5 CAPITAL BUDGETING The learning objectives of this chapter are to: introduce capital budgeting and explain why a separate capital budget is needed; deﬁne capital assets, in both theory and practice; S explain the time value of money (TVM) concept and discuss the basic tools of TVM, including compounding and discounting, present M I present the tools of investment analysis, including net present cost, annualized cost, net present value, and internal rate of return; deﬁne and discuss cost-beneﬁt analysis; and T deﬁne and discuss payback and accounting rate of return. H , and future value, and annuities; A D As discussed in Chapter 2, when an operating budget is prepared, it includes costs that the Acoming year. Sometimes, however, the organization organization expects to incur for the spends money on the acquisition of M resources that will provide it with benefits beyond the INTRODUCTION coming year. A capital asset is anything the organization acquires that will help it to provide goods or services in more than one fiscal year.1 When organizations contemplate the acquisition of capital assets, special2attention is often paid to the appropriateness of the decision. The process of planning for the purchase of capital assets is often referred to as capital budgeting. A capital budget0is prepared as a separate document, which becomes part of the organization’s master budget. 0 In some organizations, all capital budgeting is done as part of the annual planning 8 and their purchase is planned for the coming year. process. Specific items are identified, In other organizations, an overall dollar T amount is approved for capital spending for the coming year. Then individual items are evaluated and approved for acquisition throughout S the year as the need for those items becomes apparent. One concern in the capital budget process is that adequate attention be paid to the timing of cash payments and receipts. Often large amounts of money are paid to acquire 1 162 Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 A fiscal year may be a calendar year, or it may be any 12-month period. December 31 is the most common fiscal year-end. However, many not-for-profit organizations and local governments begin their fiscal year on July 1, or September 1, rather than January 1. The federal government begins its year on October 1. Generally, the fiscal year is chosen so that the end of the year coincides with the slowest activity level of the year. This allows accountants to take the time needed to summarize the year’s activity. Governments may choose a fiscal year that allows sufficient time for the body that approves the budget to review, revise, and adopt the budget by the beginning of the fiscal year. This requires coordination between the choice of the fiscal year-end and the time of the year that the legislative body is in session. Chapter 5 • Capital Budgeting 163 capital items well in advance of the collection of cash receipts earned from the use of those items. When an organization purchases a capital asset, it must recognize that by using cash today to acquire a capital asset, it is forgoing a variety of other potential uses for that money. At a minimum, cash could be put in an interest-earning account, and in the future the organization would have the original amount plus interest. As a result, paying $1,000 today cannot be equated with receiving $1,000 several years from now. One would only give up $1,000 today if the benefit to be realized from doing so is worth at least the $1,000 plus the interest that could be earned. This gives rise to a concept referred to as the time value of money (TVM). Based on the TVM concept discussed in this chapter, the financial appropriateness of an investment can be calculated. The discussion in this chapter examines TVM techniques for investment analysis, including net present cost, annualized cost, net present value, and internal rate of return. The chapter then examines an approach called cost-benefit analysis which governS ments often use in evaluating capital budgeting decisions. M The chapter concludes with a discussion of the payback and accounting rate of I but since they are sometimes return approaches. Both approaches have their limitations, used the reader should be aware of the methods and their T drawbacks. H , ISBN 1-323-02300-3 WHY DO WE NEED A SEPARATE CAPITAL BUDGET? Assume that the Hospital for Ordinary Surgery (HOS) is considering adding a new wing. The hospital currently has annual revenues of $150 million and annual operating expenses of $148 million. The cost to construct the Anew wing is $360 million. Once opened, the new wing is expected to increase the annual revenues and operating costs of HOS by $70 million and $20 million, respectively, D excluding the cost of constructing the building itself. A The operating budget for HOS would include $220 million in revenue (i.e., the M original $150 million plus the new $70 million). If the entire cost of the new wing is charged to operating expenses, the total operating expenses would be $528 million (i.e., $148 million of expenses, the same as last year, plus $20 million in new operating 2 expenses, plus the $360 million for the new building). This would result in a loss of 0 the project might be rejected as $308 million for the year. This amount is so huge that being totally unfeasible. 0 However, the benefit of the $360 million investment in the new wing will be real8 that provide benefits beyond ized over many years, not just one. When large investments the current year are included in an operating budget,Tthey often look much too costly. However, if one considers their benefits over an extended period of time, they may not be too costly. The role of the capital budget is to pull theS acquisition cost out of the operating budget and place it in a separate budget where its costs and benefits can be evaluated over its complete lifetime. Suppose that the top management of HOS, after careful review and analysis, decides that the benefits of the new hospital wing over its full lifetime are worth its $360 million cost. Based on the recommendation of chief operating officer (COO) Steve Netzer, as well as the hospital’s chief executive officer (CEO) and chief financial officer (CFO), the Board of Trustees of HOS approves the capital budget, including the cost of construction of the new wing. The cost of that capital asset will be spread out over its useful life, with a portion included in the operating budget each year. The process of spreading out the cost of a