Allowing for differential timing in cost analyses: discounting and annualization

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1 HEALTH POLICY AND PLANNING; 17(1): Oxford University Press 2002 How to do (or not to do)... Allowing for differential timing in cost analyses: discounting and annualization DAMIAN WALKER AND LILANI KUMARANAYAKE Health Policy Unit, London School of Hygiene and Tropical Medicine, London, UK There are differences in timing related to when costs of certain inputs are incurred and when they are used over the lifetime of a programme. This paper looks at the issues related to the comparison of cost data over time focusing on discounting and annualization adjustments, which are used by economists to calculate financial and economic costs. The process of discounting is used to deal with the notion of time preference. Time preference implies that future costs are worth less, and hence discounted more, to reflect individual and societal preferences to have resources and money now rather than in the future. While discounting is appropriate in many situations, it is also useful to compute an annual equivalent cost when recurrent costs of an intervention are incurred, or are expected to be incurred, in subsequent years. This approach has the added benefit of illustrating how capital items are actually used during the lifetime of an intervention. This paper presents methods to both discount and annualize costs, and discusses rules-of-thumb to decide when to make these adjustments. Key words: cost, differential timing, discounting, annualization Introduction: costs over time Economists define a cost as the value of resources used to produce a good or service. However, the way these resources are valued can differ. There are two main approaches with respect to the valuation of these resources: financial and economic costing. Financial costs represent actual monetary flows on goods and services purchased. Costs are thus described in terms of how much money has been paid for the resources used by the project or service (Kumaranayake et al. 2000). Economic costs recognize that the cost of using resources also means that these resources are then unavailable for productive use elsewhere and are effectively being tied-up. There are three main ways in which economic costs differ from financial costs (Creese and Parker 1994): economic costs include the estimated value of donated goods or services; economic costs capture the cost of a good when the price does not reflect the cost of using it productively elsewhere; and economic costs also allow for people s preference for receiving goods and services now rather than later (or equivalently, for postponing spending). Economic costs are important when considering issues related to the sustainability or replicability of projects, as well as being a component of cost-effectiveness decision-making where choices are made regarding the allocation of scarce resources. This paper looks at the issues related to the comparison of cost data over time focusing on discounting and annualization adjustments, which are used by economists to reflect the timing with which resources are consumed (or costs incurred) in the implementation of a programme. The other adjustment needed when looking at cost data over time is to adjust for inflation and this topic has already been the focus of an earlier How to do (Kumaranayake 2000). Discounting s or inputs are defined as goods that last for more than one year and typically have a unit cost greater than US$100 (Creese and Parker 1994). refer to inputs or goods used in delivering a service or project, which when used last less than one year. Typically in most projects for which a cost analysis is being undertaken, both capital and recurrent items are used. In addition, if one looked at the actual pattern of expenditure, we would find that all the capital items are typically bought at the beginning of the project (although capital items can clearly be bought at anytime during a project), and recurrent items throughout the lifetime of the project. Thus the expenditure of a project over its lifetime could follow a pattern such as shown in Table 1. This type of analysis and presentation of data is helpful for budgetary purposes, but fails to capture the opportunity cost borne by spending money in present and future periods; if we spend money in the current time period, we forego the opportunity of investing this money and earning interest. Therefore, in general, we prefer to delay spending to the future as much as possible and this is known as time preference. 1 The notion of time preference implies that future costs (and benefits) are worth less, and hence discounted more, to reflect the individual and societal preference to have resources and money now rather than in the future. For example, if there were two health interventions that both had the same effects, but one cost $100 in year 1, and the other cost $100 in year 2,

