10. discounted cash flow analysis

ANPR350/450 – Sheep Management __________________________________________ 10-1 ©2009 The Australian Wool Education Trust licensee for educational activities University of New England

10. Discounted Cash Flow Analysis

D. Cottle and E. Fleming

Learning objectives At the end of this topic you should be able to:

• Demonstrate a thorough understanding of the concept of discounted cash flow analysis • Apply discounted cash flow analysis to investment decisions in the sheep enterprise, covering

the valuation of rams, disease outbreaks, investment in research and development (R&D) and valuing environmental change.

Key terms and concepts Discounted cash flow analysis, discount rate, disease outbreaks, benefit-cost ratio, internal rate of return, net present value, R&D, sustainable development, valuing livestock

Introduction to the topic The primary focus of this topic is on the application of discounted cash flow (DCF) methods to make investment decisions in the sheep enterprise. Methods are introduced for carrying out investment analyses using DCF analysis, with three popular criteria – net present value, benefit-cost ratio and internal rate of return – outlined and used in three brief case studies. The case studies are provided to demonstrate how DCF analysis can improve decision making in the sheep enterprise and in public decision making.

10.1 What is discounted cash flow analysis? DCF analysis is the analysis of a set of alternative investments whose expected future cash flows have been discounted to their present values. DCF is widely used where the impacts of an investment, or series of investments, extend over a long period. By a long period we mean many years. The need to express all cash flows in present value terms arises from the time-value of money, which can be looked at from two different points of view. The first point of view is that of an investor, recognising that there is an opportunity cost of capital, or the best alternative use to which money could be put – refer to Topic 8. If a sheep farmer does not invest in new sheep yards, he or she could invest the money in Treasury bonds (long-term debt securities), bank deposits or the stock market, among numerous alternatives, and earn income from these investments. By investing in new sheep yards, the farmer is forgoing the opportunity to earn money from these other investments but may reduce further costs. The second point of view is that of a consumer, who has time preferences: he or she would prefer to consume now rather than have to wait until some time in the future. We can measure this preference as the individual time preference rate, or the rate needed to compensate a consumer for, say, buying a car now rather than waiting to buy one a year into the future.

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10.2 What period is selected for a DCF analysis? As indicated in the previous section, DCF analyses are used for investments that take place or have impacts over many years. How is the term of the analysis selected, given that the impacts of many on-farm investments can be expected to continue indefinitely? Take the example of an investment in the genetic improvement of the sheep flock. Such an investment may provide benefits to the farmer many decades into the future. There are two rules of thumb commonly used to define the term of the analysis. The first rule is to choose the length of time until the major fixed asset purchased in the investment requires replacement. For example, investment in a new set of sheep yards that are expected to last 20 years suggests that the length of the analysis should be 20 years. For major assets with extremely long lives. The second rule of thumb can be invoked, namely that any values extending beyond about 40 years are going to be trivial when discounted to present values. Therefore, choose this period as the maximum term for any analysis.

10.3 Selecting the discount rate and discount factor Which discount rate? A discount rate is defined as the rate of compound interest at which future cash flows are adjusted to their equivalent current values. In a perfectly operating financial market, the opportunity cost of capital should equal the individual time preference rate. Either rate should then provide us with a suitable discount rate. The problems in choosing an appropriate discount (or interest) rate for a farmer are that (a) there are many interest rates or rates of returns on investments in Australian financial markets to choose from, and (b) virtually all of them contain a risk premium. A risk premium is defined as a measure of the combined effects of risk and risk aversion (the willingness to forgo some expected return for a reduction in risk) on the return required by an investor. Put another way, it is the amount of money the investor is prepared to forgo to earn a lower return that is more certain. Ideally, the discount or interest rate chosen for DCF analysis should be risk-free. While no investment is entirely risk-free, the target cash rate of the Reserve Bank of Australia is as close as you can get to risk-free. But the problem with using this rate is that it is set by the Bank rather than the market and is a short-term rate. Other potential reference rates that are close to risk-free (that is, those investments with Triple A rating) are the rates for bank-accepted bills (a short-term rate) and the rates for Treasury bonds and certain corporate bonds (long-term rates). Long-term rates are preferable to use because on-farm investments are typically long-term in nature. Accounting for inflation Another concern in selecting the discount rate is in purging it of any inflationary element. Inflation is an increase in the general level of prices of goods and services without a real increase in aggregate demand or a real decrease in aggregate supply. It creates difficulties for DCF analysis because the values of outcomes appear to increase while true values do not. Therefore, market (or nominal) values do not measure the true values of cash inflows and cash outflows. Real values are values with the purchasing power of money held constant, relative to a specific point in time. They therefore exclude inflationary effects and comparisons between them are meaningful because a dollar at each point in time has the same purchasing power. So long as all prices in the economy increase at the same rate, it is valid to use either real or nominal values as relativity is maintained. But real values are easier to understand and more relevant to today’s decisions, and are usually preferred to nominal values. They are more accurate when relative prices of inputs and outputs are diverging over time.


Interest rates include a component for expected future inflation rates. We can calculate a real interest rate (approximately) as:

i = r + fe,

where i is the real interest rate, r is the selected market, interest rate, and fe is the expected inflation rate over the term of the investment. The discount factor (DF) is a number used to convert future cash flows to their equivalent current values. It is derived from the discount rate (r), using the following formula:

DF = 1/(1+ i)n

where n is the number of years into the future over which the cash flow occurs. A cash flow in a year, say year 4 from the time of the investment, is discounted to its present value by multiplying the actual amount of the flow (C) in that year by the discount factor for the prevailing discount rate:

P = C x DF.

Consider the following example. Assume a real discount rate (i) of 5 per cent (0.05 in decimal terms) in the above situation, and a cash inflow of $5000 in year 4. Calculate the discount factor and the present value of the cash flow. The discount factor is:

1/(1+.05)4, = 0.822702.

The present value of the cash flow is:

$5000 x 0.822702, = $4113.51.

As expected, the present value of this future cash flow is quite a deal less than the nominal amount received, reflecting the time value of money and its effect through discounting. Clearly, the discount factor must lie between zero and one, where one would be the discount factor used for cash flows in the current period.

10.4 Criteria for DCF analysis There are three popular criteria used in DCF analysis, each with its own advantages and disadvantages:

• Net present value • Internal rate of return • Benefit-cost ratio.