capital asset over the years the asset is used is called amortization, a general term that refers to any allocation over a period of Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 164 Part II • Planning time. Amortization of the cost of a physical asset is referred to as depreciation. Each year a portion of the cost of the asset is treated as an expense called depreciation expense.2 The aggregate amount of the cost of an asset that has been charged as an expense over the years the asset has been owned is referred to as accumulated depreciation. For example, if HOS builds the new hospital wing for $360 million and expects it to have a useful lifetime of 40 years, the depreciation expense each year would be $9 million ($360 million 40 years).3 Rather than showing the full building cost of $360 million as an expense in the first year, only $9 million is shown as an expense for the first year. After owning the building for three years, the accumulated depreciation will be $27 million ($9 million 3 years).4 DEFINITION OF CAPITAL ASSETS: THEORY AND PRACTICE In theory, a capital asset is any resource that will benefit the organization in more than one fiscal year. This means that, inS theory, if we were to buy something that will last for just six months, it could be a capital Mitem if part of the six months falls in one year and part falls in the next. In practice, however, organizations only treat items with a lifetime of more than one year as being capitalI assets. This is done to keep the bookkeeping simpler. Similarly, most organizations only T treat relatively costly acquisitions as capital assets. In theory, there should be no price limitation. A ballpoint pen purchased for 50 cents can be a capital asset if its life extends H from one accounting year into the next. However, no organization would treat the pen as, a capital asset. The pen would simply be included in the operating expenses in the year it is acquired. This is because its cost is so low. The cost of allocating 25 cents of depreciation in each of two years would exceed the value of the information generated by that allocation. A What about something more expensive like a $200 report-binding machine? In D not treat a $200 machine that is expected to last practice, most organizations would for 10 years as a capital asset. TheAreason is that even though it will last for more than 12 months, it is relatively inexpensive. If we were to depreciate it, we could divide the M $200 cost by 10 years and come out with a charge of $20 per year. For some very small organizations, the difference between charging $200 in 1 year and zero in the subsequent 9 years versus charging $20 per year for 10 years might be significant. However, that 2 would generally not be the case. 0 perfectly accurate. Compromises are made in Accounting information is rarely the level of accuracy based on the0cost of being more accurate and the value of more accurate information. Some estimates are unavoidable. Did we use half of the ink of the 50-cent pen in each of two years? 8 Perhaps we used 40 percent of the ink one year and 60 percent of the ink the next. A truly T correct allocation would therefore require charging S 2 Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 At times, an organization may own a capital asset that does not have physical form, such as a patent. The allocation of the cost of such an asset is simply referred to by the generic term amortization. Some assets literally empty out (e.g., oil wells, coal mines) and amortization of the cost of such assets is referred to as depletion. 3 This example has been somewhat simplified. In most cases, we would expect the building to still have some value at the end of the useful lifetime. That residual, or salvage, value would be deducted from the cost before calculating the annual depreciation expense. For example, if we expect the building to be worth $40 million after 40 years, then only $320 million ($360 million cost less $40 million salvage) would be depreciated. The annual depreciation would be $8 million ($320 40 years) instead of $9 million. 4 From an economic perspective, true depreciation represents the amount of the capital asset that has been consumed in a given year. We could measure that by assessing the value of the asset at the beginning and end of the year. The depreciation expense would be the amount that the asset had declined in value. In practice, it is difficult to assess the value of each capital asset each year. Therefore, accounting uses simplifications such as an assumption that an equal portion of the value of the asset is used up each year. Alternatives, referred to as accelerated depreciation methods, are designed to better approximate true economic depreciation. They are discussed in Appendix 11-A at the end of Chapter 11. Chapter 5 • Capital Budgeting 165 40 percent of the cost of the 50-cent pen in one year and 60 percent of the cost the next year. Similarly, we do not know exactly how much of the binding machine is used each year. Will it really last 10 years, or will it last 11 years? Accounting records should be reasonable representations of what has occurred from a financial viewpoint and should allow the user of the information to make reasonable decisions. It is true that charging the full $200 cost in the year of purchase will overstate the amount of resources that have been used up in that year. However, it is easier to do it that way. The organization must weigh whether the simplified treatment is likely to create a severe enough distortion that it will affect decisions that must be made. For the 50-cent pen, that is never likely to happen. For a $360 million building addition, by contrast, treating the full cost as a current year expense would likely affect decisions. The hard part is determining where to draw the line. Organizations must make a policy decision regarding what dollar level is so substantial that it is worth the extra effort of depreciating the asset (allocating a share of its cost to each year it is used) rather than charging it all as S an expense in the year of acquisition. To most organizations, the difference between charging $200 in one year or $20 a M year for 10 years will not be large enough to affect any decisions. In some organizations, I the difference between charging $50,000 in one year versus $5,000 per year for 10 years would not be large enough to affect any decisions. A cutoff of $1,000, or $5,000, or even T $10,000 would be considered to be reasonable by many public, health, and not-for-profit H organizations. Many organizations use even higher levels. , WHY DO CAPITAL ASSETS WARRANT SPECIAL ATTENTION? It seems reasonable to include just one year’s worth A of depreciation expense in an operating budget. However, that does not fully explain why a totally separate budget D to be special approaches for is prepared for capital assets, or why there should need evaluating the appropriateness of individual capital asset A acquisitions. Some additional reasons that capital assets warrant special attention are: M ISBN 1-323-02300-3 • the initial cost is large, • the items are generally kept a long time, • we can only understand the financial impact if we2evaluate the entire lifetime of the assets, and 0 • since we often pay for the asset early and receive payments as we use it later, the 0 time value of money must be considered. 