8.1 Introduction
8.2 The principles of partial analysis
8.3 The principles and criteria of benefitcost analysis
This chapter deals with the ways of comparing costs and benefits, so as to be able to decide whether a particular project, programme or measure should be undertaken or not. The economic analysis of a project is undertaken last, summarising all the available information and putting monetary values on it. Before this is done, the project's feasibility must be established from three points of view.
· Technical. The types of expenditure, numbers of staff and timing must all be adequate to ensure that the project fulfils its objectives.
· Social. The project must be acceptable to the farmers and livestock owners involved and must respond to the needs they have.
· Institutional and management aspects. For the project to function successfully in the institutional setup provided, the organization and management planned must be viable.
The economic analysis needs to look at the project from the points of view of the nation (economic appraisal) and of all the individuals concerned (financial appraisal). A project can be profitable from the point of view of the national economy while still offering inadequate incentives to the livestock producers or the civil servants involved.
The techniques for evaluating a project after its implementation (expost analysis) are exactly the same as those used for its appraisal undertaken before its implementation (exante analysis). The appraisal looks at the expected profitability of the project. The evaluation monitors the actual performance and compares it with the expected performance.
When deciding whether to implement any measure, be it a minor change on an individual farm or a major disease control programme, the underlying principle for laying out the costs and benefits is the same: the situation with the change is compared to that without the change. Itemised under each heading will be:
Costs 
Benefits 
Extra costs incurred 
Costs saved 
Revenue foregone 
Revenue gained 
This approach is called partial analysis. It can be applied on an annual basis, using budgets to guide shortterm decisions, or it can be applied to longterm projects, using benefitcost analysis.
In the partial analysis of disease control programmes, the extra costs of introducing a new programme over time are compared to the benefits of a reduction in the direct and indirect losses due to a disease plus the costs saved as a result of the change in the control policy. In Table 51 the approach has been used to analyse different disease control policies.
Table 51. Partial analysis of the costs and benefits of different disease control policies.
Project/policy 
Costs 
Benefits 
Do nothing 
Unchecked morbidity and mortality. 
No downside risk of making matters worse. 
Treatment of diagnosed cases 
Surveillance, treatment and diagnosis costs. 
Reduction in morbidity and mortality. 
Control of the disease 
Annually recurring cost of a systematic programme depending on the nature of control. 
Reduction in morbidity and mortality, plus the costs of the previous programme, if any, that are saved. 
Eradication of the disease 
Onceandforall cost of the programme, which includes survey, diagnosis and followup. 
As above, with morbidity and mortality eliminated and costs of a previous programme saved in perpetuity. 
When listing costs and benefits over time it is important to realise that the situation "without" the project is not likely to have remained static: otherwise there is a danger that all change taking place will be attributed to the project. Figure 13 illustrates the errors in estimation that can arise as a result.
In each example the vertically shaded area "B" represents the benefits due to the project. If it was erroneously assumed that the situation without the project was static, fixed at the output level of Oa prevailing when the project started, the whole of "A" plus "B" would be taken as the value of benefits, a considerable overestimate represented by the horizontally shaded area "A".
8.3.1 The role of the discount rate
8.3.2 Dealing with inflation
8.3.3 Layout of a benefitcost analysis
8.3.4 The decisionmaking criteria
8.3.5 Dealing with risk and uncertainty
8.3.6 The scope of a benefitcost analysis
Benefitcost analysis is based on discounting the benefits and costs attributable to a project over time and then comparing the present value of costs (PVC) with the present value of benefits (PVB). The present value of benefits is the sum of the discounted values of benefits in each year. Thus:
_{}
and similarly:
_{}
where:
n = number of years being considered
t = each individual year
i = the discount rate expressed as a decimal fraction
_{} for every value of t from t = 1 to t = n.
In benefitcost studies, the discount rate chosen should theoretically reflect the real rate of interest (or of return) on investments. It can be one of the following:
· A rate comparable to the real rate of interest that could be earned if the sum involved was put into a bank or invested in another project; or· A social time preference rate (STP), reflecting the preference society has for present as opposed to future consumption, or the relative value it puts on the consumption of future generations; or
· An accounting rate of interest (ARI), which is such rate that all the available investment funds are used up if all the projects earning less than that rate of return are rejected and the remaining projects are implemented.
The discount rate can thus be thought of as a "price" set on the use of money. It is in fact the opportunity cost of capital. Discounting should be regarded as a process whereby future values are converted to present values by deducting the minimum acceptable return (or interest) earned in an alternative investment.
The discount rates usually chosen for projects in developing countries range from 8 to 12%. Generally, the agency responsible for project evaluation or the central planning office of the country concerned will fix the rate it considers suitable. Otherwise the evaluator is best advised to use 10% or 12%, or to try out two rates of, say, 8% and 12% to see how much the choice of discount rates affects the overall result.
Figure 13. Estimating benefits over time with and without a project and with and without a production ceiling. A. Without production ceiling
Figure 13. Estimating benefits over time with and without a project and with and without a production ceiling. B. With production ceiling
It should be noted that since the process of discounting makes future receipts and expenditures look progressively smaller relative to present incomes, the choice of a high discount rate will penalise projects with high initial expenditures and a low level of benefits over a long period. Disease eradication projects often fall into this category. This problem should be acknowledged while realising that a reasonably high discount rate does often need to be applied in order to reflect the opportunity cost of capital.
The objective of a benefitcost analysis is to assess the profitability or economic feasibility of an investment from today's point of view. As long as relative prices do not change, inflation is not included and estimates are made on the basis of today's prices, so all prices may be converted to constant values for a single base year. This further explains why the real and not the market rate of interest is used as a discount rate, since the prices chosen do not reflect inflation.
For an exante appraisal, the current year, generally year 0, is used as a base year. In an expost evaluation, the prices at the time the project was appraised, which is generally year n, are mostly used. Price indices can then be used to convert all benefits and costs to year n or year 0 values. If a change in relative prices is expected, the price of those items which are getting cheaper or more expensive over time can be decreased or increased as necessary, bearing in mind that the changes in their level should be calculated relative to the prices of other goods which are fixed, not in simple monetary terms. Thus, if over a year all prices go up 10% and the price of a particular good goes up 15%, then, in constant terms, the price has increased by 5% only. In practice, such calculations are fairly complex and, unless reliable information about an expected price change at a very different rate from that for other items exists, it is simpler and safer to use presentday price levels.
Table 52 shows how a bereftcost analysis can be set out and gives the notation used for the mathematical formulation of the decision criteria.
In setting out benefits, it is often convenient to divide them under different headings, such as direct losses due to disease saved, indirect losses and costs of previous policy avoided etc. Further subdivision can be made into, say, meat or milk production, losses due to infertility or weight loss etc. The sum of benefits in each year is called gross benefits.
Sometimes it is convenient to deduct production costs, which may be the variable costs of production or the cost incurred by the producers themselves, from each source of benefit. Benefits are then described as net benefits. Often this is done implicitly, since benefits are calculated in terms of extra income due to producers. For example, in a disease control project, a reduction in mortality will mean that more animals are produced and sold for meat and more milk is produced. Thus extra production will involve producers in extra variable costs for feed, veterinary care etc. If these are deducted from output, which is then seen as extra income, the benefit items listed would be net benefits, which would be compared to the rest of costs, called total costs. If the extra costs are separately listed as production costs, the comparison would be between gross benefits and gross costs.
Table 52. The layout of a benefitcost analysis.
a) Undiscounted values
Years 
Individual benefits BI_{t} 
Sum of benefits B_{t} 
Capital costs CC_{t} 
Operation and maintenance costs OM_{t} 
Production costs PC_{t} 
Sum of Costs C_{t} 
Incremental benefit (Cash flow) B_{t}C_{t} 
0 







