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Chapter 6

Investment Appraisal

Abstract

This chapter describes the investment appraisal, which is a part of the business case. It includes the calculations for return on investment and net present value using the discounted cash flow method. Also discussed are payback, internal rate of return and cost/benefit analysis. The chapter contains a discount factor table and worked examples.

Keywords

Cost/benefit analysis; Discounted cash flow; Internal rate of return; Investment appraisal; Net present value; Return on investment

The investment appraisal, which is a part of the business case, will, if properly structured, improve the decision-making process regarding the desirability or viability of the project. It should examine all the realistic options before making a firm recommendation for the proposed case. The investment appraisal must also include a cost/benefit analysis and take into account all the relevant factors such as:

• Capital costs, operating costs and overhead costs

• Support and training costs

• Dismantling and disposal costs

• Expected residual value (if any)

• Any cost savings that the project will bring

• Any benefits that cannot be expressed in monetary terms

To enable the comparison to be made of some of the options, the payback, return on capital, net present value (NPV) and anticipated profit must be calculated. In other words, the project viability must be established.

Project Viability

Return on Investment

The simplest way to ascertain whether the investment in a project is viable is to calculate the return on investment (ROI).

If a project investment is £10,000 and gives a return of £2000 per year over 7 years,

$\begin{matrix} The average return/year = \frac{(7 \times £ 2000) - £ 10,000}{7} \\ = \frac{£ 4000}{7} = £ 571.4 \end{matrix}$ $\begin{matrix} The average return/year = \frac{(7 \times £ 2000) - £ 10,000}{7} \\ = \frac{£ 4000}{7} = £ 571.4 \end{matrix}$

The ROI, usually given as a percentage, is the average return over the period considered × 100, divided by the original investment, i.e.,

$\begin{matrix} Return on investment = \frac{average return \times 100}{investment} \\ = \frac{£ 571.4 \times 100}{£ 10,000} = £ 5.71 \end{matrix}$ $\begin{matrix} Return on investment = \frac{average return \times 100}{investment} \\ = \frac{£ 571.4 \times 100}{£ 10,000} = £ 5.71 \end{matrix}$

This calculation does not, however, take into account the cash flow of the investment, which in a real situation may vary year by year.

Net Present Value

As the value of money varies with time due to the interest it could earn if invested in a bank or other institution, the actual cash flow must be taken into account to obtain a realistic measure of the profitability of the investment.

If £100 were invested in a bank earning an interest of 6%:

The value in 1 year would be £100 × 1.05 = £106

The value in 2 years would be £100 × 1.06 × 1.06 = £112.36

The value in 3 years would be £100 × 1.06 × 1.06 × 1.06 = £119.10

It can be seen therefore that, today, to obtain £119.10 in 3 years it would cost £100. In other words, the present value (PV) of £119.10 is £100.

Another way of finding the PV of £119.10 is to divide it by 1.06 × 1.06 × 1.06 or 1.191 or

$\frac{£ 119.10}{1.06 \times 1.06 \times 1.06} = \frac{£ 119.10}{1.191} = £ 100.$ $\frac{£ 119.10}{1.06 \times 1.06 \times 1.06} = \frac{£ 119.10}{1.191} = £ 100.$

If instead of dividing the £119.10 by 1.191, it is multiplied by the inverse of 1.191, one obtains the same answer, since

$£ \frac{119.10 \times 1}{1.191} = £ 119.10 \times 0.840 = £ 100$ $£ \frac{119.10 \times 1}{1.191} = £ 119.10 \times 0.840 = £ 100$

The 0.840 is called the discount factor or present-value factor and can be quickly found from discount factor tables, a sample of which is given in Fig. 6.1.

It can be noticed from these tables that 0.840 is the PV factor for a 6% return after 3 years. The PV factor for a 6% return after 2 years is 0.890 or

$\frac{1}{1.06 \times 1.06} = \frac{1}{1.1236} = 0.890$ $\frac{1}{1.06 \times 1.06} = \frac{1}{1.1236} = 0.890$

In the earlier example, the income was the same every year. In most of the projects, however, the projected annual net cash flow (income minus expenditure) will vary year by year, and to obtain a realistic assessment of the NPV of an investment, the net cash flow must be discounted separately for every year of the projected life.

The following example will make this clear.

Year	Income (£)	Discount Rate (%)	Discount Factor	NPV (£)
1	10,000	5	1/1.05 = 0.9523	10,000 × 0.9523 = 9523.8
2	11,000	5	1/1.05² = 0.9070	10,000 × 0.9070 = 9070.3
3	12,000	5	1/1.05³ = 0.8638	12,000 × 0.8638 = 10,365.6
4	12,000	5	1/1.05⁴ = 0.8227	12,000 × 0.8227 = 9872.4
Total	45,000			39,739.1

One of the main reasons for finding the NPV is to be able to compare the viability of competing projects or different repayment modes. Again, an example will demonstrate the point.

A company decides to invest £12,000 for a project which is expected to give a total return of £24,000 over 6 years. The discount rate is 8%.

There are two options of receiving the yearly income.

1. £6000 for years 1 and 2 = £12,000		2. £5000 for years 1, 2, 3 and 4 = £20,000
£4000 for years 2 and 3 = £8000		£2000 for years 5 and 6 = £4000
£2000 for years 5 and 6 = £4000
Total	£24,000		£24,000

The DCF method will quickly establish the most profitable option to take as will be shown in the following table.