Because there is usually insufficient capital to invest in all profitable alternatives on the farm, one or more must be selected from those available. Alternatives need to be ranked by the three main criteria, but they might give different results. Cut-offs, in terms of whether a particular investment is accepted or rejected, are the same for all criteria. But the acceptable investment alternatives could be ranked differently. It is desirable to use all three measures, and most available software will generate all three. It is useful for an R&D provider to have in-house expertise on these matters and access to texts such as Gittinger (1982) and Sinden and Thampapillai (1995). Each of these criteria is now defined and its merits briefly discussed.


Net present value (NPV) The net present value (NPV) criterion is equal to the present value of benefits minus the present value of costs. The present value of a future outcome is:

PV = Σ (Xt × WTt)

where: PV is the present value Xt is a cash inflow received or cash outflow paid in time t WTt is the weight for time period t (where t is normally taken to be a year for a long-term

investment) Σ is the summation sign.

Alternatively, it can be defined as the sum of Xt × DFt, where DFt is the discount factor for time t. Note that the NPV can be calculated directly using Excel. Click on the ‘Insert Function’ icon, and select ‘NPV’ from the ‘Financial’ category. You will be asked first to enter the discount rate you wish to use. Ensure you enter it in decimal form. For example, 6 per cent would be entered as 0.06. You will then be asked to enter ‘Values’, which is an array of numbers representing the net cash flow (cash inflow minus cash outflow) for each period (cell references are normally entered for this purpose). While this is a convenient and quick way to obtain the answer, it pays to do the calculation manually in terms of understanding how the NPV is calculated. In general, the NPV criterion is the preferred measure to use because it is mathematically the soundest measure and is easy to understand once cash inflows and outflows are expressed in present-day terms. But there are circumstances when it is inferior to other criteria. In particular, it is a less convenient method to use when the farmer has to decide between alternative farm investments and the investor has a fixed budget. Consider a situation where the capital available to spend on R&D is scarce. The NPV is not a useful measure for comparing projects of different sizes because bigger projects tend to have higher NPVs than smaller ones. Internal rate of return (IRR) The internal rate of return (IRR) is the discount rate at which the present value of benefits equals the present value of costs. It can also be calculated directly using Excel. Click on the ‘Insert Function’ icon, and select ‘IRR’ from the ‘Financial’ category. You will be asked to enter ‘Values’, which is an array of numbers or reference to cell numbers containing the data for which you want to calculate the IRR. You are also asked to nominate an IRR that is close to the estimate you expect. Note the relationship between the NPV and IRR, shown in Figure 10.1. The IRR is the rate that applies when the NPV equals 0. At point A, NPVa is considerably greater than zero, and so the IRR is clearly going to be greater than the discount rate ia. At point B, NPVb is lower but still greater than zero, and so the IRR will also be greater than the discount rate ib. At point D, NPVd has declined to a negative value, which means that the IRR must be higher than id. The NPV is exactly equal to zero at point C and so the IRR has now been identified as ic. Figure 10.1 The relationship between the internal rate of return and net present value. Source: Sinden and Thampapillai (1995).


0

Netpresent value

($)

Rate of discount (i)

Cic

Internal rate of return

NPVa

NPVd

NPVb

_

A

B

D

ia ib id

+

The IRR is a useful and widely applied method that is readily understood by farmers as a rate of return on investment. But two arguments against it concern problems with its calculation for particular streams of cash flow. First, it can provide misleading results under some configurations of benefits and costs in that there might be more than one internal rate of return for an investment alternative, particularly with unconventional cash flows. Second, it can be unstable at high rates of return, leading to incorrect investment decisions. Also, it will not yield an estimate if there is no period with a negative cash flow. However, the IRR does allow comparison of projects of different size. It is often said that it also has the advantage of avoiding the need to specify a discount rate, which is true in terms of the calculation. But a discount rate is still needed to compare with the estimated IRR for the purpose of making a decision about whether an investment should be undertaken. Benefit-cost ratio (BCR) The benefit-cost ratio (BCR) is the ratio of the present value of benefits to the present value of costs. In Figure 10.1, the BCR will be greater than 1 for NPVa and NPVb, and less than one for NPVd. It will be exactly equal to one when NPV is equal to zero and the IRR is ic. Like the IRR it is easy to understand, and it is also easy to estimate. It is a more reliable criterion to maximise net returns when the farmer has a fixed capital budget and is deciding between investments in projects of different sizes. Its major disadvantage is that it can sometimes provide incorrect decisions in the comparison of mutually exclusive investments.

10.5 Identifying inflows and outflows for an investment in

the sheep enterprise Changes in outputs and inputs The outputs derived from an investment in a sheep enterprise are measured as the changes in total outputs on the farm brought about by the investment. These changes should be recorded for the length of the investment period. The inputs used in an investment in a sheep enterprise are measured as the changes in total inputs on the farm brought about by the investment. These changes should also be recorded for the length of the investment period. In measuring changes in both outputs and inputs, a common error is to confuse the ‘without’ situation with no change from the present. There are usually influences causing changes in inputs and outputs exogenous to the investment being analysed that need to be incorporated in the ‘without’ situation. Consider the example of a soil conservation project aimed at preventing any further degradation so that output remains unchanged. If you simply took output as constant and included the project costs incurred, the project may appear to be economically undesirable. But the economic evaluation might look quite different once you properly include the decline in output from degradation in the ‘without’ situation.


Pricing outputs and inputs The private cost of a good or service used as an input in an investment in a sheep enterprise reflects the willingness to pay by the farmer. Similarly, the private benefit of an output produced in a sheep enterprise reflects the willingness of the buyer to pay for the farmer’s product. These private costs and benefits are typically market prices for use in a DCF analysis. It is reasonably assumed that individual producers in aggregate face a perfectly elastic demand curve for their outputs and perfectly elastic supply curve for their inputs (see Topic 8). This means that they are price takers: their input and output prices will not alter regardless of how much output they sell and how many inputs they buy. Exclusion of sunk costs Sunk costs are those costs that have already been incurred, and cannot be avoided or changed. When making a resource allocation decision, these costs should be excluded from the analysis. Unpriced outcomes When considering whether an investment in the sheep enterprise is worthwhile, it is often important to take into account any significant unpriced outcomes. Such outcomes, which could be either positive or negative, are those that do not have a market price but which affect the farmer’s welfare. They should be included in the analysis of an investment decision. Various methods exist that could be used to make these valuations, but you are not required to know them in this unit.