2 How to do (or not to do) 113 Table 1. Expenditure of a hypothetical project by year Item Year 1 Year 2 Year 3 Year 4 Year 5 Car $ Nurse $5 000 $5 000 $5 000 $5 000 $5 000 Drugs $ $ $ $ $ Fuel $700 $700 $700 $700 $700 Total annual expenditure $ $ $ $ $ Total expenditure $ Note: figures are assumed to be presented in constant or real terms. For discussion see Kumaranayake (2000). we would prefer the intervention that would have the costs in year 2 (Togerson and Raftery 1999), if we allow for time preference. 2 In order to adjust for this time preference, the practice of discounting is used. When discounting, the present value of all costs is calculated taking into account when these costs are incurred and their opportunity cost. In general, we have some rate r, the discount rate, representing either the real rate of return in the private sector or some social rate of time preference, for example 5% (Drummond et al. 1997) see below for a discussion on where an appropriate discount rate can be obtained from. Through the process of discounting, time preference is taken into account by applying a discount rate to costs 3 and expressing them in terms of their present value. The present value of costs incurred in year n is equal to costs in year n, divided by 1 plus the discount rate (expressed as a decimal) to the power of n. That is for costs in year n, the present value is obtained by: Present value of year n costs = (costs of year n) / (1 + r) n This is equivalent to saying that the costs of year n have been multiplied by: 1 / (1 + r) n which is known as the discount factor. Table 2. Discount factors for present value calculations for a discount rate of 5% Year (1+ r) t Discount factor = 1 / (1+ r) t 1 (1 + 0) = ( ) = ( ) 2 = ( ) 3 = ( ) 4 = Note: assumes that costs occur at the beginning of each year. An alternative assumption is that costs all occur at the end of each year, in which case year 1 costs need to be discounted. So if our discount rate is 5%, then our discount factors for different years are shown in Table 2. Notice that as the number of years increase (e.g. costs are further in the future), the discount factor decreases due to a denominator increase, and therefore costs are reduced or discounted more. In other words, the opportunity cost of resources consumed further in the future is lower than that of their present use, and so we find that $1 in the future is worth less than $1 in present value terms today. Notice that the calculation of the discount factor is reliant on the specification of the exact time period in the future (n) and the discount rate (r). For the hypothetical project presented in Table 1, we can calculate the present value of costs in year 3 for a 5% discount rate as: Present value of year 3 project costs = $ /( ) 2 = $ = $ Then the net present value of the project shown in Table 1 is given by the following calculation and shown in Table 3: Net present value = present value of year 1 project costs + present value of year 2 project costs + present value of year 3 project costs + present value of year 4 costs + present value of year 5 costs = $ ($ ) + ($ ) + ($ ) + ($ ) = $ $ $ $ $ = $ Present value calculations become important as we start to compare alternative projects or programmes with different patterns of spending over time, and also with outcomes which are spread out through time. Note that the application of a 5% discount rate has resulted in an 8.05% difference between the undiscounted ($88 500) and discounted ($81 372) total

3 114 How to do (or not to do)... Table 3. Expenditure and present value of a hypothetical project by year Item Year 1 Year 2 Year 3 Year 4 Year 5 Car $ Nurse $5 000 $5 000 $5 000 $5 000 $5 000 Drugs $ $ $ $ $ Fuel $700 $700 $700 $700 $700 Total annual expenditure $ $ $ $ $ Total expenditure $ Present value calculation (at discount rate of 5%) $ $ $ $ $ Net present value $ Note: figures are assumed to be presented in constant or real terms. For discussion see Kumaranayake (2000). Also assumes that costs occur at the beginning of each year. costs. 4 This reflects the fact that we value spending in future periods less than in the present period. Annualization In Tables 1 and 3, the total costs of the project were obtained by adding up the annual costs for each year of the project. However, when recurrent costs are similar each year, it is often useful to compute an equivalent annual cost of a project. In addition, there are often differences in timing related to when costs of certain inputs are incurred and when they are used over the lifetime of a programme. For example, the purchase of capital items often occurs at the beginning of an intervention, but the services from, or effect of, their use will be over the duration of the project, which could last several years. For recurrent input categories, the purchase and use of the items will be reflected completely in the current year s costs. But in order to compute the equivalent annual cost we need to add capital and recurrent inputs together in a