8 pen, the binding machine) are Since small capital expenditures (e.g., the ballpoint often not treated as capital assets, the items that are T included in the capital budgeting process are generally expensive. When the cost of an item is high, a mistake can be costly. Long-term acquisitions often lock us in, and aSmistake may have repercussions for many years. For example, suppose that HOS unwittingly buys 10 inferior patient monitors for $50,000 each. As we use them, we learn of their shortcomings and hear of another type of monitor that we could have purchased that performs better. Although we may regret the purchase, we may not have the resources to be able to discard the monitors and replace them. We may have to use the inferior machines for a number of years. To avoid such situations, the capital budgeting process used by many organizations requires a thorough review of the proposed investment and a search for alternative options that might be superior. The impact of capital acquisitions can only be understood if we consider their full lifetime. Suppose that a donor offers to pay the full cost for a new, larger, wonderful building for the organization. Do we need to look any further? The building will be free! Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 166 Part II • Planning However, that is not quite correct. Perhaps the new building will cost money to operate (for heat, power, maintenance, security, etc.) but will not generate any additional revenue or support for the organization beyond the donation to acquire it. The operating costs of the building must be considered. Capital budgets should consider all revenue and expense implications of capital assets over their useful lifetime. Governments face similar issues when they determine whether they should build a new school. Analysis of the feasibility of the new school building must consider whether we will be able to afford to run it once it is built. Governments must try to assess the likely impact of the added annual operating costs on the tax structure of the town, city, county, or state. Thus, capital budgeting takes a broad view, considering all the likely impacts of making a capital acquisition. A last, and critical, issue relates to the timing of payments and receipts. Often capital assets are acquired by making a cash payment at the time of acquisition. However, the cash the organization will receive as it uses the asset comes later. In the meantime, there is a cost for the money invested S in the project. Since cash is not available for free, we must consider the rent we pay for it. M When we use someone’s office or apartment, we pay rent for it. When we use I for that use. Rent paid for the use of someone’s someone’s money, we also pay rent money is called interest. For capitalTassets, the rental cost for money used over a period of years can be substantial, and its effect must be considered when we decide whether it makes sense to acquire the item. H In fact, there is an opportunity , cost for all resources used by an organization. Each resource could be used for some other purpose. We often refer to the opportunity cost of using resources in an organization as the cost of capital. Part of the cost of capital is reflected in the interest that the organization A pays on its debt. However, there is also a cost of using the resources that the organization owns. If they are not used to buy a particular capital D else. Thus, whenever a capital asset is purchased, asset, they could be used for something we must consider the cost of the money A used for that purchase. Calculations related to the cost of capital or cost of money are referred to as time value of money computations. M THE TIME VALUE OF MONEY 2 Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 A dollar today is not worth the same amount as a dollar at some future time. Imagine 0 someone $10,000 today with the expectation that whether we would be willing to lend they would give us back $10,000 in0five years. Would we consider that to be a reasonable investment? Probably not. If we had instead invested the money in a safe bank account or U.S. Treasury security that pays8interest, at the end of five years we would have our $10,000 plus interest. Getting $10,000 T in five years is not as good as having $10,000 today. This gives rise to a concept referred to as the time value of money (TVM). Suppose that the Museum of Technology S is considering buying computers for an exhibit for $50,000. The money would come from cash that the museum currently has. It will be able to charge $12,000 per year in special admissions fees for the exhibit for five years. At that point, the exhibit will be closed and the computers will be obsolete and will be thrown away. If the museum uses a capital budget, the initial cash outlay will be $50,000, and the full five years of revenues will also be shown. The $12,000 of admission revenues per year for five years total to $60,000. However, can we compare the $50,000 to acquire the exhibit with the $60,000 that we will receive and conclude that there will be a $10,000 profit from the exhibit? No. The two numbers appear to be comparable, but the cash is paid and received at different times. A dollar received at some point in the future is not worth as much as a dollar today. We will need some mechanism to help us make a reasoned comparison. Chapter 5 • Capital Budgeting 167 It is sometimes easier to understand TVM mechanics using a time line such as the following: 0 1 2 3 4 5 ($50,000) $12,000 $12,000 $12,000 $12,000 $12,000 The $50,000 initial cost is spent at the very beginning of the project, or time 0. It is shown in parentheses to indicate that this