1 







2 















n 







2 b) Discounted values

Bi_{t} / (1+t)^{t} 
B_{t} / (1+t)^{t} 
CC_{t} / (1+t)^{t} 
OM_{t} / (1+t)^{t} 
PC_{t} / (1+t)^{t} 
C_{t} / (1+t)^{t} 
B_{t } C_{t} / (1+t)^{t} 
0 







1 







2 















n 







Totals 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
Rather than discounting all the benefits and costs, usually it is sufficient discount the gross or the net benefits and the gross or the total costs, or the annual incremental benefit if an internal rate of return is required (see following section). Discounting individual benefit and cost sources is only useful if it is desired to examine the share of the individual sources of benefits in the total benefit. To do this the individual present values:
_{}
must be expressed as a percentage of the present value of the gross (GB) or net benefits (NB):
_{}
After the discounting has been completed, the present value of the benefits (PVB) is compared to the present value of all the costs (PVC). Obviously for a project to be considered profitable at a given discount rate, the present value of benefits should exceed that of costs i.e. PVB > PVC, or, if a discount rate is found such that the present value of the benefits is equal to the present value of costs, the discount rate should exceed the opportunity cost of capital. In other words, when "interest" is deducted by discounting at a rate high enough for PVB = PVC, then that interest or rate of return should be higher than the minimum acceptable return ® earned in an alternative use of money. Thus if PVB = PVC, then i > r, where i is discount rate used to calculate PVC and PVB, and r is the minimum acceptable discount rate.
From this, three decisionmaking criteria emerge:
· The net present value (NPV). This is sometimes called "net present worth", and it is obtained by subtracting the present value of costs from that of benefits i.e. NPV = PVB  PVC or, mathematically:
_{}
where:
t = individual years,
n = number of years over which the project is evaluated,
B = the sum of benefits in a given year,
C = the sum of costs in a given year, and
i = the discount rate expressed as a decimal.
For a project to be acceptable, PVB > PVC i.e. the net present value should be positive.
The net present value gives a good idea of the total profit, in present value terms, of the project. Difficulties arise when net present values are used to rank projects, since a large project with a relatively low net present value would look as profitable as a far smaller project with a relatively high net present value in comparison to its overall level of costs and benefits.
· The benefitcost ratio (B/C), which is obtained by dividing the present value of benefits by the present value of costs i.e. B/C = PVB/PVC or, mathematically:
_{}
For a project to be acceptable, the bereftcost ratio should be greater than 1.
The benefitcost ratio is a very useful criterion for ranking projects of different sizes, and it is relatively easy to calculate. However, the ratio will be different when net benefits are compared to total costs from that obtained when gross benefits are compared to gross costs.
· The internal rate of return (IRR), which is that discount rate i for which PVB = PVC. In mathematical terms, the IRR is that i for which: n
_{}
If i > r, i.e. IRR exceeds the minimum acceptable rate or the opportunity cost of money, the project is acceptable.
The internal rate of return is a useful criterion for comparing projects, especially since it can be expressed as an annual percentage rate of return. An internal rate of return cannot be calculated if:
 the annual incremental benefit or cash flow, B_{t}  C_{t}, is always >= 0 for every year, since in that case it would be impossible for the sum
_{} to equal zero.
 the annual cash flow, B_{t}  C_{t}. changes from negative to positive more than once over the years. In this case an IRR may exist for every change of sign.
An IRR can only be calculated for those cases where costs exceed benefits in the first years of the project. These cases are by far the most common.
Tables 53 and 54 give examples of how these three criteria can be obtained. The internal rate of return can only be calculated by trying out different discount rates until an NPV closer to 0 than that for the discount rates immediately above and below it is obtained. The method is illustrated in Table 53 and described below:
· Check that the undiscounted sum of the benefits exceeds that of the costs. If not, the project will not be profitable at any discount rate. From Table 53, the sum of benefits is 58 000 and the sum of costs is 46 250.· Check that costs exceed benefits for some years. In Table 53, costs exceed benefits in years 1,2 and 3.
· Check that the annual cash flow (B_{t}  C_{t}) changes from negative to positive only once. In Table 53, it changes from negative to positive after year 3 and never thereafter.
· Calculate the NPV at the usual discount rate. Check if this is positive or negative. In Table 53, NPV is 3264 at 12 %.
· If the NPV is positive, try a higher discount rate. If the NPV is negative, try a lower one. Continue until you arrive at an NPV of the opposite sign to the previous one. In Table 53, at a discount rate of 10%, the NPV is 1850. At a discount rate of 6%, the NPV is 2008.
Table 53. Derivation of the benefitcost ratio, the net present value and the internal rate of return using a 12% discount rate.
Year 
Capital 
Operations and maintenance 
Production costs 
Sum of costs 
Discount factor 
PVC 
Sum of benefits 
Discount factor 
PVB 
PVB  PVC 
1 
10 000 
 
 
10 000 
.893 
8 929 
 
.893 
 
8 929 
2 
5 000 
 
 
5 000 
.797 
3 986 
 
.797 
 
3 986 
3 
5 000 
750 
600 
6 350 
.712 
4 520 
2 000 
.712 
1 424 
3 096 
4 
 
1 500 
1 200 
2 700 
.636 
1 716 
4 000 
.636 
2 542 
826 
5 
 
1 500 
1 200 
2 700 
.567 
1 532 
5 500 
.567 
3 121 
1 589 
6 
3 000 
1 500 
1 200 
5 700 
.507 
2 888 
8 000 
.507 
4 053 
1 165 
7 
 
1 500 
1 200 
2 700 
.452 
1 221 
8 000 
.452 
3 619 
2 397 
8 
 
1 500 
1 200 
2 700 
.404 
1 090 
8 000 
.404 
3 231 
2 141 
9 
3 000 
1 500 
1 200 
5 700 
.361 
2 055 
8 000 
.361 
2 885 
829 
10 
 
1 500 
1 200 
2 700 
.322 
869 
14 500 
.322 
4 669 
3 799 
Total 
26 000 
11 250 
9 000 
46 250 

28 807 
58 000 

25 543 
3 264 
At 12% discount rate: 
At 10% discount rate: 
At 8% discount rate: 
At 6% discount rate: 
Net present value = 25 54328 807= 3264 
NPV = 1850 
NPV = 116 
NPV = 2008 
Benefitcost ratio = 25 583/28 807= 0.89 

Internal rate of return = 7.891%. 
Table 54. Present value of costs and benefits of sheep scab control in Lesotho in 1974/5 (prices in 1981/2 maloti).
a) Discounted at 10%
Year 
Costs 
Benefits 
(M) 
(M) 

