of capital (WACC) of 10% and has appraised various projects, each requiring a similar investment, and found that the IRRs are:

1. 18%
2. 13%
3. 11%
4. 8%

Logically the entity should undertake projects a, b and c because it can make a return on all of them. It should not invest in project d, because it makes a return of less than the WACC.

Calculating the IRR on a project

There is a function in Excel to calculate the IRR of a cash flow. In the real world that is very useful and a simple example can demonstrate how this works.

Assume that you were asked to calculate the IRR of the cash flows in the exercise in paragraph 21.5. The easiest way to do this is to put them in an Excel table and then change the WACC until the NPV is as close to zero as it is reasonably possible to get. This is the result:

The IRR of this project is 14.01%, which is above the required 10% WACC, so the company should undertake the project. This is, unsurprisingly, the same message as NPV provides.

The big advantage of IRR calculations over NPV is that, in principle, project ranking is easier to achieve, irrespective of the sum invested.

The downside of IRR is that the rate of return does not take into consideration the scale of resources the project requires. This can produce misleading impressions of desirability when in reality resources are limited.

There is another problem with IRR in the real world. Few projects have known lives. In addition, few have known, or even predictable, cash flows. IRR can therefore not be as easy to calculate as examples might imply. They can also have multiple IRRs, because the rates of return might vary over the project’s life. As a result, they are relatively rarely used in practice.

Worked example: IRR calculated using formulas

It is time-consuming to use a trial-and-error approach to calculating IRR without programming. We can use a formula to help us.

IRR = ra + (NPVa/(NPVa − NPVb))(rb − ra)

ra = lower discount rate chosen

rb = higher discount rate chosen

NPVa = NPV at rate a

NPVb = NPV at rate b

Assume a two-year project with an initial outlay of €8,000 and cash inflows of €5,000 in years 1 and 2. The company has a WACC of 12%.

Note: Apply two different discount rates where we expect one positive and one negative NPV as we aim to estimate where the NPV crosses the zero axis.

Substitute the results into our formula.

IRR = ra + (NPVa/(NPVa − NPVb))(rb − ra)

IRR = 5% + (1,295/(1,295 − (−365))(20% − 5%)

Estimated IRR = 16.7%

As the estimated IRR is in excess of the WACC, the company should pursue the project.

21.6 Summary

• Four main approaches to project evaluation have been reviewed in this unit. One is a profit-based method – the accounting rate of return (ARR) – and three are cash-based methods: payback, net present value (NPV) and the internal rate of return (IRR).
• The ARR method is based on the logic in return on capital employed calculations. It does not account for the timing of cash flows or required rates of return and often ignores key relevant financial information.
• Cash-based methods are not limited to physical cash flows and include opportunity costs, sunk costs, committed costs, and unchanged costs. NPV and IRR calculations reflect the expectations of the supposedly rational funders of an entity by using cost of capital discount factors.
• In contrast, the payback method considers the timing of cash flows and determines the time needed to repay initial investment from projected net cash inflows. It focuses on the shortest payback period, adjustable for risk–return trade-offs. While it is simple to calculate and emphasises liquidity, it does not consider required rates of return.
• NPV calculations consider the required rates of return using discount factors based on funder expectations. A positive NPV indicates that returns on an investment exceed expectations. The higher the NPV, the more attractive the project, while a negative NPV means funder expectations are not met.
• The IRR method of capex appraisal identifies the yield achieved relative to initial expectations and calculates the discount rate that results in a zero NPV. This appears to be a useful tool, but it can be misleading when comparing projects of different sizes, which is why it is less popular than NPV in practice.
• All these techniques are limited by the fact that they rely on estimates about what will happen in the future while things may happen very differently in reality. In addition, there are often non-financial considerations to take into account when making the final decision on capital expenditure. The management accountant can help inform the capital expenditure decision-making process, but the final decisions are made by managers, all of whom have their own preferences and opinions which might override what is suggested by the use of any of these techniques.