amount is being paid out, rather than being received. Each year there is a total of $12,000 collected in admissions fees. In this example, we are assuming that $12,000 is collected at the end of each of the five years. For example, the $12,000 shown at time period 1 on the time line is received at the end of the first year. Although a time line, as it appears above, is a helpful conceptual tool, in practice managers tend to do their calculations in a spreadsheet,Ssuch as Excel. The same information in Excel might be shown as: M I T H , To evaluate the investment, we use a methodology that is based on compound interest calculations. If the museum had borrowed theA$50,000 for the exhibit, it would be clear that in addition to the cost of the exhibit, the D admission fees would have to be enough to pay the interest that the museum would pay on the money it borrowed. A money. It is using money it In this example, however, the museum has not borrowed already has. M However, TVM calculations are still required. Why? Because the museum could have put the money into some safe investment and earned a return if it did not open the proposed exhibit. In every case that a capital acquisition is considered, we must 2 recognize that the acquisition is paid for either by borrowing money (and therefore 0 paying interest) or by deciding not to invest the money elsewhere (and therefore failing to earn a return). There is a cost-of-capital opportunity cost for all capital asset 0 purchases. If this were not the case, we would not mind lending our own money to 8 someone at a zero interest rate. ISBN 1-323-02300-3 Compounding and Discounting T S TVM computations are based on the concepts of compounding and discounting. Compound interest simply refers to the fact that when money is invested going forward in time, at some point the interest earned on the money starts to earn interest itself. Discounting is just the reversal of this process as we go backward in time. Compounding and discounting can be applied to any returns for an investment, whether earned as interest on a bank account or profits on a venture. For example, suppose that Meals for the Homeless invests $100 of cash in a certificate of deposit (CD) that offers to pay 6 percent per year for two years. Notice that the interest was stated as an annual rate. All interest rates are annual unless specifically stated otherwise. What will the value be after two years? Six percent of $100 is $6. If we earned $6 a year for two years, we would have a total of $12 of interest and would end the two years with $112. That assumes that the CD pays simple interest. By simple interest, we Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 168 Part II • Planning mean the initial investment earns interest, but any interest earned does not in turn earn interest. We can see the simple interest process as follows: $100.00 investment .06 interest rate $ 6.00 interest/year $ 6.00 interest/year 2 years $ 12.00 interest for 2 years $100.00 investment 12.00 interest for 2 years $112.00 ending value By contrast, what if the CD compounds interest annually? In that case, at the end of one year interest would be calculated on the $100 investment. That interest would be $6 (i.e., 6% of $100 $6). At that point, the $6 of interest would be added to the initial investment. In the second year, we would earn 6 percent of $106. That comes to $6.36. The total investment at the end of two years would be $112.36. The difference between simple and compound interest seems to be a minor point, because it adds up to only $.36 in this example. We can see the compound interest process as follows: $100.00 .06 S $100.00 6.00 M $106.00 .06 $106.00 6.36 $ 6.00 $I106.00 $ $112.36 6.36 T this year for our retirement in an 8 percent investSuppose that we invested $10,000 ment. Assume that we plan to retire H in 40 years. Eight percent of $10,000 is $800. If we earned $800 per year for 40 years, that would be $32,000. Together with the initial invest, ment of $10,000, we would have $42,000 in the retirement account using simple interest. By contrast, assume that the 8 percent interest was compounded annually. That is, every year the interest earned so far is added to the principal and begins earning interest itself. Then, the total investment atA the end of 40 years would be worth $217,245. If the interest were compounded quarterly, D the total would be $237,699 (see Table 5-1)—quite a difference from $42,000. The compounding of interest is a powerful force. Note that A how frequently the interest is calculated. The total with simple interest, it does not matter is $42,000 with annual or quarterlyM calculations. Compound interest is a valuable concept if we would like to know how much a certain amount of money received today is likely to be worth in the future, assuming that 2 Often, however, our concern is figuring out how we could earn a certain rate of return. much an amount to be received in the future is worth today. For example, the Museum of 0 Technology is trying to decide if it makes financial sense to invest $50,000 today to earn admission revenues of $12,000 per0year for the next five years. We are concerned with taking those future payments of $12,000 8 each year and determining what they are worth today. The approach needed for this calculation is called discounting. Discounting is the reverse ofTcompounding. If we expect an investment to earn $60,000 five years from now, howS much is that worth today? Is it worth $60,000 today? No, because if I had $60,000 today, I could earn interest and have more than $60,000 five years from now. It is worth less than $60,000. We need to remove the simple interest that has been earned on the original amount and also the compound interest that has been earned on the interest. Discounting is a process of unraveling or reversing all of the compound interest that would occur between now and the future payment. Table 5-1 $10,000 Invested at 8 Percent for 40 Years Compound Interest Annual Interest Calculations $42,000 $217,245 Quarterly Interest Calculations $42,000 $237,699 Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 Simple Interest Chapter 5 • Capital Budgeting 169 Present Value Versus Future Value When interest computations are done for compounding and discounting, one often speaks of the present value (PV) and the future value (FV). The PV represents the beginning point for an investment. It is when the investment starts. The FV represents a time after the investment’s start when an amount of money will be paid