10.6 Incorporating risk in DCF analysis Not all farm investments have the same level of certainty of outcome, and many farmers are risk-averse. So it is advisable for a farmer to take into account any risks associated with these investments. Long-term investments on the farm are particularly prone to uncertain outcomes. Managing risk on sheep farms is quite a complex undertaking that is not dealt with in this topic. The recommended approach is covered in detail in Topic 11, and is also pertinent to managing risky farm investments.

10.7 Valuing livestock The comparative economic value of flock and stud rams can be calculated using selection index theory in combination with other algebraic techniques, including discounting. Cottle (1986) calculated that if flock rams are used for three years, then compared to the price of a ram with average figures, a general guideline (using 1986 financial values) was: 1 micron finer = $64; 10% GWP = $88; 10% BWP = $82 For stud rams the relative value of each ram sired by the purchased ram was: 1 micron finer: $24; 10% GWP = $33; 10% BWP = $31 where GWP = greasy wool percentage and BWP = bodyweight percentage For example, a flock ram with figures of 104% GWP, 111% BWP and -1 micron would be worth about $190 more than the price of an average ram from the stud. Introduction An estimated breeding value (EBV) for an animal is the estimate of that animal's genetic worth for a particular trait or index of traits. EBVs can be expressed in physical units (for example, kilograms of greasy fleece weight) or as deviations from a flock mean (for example, -2 microns fibre diameter). NSW Merino studs offering sale rams with objective measurement data in their sale catalogues provide a mixture of information. The figures on rams that were most often given were GWP (greasy fleece weight expressed as a percentage, with the stud's measured average given the value of l00% in the 1990s), FD (fibre diameter expressed as a deviation from the stud's measured


average micron) and BWP (hogget bodyweight expressed as a percentage, with the stud's measured average given the value of 100%). EBVs (in 1987) of a ram could be calculated as: EBV = (13.4 x (GWP – l00)/ 100) + (12.5 x (BWP – l00)/ 100) - (1.0 x FD) (1) Or EBV = ($8.71 x GGFW) + ($0.50 x GHBW) - ($2.40 x GFD) (2) where GGFW, GHBW and GFD are the estimated genetic values of the ram for greasy fleece weight, hogget bodyweight and fibre diameter respectively. Thus an animal with one extra unit of the index or EBV will return $1 extra revenue from its lifetime performance. The economic values (lifetime returns) are based on a flock with four age groups, which results in 5.85 shearings per animal lifetime, with wool returns discounted relative to the time the animal is 1.5 years of age. Methods Direct returns The use of a ram with an EBV of +1 will result in progeny with an EBV of +0.5, if he is mated to a random sample of ewes from the flock. Thus every sheep sired by the ram would be expected to return an extra 50c which is received when the animal is 1½ years of age but is accrued during its lifetime. Table 10.1 shows the present value of 50 cents earned in 2 to 8 years time and is the increased value of each additional sheep sired by a ram with an EBV of +1, compared to progeny from a ram with the flock's average figures. Table 10.1 Present value of a future cash flow of 50 cents discounted at 10% per annum. Source: Cottle and Fleming, authors’ example. Years From Now Present Value of Future 50c

2 3 4 5 6 7 8 41.3 37.6 34.2 31.0 28.2 25.7 23.3

If the producer mates the ram to 50 ewes each year for four years and gets a 78% marking (39 lambs) then the value of the 1 unit in the ram's EBV is:

39 x (41.3 + 37.6 + 34.2 + 31.0) cents = $56.20.

Table 10.2 shows the value of this premium if the ram is used for one to four years. Table 10.2 Relative value of one unit of EBV of a ram used for one to four years. Direct returns on offspring. Source: Cottle and Fleming, authors’ example. Years of Use of Ram Relative Present Value (=$)

1 2 3 4 16.11 30.77 44.11 56.20

Flock rams - indirect returns The values shown in Table 10.2 only show the increased returns from sheep sired by the ram. They do not take into account the fact that progeny from the progeny the ram has sired will be superior. If these progeny are retained for breeding purposes there will be further indirect effects, which will be further diluted, i.e. a 'line' of progeny is produced. If it is assumed that the ram bought is a flock ram and only female progeny are used as breeders then it is possible to calculate the discounted economic value of these accumulated indirect effects, as well as the direct returns for offspring. James (1980) developed an expression for the value of a purchased sire using matrix algebra. If returns are realised at an age Y in both sexes, each unit of breeding value in the sire is worth:


(rY+1 JP / 2) (1 - rtWt / 1 - rW) (3) where t = time from the sire's initial use (years) W = survival rate of rams (fraction per year) r = 1 / (1 + d) (the discount factor); d = discount rate (fraction) P = number of progeny produced by each ram J = matrix of genetic contribution of the sire (total / direct). Note the change in notation for the discount rate and discount factor, to be consistent with the reference from which it is taken, namely James (1980). If it is assumed that P = 39, d = 0.1, Y = 1, W = 0.95 and ewes are bred for four years, then (3) has the values shown in Table 10.3. Table 10.3 Relative value of one unit of EBV of a ram: Returns from all future offspring related to the ram. Source: Cottle, (1986). Years of Use of Ram Relative Present Value (=$)

1 2 3 4 25.14 46.84 65.59 81.77

Stud rams The values in Table 10.3 only show the increased returns from sheep bred from ewes related to the ram or directly from the ram. If the ram is a stud ram then future returns may also be gained from rams bred from this ram. Rams bred immediately from the purchased ram receive half of their genes from the ram and start producing their returns two years later. Therefore, each unit of breeding value of the purchased sire realised from his sons born in the first year of his use is worth: (rY+3JP / 4)(1 - rtWt) / (l - rW) (4) A similar approach could be used to evaluate rams bred in the future, more distantly related to the purchased ram. For example rams born 2.5 years in the future from the purchased ram's ewe offspring would increase the breeding value of the purchased sire by (rY+5JP / 8) (1 - rtWt) / (l - rW). All possible combinations cannot be considered here. If the previous assumptions are used then (4) has the values shown in Table 10.4. If the ram is used to breed some rams for the flock the value of an EBV of +I, if all rams are used for a set number of years, is approximated by averaging the appropriate values in Table 10.4. The value of each bred ram is shown in Table 10.5. Table 10.4 Relative value of one unit of EBV of a stud ram: Returns from each son of the ram. Source: Cottle, (1986).