consistent fashion; the process of annualization allows us to do so. There exist two approaches for doing this depending on whether the analyst seeks to estimate financial or economic costs. Depreciation and financial costs Given that there is a flow of services from capital items throughout the lifetime of projects, we can compute the value of this flow of services for each year and add them to the recurrent costs. Depreciation refers to the amount of capital that is used-up in one year. The simplest approach to depreciation is to assume that the services from the capital item are divided equally over the useful life of the capital item. 5 This is known as straight-line depreciation. Thus the annual cost of capital is now the current or replacement cost of the capital item, 6 divided by its expected useful life. 7 In this example, we assume that the useful life of the vehicle is 5 years. The annual financial costs of our hypothetical project are presented in Table 4. In this example, we see that the effect of depreciation is to value the capital resources according to the extent to which they are used in a particular time period. We now see that the annual costs of the intervention are the same across the 5 years, but the total expenditure remains the same ($88 500). Table 4. Calculation of annual financial cost using straight-line depreciation of capital items Item Year 1 Year 2 Year 3 Year 4 Year 5 Car $2 000 $2 000 $2 000 $2 000 $2 000 Nurse $5 000 $5 000 $5 000 $5 000 $5 000 Drugs $ $ $ $ $ Fuel $700 $700 $700 $700 $700 Total annual expenditure $ $ $ $ $ Total expenditure $ Note: figures are assumed to be presented in constant or real terms. For discussion see Kumaranayake (2000).

4 How to do (or not to do) 115 Table 5. Calculation of equivalent annual cost [(1 + r) n 1] / [r (1 + r) n ] Item Car $2 310 Nurse $5 000 Drugs $ Fuel $700 Total annuyal expenditure $ Equivalent annual cost Note: Economic equivalent annual cost calculation based on a useful life of 5 years for a car, and a 5% discount rate; the corresponding annualization factor is We assume that the expenditures for recurrent items reflect their opportunity costs. Valuation of capital items: opportunity cost and annualization In Table 4, we undertook an analysis where we valued the capital item in terms of how much was consumed or depreciated within a particular period. However, for economists the value of a resource must also take into account its opportunity cost. Simply taking into account depreciation is not adequate if one is interested in economic costs, which must take into account the value of alternative opportunities for using the resources tied-up in the capital inputs. The alternative to spending money in year 1 is that this money could be invested elsewhere and gain some profit or real rate of return (which could be simply the rate of interest earned in a bank). Thus valuing the capital item according to its opportunity cost of capital would also reflect the foregone income from investing in a bank and earning interest. In order to determine the annual economic cost of a capital item in any year, the strict procedure would be to add the annual cost of depreciation to the annual interest that could be obtained by investing the undepreciated portion of the capital for each year. However, this estimate is highly contingent on the age of the capital item (e.g. the greater the undepreciated portion, the higher the opportunity cost). Depending on the pattern of depreciation, with the exception of straight-line depreciation, we may obtain a very distorted view of average annual costs, particularly for analyses where one year is chosen as the basis of comparison between alternatives. Therefore, the process of annualization values the cost of capital by estimating an average combination of depreciation and interest on the undepreciated portion over the useful life of the capital item (Lewin 1983). This procedure produces an equivalent annual cost of capital, which can be used in an economic cost analysis. The annualization calculation In order to annualize the cost of a capital item we would need to know its replacement cost, the useful life of the capital item for depreciation purposes and the discount rate. We would then be able to obtain the value of capital for one time period by dividing the replacement cost of capital by the annualization factor given by: where r is the discount (interest) rate and n is the useful life of the capital item. In practice, annualization factor tables are available that show the annualization factor for a particular discount rate and n (e.g. Creese and Parker 1994; Drummond et al. 1997; Kumaranayake et al. 2000). To calculate the economic cost of capital on an annualized basis using the annualization factor tables, we adopt the following approach: 8 Estimate the current value of the capital item as the amount you would have to pay to purchase a similar item now (i.e. the replacement value rather than the original price see footnote 