1975/76 
307 796 
0 
1976/77 
700427 
0 
1977/78 
391809 
552650 
1978/79 
463818 
1 675 243 
1979/80 
297 348 
1 675 243 
1980/81 
329525 
1 675 243 
1981/82 
242 982 
590 310 
Total 
2 733 705 
2 818 203 
Benefitcost ratio = 1.03
Net present value = M 84 498
b) Discounted at 12%
Year 
Costs 
Benefits 
(M) 
(M) 

1975/76 
302 378 
0 
1976/77 
675 836 
0 
1977/78 
371462 
523 950 
1978/79 
431 901 
1532650 
1979/80 
271492 
1532650 
1980/81 
296222 
1532650 
1981/82 
214089 
520117 
Total 
2 563 380 
2 576 717 
Benefit cost ratio = 1.01
Net present value = M 13 337
Note: To calculate internal rate of return we need to find an NPV closer to 0 than the above values:
NPV at 12.5% =  M 3062
NPV at 12.3% = +M 4829
Using the formula given above:
IRR=12.3 + (12.5  12.3) x 4829 / (4829+3062) =12.42
Thus the internal rate of return for the sheep scab control programme in Lesotho was 12.42%.
· Calculate IRR using the following formula:
IRR = Lower DR +(Difference between the DRs) x (NPV at the lower DR) / (The sum of the absolute values of the two NPVs)
From Table 53:
 Lower DR = 6%; NPV = 2008
The absolute value of 2008 is 2008. Higher DR = 10%; NPV = 1850
The absolute value of1850 is 1850.
Thus:
IRR = 6 + [(10  6) x 2008] / (2008+1850) = 8.08
The actual IRR is 7.891%. The closer the two discount rates used are, the more accurate is the result obtained.
Risk and uncertainty can be dealt with by applying the probability of a particular outcome, or by doing a sensitivity analysis to see how different values or outcomes affect the overall results. Contingency allowances can also be used, especially for estimating costs.
A sensitivity analysis is usually undertaken if there is a great deal of uncertainty as to the values of particular parameters, but no probability can be attached to their attaining certain values. The analysis uses different values for the relevant item in the calculations to illustrate how sensitive the results are to the assumptions made about the value of a particular parameter.
The items for which different values are most commonly tried are:
· Discount rates. Several discount rates may be tried, if an internal rate of return is not being calculated. This is especially important for projects (e.g. disease eradication projects) which have high initial capital costs and benefits extending far into the future. Such projects can be said to be disadvantaged by the use of high discount rates, since the high initial costs are then given a relatively higher value in comparison to the future benefits.
· Prices. Several prices, which may be shadow prices or various market prices, may be tried out. A full recalculation of the project with the new price is not necessary; one can simply determine the percentage of costs or benefits which are accounted for by that item each year. The percentage is the same for both the discounted and undiscounted costs and benefits in a particular year. The overall total for costs or benefits cannot be used, unless the percentage accounted for by that item is constant from year to year. Having determined the percentage of the total (say X%) accounted for by that item, and if the percentage change in price is Y%, then the total cost (TC) for that year is multiplied by:
1 + (X/100 x Y/100)
where Y can obviously be positive or negative, since it can represent an increase or a decrease.
· Estimates of benefits. Since the extent of the benefits realised by a project are often open to doubt, it is useful to make high and lowlevel estimates of benefits (optimistic versus pessimistic projections). These give an upper and lower limit within which the real performance of the project is expected to fall. Some indication of this nature is necessary in almost all costbenefit studies.
Alternatively, a breakeven analysis can be done to determine what level benefits must reach to cover costs. The analysis uses the present value of costs to estimate the present value of benefits needed to cover the costs.
If either the level of benefits is totally unknown or else the same level of benefits can be attained by several different methods, the cost effectiveness of the different methods can be analysed by comparing the present values of costs.
· Estimates of costs. Uncertainty in estimating costs can be dealt with by trying different assumptions or sets of prices, or by making contingency allowances.
Once the present values of benefits and costs have been determined, the effects of increasing or decreasing these by certain percentages can be examined. Thus at its simplest, sensitivity analysis may consist of, say, looking at the effect of a 10% cost overrun or a 20% shortfall in expected benefits.
The number of years covered by a costbenefit analysis depends on:
· The requirements of the project, its duration and how long it will take before investments and subsidies stop and the project shows a return.· The feasibility of estimating costs and benefits with any accuracy beyond a certain number of years.
· The fact that by using a discount rate the value of future income is reduced to very small amounts after a number of years. At a 10% discount rate after 12 years, an item is worth less than a third of its face value; after 25 years less than a tenth; and after 50 years less than a hundredth (see appendix 1, Table 1).