Table 10.5 Relative value of each ram bred from stud rams with one unit of EBV. Source: Cottle, (1986). Years of Use of all Rams Relative Present Value (=$)

1 2 3 4

10.38 18.46 24.70 29.44

Year of Use of the Purchased Ram

First Second Third Fourth

Years of Use of His Sons

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

Relative Present Value ($)

10.38 19.34 27.09 33.77 9.44 17.58 24.62 30.70 8.58 15.99 22.39 27.92 7.80 14.53 20.35 25.37


The figures shown in Tables 10.3 and 10.5 relate to the predicted increased returns from using superior rams. They obviously cannot take into account the sociology and publicity purposes of ram purchases. If the rams are used in an A.I. programme then P increases dramatically and hence the relative values also increase. For the commercial ram purchaser, however, the values in Tables 10.3 and 10.5 provide an interesting yardstick in determining the price or auction value of rams. Assume the value of a ram that has average figures (i.e. 100% GWP, 100% BWP 0 micron) is given as $150. What are the predicted extra returns to be gained, and hence theoretical price premium, for the following three rams (1984 'Avenel' ram sale)? Ram 1 104% GWP, -I FD, 111% BWP Ram 2 117% GWP, -2 FD, 109% BWP Ram 3 112% GWP, +1 FD, 127% BWP Using (1): EBV(Ram 1) = (13.4 x .04 + 0.11 x 12.5 + 1 x 1) = 2.9 EBV(Ram 2) = (13.4 x 0.17 + .09 x 12.5 + 2 x I) = 5.4 EBV(Ram 2) = (13.4 x 0.12+ 0.27 x 12.5 -1 x 1) = 4.0 Assume that all rams are kept for three years. If the three rams are flock rams the predicted extra returns from the rams are: Ram 1 = 2.9 x 65.59 = $190 Ram 2 = 5.4 x 65.59 = $354 Ram 3 = 4.0 x 65.69 = $262 Thus the rams should be valued at $340, $504 and $412 respectively. They were actually sold for $375, $350 and $850, respectively, which suggests a poor relationship between the objectively measured figures and price in this case. If these rams were used to breed rams, each ram offspring would increase returns due to their genetic relationship with the purchased ram by $72, $133 and $99 for Rams 1, 2 and 3 respectively. The above calculations show a specific example of how the objective value of rams could be assessed. As an extension guideline, using the assumptions given in this paper, the value of rams can be summarised as follows: If flock rams are used for three years, then: 10% GWP = $88 10% BWP = $82 1 micron finer = $64 If kept for four years, then: 10% GWP = $110 10% BWP = $102 1 micron finer = $80 Some of the more important assumptions made by Cottle (1986) are that the net return from wool is $21 kg greasy wool, the clean price differential for fibre diameter is 16 cents/micron category, the average GFW is 6 kg and average HBW is 50 kg. If stud rams and flock rams are used for 3 years then the value of each ram sired by the purchased ram is: 10% GWP = $33 10% BWP = $31 1 micron finer = $24 At the 1984 'Avenel' auction the top-priced ram was bought for $2,200. This ram had figures of 125% GWP, -2 FD, 120% BWP. By the above calculations the ram's EBV was 7.85, thus his flock ram value was approximately $150 + $515 = $665. The ram would need to sire 8 rams kept for breeding to pay his way. This is possible and hence his price was not necessarily extravagant.

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For a ram to be worth $10,000 the average wool cut of the stud would need to be extremely high and/or a large number of rams would need to be bred from the sire. For example if the top-priced ram mentioned above came from a stud with an average GFW of 7kg, the ram's EBV would be 8.4, his flock ram value would be approximately $200 + (8.4 x 65.5) = $752, and he would need to sire 45 rams (i.e. 12 every year) that were used for breeding. This assumes the bred rams are not sold but used to increase production. The guidelines presented here allow any ram breeders, e.g. studs and group breeding schemes, to place an economic value on any ram based on his objective measurements. This should promote a more financially equitable distribution of genetic material. Wade and Goddard extended the above analysis in 1994. A discounting approach can also be used to compare the value of cast for age ewes against cull hoggets (see Cottle 1993).

ANPR350/450 – Sheep Management _________________________________________ 10-11 ©2009 The Australian Wool Education Trust licensee for educational activities University of New England

10.8 Disease outbreaks To estimate the expected value of losses from a disease outbreak, a probability distribution of disease outbreaks occurring over the relevant planning period has to be estimated (Malcolm 2003, see http://www.agrifood.info/perspectives/2003/Malcolm.html). Then the estimated cost of the outbreak is multiplied by the probability of it occurring during this time. If the planning horizon is 20 years, and the disease event which is concluded within one year is considered to have an equal probability of occurring in any of those 20 years, and if it were to occur once it could not occur again, then the probability of the event occurring in any single year would be 1/20. The expected value of the distribution of disease outbreak possibilities would be the discounted cost of the outbreak if it were to occur in each of the years multiplied by the probability of it occurring in the year. Suppose the loss were to occur in year i with an economic cost li. with an annual discount rate r and a probability pi of occurrence and having occurred there is no further loss, then the expected present value of the loss E(L) is: E(L) = SUMi=1 to ¥ pi [li / (1 + r)i] equation 1

Equation 1 can be re-written as:

E(L) = SUMi=1 to ¥ [pi / (1 + r)i] li equation 2 The term [pi / (1 + r)i] in equation 2 is a ‘discounted probability', denoted by pi

*. The same numerical result for E(L) is obtained using either equation 1 or equation 2. When the loss li is constant no matter when the event occurs then: E(L) = SUMi=1 to ¥ pi

* li = l SUMi=1 to ¥ pi* = l p* E(L) = SUMi=1 to ¥ pi

* li = l SUMi=1 to ¥ pi* = l p*

Where the total discounted probability is: Where, the total discounted probability is:

p* = SUMi=1 to ¥ [pi / (1 + r)i] < 1.0 p* = SUMi=1 to ¥[pi/(1 + r)i] < 1.0

Notice that SUM pI = 1.0 but SUM ¥ pI* < 1.0. Notice that SUM pI = 1.0 but SUM ¥ pI

* < 1.0. One can interpret p* as follows. In terms of expected discounted loss an event with a probability distribution (pI ) is equivalent to an event which happens at the present with probability p* or not at all. Combining the discounting formula (PV = $Cost / ((1 + discount rate) / 100) x the number of years), and the formula for the probability of the random event, the algebra reduces to: 100 / ((number of years x discount rate) + 100). For instance, when number of years is 10, and discount rate is 4 per cent , the solution is 100/140 = 0.714. When number of years is 20 and discount rate is 5 per cent, the solution is 100/200 = 0.5. The interpretation is that in considering the discounted cost of a one in 20 year disease outbreak discounted at 5 per cent, we can equivalently consider the event to occur in the coming year with a probability of 0.5 or not at all. The discounted probability of the event occurring is 0.5. This figure is multiplied by the cost that it has been estimated will be incurred when the disease outbreak does occur.

