Vijaya R. Sharma, Ph.D.

vijaya.sharma@colorado.edu

June 12, 2000

Estimation of annual social cost of a program begins with acquiring the annual expenditure schedule of the program. The evaluator examines each cost item in the schedule from social perspective and adjusts them by valuing all uses of resources at competitive market prices, converting capital expenditures to equivalent annual costs, and excluding transfer payments and unrelated costs. For programs that lump together costs of severe emotional disturbance (SED) services with costs of other services, the evaluator also has to separate out from the expenditure schedule the share of costs incurred on services to children with SED. This can be done either by microcosting of care, determining quantity and unit cost of each resource used in the care of children with SED, or by adopting other simpler, but less precise, methods.

It is important to distinguish between private costs and social costs of care. Costing of the same activity may end up with two different estimates, depending upon whose perspective is taken in preparing the estimate. If the estimate is prepared from the perspective of a particular program, only those items are included that are considered costs by the program. Such estimates are then called private costs. In contrast, estimates prepared from the general social perspective are called social costs of care. This paper discusses methods of estimating social costs of care offered by programs to children suffering or at risk of suffering from severe emotional disturbance (SED).

Below we present some examples to explain how the same expenditure of a program would be treated differently for estimation of private cost and social cost. For convenience of discussion, these examples are grouped into three types ¾ operating expenditures, capital expenditures, and externalities.

Operating expenditures are expenditures on resources that provide services for a year or less, like salaries and wages paid to labor resources, costs of supplies and consumables, and costs of fuels and utilities.

Example 1: A clinic pays a worker the federal minimum wage.

Private cost to the clinic is the actual federal minimum wage paid, but the social cost would be the competitive market wage that would have prevailed in the absence of the federal minimum wage law. Competitive market prices or wages reflect true value of resources, but lack of competition and/or government controls in a market can distort the ability of prices to convey true value of resources.

Example 2: A hospital buys linen supplies for $107, inclusive of 7% sales tax.

Private cost of supplies to the hospital is the actual amount paid by the hospital ($107), whereas the social cost would only be $100, the true value of linen. $7 of sales tax is not a cost to society, because it is not a payment for any resource. Tax is simply a legally mandated payment, a transfer of resources from the hospital to the taxpayers. Therefore, taxes and other transfer payments have to be excluded from social costs.

Example 3: A clinic dispenses drugs to indigent free-of-cost, under a program financed by major drug manufacturers.

Private cost of drugs to the clinic is zero, because it is drug manufacturers, not the clinic, that pay the cost. However, the social cost of the activity is the competitive market price of drugs that were dispensed. For social cost, it does not matter who pays the cost.

Example 4: A psychiatrist volunteers her services to a rural clinic one-day a week.

Private cost of the psychiatrist's services to the clinic is zero, since the clinic does not pay salary to the psychiatrist. In fact, the psychiatrist bears the cost of her volunteer work, by sacrificing the potential income she could have earned from her services during that time. Therefore, the social cost would be the loss of potential income to the psychiatrist or the competitive wage the clinic would have had to pay if it hired a psychiatrist for one-day a week. This is again another example of including use of a resource in social cost, irrespective of who bears the cost for the resource.

Example 5: A residential care program refers a resident to a specialist. A staff accompanies the resident.

Private cost to the program would be the sum of expenditures the program pays for this activity. Obviously, the program pays the staff's travel and time costs. If the program also pays the specialist's fees and the resident's travel expenditures, they would be included in private cost. On the other hand, the time cost of the resident for obtaining specialist services would not be included in private cost, because the resident, not the program, sacrifices the alternative use of this time. Once again, for social cost it does not matter who is paying what; therefore, the social cost would include all of the above expenditures ¾ specialist's fees, staff's travel and time costs, and the resident's travel and time costs. Note that the resident's time cost is not a monetary cost or out-of -pocket expense; yet, the value of the time spent on travelling and getting services of the specialist is included in social cost, because the resident is sacrificing other things that could have been done during this time.

How would you put a value on the time of the resident? It depends upon what is the next best thing the resident could have done if not seeking the specialist's services. If this time came at the expense of working time, the value of time would be the wage the resident could have earned. On the other hand, if SED has rendered the resident temporarily disabled from job and even household chores, the value of time may be considered zero.

Capital expenditures are expenditures on purchases of buildings, machinery, and equipment that last and provide services over a number of years. In case of operating expenditures, programs pay for a resource in the year when the services of the resource are realized. In case of capital expenditures however, programs pay the price of a capital asset now, but receive services of the asset now and also in future, over the life period of the asset. Therefore, the initial purchase price of the asset has to be distributed over its life period, to estimate its equivalent annual cost.