Year	Discount Factor	Cash Flow A (£)	NPV A (£)	Cash Flow B (£)	NPV B (£)
1	1/1.08 = 0.9259	6000	5555.40	5000	4629.50
2	1/1.08² = 0.8573	6000	5143.80	5000	4286.50
3	1/1.08³ = 0.7938	4000	3175.20	5000	3969.00
4	1/1.08⁴ = 0.7350	4000	2940.00	5000	3675.00
5	1/1.08⁵ = 0.6806	2000	1361.20	2000	1361.20
6	1/1.08⁶ = 0.6302	2000	1260.40	2000	1260.40
Total		24,000	19,437.00	24,000	19,181.50

Clearly, A gives the better return, and after deducting the original investment of £12,000, the net discounted return for A = £7437.00 and for B = £7181.50.

The mathematical formula for calculating the NPV is as follows:

If NPV	=	Net Present Value
r	=	the interest rate
n	=	number of years the project yields a return
B1, B2, B3, etc.	=	the annual net benefits for years 1, 2 and 3, etc.
NPV for year 1	=	B1/(1 + r)
for year 2	=	B1/(1 + r) + B2/(1 + r)²
for year 3	=	B1/(1 + r) + B2/(1 + r)² + B3/(1 + r)³ and so on

If the annual net benefit is the same for each year for n years, the formula becomes

$NPV = B / {(1 + r)}^{n} .$ $NPV = B / {(1 + r)}^{n} .$

As explained previously, the discount rate can vary year by year, so the rate relevant to the year for which it applies must be used when reading off the discount factor table.

Two other financial calculations need to be carried out to enable a realistic decision to be taken as to the viability of the project.

Payback

Payback is the time taken to recover the capital outlay of the project, having taken into account all the operating and overhead costs during this period. Usually, this is based on the undiscounted cash flow. Knowledge of the payback is particularly important when the capital must be recouped as quickly as possible, as would be the case in short-term projects or projects whose end products have a limited appeal due to changes in fashion, competitive pressures or alternative products. Payback is easily calculated by summating all the net incomes until the total equals the original investment (e.g., if the original investment is £600,000, and the net income is £75,000 per year for the next 10 years, the payback is £600,000/£75,000 = 8 years).

Internal Rate of Return

It has already been shown that the higher the discount rate (usually the cost of borrowing) of a project, the lower the NPV. Therefore, there must come a point at which the discount rate is such that the NPV becomes zero. At this point, the project ceases to be viable and the discount rate is the internal rate of return (IRR). In other words, it is the discount rate at which the NPV is 0.

While it is possible to calculate the IRR by trial and error, the easiest method is to draw a graph as shown in Fig. 6.2.

Figure 6.2 Internal rate of return (IRR) graph.

The horizontal axis is calibrated to give the discount rates from 0 to any chosen value, say 20%. The vertical axis represents the NPVs, above and below the horizontal axis denoted by (+) and (−).

By choosing two discount rates (one low and one high), two NPVs can be calculated for the same envisaged net cash flow. These NPVs (preferably one +ve and one −ve) are then plotted on the graph and joined by a straight line. Where this line cuts the horizontal axis, i.e., where the NPV is zero, the IRR can be read off.

The basic formulae for the financial calculations are given in the following.

Investment appraisal definitions

NPV	=	summation of PVs − original investment
Net income	=	incoming moneys − outgoing moneys
Payback period	=	no. of years it takes for net income to equal original investment
Profit	=	total net income − original investment
Average return/annum	=	$\frac{total net income}{no . of years}$ $\frac{total net income}{no . of years}$
Return on investment (%)	=	$\frac{average return \times 100}{investment}$ $\frac{average return \times 100}{investment}$
	=	$\frac{net income \times 100}{no . of years \times investment}$ $\frac{net income \times 100}{no . of years \times investment}$
IRR	=	% discount rate for NPV = 0

Cost/Benefit Analysis

Once the cost of the project has been determined, an analysis has to be carried out which compares these costs with the perceived benefits. The first cost/benefit analysis should be carried out as part of the business case investment appraisal, but in practice such an analysis should really be undertaken at the end of every phase of the life cycle to ensure that the project is still viable. The phase interfaces give management the opportunity to proceed with or, alternatively, abort the project if there is an unacceptable escalation in costs or a diminution of the benefits due to changes in market conditions, such as a reduction in demand caused by political, economic, climatic, demographic or a host of other reasons.

It is relatively easy to carry out a cost/benefit analysis where there is a tangible deliverable producing a predictable revenue stream. Provided there is an acceptable NPV, the project can usually go ahead. However, where the deliverables are intangible, such as better service, greater customer satisfaction, lower staff turnover, higher staff morale, etc., there may be considerable difficulty in quantifying the benefits. It will be necessary in such cases to run a series of tests and reviews, and assess the results of interviews and staff reports.

Similarly, while the cost of redundancy payments can be easily calculated, the benefits in terms of lower staff costs over a number of years must be partially offset by lower production volume or poorer customer service. Where the benefits can only be realized over a number of years, a benefit profile curve as shown in Fig. 6.3 should be produced, making due allowance for the NPV of the savings.

Following is a list of some of the benefits that have to be considered, from which it will be apparent that some will be very difficult to quantify in monetary terms:

• Financial

• Statutory

• Economy

• Risk reduction

• Productivity

• Reliability

• Staff morale

• Cost reduction

• Safety

• Flexibility

• Quality

• Delivery

• Social

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Table of Contents for Chapter 6. Investment Appraisal

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