10.9 Net present value of R&D Procedures for BCA can be broken down into a number of steps representing components for typical agricultural R&D evaluation. The following is a typical set of seven steps: Step 1 Identify and describe best estimate or estimates of outcomes from the R&D and the ‘without scenario’. The starting point of these analyses is to identify what is the difference, with and without the R&D being conducted. This can be difficult and may require some training or support from an experienced analyst able to probe and ask the right questions. As mentioned above, one common


error is to confuse the ‘without’ situation with no change from the present. There usually are influences which will be causing changes in productivity and product quality irrespective of the R&D being evaluated. These must be represented in the ‘without’ situation. Representation of more than one plausible outcome of the R&D investment is often appropriate for dealing with uncertainty of future outcomes. A probability needs to be estimated for each outcome. The simplest example of this is two outcomes, success and failure. However, more outcomes can be specified. For example, it may be specified that an agronomic project has a 0.3 probability of achieving a 20% increase in yield, a 0.5 probability of achieving a 10% increase in yield, with failure having a probability of 0.2. Step 2 Estimation of net benefits per unit for each industry outcome. The unit in this case could be a hectare, an animal, a farm, etc. In the case of the above example it would be a simple gross margin of the yield increase; in other cases a more sophisticated analysis may be required. Step 3 Calculate potential benefits. This is done by scaling up from the benefit per unit to whole industry which is potentially affected. Frequently units are not homogeneous. It is then necessary to represent more than one kind of unit (e.g. different kinds of farms or different types of soil) and scale up each by multiplying by the number of units each represents. Step 4 Account for the probability of realising each outcome. Where more than one outcome is specified, weight the benefits of each outcome by multiplying by the probability of success of the outcome. Step 5 Account for adoption. Specify parameters for adoption over time. Accounting for adoption in the calculation converts potential benefits in each year to estimates of actual benefit. Step 6 Account for R&D costs. Enter R&D costs for each year. Step 7 Convert dollars of different years to a common value. Discount all benefits and costs, bringing them to the present year’s value. The discount rate is included in calculations to represent the differences of value of dollars in one year versus the next. It is not simply a case of allowing for inflation, but representing the opportunity costs.

10.10 Valuing environmental change (ANPR450 students) Public policy on environmental and sustainability issues deserves detailed and formal analysis – because the issues are more complex, there is uncertainty about the costs and outcomes, the decisions may be unrepeatable and irreversible and the decisions involve larger groups of people – including people outside the direct and immediate realms of the policy, such as future generations. In addition to the points already covered, formal BCA of public expenditures, for environmental and sustainability or any other purposes, has the further advantage of making the process transparent. That gives all stakeholders an opportunity to scrutinise the analysis and to provide feedback on the assumptions made and the issues considered.

One common information gap with BCA is a lack of data on the incremental impacts of programs. BCA practitioners are often presented with pre-determined policy packages and asked to compare “this program package and its costs” against “that environmental outcome and its benefits”. In reality, what environmental programs can offer is an increased chance or probability of outcomes and benefits. In cases where programs are divisible beyond some threshold, the environmental policy task is to determine not just what program but also how much of each program. Data on incremental program benefits and costs are needed for that dual policy task.


In the absence of binding financial constraints, investment in a conservation program should continue increasing up to the point that the incremental gain in benefits just equals the incremental increase in costs. Prior to that level of expenditure, the community will not achieve its maximum environmental benefits for its program expenditure. This rule applies to individuals and the community and to all forms of expenditure.

Judgments about environmental programs cannot ultimately be made without considering the benefits and costs of other forms of expenditure. In that regard environmental policies face a timing problem in contrast to, say, social security expenditures where cost and benefit flows often coincide. But an environmental program, such as land retirement for biodiversity objectives, will typically require cost outlays up front while its benefits may not happen for a considerable time later. To compare programs with different impact time paths, it is necessary to use discounting.

Table 10.6 The Tyranny of Discounting.

Discount Rate

(% pa)

Years to Receiving Single $100 Payment

1 10 20 30 40 50

Net Present Value of Benefit ($)

1 99 91 82 74 67 61

5 95 61 38 23 14 9

10 91 39 15 6 2 1

Table 10.6 shows the discounted net present value of a single $100 payment received at the end of the period of years. At a real discount rate of 5%, the NPV of the distant benefit dwindles quite a lot. Differences in discount rates can cause project outcomes to switch from showing net benefits to net costs in present value terms.

Social or community discount rates are usually lower than the rates applicable to individuals. The community as a whole can afford to take more risks and to wait longer than an individual for benefits. As a result, governments will tend to place less weight on current benefits and cost outlays and relatively more weight on future benefits than would most individuals. However, governments can manage economic policies to maximise their chances of re-election. In doing so, they are responding to the shorter time horizons and higher discount rates of the voters who elect them. People may be greedy and place relatively little weight on the impacts of their choices upon other people or future generations.

In a democracy with efficient product, capital and political markets, the opportunity cost of money to government and the community would be indicated by government bond rates. Reflecting this, the Victorian Department of Treasury and Finance advises government agencies to use the Treasury Corporation of Victoria (TCV) fixed interest stock yield as the rate for discounting purposes (http://www.tcv.vic.gov.au/page/Market_Activity/Interest_Rates/Current_Interest_Rates/). The ten-year rate was quoted at a nominal rate of 4.85% per year for December 2011. Assuming an underlying annual rate of inflation net of GST effects of around 2%, the TCV rate is roughly equivalent to a real rate of 2.85%. Government Bond rates are generally lower than the spectrum of market interest rates available to other borrowers.