or received. Time Value of Money Calculations Although we could calculate interest by laboriously multiplying the interest rate by the amount of money invested over and over for the number of compounding periods, our life is made somewhat simpler by the mathematical development of formulas for interest calculations. For example, using the following notation PV FV i or rate N or nper present value future value S interest rate M number of periods I T N FV PV(1i) H (5.1) , in the future (FV) is equal to This formula says that the amount that we will have the FV can be calculated from the following formula: the amount we start with (PV), multiplied by the sum of one plus the interest rate (i) raised to a power equal to the number of compounding periods (N). For example, supAwould have after two years if we pose that we want to calculate the amount of money we invested $100 today (called time period 0) at 6 percent D compounded annually. A time line for this problem would look 0 A M 1 6% ($100) 2 FV 2 period 0, and expect to get an We are investing (paying out) $100 at the start, time amount of money, FV, two years in the future. The 6 percent 0 interest rate is shown on the time line between the start and the end of the first compounding period. We could use the formula from Equation 5.1 to solve this problem as0follows: 8 FV $100 (1 .06) 2 T $100 [ (1.06) ( 1 .06 )] S .36 $100 ( 1.1236 ) $112 This simply formalizes the process that we followed earlier. Similarly, for the retirement investment calculated earlier with quarterly compounding, the time line would be as follows: 0 1 2% ISBN 1-323-02300-3 $(10, 000 ) 2 159 160 … FV The number of compounding periods, N, is 160. This is because the investment is compounded quarterly for 40 years. There are four quarters in a year. Therefore, four compounding periods each year for 40 years results in a total of 160 periods (4 * 40 = 160). Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 170 Part II • Planning Note that time periods and interest rates must be adjusted for the compounding period. The annual interest rate must be divided by the number of compounding periods per year to get the interest rate per period. The number of compounding periods per year must be multiplied by the total number of years to get the total number of compounding periods. Using the formula to solve for the FV, we find the following: FV $10,000 (1 .02)160 $10, 000 (1.02 )160 $10, 000 (23.7699 ) $237,699 This is the result seen in Table 5-1. The interest rate, i, is .02, or 2 percent. This is because of the quarterly compounding. The interest rate of 8 percent per year (as used earlier for this retirement example) must be divided by four, the number of quarters in each year, to get the quarterly interest rate. Rather than multiply 1.02 times itself 160 times, it would be S or a computer spreadsheet program such as Excel. simpler to use a handheld calculator For discounting, the process is just reversed. If we start with the same formula, M I FV PV(1i) N T the PV: we can rearrange the equation to find H FV , PV (1 i)N (5.1) (5.2) If someone offered to pay us $237,699 in 40 years, how much would that be worth A could invest money at 8 percent per year, comto us today if we anticipate that we pounded quarterly? The time line would D be as follows: 0 1 2% PV A2 M 159 160 … $237,699 We could use Equation 5.2 to solve for the PV, as follows: 2 0PV $237,699 (1.02)160 0 $237,699 8PV 23.7699 T $10,000 discounting S is merely a reversal As we can see, of the compounding process. If we invest $10,000 today, it would grow to $237,699 forty years in the future at 8 percent interest with quarterly compounding. Making the same assumptions, then, $237,699 paid 40 years in the future is worth only $10,000 today. Financial calculators and electronic spreadsheet software programs, such as Excel, have been programmed to perform TVM computations. Since most managers usually do their TVM computations using Excel or similar spreadsheet programs, that is the approach we will take in this chapter. For those interested in learning how to use calculators for TVM computations, see Appendix 5-A. Using Computer Spreadsheets for TVM Computations Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 A number of different computer spreadsheet software programs can be used to solve TVM problems. They are particularly useful for the more complicated calculations where using a calculator may be impractical. Some of the most popular spreadsheets are Microsoft Chapter 5 • Capital Budgeting 171 Excel, Lotus 1-2-3, Apple iWork Numbers, and Google Spreadsheets. Appendix 5-B provides examples of how to solve TVM problems with Excel. The approach of other spreadsheets is similar. Consider the problem of finding the future value of $100 invested for two years at 6 percent. Using Excel, begin by entering the data that will be used to solve the problem. In this example, the problem could be set up as shown in Figure 5-1. This figure shows the data you have, the variable FV that you are looking for, and indicates where the answer will be shown. Once data have been entered, move the cursor to the cell where you want the solution to appear (in this case, Cell D10). Type an equal sign followed by the variable we are trying to find, followed by an open parenthesis, as follows: = FV( Once you have done that, Excel will show the complete formula for computing the S on, you will see: present value. On the screen near the cell you are working M I This will guide you in providing Excel with the data needed to solve for the FV. Following the open parenthesis you have typed, you next insert T the rate (interest rate), nper (number of compounding periods), and PV (present value). HWe have not yet discussed pmt, but for now we can leave a blank space and extra comma for that variable, or we can , use a value of zero for the pmt variable. Type refers to whether the payments come at FV(rate, nper, pmt, pv, type) the beginning or end of each period. This pertains primarily to annuities, which will be discussed below. For now, we can ignore it as well and the value for type can be A omitted. D interest rate should be shown in Two things should be noted in Figure 5-1. First, the the spreadsheet as 6% (see Cell D5). In Excel, it is critical A that the rate be entered either with a percent sign, such as 6%, or as a decimal, such as .06. If you enter 6 rather than 6% M the answer will be grossly incorrect. Second, the PV in the formula should be entered as a negative number. Excel follows the logic that if you pay out something today, you will get back something in the future. So if the FV is to be a positive amount, representing a2receipt of cash in the future, the PV must be a negative amount, representing a payment 0 of cash today. You cannot have a positive number for both the PV and the FV because that would imply that we receive money at the beginning, and then we receive money at0the end. That is not logical. Either B A 8 T D S C 1 2 Future Value Calculation ISBN 1-323-02300-3 3 4 PV = 5 = = 6% 6 rate nper 7 pmt 8 9 10 11 FV = ??? FV = FIGURE 5-1 $ 100 2 0 Initial Data Entry Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 172 Part II • Planning fx =FV(D5,D6,D7,–D4) SUM A B C D E F 1 2 Future Value Calculation 3 4 PV = 5 rate = 6% 6 nper = 2 7 pmt = 0 8 FV = ??? 