Introduction

• Project appraisal – the problem
• Project appraisal – steps to a solution (1)
• Project appraisal – steps to a solution (2)
• Project appraisal – present value (PV)
• Project appraisal – internal rate of return (IRR)
• Project appraisal – summary

The social object of skilled investment should be to defeat the dark forces of time and ignorance which envelope our future.

JOHN MAYNARD KEYNES (1883–1946)

Introduction

The need for a company to earn a return on its investment has been covered in detail. It is clear that this return must meet market expectations if the standing and value of the company is not to suffer.

One of management’s critical functions is planning the future of the business to ensure that an adequate rate of return is maintained. Essential to this is adequate new productive investment, as it is the return on this new investment that will provide the ongoing profits on which the company depends. Therefore a careful selection process needs to be applied to competing investment proposals so that only the best qualify.

In the past, many approaches have been adopted to assist managers in this selection. One very well tried and tested one that is still in use, is ‘pay-back’. Simply calculate the number of years that the project will take to pay back the money invested in it. As a rule of thumb it can provide a useful ‘fix’ on a project. However, it is not a mathematically sound approach. Some accounting-type measures have also been used in the past that are mathematically suspect.

This chapter is about the sound and tested techniques used now by all major companies to assist them with investment decisions. It illustrates the various measures and ratios that have proved to be effective in selecting and ranking investment projects.

Project appraisal – the problem

The standard investment profile is that of a large initial cash out-flow followed by a stream of cash in-flows for a certain number of years (section A of figure 16.1). The investor hopes that the in-flows will both repay the initial investment and yield an adequate surplus. The problem has been how to relate the immediate cash outlay with the stream of future repayments so as to determine the true rate of return.

In section B of figure 16.1, the financial numbers are given for Investment ‘X’. The investment is $1,000 and the stream of repayments over five years add up to $2,000. What, then, is the rate of return on the investment (ROI)? The increase in value over the five years is 100 per cent, which could be interpreted as 20 per cent per annum. Is this a correct interpretation? Is the return adequate and how is it affected by inflation? These are the questions investors commonly ask. Before answering them, let us look at one more example.

Section C of figure 16.1 shows the cash flows of Investment ‘Y’. The investment here of $1,000 and total repayments of $2,000 is the same as before. However, the pattern of repayments is quite different. For each of the first four years the cash in-flows are $200 but in Year 5 the initial investment of $1,000 is repaid in addition to the annual amount of $200. In other words an investment of $1,000 gives an annual return of $200 and, at the end of its life, the original investment of $1,000 is also repaid in full. This is the pattern of cash flows we would realize if we were to invest in a fixed interest security yielding 20 per cent. The true return on this project is 20 per cent.

When we look back at Investment X, we see that we do not get our investment back in one lump at the end of the period – it is spread over each year. The yearly cash repayments, then, are both paying interest on the investments and repaying the principal. This is the pattern of returns given by a commercial investment such as a piece of equipment that wears out to nothing over a five-year period. The return to the investor here cannot be assessed so easily.

Figure 16.1 Investment profiles

Project appraisal – steps to a solution (1)

The difficulty in assessment arises because of the timing of the cash flows. As already stated the cash flows tend to follow the pattern of a large cash out-flow followed by a stream of smaller cash in-flows over a series of future time periods.

We designate these periods as:

• Period 0: today
• Period 1: one year hence
• Period 2: two years hence, etc.

We know instinctively that money to be received at some distant time in the future has not the same worth as money in our hands now. This is the well-known principle referred to as ‘The time value of money’. Because of it we cannot make direct comparisons between sums of money that fall into different time periods.

We have to use a mechanism to express the value of all cash flows at one specific time period. The period most often selected is Period 0.

This approach is illustrated in figure 16.2. Each of the future cash flows is converted into what is called its ‘present value’ by the application of a ‘discount factor’. The means of calculating this discount factor is shown in the next section.