There are two components of equivalent annual cost ¾ depreciation cost and opportunity cost of capital. Depreciation cost is the gradual decline in value of asset, caused by physical wear and tear and/or technological obsolescence. Suppose an asset purchased at $110 has a life period of 5 years and resale value of $10 at the end of the life period. Then, the total loss in value of the asset over 5 years is $100. Or, one could say that the annual depreciation cost of the asset is $20 per year for 5 years.

Opportunity cost of capital considers the fact that the price of an asset has to be paid at the time of purchase, in advance of obtaining services over the life period of the asset. Thus, capital is tied up for services that would be utilized only in future. The opportunity cost of this capital is the annual rate of return that could have been earned by investing this capital elsewhere. Equivalent annual social cost of a capital expenditure includes both depreciation cost and opportunity cost of capital. To explain the method of calculating equivalent annual cost, we will first define discount factor and annuity factor.

Discount factor helps converting a future sum of money into its present value. Consider an example. An amount of $121 that would be received two years from today is not considered worth $121 today. Any one who is given a choice between receiving $121 today or receiving it two years later, is likely to choose to have it today. People generally have a positive rate of time preference. Everything else the same, they prefer receiving benefits sooner than later. Also, a person who has $100 today has the option of investing the amount at the going annual rate of interest (say 10 percent) and multiply it to $121 in two years. Therefore, $100 today is equivalent to $121 two years from today. Alternatively, $121 that would be received two years from today is equivalent to only $100 today, when the rate of interest (more precisely, discount rate) is 10% per year. Thus, to convert $121 to its present value, the future sum has to be multiplied by a discount factor 0.8264. Discount factor is the factor by which a future sum is multiplied to calculate its present value and the process of calculating present value is called discounting. The appendix of this paper provides a table of values of discount factor for different discount rates and years. Note that the discount rate is indeed the opportunity cost of capital.

Annuity factor is the factor by which current capital expenditure is divided to obtain equivalent annual cost. Consider the following table, which shows that the total present value of a sum of $10 paid every year for 3 years is $27.23 when the discount rate is 5% per year. This also means that $27.32 spent today on a capital asset would be considered equivalent to an annual cost of $10 every year for 3 years (this is assuming that the life period of the asset is 3 years with zero resale value). One can divide $27.23 by an annuity factor 2.7232 and obtain the equivalent annual cost of $10. The appendix of this paper also provides a table of values of annuity factor.

Table 1: Present Value of Uniform Annual Payments

(Discount Factor 5% per year)

Armed with the understanding of annuity factor, let us now consider a few examples of capital expenditures to see how they would be separately treated for estimating private cost and social cost.

Example 6: A government-operated clinic purchases an X-ray machine for $30,000 from its annual budget. Life period of the machine is 6 years, and estimated resale value at the end of life period is $3000. Consider discount rate of 5% per year.

A government-operated program is likely to show the entire purchase price of the machine as its private cost in the year of purchase itself. If so, the private cost would be $30,000. However, the equivalent annual social cost would be equal to $5,469.50 for 6 years and is calculated as follows.

1. Present value of resale value = resale value x discount factor (5%, 6 years)

= $3000 x 0.7462 = $2238.60

2. Capital expenditure, net of present value of resale value

= $30000 - $2238.60 = $27761.40

3. Equivalent annual social cost

= Capital expenditure (net of resale value) ¸ annuity factor (5%, 6 years)

= $27761.40 ¸ 5.0757 = $5469.50

Example 7: A commercial clinic purchases an X-ray machine for $30,000 from its own financial resources, without borrowing money for this purpose. Life period of the machine is 6 years, and estimated resale value at the end of life period is $3000. Consider discount rate of 5% per year.

Unlike a government-operated program, a commercial program does not charge the entire purchase price on the year of purchase. It spreads the purchase price over the life period of the machine in the form of depreciation cost. Assuming a straight-line depreciation method (see Footnote 2), the purchase price, net of resale value, i.e., $27,000 is allocated equally over 6 years, resulting into annual depreciation cost of $4,500 each year for 6 years. This amount would show up as the annual private cost of the capital expenditure. Note that private cost ignores the opportunity cost of its capital, as it does not use discount or annuity factor. In contrast of this private cost, the annual social cost of the capital expenditure would be exactly the same as in Example 6, i.e., $5,469.50 each year for 6 years.