9 10 FV = 11 12 $ 100 =FV(D5,D6,D7,–D4 ) FV(rate, nper, pmt, [pv], [type]) S FIGURE 5-2 Using Formulas M in Future Value Calculations I you pay out money at the start and receive money later, or vice versa. We can accomplish T could show the value for the PV in Cell D4 as being this in several ways. In Figure 5-1, we a negative $100, or when we complete H the formula for FV, we can refer to the cell reference for the PV with a minus sign in front of it. That is, we can enter the PV into the FV formula as either 100 or else by ,the cell reference to D4. It is important to get into this habit. In many TVM calculations, not entering opposing signs for cash inflows and outflows will produce an error. A Each variable can be inserted as either a numeric value or a cell reference. Given the cell locations of the raw data inDthe worksheet in Figure 5-2, a cell reference formula to solve the above problem would be: = A FV(D5, M D6, D7, D4) An advantage of a formula that uses the cell references is that it will automatically recalculate the future value if the numeric value in any of the indicated cells is changed. 2 If we were to change the rate in Cell D5 from 6% to 8%, a new future value would 0 immediately appear on the worksheet. Alternatively, we could insert the values directly with rate as 6%, nper as 2, and PV 0 as 100 as shown below. 8 T The advantage of this approach S is that it not only will calculate the answer in your = FV(6%, 2, 0, -100) Excel spreadsheet, but it can also be communicated to a colleague who can tell exactly what information you have and what you are trying to calculate. Anyone can drop this into their spreadsheet without needing to know the specific cells in which the raw data appear in your spreadsheet. TVM Excel problems will be discussed in the form of providing the basic Excel formula, as well as the numeric value formula, for a variable, such as: = FV(rate, nper, pmt, pv, type) = FV(6%, 2, 0, -100) Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 Note that if you enter FV(6%, 2, 0, 100) into an Excel spreadsheet cell and press the Enter key, the solution of 112.36 will automatically be calculated. Excel can be used to solve for other TVM variables as well as the FV. See Appendix 5-B for a detailed discussion. Chapter 5 • Capital Budgeting 173 Annuities Although there are many times that we anticipate paying or receiving a single amount of money paid at one point in time, sometimes capital assets result in a number of cash flows over a number of different compounding periods. For example, one might wish to determine the maximum amount that should be paid for a piece of equipment to result in receipts of $3,000, $5,000, and $7,000 over the next three years. 0 1 2 3 (PV) $3,000 $5,000 $7,000 To find out how much this is worth today, we would have to add up the present value of each of the three payments. Essentially, one could break the preceding time line down into three separate problems, as illustrated below: 0 1 (PV) $3,000 0 1 (PV) 2 2 S M I T H , 3 3 $5,000 A 3 D (PV) A $7,000 M Then, add the PV solutions from the three problems together. 0 1 2 ISBN 1-323-02300-3 However, if all three payments are exactly the same and come at equally spaced periods of time, the payments are referred to as an annuity. Computations are somewhat 2 easier for this special case. Although we may think of annuities as being annual 0 payments, that is not necessarily the case for TVM computations. An annuity is any amount of money paid at equal time 0 intervals in the same amount each time. For example, $110 per week, $500 per month, 8 and $1,250 per year each represent annuities. In notation, an annuity is often referred to as PMT, T an abbreviation for payment. Formulas have been developed that can be used to calculate both the future value S 5 These formulas have been and the present value of a stream of annuity payments. included in spreadsheet computer software programs and in handheld calculators that perform TVM computations. Note that annuities generally assume the first payment is made at time period 1, not time period 0. An annuity with the first payment at time period 1 is referred to as an ordinary annuity or an annuity in arrears. Some annuities, such as the rent one pays on an apartment, are called annuities in advance, and the first payment is made at the start, or time period 0. Computer spreadsheets assume annuities are ordinary (first payment at time period 1), unless the user indicates the type of annuity. The present value of an annuity of $1 equals {(1 – [1/(1 + i)N])/i} and the future value of an annuity of $1 equals {[(1 + i)N – 1]/i}. 5 Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 174 Part II • Planning Suppose that we expect to receive $100 per year for the next two years. We could normally invest money at an interest rate of 10 percent compounded annually. What is the present value of those payments? If we put our cursor in an Excel cell, and type PV( we will then see the formula that needs to be completed for Excel to solve for the PV. It will appear as: PV(rate, nper, pmt, fv, type) Using the time line and a spreadsheet, we can solve the problem as follows: 0 1 2 $100 $100 10% (PV) PV PV(rate, nper, pmt, fv, type) PV(10%, 2, 0, 100) S 173.55 M The result shown here indicates I that receiving two annual payments of $100 each for the next two years is worth $173.55 today if the interest rate is 10 percent. The $173.55 T is shown as a negative number because you would have to pay that amount today to receive $100 a year for two years. How much would those two payments of $100 each be H worth at the end of the two years? , 1 0 2 10% FV $100 A $100 (FV) D FV(rate, nper, pmt, pv, type) A FV(10%, 2, 100) M = = = -210.00 Observe that there is a great deal of flexibility. If we know the periodic payment, 2 interest rate, and number of compounding periods, we can find the FV. However, if we know how much we need to have 0 in the future and know how many times we can make a specific periodic payment, we can calculate the interest rate that must be earned. Or 0 have to keep making payments to reach a certain we could find out how long we would future value goal. Given three variables, 8 we can find the fourth. For example, suppose that we are going to invest $100 a year for five years and we want it to be worth $700 at the end T of the fifth year; what interest rate must we earn? If we put our cursor in an Excel cell, and type Rate( we will then see the formula that needs to be completed for Excel to solve S for the rate. It will appear as: Rate(nper, pmt, pv, fv, type, guess) Using the time line and a spreadsheet, we can solve the problem as follows: 1 2 3 4 5 ($100) ($100) ($100) ($100) ($100) $700 0 ?