These present values are now directly comparable. They have been standardized. They are summed together to give a total present value of all future cash in-flows. This amount in turn can be directly compared with the investment’s initial cash out-flow. From this comparison we come to a conclusion about the worth of the investment project.

Figure 16.2 Project appraisal – setting out the problem

Project appraisal – steps to a solution (2)

We can approach this question by asking the question ‘If I had $100 available for deposit in the bank at an interest rate of 10 per cent, what would it be worth one year from now?’ The answer is of course $110.

Therefore $100 is the present value of $110 due in year 1 at a rate of 10 per cent (expressed as a decimal = 0.1). We can bring any value back from the future to the present by applying a factor related to the interest rate. In this case we divide the future value by (1 + decimal interest rate), i.e., $110/ 1.1 = $100. (It is mathematically identical to multiply by the discount factor .909, i.e., 1/1.1.)

If the future cash flow was positioned in Period 2, then we would have to do the calculation twice, i.e., . In reality we do not make two calculations, we apply a factor that has the equivalent effect.

Figure 16.3 illustrates the effect of taking the value of a present sum of money either forward in time or back in time.

Centrally placed is the box showing $100 which is aligned with the Period 0. Periods going forward into the future and back into the past are shown on the right- and left-hand sides of zero respectively. An interest rate of 10 per cent is used here to keep things simple. As we move to the right of the central zero point, the interest factors are 1.100, 1.210 and 1.331, which is 10 per cent compounded for years +1, +2 and +3.

When applied to the sum of $100 they tell us that the equivalent is $133.1 at the end of Year 3.

To the left of the model, the factors are 0.909, 0.826 and 0.751. This last one tells us that $100 carried back three years has a present value of $75.1.

The investment appraisal technique relies mainly on the factors to the left of centre, i.e., the discount factors.

To carry out our analysis we first select an appropriate interest rate. A higher rate would give a lower discount factor and vice versa. (See appendix 4 for relevant interest rate tables.) We can calculate the present or future value of any sum of money due in any period past or future by using such tables.

Figure 16.3 Project appraisal – effects of time on value of a cash flow

Project appraisal – present value (PV)

Figure 16.4 shows an example of a three-year project:

Investment		$5,000
Return in:	Year 1	$1,500
	Year 2	$3,500
	Year 3	$1,400

We wish to ascertain if the rate of return on this investment is greater or less than 10 per cent.

In figure 16.2, we saw the method for setting out the problem;figure 16.4 shows how the 10 per cent discount factors are applied to the stream of returns. Each future payment is connected by an arrow back to the present time, showing the conversion of future cash flows into present-day values. The discount factor for one year at 10 per cent is 0.909, for two years it is 0.826, etc.

The present value of each conversion is shown, i.e., $1,364 for year 1, etc. All individual present values are summed to give a total $5,309. The technical name for this amount of $5,309 is the present value (PV) of the project’s future cash flows.

This sum can now be directly compared with the initial investment of $5,000. Cash in-flows are shown positive and out-flows negative. The positive sum of $5,309 is offset against the negative sum of $5,000 to give a net present value (NPV) of $309 (positive).

Figure 16.4 Project appraisal – calculating present value 1

The meaning of Net Present Value (NPV)

In figure 16.5 we have set up a schedule for a hypothetical bank loan that carries an interest rate of 10 per cent. The amount of the loan is equal to the project NPV of $5,309. The loan repayment schedule shows payments that are equal to the project’s cash flows of $1,500, $3,500, and $1,400.

Over the period of the loan the bank charges annual interest at the rate of 10 per cent on the outstanding balance. The schedule shows for each of the three years:

a the interest charge

b the repayment and

c the closing balance.

At the end of Year 3 the balance on the loan is exactly zero. This shows that the three repayments have done two things:

1. they have repaid in full the initial loan of $5,309 and
2. they have also paid the bank 10 per cent interest each year on the amount outstanding.

The column headed ‘Bank cash movements’ will clarify the example further. The bank has had one cash out-flow of $5,309 followed by three cash in-flows of (1) $1,500, (2)$3,500, (3) $1,400 and it has earned exactly 10 per cent on the whole operation. Note that the bank has not earned 10 per cent interest on $5,309 for three years, but only on the outstanding balance each year.