Example 8: A commercial clinic purchases an X-ray machine for $30,000. For this purpose, it uses its own equity capital of $20,000 and borrows the rest $10,000 at an annual interest rate of 6% per year for 6 years. Life period of the machine is 6 years, and estimated resale value at the end of life period is $3000. Consider discount rate of 5% per year.

Private cost of the capital expenditure would include annual depreciation cost $4,500 (as calculated in Example 7), and it would also include average annual interest cost of $367.40 on the borrowed money. Note that the private cost would not include the opportunity cost of $20,000 of equity capital (the foregone interest income that would have been earned if this capital was invested elsewhere.) On the other hand, the annual social cost would still be the same as that in the previous two examples.

Example 9: A commercial clinic purchases a land for $30,000. For this purpose, it uses its own equity capital of $20,000 and borrows the rest $10,000 at an annual interest rate of 6% for 6 years. Land is a nondepreciable asset; therefore, its resale value would be $30,000 whenever sold. Consider discount rate of 5% per year.

Since land is a nondepreciable cost, the private cost would not have depreciation cost, but only the average annual interest cost of $367.40 each year for 6 years. The social cost too would exclude depreciation cost and include only the opportunity cost of capital. Let us calculate this, following the steps illustrated in Example 6.

4. Present value of resale value = resale value x discount factor (5%, 6 years)

= $30000 x 0.7462 = $22386

5. Capital expenditure, net of present value of resale value

= $30000 - $22386 = $7614

6. Equivalent annual social cost

Note that $1500 (the calculated annual social cost) equals the potential interest income that could have been earned by investing the equity capital of $30,000 at 5% interest, which is the opportunity cost of capital at discount rate of 5%.

Estimation of social cost is relatively easy when a program serves only children with SED, for example a substance abuse rehabilitation program for children. Since all services of the program are dedicated to the target population, total annual expenditure of the program is its annual private cost of care of children with SED. The task then is to acquire the annual expenditure schedule from the account section of the program and to examine individual cost items from social perspective. Upon examination, many cost items may be accepted as social costs, but some may have to be adjusted or even excluded. For explaining the process of examination and adjustment of private costs, we take the help of a hypothetical schedule (Table 1) of annual expenditures of a clinic that provides services exclusively to children with SED.

Table 1: Annual Expenditure in 1999 and Estimation of Social Cost

The first three columns of Table 1 show the cost items and the annual expenditures under each item in 1999. The last column presents the corresponding social costs after each cost item has been examined and adjusted. The general principles involved in adjustments are explained below.

Cost items 1 through 6 in the table are included in both private costs and social costs, because they entail use of resources from social perspective too. We have assumed that resources under these cost items have been valued at their competitive market prices; therefore, no adjustment is necessary. However, if the evaluator has reasons to believe that wages, fees, or prices of food, drugs, or utilities are not in accordance with what would be expected in a competitive market, they would have to be revised with estimated competitive wages or prices.

Accountants of a program consider use of a resource a cost only when the program pays money for the resource. If money is not paid, it is not a cost. Consider Items 7 and 8 in the table. The use of a donated building space and the use of voluntary services of a front desk clerk are not shown as private costs, because the clinic does not pay rent or salary for them. To the society however, these costs imply use of resources that have alternative uses. Use of any resource, even if not paid by the program, needs to be valued at competitive market prices and included in social costs. From social perspective, what matters is whether a resource has been used; it does not matter whether money is being paid or who is paying for the resource. In the social cost column therefore, these resources are valued at competitive market prices, estimated at $4,000 per month for the donated building space and $2,000 per month for the services of the front desk clerk.

Accountants consider a monetary payment a cost, even when the payment entails no use of resource. Consider Item 9 in the table, the clinic shows cash contributions to charities as a cost. To the society however, they are not costs but transfer of resources from the clinic to charitable organizations. Another example of such a cost item would be payment of sales taxes by programs (not shown in the table). Tax is not a cost to society because it is not a payment for any resource; it is simply a legally mandated payment, a transfer of resources from the program to the taxpayers. Therefore, taxes and other transfer payments need to be excluded from social costs. In the table, if expenditures on food, drugs, fuel, and utilities reported under Items 4 and 5 include payment of sales taxes, tax amounts would have to be deducted.

Some programs, especially those operated by government, may not distinguish between capital expenditures and operating expenditures, as has been assumed in the table above.