% Rate(nper, pmt, pv, fv, type, guess) Rate(5, 100, 0, 700) 16.9% Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 Rate Chapter 5 • Capital Budgeting 175 If we are investing $100 each year, we pay that money out into the investment, so it is shown as a negative amount. The $700 will be received at the end, so it shown as a positive amount. As you can see, we have calculated that if we pay out $100 a year for five years, in order to receive $700 at the end of the fifth year, we would have to earn a rate of 16.9 percent per year. If we did not enter opposing signs for the PMT and FV, the spreadsheet would not be able to calculate Rate and would give you an error message. Similarly, we can solve for the number of periods. Suppose we know that if we are investing $100 a year, we can earn a 16.9 percent annual rate of return, and we want to have $700 at the end of our investment. We can find the number of periods before we will accumulate the desired amount. If we put our cursor in an Excel cell, and type Nper( we will then see the formula that needs to be completed for Excel to solve for the Nper. It will appear as: Nper(rate, pmt, pv, fv, type) Using the time line and a spreadsheet, we can solve the S problem as follows: 0 M N I … ($100) ($100) ($100) T $700 H Nper(rate, pmt, pv, fv, type) , 700) Nper(16.9%, 100, 0, 1 2 16.9% Nper 5 We see that if we invested $100 a year at 16.9 percent, Ait would take five years for it to grow to $700. D We can also solve for the payment. Suppose we need $700 in five years and believe A We can find the amount we that we can earn 16.9 percent per year on our investment. will need to invest each year to reach that goal. If we put M our cursor in an Excel cell, and type PMT( we will then see the formula that needs to be completed for Excel to solve for the PMT. It will appear as: PMT(rate, nper, pv, fv, 2 type) 0 problem as follows: Using the time line and a spreadsheet, we can solve the 0 1 16.9% (PV) PMT 0 4 8 T PMT(rate, nper, pv, Sfv, type) 2 3 5 ($700) = = PMT(16.9%, 5, 0, 700) = -100.00 We would have to invest $100 a year for 5 years at 16.9 percent, in order to have $700 at the end of the five-year period. ISBN 1-323-02300-3 Cash Flow Versus Revenue and Expense Note that TVM computations are always done based on cash flow rather than accrual-based revenues and expenses. This is because we can only earn a return on resources that are actually invested. For example, interest on a bank account is calculated from the time that money is deposited. Therefore, one should remember that all TVM computations are based on the timing of cash receipts and payments rather than the recording of revenues and expenses. For this reason TVM calculations are often referred to as discounted cash flow analyses. Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 176 Part II • Planning CAPITAL ASSET INVESTMENT ANALYSIS Investment analysis for the acquisition of capital assets requires careful consideration of the item to be acquired. Alternatives should be examined so that we can be assured that we are making an appropriate selection. Several different analytical approaches can help evaluate alternatives: net present cost, annualized cost, net present value, and internal rate of return. In some cases, there may be qualitative benefits from an investment, even though it does not have a solid financial result. Public, health, and not-for-profit organizations may decide that something is worth doing, even if it loses money, because of its benefit to the organizations’ clientele. Management must decide whether to invest in a capital asset because of its nonfinancial benefits after considering all factors. Four general issues should always be considered in evaluation of alternative capital investments. First, the evaluation should include all cash flows. The consideration of all cash inflows and cash outflows is essential to the calculation. Second, the TVM must be S considered. Since the flows of the same number of dollars at different points in time are M clearly consider not only the amount, but also the not equally valuable, the analysis should timing of the cash flows. Third, there I should be some consideration of risk. The expected receipt of a cash interest payment in 10 years from a U.S. Treasury bond investment is T expected to be received in 10 years from a current much less risky than a similar amount start-up business, which may not even H survive for 10 years. There should be a mechanism to incorporate different levels of risk into the calculation. Fourth, there should be a , on the organization’s priorities. These issues are mechanism to rank projects based addressed below. A D that it must acquire a new piece of equipment Many times an organization will find and is faced with a choice amongAseveral possible alternatives. For example, suppose that Leanna Schwartz, executive director of Meals for the Homeless, is trying to decide M between two new industrial-size refrigerators. It has already been decided that the unit Net Present Cost currently owned is on its last leg and must be replaced. However, several good units are available. Either of the two models would be acceptable, and Schwartz has decided to 2 choose the less costly option. 