One of the key areas of long-term decision-making that firms must tackle is that of investment - the need to commit funds by purchasing land, buildings, machinery and so on, in anticipation of being able to earn an income greater than the funds committed. In order to handle these decisions, firms have to make an assessment of the size of the outflows and inflows of funds, the lifespan of the investment, the degree of risk attached and the cost of obtaining funds.
The main stages in the capital budgeting cycle can be summarised as follows:
- Forecasting investment needs.
- Identifying project(s) to meet needs.
- Appraising the alternatives.
- Selecting the best alternatives.
- Making the expenditure.
- Monitoring project(s).
Looking at investment appraisal involves us in stage 3 and 4 of this cycle.
We can classify capital expenditure projects into four broad categories:
- Maintenance - replacing old or obsolete assets for example.
- Profitability - quality, productivity or location improvement for example.
- Expansion - new products, markets and so on.
- Indirect - social and welfare facilities.
Even the projects that are unlikely to generate profits should be subjected to investment appraisal. This should help to identify the best way of achieving the project's aims. So investment appraisal may help to find the cheapest way to provide a new staff restaurant, even though such a project may be unlikely to earn profits for the company.
Investment appraisal methods:
One of the most important steps in the capital budgeting cycle is working out if the benefits of investing large capital sums outweigh the costs of these investments. The range of methods that business organisations use can be categorised one of two ways: traditional methods and discounted cash flow techniques. Traditional methods include the Average Rate of Return (ARR) and the Payback method; discounted cash flow (DCF) methods use Net Present Value (NPV) and Internal Rate of Return techniques.
Traditional Methods
Payback:
This is literally the amount of time required for the cash inflows from a capital investment project to equal the cash outflows. The usual way that firms deal with deciding between two or more competing projects is to accept the project that has the shortest payback period. Payback is often used as an initial screening method.
Payback period = Initial payment / Annual cash inflow
So, if £4 million is invested with the aim of earning £500 000 per year (net cash earnings), the payback period is calculated thus:
P = £4 000 000 / £500 000 = 8 years
This all looks fairly easy! But what if the project has more uneven cash inflows? Then we need to work out the payback period on the cumulative cash flow over the duration of the project as a whole.
Payback with uneven cash flows:
Of course, in the real world, investment projects by business organisations don't yield even cash flows. Have a look at the following project's cash flows (with an initial investment in year 0 of £4 000):
| Year | Cash flow (£ 000) | Cumulative cash flow (£ 000) |
| 0 | (4000) | (4000) |
| 1 | 750 | (3250) |
| 2 | 750 | (2500) |
| 3 | 900 | (1600) |
| 4 | 1000 | (600) |
| 5 | 600 | Zero |
| 6 | 400 | 400 |
The payback period is precisely 5 years.
The shorter the payback period, the better the investment, under the payback method. We can appreciate the problems of this method when we consider appraising several projects alongside each other.
| Year | Project | 1 | 2 | 3 | 4 | 5 | 6 |
| 0 | (50) | (100) | (80) | (100) | (100) | (100) | |
| 1 | 5 | 50 | 40 | 40 | 30 | 5 | |
| 2 | 10 | 30 | 20 | 30 | 30 | 10 | |
| 3 | 15 | 20 | 20 | 20 | 10 | 15 | |
| 4 | 20 | 10 | 20 | 10 | 10 | 40 | |
| 5 | 20 | 20 | 5 | 20 | 40 | ||
| 6 | 10 | 20 | 10 | 40 | 30 | ||
| Payback period (Yrs) | 4 | 3 | 3 | 4 | 3 | 3 | |
You can see that the payback period for four of the projects (2, 3, 5 and 6) is three years. In this case, then, the four projects are of equal merit. But, here we must face the real problem posed by payback: the time value of income flows.
Put simply, this issue relates to the sacrifice made as a result of having to wait to receive the funds. In economic terms, this is known as the opportunity cost. More on this point follows later.
So, because there is a time value constraint here, the four projects cannot be viewed as equivalent. Project 2 is better than 3 because the revenues flow quicker in years one and two. Project 2 is also better than Projects 5 and 6, because of the earlier flows and because the post-payback revenues are concentrated in the earlier part of that period.
OK, so it's clear that the payback method is a bit of a blunt instrument. So why use it?
Arguments in favour of payback
Firstly, it is popular because of its simplicity. Research over the years has shown that UK firms favour it and perhaps this is understandable given how easy it is to calculate.