Reflecting the interest rate differentials and other factors, the private discount rates applied by individuals, such as landowners, are likely to be higher than the social discount rate applicable to Australia as a whole. And individual landowners under financial pressure would evaluate alternative cost and income streams at even higher discount rates than their more fortunate colleagues. For financially pressed landowners the opportunity costs of achieving an income gain or avoiding a cost in the short run would, in some cases, include the chance of bankruptcy and all the associated financial and personal costs.

Clearly, differences about the discount rates applied by individuals and the community can be a source of conflict in resolving environmental policy issues and matters related to sustainable


production. For that reason, there may be advantages in bid systems for determining any payments to landowners for participating in initiatives such as land retirement programs. A bid system should, at least implicitly, reflect the private discount rates of landowners through the payments they are prepared to accept, for example, for altering their land management practices. In that way, the ultimate policy outcomes would be more likely to reflect both the discount rates and time preferences of the community as well as individual landowners affected by the policy.

Spillovers or externalities Pollution, loss of biodiversity due to overgrazing and damage to roadsides due to salinity caused by excessive irrigation are examples of negative externalities. In the case of rural industries such as wool, R&D and generic promotion are both likely to generate positive externalities. A beekeeper’s bees also generate positive externalities by pollinating nearby crops.

Figure 10.2 illustrates the case of a negative externality. The figure shows the market demand curve for the product causing the externality – let’s say it is wool produced by sheep grazing on sensitive country.

By definition, the demand curve shows the value to consumers of each last unit of the item produced and so measures the per unit marginal or incremental community-wide benefits from consuming or using that wool.

Figure 10.2 The case of negative externalities.

There are two supply curves. The standard aggregate industry supply curve is labelled “Supply = MPC”, where MPC stands for marginal private costs. Again, by definition at each level of production this supply curve shows the per unit marginal costs of the activity that accrue to the firms or individuals carrying on that production activity. Now assume that sheep grazing on sensitive country contributes to a loss of biodiversity, which represents a negative externality attributable to the grazing activity. The private costs shown by the Supply = MPC function exclude the costs to the community of this loss of biodiversity.

So from the community-wide perspective the marginal or incremental costs of the activity from this grazing are higher than the private costs and are shown by the function “Supply = MSC” where MSC stands for marginal social costs.

Left to the market, a quantity of Q0 will be produced at a price of P0. But the community optimum taking account of the externality – or the true costs to the community – is where output is Q1 produced at a price of P1. So the consequence of externalities is that either too much – negative spillovers – or too little – positive externalities – of the particular product or service is produced.

Figure 10.3 illustrates the case of a negative externality after the imposition of a tax. The negative externality could be environmental pollution due to greenhouse gas emissions, it could be environmental damage from grazing sheep on sensitive country, or the discharge of excess fertiliser onto neighbouring land, or then again it could be damage to roadsides arising from salinity caused by excessive irrigation.

Supply = MSC

Supply = MPC

Demand = MSB

Price

QuantityQ1

P0

Q0

P1

00


Figure 10.3 Externalities and a pollution tax.

As before, in the absence of any intervention by government, a quantity of Q0 will be produced at a price of P0 and the community optimum taking account of the externality is where output is Q1 produced at a price of P1. But now the government has imposed a “pollution” tax so as to bring marginal private costs up to the level of marginal social costs. The level of the tax is given by P1 – P2. A tax of that amount forces the external costs of the pollution onto the polluter so that the firm’s production decisions with the tax imposed do accurately reflect the full costs of the activity –both the private costs and the social costs of the externality. The result is that a new market equilibrium is established at an output of Q1 produced at P1.

What are the effects of this tax?

First of all, the results of this negative externality are:

• Production of the externality-causing activity is too high. • Too much external damage – loss of biodiversity or whatever – occurs. • The price of the externality-causing product is too low. • There is no incentive to reduce the external damage. • Recycling or reuse of the polluting or damaging substances – greenhouse gasses with

electricity generation – is discouraged because their release into the environment is too cheap.

Demand curves show willingness to pay or value to consumers and supply curves show incremental production costs and revenue or value equals price times quantity. Thus it is possible to put monetary values on the impacts listed above and so to determine the distribution of the gains and losses due to the imposition of the pollution tax. Two definitions of “economic surplus” are required:

• Consumer surplus is the difference between the aggregate amount that a consumer would be willing to pay for some given quantity of a product or service and the amount the consumer actually pays;

• Producer surplus is the difference between a producer’s total revenue for some amount of output and the incremental costs of producing that output.

Both of these measures of economic surplus can be viewed as “icing on the cake” of consumption and production. Consumer surplus arises from the fact that people generally place a relatively high value on consuming the first unit of something and then progressively reduce their valuation of additional units of consumption. This result is known as the diminishing marginal or incremental utility of consumption.

In terms of Figure 10.3, the valuation P1 on Q1 units of consumption is greater than the value of P0 on the greater quantity Q0. However, without any pollution tax, everybody in the market can buy Q0

Supply = MSC

Supply = MPC

Demand = MSB

Price

Quantity

A B

C D

E

Q1

P0

Q0

P2

P5

00

x

y

z

P4

P3

P1


at P0. So the consumer surplus is given by the area P3yP0 which in mathematical terms equals ((P3 – P0)*Q0)/2.

The definition of producer surplus follows along similar lines but is based on the notion that after some point, the unit costs of production increase incrementally. Again in terms of Figure 10.3, and working on the curve labelled Supply=MPC – at P2 for example, the unit cost of producing Q1 units is less than P0 the per unit cost of producing the larger quantity of Q0. However, producers are paid P0 for all the units of output making up the total quantity Q0 including Q1. So their producers surplus is given by the area P5P0y and the total value is given mathematically as ((P0 – P5)*Q0)/2.

In terms of the various shaded and labelled areas in Figure 10.3, the welfare gains (+) and losses (–) to the various groups involved are:

Consumer surplus: – A – B

Producer surplus: – C – D

Government tax revenue: + A + C

Net pollution reduction: + B + D + E

Net community gain: + E

The net community gain is the straightforward result of the community not consuming any units of the product where marginal social costs exceed the marginal social benefits at production levels beyond Q1.