Consider Item 10, the purchase of new copiers in 1999. The entire purchase cost ($5000) has been shown as that year's annual expenditure, in spite of the fact that copiers are expected to provide services over their life period, the next five years. For estimating annual social cost, the initial purchase price ($P) of a piece of capital equipment should be distributed as equivalent annual costs ($E) over the life period of the equipment, by using an appropriate annuity factor (A), such that E = P/A. The value of the annuity factor depends on the life period of the equipment and on the annual interest rate (more precisely, discount rate), and this value can be found from discount and present value tables. For copiers, the initial purchase price (P) is $5000 and the value of annuity factor (A) is 4.3295 for 5-year life period and 5% discount rate; therefore, the equivalent annual cost (E) would be $1155 (=$5000/4.3295). Instead of accounting the entire purchase cost ($5000) in the year of purchase, this method spreads the cost into a stream of equivalent annual costs ($1155) over the life period of the copiers (5 years). This equivalent annual cost is then the annual social cost of new copiers purchased in 1999.

Now consider Item 11 in the table. There was an X-ray machine donated to the clinic in 1999. Since the clinic did not pay for the machine, it does not show up as a private cost. However, we need to value the machine at its competitive market price (say, $50,000) and calculate the equivalent annual cost, as we did above with copiers. Assuming its life period of five years and at a discount rate of five percent, the social cost of the donated X-ray machine would be the equivalent annual cost of $11,549 (E=50000/4.3295).

Item 12 in the table is the depreciation cost of existing capital equipment, and Item 13 is the amount of interest and principal repayments on borrowings that were made to purchase capital equipment in earlier years. Depreciation cost in a conventional account is mostly determined by tax considerations, instead of actual depreciation of equipment. Also, accountants show interest costs on borrowed capital, but they ignore the opportunity cost of equity capital of the owner of the clinic. In contrast, social costs include opportunity cost of all capital, whether borrowed or owner's equity. The equivalent annual cost calculation discussed above accounts for both, actual depreciation and opportunity cost of capital. Therefore, this method can be used for determining social costs of existing equipment too.

For simplicity, assume that all existing pieces of equipment have six years of remaining useful life, and assume that their current market value is $80,000. The value of annuity factor for a life period of six years and at five-percent discount rate is 5.0757. Then, the equivalent annual cost, i.e., the annual social cost for Items 12 and 13, would be $15,761 (=80000/5.0757) every year for the next six years. If the existing pieces of equipment differ in remaining life periods, it would be convenient to group capital equipment by life periods and do the equivalent annual cost calculation separately for each group.

Consider Item 14 in the table, expenditures on consumer satisfaction survey. This cost item is unrelated to use of resources on care of children with SED. Another mostly encountered unrelated cost item is expenditures on research and training. All unrelated private costs should be excluded from social costs.

The bottom two rows of the table calculate and compare the average annual private costs and the average annual social costs of care per child and per child-day of care. Computation of social costs in this table is based exclusively on the annual expenditure schedule of the clinic; therefore, the calculated average social costs might only be reflecting a part of the full social cost of care. This is likely if other agencies or individuals also provided resources to the care of the clinic. A complete accounting of social cost requires inquiring whether resources were used by other agencies or individuals also in the delivery of services of the clinic or in receiving services of the clinic. For example, some programs may not show costs of drugs and outside lab works in their account if the programs do not pay these costs. To further illustrate this point, let us consider two programs that offer identical services. However, assume that one program provides services at the homes of consumers and another program provides services at its clinic. The private costs of the first program would include travel expenses incurred by providers to deliver services to consumers, but the private costs of the second program would not include travel expenses incurred by consumers to receive services from providers. From society's perspective, travel expenses are integral component of costs of care, irrespective of who pays them. Therefore, the evaluator should identify all other agencies and individuals, besides the program, that are involved in providing resources for care and should add costs incurred by them to the annual cost of the program.

Estimating social costs of care to children with SED in programs that offer non-SED services too and serve adult consumers also is relatively more difficult. An example is services to children with SED in a general hospital. Under each cost heading of private costs, a nonexclusive program is likely to have summed up all resources used, with no indication of how much of these resources were used for SED services to children. Therefore, precise estimation of social cost would require microcosting of care, which involves identification of each resource used in the SED care to children and determination of its quantity and unit cost. In the following paragraphs, we first discuss microcosting and then few other methods which are likely to be less expensive but less precise than microcosting. Which method of estimation is adopted is the choice an evaluator has to make depending upon the availability of data, time, and budget for estimation and the desired level of precision of estimation.