6); Estimate the total number of years of useful life the item can realistically be expected to have (n) (footnote 7); Find out the discount rate used by the Economic Planning Office or Ministry of Finance (r); Find out the annualization factor, determined by the discount rate and useful life of the item, by consulting a standard table; Calculate the annual cost by dividing the current value of the item by the annualization factor. For example, for a single $ piece of equipment with a useful life of 10 years, the approach above would be applied as follows: 9 Discount rate: 5% Annualizing factor (from standard table based on n = 10, and r = 5%): Calculation of annual economic cost: $20 000/7.722 = $2590 (rounded figure). To compare this economic cost with the corresponding financial cost, where we have only allowed for depreciation, note that the latter would be $20 000/10 = $2000 per year. The difference between these two figures reflects the opportunity cost of tying-up the funds in purchasing the capital equipment, and this is why the economic costs for capital are higher than the financial costs. Table 5 presents the economic equivalent annual cost of the hypothetical project, using the above method to value capital items. Note again that the economic costs are higher than the financial costs in Table 4, reflecting the inclusion of opportunity costs ($ vs. $17 700). Discounting to present value and annualization When considering the costs of continuing an intervention (e.g. Expanded Programme on Immunization), it is common to estimate an equivalent annual cost (assuming operating costs are similar over time). Conversely, estimating the costs of a discrete project usually involves calculating the net present value. However, occasionally it may be useful to estimate the cost of an intervention or project over several time periods, for example 2 or 3 years (i.e. greater than 1 year and less than its useful life). In these instances it is possible to annualize capital items and discount appropriately in order to compute the net

5 116 How to do (or not to do)... present value of an intervention across any specified number of years. 10 However, it should be stressed that this type of analysis is only valid if the intervention will continue for the foreseeable future. Otherwise, a resale value should be estimated and incorporated into the analysis to compute the net present value; failure to do so will result in over-estimating the cost of the intervention. Further guidance on the choice between discounting and annualizing is provided below. Annualization and discounting: some rules of thumb Annualization and discount factor tables and choice of discount/interest rate Annualization and discount factor tables, which present the factors by both the discount rate and various years, are readily available (e.g. Drummond et al. 1997). Therefore, it is relatively easy to undertake the annualization or present value calculation. The more difficult decision is the selection of the discount rate. The choice of discount rate is particularly critical since it can significantly influence the relative costs and cost-effectiveness of strategies being compared. The choice of discount rate should be consistent with the rate used by the Economic Planning Office or Finance Ministry of the country in question. If there is no particular recommended rate for the country then a rate can be taken from economic project appraisals done for that country by other organizations such as the World Bank. A more complex approach would be to calculate the real rate of interest, e.g. the rate of interest that would be obtained by depositing the money in the bank minus the rate of interest. The real rate of interest would provide an indication of the opportunity cost of capital to the economy in real terms. The information required can usually be obtained from the Central Economic Planning Office, the Finance Ministry or the Central Bank. Alternatively, a simpler approach is to use a rate consistent with the existing literature, which has the advantage of facilitating comparability between different studies. In general, rates used in the literature vary from 2 10%, although most recently rates of 3 and 5% have been extensively used and recommended (Gold et al. 1996; Drummond et al. 1997). Historically, a 10% rate has been used in evaluations reflecting long-term interest rates in the American bond market (Lewin 1983). Whatever rate is chosen, the effects of using different rates should be explored by conducting sensitivity analyses, such as in Tables 6 and 7. Choice of method The exact nature of the adjustment to the cost data is linked to the ultimate uses for which a cost analysis is undertaken. Cost analysis is a tool that can provide useful insight on the functioning of projects, as well as being a key component of economic evaluation. In particular, analysis of the costs of health care programmes may be undertaken for a number of reasons: (1) Budgeting. For the