The Commonwealth Government’s current excise tax on petrol is criticised for contributing to the high cost of fuel. However it can be viewed as a tax on carbon emissions such as might be designed explicitly for ameliorating greenhouse gas emissions. It may have been designed to raise revenue but its effect is to encourage people to buy smaller cars and use less petrol. That does not mean the excise tax is set at the optimal level in terms of a greenhouse gas pollution tax.

A government could also achieve the same reduction in the pollution/externality by setting appropriate industry standards. A standard that limited the cost of the externality to P1 – P2 would also reduce output to the socially desirable level Q1 with the following distributional consequences:

Consumer surplus: – A – B

Producer surplus: + A – D

Government tax revenue: + 0

Net pollution reduction: + B + D + E

Net Community gain: + E

With a regulated standard, the community gain is as before, but producers do better.

In effect, producers end up with some of the revenue that under a tax would otherwise have accrued to government. Thus polluting industries prefer to be regulated via standards rather than through the imposition of taxes. If the pollution can be managed through some form of pollution abatement equipment, then a Pigovian tax (named after economist Arthur Pigou who developed the concept of economic externalities) and the standard should be imposed directly on the pollution rather than the production activity that causes it.

Optimal externality The source of externality or the externality itself should not be banned but managed. Without proper management, wool scouring causes some environmental pollution. But a ban on scouring would mean no wool industry.

Figure 10.4 shows the marginal or incremental damage increasing as the amount of pollution increases. The pollution in this case may be pollution of a local creek due to the drift of a chemical spray that has been used on a nearby crop. Very small amounts of the pollution will be diluted by the volume of water in the creek so the environment effectively “absorbs” the pollution. But the story will be very different if a whole drum or a truckload of the chemical spills into the creek.

The figure also shows the marginal or incremental costs of controlling the pollution. The control costs increase as the amount of pollution is reduced. The control costs are highest when all the pollution has been eliminated – that is, when pollution = 0.


The economically efficient solution is where the marginal control cost just equals the marginal damage cost (full cost) at a cost of P0 and pollution of Q0. It is not efficient to accept more pollution than Q0 – positions to the right of Q – because there the control costs are less than the marginal damage costs. To the right of Q0 it pays to increase the control effort. And to the left of Q0 the marginal control cost is greater than the marginal damage cost, so it is not worth preventing pollution less than Q0.

Figure 10.4 The economically optimum externality. Source: Tietenberg (1988).

In general it is not economic to avoid pollution or land-degrading activities completely. Nevertheless, sometimes the optimal level of pollution may be zero, for example nuclear wastes near densely populated areas. Furthermore, the optimal levels of pollution from any given activity will vary from place to place if there are site-specific differences in the control and damage costs.

This is not a recipe for being reckless in the face of uncertainty about the future. Recognition of that has led to the acceptance of the precautionary principle, which states that:

Where there are threats of serious or irreversible environmental damage, lack of full scientific certainty should not be used as a reason for postponing measures to prevent environmental degradation. (Industry Commission, 1998, p.61)

How serious the threat must be or how serious the potential damage must be are matters of judgment. But the Industry Commission (Industry Commission, 1998 p 62) pointed out:

…the precautionary principle clearly shifts the burden of proof associated with development projects. The proponent of the development in question must prove that harm will not occur rather than the opponent prove that it will. Has that principle been applied to fracking coal seam gas and water quality?

The Industry Commission goes on to indicate that the preceding quote does not mean:

…all developments with uncertain ecological impacts should not proceed as that would be to forego benefits for current and future generations without justification. But it does mean that all options need to be explored when considering a significant irreversible action of unpredictable future consequences. Further, such action should only be undertaken when large social costs would otherwise be incurred by the current generation. (Industry Commission, 1998 p. 62)

Marginal Cost $

Quantity of PollutionQ0

P0

Marginal Conrtol Cost

MarginalDamage

Cost

Total Damage Cost

Total Control Cost

Increasing Control Increasing Pollution


Readings

1. Cottle, D. 1993, ‘Is it best to purchase cast-for-age ewes or cull maidens?’, Wool Technology and Sheep Breeding, vol 41(2), pp 91-98.

2. Davis, G.P. and DeNise, S.K. 1998, ‘The impact of genetic markers on selection’, Journal of Animal Science, vol 76, pp 2331–2339.

3. Malcolm, B., 2003. 'What price animal health - and whose problem is it anyway?' Agribusiness Perspective Papers, 2003. Paper 59. ISSN 1442-6951. Retrieved May 20th, 2007 from http://www.agrifood.info/perspectives/2003/Malcolm.html.

4. Nitter, G., Graser, H.U. and Barwick, S.A. 1994, ‘Evaluation of advanced industry breeding schemes for Australian beef cattle. I. Method of evaluation and analysis for an example population structure’, Australian Journal of Agricultural Research vol 45(8), pp 1641-1656.

5. Trapnell, L.N., Ridley, A.M., Christy, B.P. and White, R.E. 2006, ‘Sustainable grazing systems: economic and financial implications of adopting different grazing systems in north-eastern Victoria’, Australian Journal of Experimental Agriculture vol 46, pp 981-992.

6. Sinden, J.A. and Thampapillai, D.J. 1995, Introduction to Benefit-Cost Analysis, Longman, Melbourne, Ch. 7.

7. Wade, C. and Goddard, M. 1994, ‘How much is a genetically superior ram worth?’ Australian Journal of Agricultural Research, vol 45, pp 403-413.

Summary This topic provides an overview of the use of technique of discounted cash flow analysis for making investment decisions in sheep enterprises and carrying out benefit-cost analyses. Components include valuing livestock, disease outbreaks and investment in R&D References

Bird, P.J.W.N. and Mitchell, G. 1980, ‘The choice of discount rate in animal breeding investment appraisal’, Animal Breeding Abstracts, vol 48(8), pp 499-505.

Brascamp, E.W. 1978, Methods on economic optimization of animal breeding plans. Rapport B-134, University Wageningen.

Cottle, D.J., 1986. 'How much is a superior ram worth?' Wool Technology and Sheep Breeding, vol 34, pp 110-112.

Cottle, D.J., 1993. 'Is it best to purchase cast-for-age ewes or cull maidens?', Wool Technology and Sheep Breeding, vol 41(2), pp 91-98.