Microcosting is generally done in two broad categories of costs — direct costs of care and indirect costs of care. Consider an example of inpatient care of a child with SED in the psychiatric wing of a hospital. Direct costs would be the costs of drugs, lab tests, services of psychiatrists, nurses, and any such material or manpower directly used in the care or services for the child. Indirect costs would be the costs of materials and manpower services shared among different units and patients (including the child in question) of the hospital. Examples of indirect costs are laundry, housekeeping, utilities, and administrative expenditures. For both direct and indirect costs, the individual cost items should be examined from social perspective, using the principles mentioned for adjustment of the annual expenditure schedule in Table 1.

Direct costs are usually broken down into direct manpower cost and direct material cost. Direct manpower cost is the sum of the costs of psychiatrists' services, costs of nursing services, costs of lab technicians' services, and costs of services of all other persons who directly served the child. Cost of services of a professional is estimated by multiplying the number of hours devoted by the professional on the care of the child with the professional's hourly salary and benefits. Direct material cost is the sum of products of quantity and price of each drug administered to the child and each material consumed on lab tests performed on the child.

Indirect costs of care are estimated by appropriately allocating shares of overhead costs to the care of the child. There is no fixed allocation rule; it depends on the type of program and the type of overhead cost being allocated. For example, an allocation basis for annual housekeeping expenditures of the hospital can be the floor area of the psychiatric wing as a proportion of the total floor area of the hospital. According to this basis, if the psychiatric wing occupies 10 percent of the total floor area of the hospital, it should share 10 percent of the annual housekeeping expenditures of the hospital. This share can then be divided by the total number of patient-days served by the psychiatric wing to determine the average housekeeping expenditure per patient-day. This average norm can then be multiplied with the number of days of care of the child with SED to estimate the housekeeping expenditures on the child's care. Similar allocation rules can be devised for other overhead costs. Laundry expenditures can be allocated on the basis of weight of laundry of the psychiatric wing to the weight of total hospital laundry. Administrative expenditures can be allocated on the basis of the number of patient-days served by the psychiatric wing as a proportion of the total patient-days of the hospital.

Microcosting can be a time-consuming process. Instead, the evaluator may use simpler, but less precise, methods of estimation. For example, cost of inpatient care of a child (considered above) may be approximated by the average cost of care per person or by multiplying the number of days of hospitalization of the child with the average per diem hospitalization charge. Per person or per diem charge is often estimated by hospitals to claim reimbursements from Medicare, Medicaid, and insurance agencies. However, these charges are likely to have been calculated from private costs. Therefore, the evaluator would have to obtain the itemwise breakdown of the charge and adjust the individual cost items for social costs, as explained for cost items in Table 1 above. Below we discuss methods of estimation for different types of programs.

The share of cost incurred on residential or inpatient care of children with SED can be approximated as below.

In addition to per diem charge, the evaluator requires information on inpatient days of services offered by the program to children with SED. If this information is not readily available, the evaluator may have to gather it from a review of individual consumer files (case notes) of each child with SED served last year. From the files, the evaluator would record the number of days of residence or hospitalization of each child. If the review of each consumer file is likely to be expensive, the evaluator may review files of only a randomly selected sample of children with SED served last year. From the review, the evaluator would calculate the average length of stay of a child and multiply it with the total number of children with SED served last year to arrive at the total number of days of residential services.

Drug costs are generally not included in per diem charges. Therefore, the evaluator may have to note drug costs also from individual consumer files and estimate average drug cost per child with SED.

Examples of such programs are ambulatory care, self-help groups, office visits to providers, traditional healing at home, and home visits of providers. Estimation procedure is similar to that of residential or inpatient care.

Prevalence of SED among children may increase cost of educating them; the interest then is to estimate the cost increase caused by SED. Counselors and teachers may be devoting more than normal counseling or teaching time with children and/or their parents to take care of their SED-related issues. The evaluator may have to conduct separate surveys of teachers and counselors to estimate average additional hours of counseling or teaching time devoted to a student with SED in an academic year. These averages then may be multiplied with average hourly salaries of counselors and teachers to find annual direct cost of care of students with SED, as shown below.

If a school has hired mental health counselors or separate personnel to take care of mental health issues. Then the annual direct cost may be estimated as below.

The above costs are direct costs, to which increase in indirect or overhead costs due to SED should be added. Indirect cost can be estimated as below.

Clientele of these institutions consist of both, target and non-target populations; therefore, the interest is to find the proportion of total expenditure of the institution that goes to services offered to children with SED.