purposes of budgeting, the cost analysis will focus on the actual monetary flows in each year, rather than an economic valuation of the resources. For budgeting purposes, an analysis similar to Table 1 is required, where the required expenditures are presented without discounting. Table 4, presenting the value of capital items in annualized terms using straight-line depreciation, is also commonly used for accounting purposes. Hence both Tables 1 and 4 are useful for budgetary analysis. (2) Efficiency and sustainability within a project. The objectives of the costing exercise may be to analyze on-going costs of an established project in order to identify potential cost savings or implications for project sustainability. By analyzing costs by input, we can understand which areas of the programme are high or low spending, and identify areas for potential efficiency improvements. If there is no reason to suspect significant annual variation of costs, capital costs should be annualized and summed to recurrent costs in order to ascertain the annual costs of a project. The analysis of both financial and economic costs (Tables 4 and 5) are useful when exploring efficiency and project sustainability issues. Tables 6 and 7. Discounting costs to calculate their present value: sensitivity analysis for choice of different discount rates Cost Discount factor with discount rate of 3% Present value calculation Net present value Note: costs are assumed to be presented in constant 2001 dollars. Again, in this example we assume that costs are incurred at the beginning of the year, and so there is no need to discount year 1. Discount rate 3% 5% 7% 10% Present value % difference from 3% present value calculation % 3.64% 6.13%

6 How to do (or not to do) 117 (3) Project expansion. Cost analysis may be used to estimate resource requirements to expand a project or intervention. In this case, the interest is in collecting information on on-going costs. However, as it is important to have a full valuation of all the resources that are currently being used, regardless of whether there is a monetary transaction, an economic cost analysis should be performed, and it is most common to estimate an equivalent annual cost such as in Table 5. (4) Project replication. Cost analysis may also be used in discussions about the feasibility of project replication. The objective of the costing exercise may be to assess the costs of a strategy relative to the other main strategies or to provide information on costs of replicating the project elsewhere. As it is important to have a full valuation of all the resources that are being used, regardless of whether there is a monetary transaction, an economic cost analysis should be used, as in Table 3. (5) Economic evaluation. When the cost analysis is being undertaken for the purposes of economic evaluation (such as cost-effectiveness analysis), economic costs are used (as in Tables 3 and 5). Where there are projects with costs and benefits occurring at different stages over time (e.g. hepatitis B vaccination, in which costs are incurred today to avoid disease in the future), the absence of discounting may skew results, particularly if benefits are presented in terms of cost savings in the future, so costs (and outcomes) should be presented in present value terms (as in Table 3). However, many evaluations choose to compare one year s cost and (usually process) outcome information across a number of alternatives (as in Table 5). Conclusion We have noted that for projects that have costs being incurred for a number of years, it is important to look at their net present value, particularly when comparing projects with different flows of costs and benefits over time. Present value calculations are important when the phasing of costs and related outcomes of a project do not occur at the same points in time. This difference between the timing of costs and benefits requires that we take our values of time preference into account when making comparisons between alternatives. We have also seen that for capital items, annualizing the costs will average their value (allowing for both depreciation and opportunity cost) over the lifetime of a project, providing an estimate of the annual equivalent capital costs of the intervention which can be added to the annual recurrent estimate. Annualization processes will reflect the value-in-use of a capital item, rather than reflecting when the item was bought. An understanding of equivalent annual costs, used in economic cost calculations, is important when considering project efficiency, expansion or replication, and cost-effectiveness. A final point is that costs (and benefits) should be presented in an explicit and transparent manner. This involves presenting data by the year in which they occur, information related to the annualization adjustment, and both discounted and undiscounted costs, so that others will be able to apply different discount rates if they wish. Endnotes 1 A similar concept applies for benefits where people prefer to enjoy benefits in the present, relative to the future. However, it should be noted that the concept of discounting benefits has aroused much controversy. There is a lack of consensus on whether benefits should be discounted at all, and among those who agree that benefits should be discounted, there is disagreement over the rate (Gold et al. 1996). An important consequence of discounting is that preventive programmes are penalised because future benefits appear devalued relative to initial investments resulting in lower costeffectiveness (see Hall et al for an example of the impact of discounting future benefits of a preventive programme). 