We will now apply these principles to our example investment project. If the initial investment were $5,309 (as in the case of the bank) the return to the investor would have been exactly 10 per cent. It follows that if we can get the same returns from a smaller initial sum, i.e., $5,000, then the return is greater than 10 per cent.

The fact that the value derived for NPV (i.e. present value of cash flows less initial investment) has come out positive means that the project is delivering a rate of return greater than the interest rate used in the calculations. If the NPV were negative, it would mean the rate delivered was less than the interest rate used.

Figure 16.5 Project appraisal – calculating present value 2

Project appraisal – internal rate of return (IRR)

The previous example has shown that the investment of $5,000 earns more than 10 per cent. We have established that when the present value of the future cash flows exceeds the investment amount, we know that the rate of return is greater than the interest rate used in the calculation.

However, we do not know what actual rate of return is being delivered by the project. Of course this is very important information and further calculations are needed to establish it.

Unfortunately, there is no mathematical way of going directly to the answer. Instead we carry out a series of tests at various rates and by degrees work our way towards the answer.

We see this approach in figure 16.6. On our first test we got a positive NPV of $309 which told us that the project was delivering a return greater than 10 per cent. A second test is carried out using 11 per cent discount factors. The present value here is $5,216, yielding an NPV of $216 positive. We conclude that the return is greater than 11 per cent.

In section B, a schedule shows calculations for interest rate values between 10 per cent and 15 per cent, as listed in column 1. In the second column the present values that correspond to these different rates are $5,309, $5,216, $5,126 and so on. Note how these amounts fall in value as higher interest rates are applied. The third column has the unchanged investment figure of $5,000 in all rows. The fourth column shows the result of deducting the investment from the present value.

The NPV at 10 per cent is $309 (positive) and at 11 per cent it is $216 (positive). Going down the column, the value remains positive as far as 13 per cent. At 14 per cent cent it becomes negative. It becomes even more negative at 15 per cent. It can be concluded from these values, then, that the investment is earning more than 13 per cent and less than 14 per cent. At approximately 13.5 per cent, the figure in the NPV column would equal zero.

This value of 13.5 per cent is the rate of return being earned by the project. It is referred to as the Internal Rate of Return (IRR).

Figure 16.6 Calculating the internal rate of return

Project appraisal – summary

The method of investment appraisal that has been described is called the discounted cash flow (DCF) technique. (see figure 16.7). To apply this technique the cash flow, positive or negative, for each time period must first be identified. Then one or both of the approaches illustrated is used:

The NPV (net present value) method

• select the required rate of interest (see below)
• apply it to the stream of cash flows to derive net present value
• if net present value is positive, select the project, otherwise do not.

The IRR (internal rate of return) method

• find the interest rate that makes net present value equal to zero
• if this rate is satisfactory, select project, otherwise do not.

In this chapter we have merely considered how to apply a mathematical technique once the cash flows from a project have been established.

In real life this is the easy part of project appraisal. It requires considerably more effort and skill to arrive at the expected cash flows. Furthermore managers will never have to physically do the calculations themselves because computer programs are available to do this for them. However, a manager must understand the reasoning behind the calculations so that he can formulate a problem correctly and interpret the results produced by the computer. The various ratios produced by these programs can help him to make sound decisions in the field of investment appraisal.

Figure 16.7 gives an outline structure of the inputs that are required to analyze an investment decision. These inputs can be grouped under four headings:

• cost of investment
• annual returns from project
• life of project
• rate of interest.

A brief description of each is given. The area for which it is hardest to input reliable data is that of ‘annual returns’. There are no rules for this. Common sense and business acumen must apply here. It is normal to test a series of scenarios to examine the sensitivity of the project to small changes in input variables. Over time the accuracy of predictions can be monitored and suitable filtering mechanisms adopted.

Figure 16.7 Discounted cash flow – the component parts