Secondly, in a business environment of rapid technological change, new plant and machinery may need to be replaced sooner than in the past, so a quick payback on investment is essential.
Thirdly, the investment climate in the UK in particular, demands that investors are rewarded with fast returns. Many profitable opportunities for long-term investment are overlooked because they involve a longer wait for revenues to flow.
Arguments against payback
It lacks objectivity. Who decides the length of optimal payback time? No one does - it is decided by pitting one investment opportunity against another.
Cash flows are regarded as either pre-payback or post-payback , but the latter tend to be ignored.
Payback takes no account of the effect on business profitability. Its sole concern is cash flow.
Payback summary
It is probably best to regard payback as one of the first methods you use to assess competing projects. It could be used as an initial screening tool, but it is inappropriate as a basis for sophisticated investment decisions.
Average Rate of Return:
The average rate of return expresses the profits arising from a project as a percentage of the initial capital cost. However the definition of profits and capital cost are different depending on which textbook you use. For instance, the profits may be taken to include depreciation, or they may not. One of the most common approaches is as follows:
ARR = (Average annual revenue / Initial capital costs) * 100
Let's use this simple example to illustrate the ARR:
A project to replace an item of machinery is being appraised. The machine will cost £240 000 and is expected to generate total revenues of £45 000 over the project's five year life. What is the ARR for this project?
ARR = (£45 000 / 5) / 240 000 * 100
= (£9 000) / 240 000 * 100
= 3.75%
Advantages of ARR
As with the Payback method, the chief advantage with ARR is its simplicity. This makes it relatively easy to understand. There is also a link with some accounting measures that are commonly used. The Average Rate of Return is similar to the Return on Capital Employed in its construction; this may make the ARR easier for business planners to understand. The ARR is expressed in percentage terms and this, again, may make it easier for managers to use.
There are several criticisms of ARR which raise questions about its practical application:
Arguments against ARR
Firstly, the ARR doesn't take account of the project duration or the timing of cash flows over the course of the project.
Secondly, the concept of profit can be very subjective, varying with specific accounting practice and the capitalisation of project costs. As a result, the ARR calculation for identical projects would be likely to result in different outcomes from business to business.
Thirdly, there is no definitive signal given by the ARR to help managers decide whether or not to invest. This lack of a guide for decision making means that investment decisions remain subjective.
A project requires a capital outlay of £900 000 and earns the following cash inflows over the following seven years:
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Inflows | 200 | 250 | 300 | 450 | 400 | 200 | 150 |
See our worked solution for these two questions.
Discounted Cash Flow Methods
Net Present Value:
The Net Present Value (NPV) is the first Discounted Cash Flow (DCF) technique covered here. It relies on the concept of opportunity cost to place a value on cash inflows arising from capital investment.
Remember that opportunity cost (see Glossary) is the calculation of what is sacrificed or foregone as a result of a particular decision. It is also referred to as the 'real' cost of taking some action.
We can look at the concept of present value as being the cash equivalent now of a sum receivable at a later date. So how does the opportunity cost affect revenues that we can expect to receive later? Well, imagine what a business could do now with the cash sums it must wait some time to receive.
In fact, if you receive cash you are quite likely to save it and put it in the bank. So what a business sacrifices by having to wait for the cash inflows is the interest lost on the sum that would have been saved.
Looked at another way, it is likely that the business will have borrowed the capital to invest in the project. So, what it foregoes by having to wait for the revenues arising from the investment is the interest paid on the borrowed capital.
NPV is a technique where cash inflows expected in future years are discounted back to their present value. This is calculated by using a discount rate equivalent to the interest that would have been received on the sums, had the inflows been saved, or the interest that has to be paid by the firm on funds borrowed.
Using Present Value Tables
Net Present Value tables provide a value for a range of years and discount rates. Notice the time scale used in the table:
| 0 | 1 | 2 | 3 | - - - - | n |
| Now | 1 year from now | 2 years from now | 3 years from now | n years from now |
The present value for 0 years is always 1, and this is not included in the present value table.
If you are looking to find the present value of £ 50 000 which you expect to receive in 3 years time, at a rate of interest of 9 %, the following steps are taken:
Step 1 Download the present value spreadsheet (you can right-click on this link and select 'save as', if you want to save the spreadsheet to your own computer)
Step 2 Look down the top column of the table ('After n years') and find 3 years.
Step 3 Look across the row titled 'At rate r' for the rate of interest of 9 %.