Dekkers, J.C.M. and Shook, G.E. 1990, ‘Economic evaluation of alternative breeding programs for commercial artificial insemination firms’, Journal of Dairy Science, vol 73, pp 1902-1919.

Gittinger, J.P. 1982, Economic Analysis of Agricultural Projects, 2nd Edition, Johns Hopkins University Press, Baltimore.

Hill, W.G. 1971, ‘Investment appraisal for national breeding programmes’, Animal Production, Vol 13, pp 37-49.

Hill, W.G. 1974, ‘Prediction and evaluation of response to selection with overlapping generations’, Animal Production, vol 18, pp 117-139.

Industry Commission (1998) A Full Repairing Lease: Inquiry into Ecologically Sustainable Development, 27 January, Report No. 60 Industry Commission.

James, J.W. 1980, ‘The analysis of sire buying policies’, Annales de Genetique et de Selection Animale, vol 12, pp 33-47.


Kinghorn, B.P. 1993, ‘Deterministic versus stochastic approaches to evaluating the design of livestock breeding programs’, In Design of Livestock Breeding Programs, (eds D. Fewson, J.W. James and G. Nitter).

Kinghorn, B.P., Barwick, S.A. Graser, H.-U. and Savicky, J., Animal Genetics and Breeding Unit, University of New England, Armidale, pp. 111-125.

Malcolm, B., 2003. 'What price animal health - and whose problem is it anyway?' Agribusiness Perspective Papers, 2003. Paper 59. ISSN 1442-6951. Retrieved May 20th, 2007 from http://www.agrifood.info/perspectives/2003/Malcolm.html.

Morley, F.H.W. 1991, ‘The discounted value to commercial flocks of selected Merino rams’, Proceedings of the Ninth Conference, Australian Association of Animal Breeding and Genetics, Melbourne, pp. 327-330.

Sinden, J.A. and Thampapillai, D.J. 1995, Introduction to Benefit-Cost Analysis, Longman, Melbourne.

Tietenberg, T. (1988), Environmental and Natural Resource Economics, 2nd Ed, Scott, Foresman, Boston. Glossary of terms Annual equivalent return (AER) An indicator of the profitability of a project on an annual

basis; this indicator allows profitability of one system/technology to be compared with another

Benefit-cost analysis (BCA) A conceptual framework for the economic evaluation of projects and programs in the public sector, differing from a financial appraisal or evaluation in that it considers all gains (benefits) and losses (costs), regardless of to whom they accrue

Benefit-cost ratio The ratio of the present value of benefits to the present value of costs of an investment

Bond A long-term debt security Benefit transfer The transfer of estimated benefits from an original

source site to a new or target site. Capital Buildings, plant, equipment, livestock and

improvements that can be used to produce output that generates future stream of cash inflows.

Consumer surplus The difference between the aggregate amount that a consumer would be willing to pay for some given quantity of a product or service and the amount the consumer actually pays

Demand schedule (curve) A schedule or curve showing the quantity of a good that an individual consumer (individual demand curve) or consumers in aggregate (market demand curve) would buy at each price, holding other things constant.

Discount factor A number used to convert future cash flows to their equivalent current values

Discount rate The rate of compound interest at which future cash flows are adjusted to their equivalent current values

Discounted cash flow analysis Analysis of a set of alternative investments whose expected future cash flows have been discounted to their present values

Discounting The process of adjusting future cash flows to their equivalent present values using a stated discount rate


Equilibrium (Consumer) The position in which the consumer is maximising his or her wellbeing, that is, the consumer has chosen the bundle of goods and services which given the consumer’s preferences, income and market prices best satisfies the consumer’s wants.

Equilibrium (Producer/Firm) The position or level of output at which the firm maximises its profits subject to any constraints such as the state of technology; for competitive firms, equilibrium is where marginal cost equals marginal revenue equals market price.

Ex-ante or prospective analysis Evaluates a potential investment based on a number of assumptions of the likely level of inputs and outputs (and their values) that will occur as the investment proceeds.

Ex-post or historical analysis Occurs after the research investment has been completed. It analyses the investment after completion with respect to benefit and cost outcomes attributable to the investment.

Externality An effect of either consumption or production which is not taken into account by the consumer or producer because it is not reflected in the prices they pay but which influences the wellbeing or costs of other consumers or producers.

Inflation An increase in the general level of prices of goods and services

Internal rate of return The discount rate at which an investment has a net present value of zero (that is, the present value of benefits equals the present value of costs of an investment)

Investment The act of capital formation to secure a stream of cash inflows in the future

Investment criteria Measures of the economic worth of an investment such as net present value, benefit-cost ratio and internal rate of return

Law of supply and demand The analytical result that under perfect competition market price will move to a level at which the quantity that consumers wish to buy just equals the quantity that firms wish to produce, so that there is no excess demand or supply.

Long run A period or length of time over which all the factors of production become variable and the firm can choose its optimum level of production and technology.

Negative externality An unpriced outcome of production or consumption – that is an externality –that represents a cost to others.

Net present value The present value of benefits minus the present value of costs of an investment or project. The lump sum value of the project expressed as the sum of discounted annual net returns.

Opportunity cost of capital The revenue forgone by not investing capital in its next best alternative use

Negative externality An unpriced outcome of production or consumption – that is an externality – that represents a cost to others.

Present value of benefits (PVB) The discounted value of benefits Present value of costs (PVC) The discounted value of costs. Producer surplus The difference between a producer’s total revenue for


some amount of output and the incremental costs of producing that output.

Risk aversion Willingness to forgo some expected return for a reduction in risk.

Risk premium A measure of the combined effects of risk and risk aversion on the return required by an investor

Sheep enterprise The production of a particular sheep output, or group of related sheep outputs, for sale or domestic use

Sunk cost A cost already incurred before an investment decision is made

Short run The period in which at least some of the firm’s factors of production are fixed.

Supply schedule (curve) A schedule or curve showing the quantity of a good that an individual firm (individual supply curve) or firms in aggregate (market supply curve) would produce at each price, holding other things constant.

Time preference rate The rate reflecting the preference of an individual to consume now rather than have to wait until some time in the future

Willingness to pay (WTP) The amount an individual is willing to pay to acquire a good or service, often elicited from stated or revealed preference approaches.

Willingness to pay A measure of the benefit a consumer/user expects to get from purchasing a good or service.

10. discounted cash flow analysis

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