2 Similarly, if one intervention resulted in 100 units of benefits in year 1 and another resulted in 100 units of benefits in year 2, we would prefer the first, if we allow for time preference. 3 Generally already in constant or real prices, so that the effects of inflation have been taken into account (Drummond et al. 1997). 4 It should be noted that in this example it has been assumed that the all costs occur at the beginning of each year, hence no need to discount year 1 costs. 5 In practice the rate of depreciation can be varied by year, e.g. using less of the capital item in the first few years would mean a lower capital cost. 6 Since we are attempting to value the flow of resources being used in a year, we use the current or replacement cost of the capital item, rather than the price at the time of purchase. This is particularly important when capital items have been acquired before the start of the project. If there is the possibility of re-sale at the end of the project, the cost of capital may be attributed as the difference between the current cost minus the value of re-sale (Drummond et al. 1997). In this example, since the capital items were acquired at the beginning of the project, we assume that the replacement cost was the same as the cost at time of purchase in constant dollars. We also assume that the item has no re-sale value. 7 The choice of the lifetime of the capital item may be related to the technical length of life (e.g. how long will it technically last?) or the useful length of life (e.g. how long will it be used for this project? or will it also be available for other projects?). 8 Adapted from Creese and Parker (1994). 9 In order to simplify this example we have assumed that the piece of equipment has no re-sale value. Otherwise a re-sale value at the end of the capital item s useful life can be assumed, which should then be discounted and subtracted from the replacement value in order to estimate the net present value (Drummond et al. 1997). 10 It should be noted that while discounting to present value and annualization are different approaches for dealing with differential timing, if we discount to obtain a present value of an annual equivalent cost, this will yield the total cost of the item (Drummond et al. 1997). References Creese A, Parker D Cost analysis in primary health care: a training manual for programme managers. Geneva: World Health Organization. Drummond MF, O Brien B, Stoddart GL, Torrance GW Methods for the economic evaluation of health care programmes. Oxford: Oxford Medical Publications. Gold MR, Siegel JE, Russell LB, Weinstein MC (eds) Costeffectiveness in health and medicine. New York: Oxford University Press. Hall A, Robertson R, Crivelli P et al Cost-effectiveness of hepatitis B vaccine in The Gambia. Transactions of the Royal Society of Tropical Medicine and Hygiene 87: Kumaranayake L The real and the nominal? Making inflationary adjustments to cost and other economic data. Health Policy and Planning 15: Kumaranayake L, Pepperall J, Goodman H, Mills A, Walker D

7 118 How to do (or not to do)... Costing guidelines for HIV/AIDS prevention strategies. Version 3. UNAIDS Best Practice Collection. Geneva: UNAIDS. Levin HM Cost-effectiveness: a primer. London: Sage Publications. Togerson DJ, Raftery J Discounting. British Medical Journal 319: Acknowledgements Both authors are members of the Health Economics and Financing Programme which is supported by programme funds from the UK Department for International Development. The authors would like to acknowledge Anne Mills of the London School of Hygiene and Tropical Medicine, and the anonymous reviewers, for their helpful comments on earlier drafts of this paper. Biographies Damian Walker is a member of the Health Economics and Financing Programme (HEFP), in the Health Policy Unit, London School of Hygiene and Tropical Medicine, London, UK. Lilani Kumaranayake is a member of the Centre on Globalization, Environmental Change and Health and HEFP, Health Policy Unit, London School of Hygiene and Tropical Medicine, London, UK. Correspondence: Damian Walker, Health Economics and Financing Programme, Health Policy Unit, Department of Public Health and Policy, London School of Hygiene and Tropical Medicine, Keppel Street, London, WC1E 7HT, UK. damian.walker@lshtm.ac.uk