Step 4 Where the row for 3 years intersects with the column for 9 % in the table, there is the relevant present value factor. In this case this is 0.772.
Step 5 Multiply £ 50 000 by 0.772 = £ 38 600
So, £ 38 600 is the present value of £ 50 000 receivable in three years at 9 %. Looked at another way, £ 38 600 is the amount which, if invested now at 9 %, will yield £ 50 000 after three years.
NPV Illustration
Calculate the present value of the following project's cash flows, using a 10 % discount rate.
| Year | Cash Flow (£) | Discount Rate | Present Value (£) |
| 0 | (75 000) | 1.000 | (75 000) |
| 1 | 10 000 | 0.909 | 9 090 |
| 2 | 25 000 | 0.826 | 20 650 |
| 3 | 35 000 | 0.751 | 26 285 |
| 4 | 35 000 | 0.683 | 23 905 |
| 5 | 30 000 | 0.621 | 18 630 |
| Net Present Value | £23 560 |
Assessing the value of NPV calculations is simple. A positive NPV means that the project is worthwhile because the cost of tying up the firm's capital is compensated for by the cash inflows that result. When more than one project is being appraised, the firm should choose the one that produces the highest NPV.
The Internal Rate of Return (IRR):
So far so good. We know that when a positive NPV is produced by our DCF calculations, a project is worthwhile. We have also seen that when there are competing projects, we should select the one that produces the highest NPV.
But sometimes a firm will want to know how well a project will perform under a range of interest rate scenarios. The aim with IRR is to answer the question: 'What level of interest will this project be able to withstand?' Once we know this, the risk of changing interest rate conditions can effectively be minimised.
The IRR is the annual percentage return achieved by a project, at which the sum of the discounted cash inflows over the life of the project is equal to the sum of the capital invested.
Another way of looking at this is that the IRR is the rate of interest that reduces the NPV to zero.
Making the investment decision
Let's set out the criteria for accepting or rejecting investment opportunities, using the NPV and IRR.
Imagine a scenario where the managers of a firm are considering whether to accept or reject an investment project, on the basis of their acquiring the funds necessary at a known rate of interest.
- The NPV approach asks if the present value of cash inflows less the initial investment is positive, at the current borrowing rate.
- The IRR approach asks if the IRR on the project is greater than the borrowing rate.
Illustration of NPV & IRR
An initial investment of £ 2 500 in a project produces cash inflows of £ 750, £ 750, £ 900, £ 900 and £ 595 at 12 month intervals. The cost of capital to finance the project is 12 %.
You are required to decide whether the project is worthwhile using:
- The Net Present Value
- The Internal Rate of Return
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Cash flow | (2500) | 750 | 750 | 900 | 900 | 595 |
1. NPV
| Year | Cash flow | Discount factor @ 12% | Present value |
| 0 | (2500) | 1.000 | (2500) |
| 1 | 750 | 0.893 | 669.75 |
| 2 | 750 | 0.797 | 597.75 |
| 3 | 900 | 0.712 | 640.80 |
| 4 | 900 | 0.636 | 572.40 |
| 5 | 595 | 0.567 | 337.37 |
| Net present value | £318.07 |
A positive NPV makes the project worthwhile because the cost of tying up the firm's capital is compensated for by the cash inflows that result.
2. IRR
The above calculation for NPV used a 12 % discount rate and produced a positive value of £ 318.07. We need to find a discount rate that produces a negative NPV. Let's try 20 %.
| Year | Cash flow | Discount factor @ 20% | Present value |
| 0 | (2500) | 1.000 | (2500) |
| 1 | 750 | 0.833 | 624.75 |
| 2 | 750 | 0.694 | 520.50 |
| 3 | 900 | 0.579 | 521.10 |
| 4 | 900 | 0.482 | 433.80 |
| 5 | 595 | 0.402 | 239.19 |
| Net present value | (£160.66) |
The IRR lies between 12 % and 20 %. But we can get much closer to the precise answer by using arithmetic.
| IRR = 12 % + Difference between the two discount rates * Positive NPV Range of +/ve to -/ve NPVs |
| IRR = 12 % + (8 % * 318.07) 478.73 |
IRR = 12 % + 5.32
IRR = 17.32 %
IRR Summary:
The value to a business of calculating the IRR is that its decision-makers are able to see the level of interest that a project can withstand. In the case where a number of projects are competing for selection, the one that is most resilient can be chosen.
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