0 are Model A, which is expensive to acquire but The two units under consideration costs less to operate; and Model B,0which is less expensive to acquire but costs more to operate: Purchase Price Annual Outlay Total Cost 8 T S Model A Refrigerator Model B Refrigerator $105,000 10,000 10,000 10,000 10,000 10,000 $155,000 $ 60,000 20,000 20,000 20,000 20,000 20,000 $160,000 Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 At first glance, Model A appears less expensive because it only requires a total outlay of $155,000 as opposed to the Model B total cost of $160,000. However, since payments are made over a period of years for each model, we cannot simply add the costs together. Rather, it is necessary to find the PV of each of the future payments. We can add those PVs to the initial outlay to determine the total cost in equivalent Chapter 5 • Capital Budgeting 177 dollars today. The total of the initial outlay and the PV of the future payments is called the net present cost (NPC). Whichever project has a lower NPC is less expensive. To determine the present values, we will need to have a discount rate to use to bring the future payments back to the present. For this example, we will assume a rate of 10 percent. (Later in this chapter, the appropriate choice of rates is discussed.) Since each of the annual payments is identical, they can be treated as an annuity: Model A: 0 1 2 3 4 5 $(10,000) $(10,000) $(10,000) $(10,000) $(10,000) 10% PV Model B: S 4 5 M 10% I PV $(20,000) $(20,000) $(20,000) $(20,000) $(20,000) T The answers can be obtained solving the problem with H Excel using the following formulas: , fv, type) Model A: PV(rate, nper, pmt, 0 1 2 3 PV(10%, 5, 10000) $37,908 A Model B: D PV(rate, nper, pmt, fv, type) A PV(10%, 5, 20000) M $75,816 The resulting present values for Models A and B tell us what the periodic payments 2 also consider the initial acquisiare equivalent to in total today. To find the NPC, we must tion price: 0 ISBN 1-323-02300-3 Model A NPC $105,000 $37,908 $142,908 0 Model B NPC $60,000 $75,816 8 $135,816 T Based on this, we see that the NPC of Model BSis less than the cost of Model A, even though Model A had initially looked less expensive before the TVM was taken into account. If we were to acquire and pay for all of the other costs related to Model A, we could pay a lump sum today of $142,908, while Model B would only require a lump sum of $135,816. We are indifferent between paying the NPC and paying the initial acquisition cost followed by the periodic payments. The lump-sum NPC total for Model B is clearly less expensive than the lump-sum NPC for Model A. This analysis can only assess the financial implications of the two alternatives. If it turned out that Model A was a more reliable unit, Schwartz would have to make a decision weighing the better reliability of Model A against the lower cost of Model B. The preceding example also assumes that the cost of operating each piece of equipment is the same each year. This is likely to be an unrealistic assumption. If the estimates are different each year, then the annuity approach could not be used. The PV for each year would have to be calculated and then added together to get the NPC. Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 178 Part II • Planning Annualized Cost The NPC method is very helpful for comparing projects that have identical lifetimes. What if investments aimed at the same ends have different lifetimes? Suppose that Model A has a five-year lifetime, but Model B has only a four-year lifetime, as follows: Purchase Price Annual Outlay Total Cost Model A Refrigerator Model B Refrigerator $ 105,000 10,000 10,000 10,000 10,000 10,000 $ 155,000 $ 60,000 20,000 20,000 20,000 20,000 $140,000 S Mto equalize the lifetimes. We could assume that each One approach would be to try time a unit wears out it is replaced.I If we repeat that process four times for Model A and five times for Model B, at the end of 20 years the two alternatives will have equal lifetimes T (see Table 5-2). H the NPC for each of these two 20-year alternatives. We could then proceed to find However, the uncertainties going forward 20 years are substantial. The purchase prices , will likely change, as will the annual operating costs. Our needs might change drastically in 10 years, making the acquisitions in the future unnecessary. As an alternative to the process A of equalizing the lifetimes, we can use an approach called the annualized cost method. In that approach, one first finds the NPC for each D into a periodic payment for the number of years alternative. Then, that cost is translated of the project’s lifetime. The projectAwith the lower annualized cost is less expensive on an annual basis in today’s dollars. M Assume that Model A lasts for five years and Consider the refrigerator example. Model B lasts for four years. All of the assumptions for Model A are the same as they were originally, so the NPC is still $142,908, as calculated earlier. Model B is different, because it now has only a four-year life: 2 Model B: 0 0 2 3 10% 8 PV $(20,000) T $(20,000) $(20,000) S the PV would be: The Excel spreadsheet formula to find 0 1 4 $(20,000) PV(rate, nper, pmt, fv, type) PV(10%, 4, 20000) $63,397 To find the NPC, we must also consider the initial acquisition price. Model B NPC $60,000 $63,397 $123,397 Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 Although the $123,397 NPC for Model B is lower than the $142,908 NPC for Model A, we are now comparing apples and oranges. Model B will only last for four years, while Model A will last for five years. We need to account for the fact that we will have to Chapter 5 • Capital Budgeting 179 Table 5-2 Equalizing Asset Lifetimes Time Period Action Model A Refrigerator Model B Refrigerator 0 Purchase Models A and B $105,000 $ 60,000 1 Annual Outlay 10,000 20,000 2 Annual Outlay 10,000 20,000 3 Annual Outlay 10,000 20,000 4 Annual Outlay 10,000 4 Purchase Model B 20,000 60,000 5 Annual Outlay 5 Purchase Model A 105,000 10,000 6 Annual Outlay 7 Annual Outlay 20,000 10 Purchase Model A 11 Annual Outlay S10,000 10,000 M 10,000 I T10,000 H10,000 105,000 ,10,000 10,000 20,000 A D10,000 10,000 A10,000 M 105,000 60,000 8 Annual Outlay 8 Purchase Model B 9 Annual Outlay 10 Annual Outlay 12 Annual Outlay 12 Purchase Model B 13 Annual Outlay 14 Annual Outlay 15 Annual Outlay 15 Purchase Model A 16 Annual Outlay 16 Purchase Model B 17 Annual Outlay 18 Annual Outlay 19 Annual Outlay 20 Annual Outlay Total Outlay 20,000 20,000 20,000 60,000 20,000 20,000 20,000 20,000 20,000 20,000 10,000 20,000 2 10,000 010,000 010,000 810,000 $620,000 T S 60,000 20,000 20,000 20,000 20,000 $700,000 replace it sooner. This is done by treating each NPC as a present value of an annuity and finding the equivalent periodic payment over its lifetime. Model A: 0 1 ISBN 1-323-02300-3 10% $(142,908) PMT 2 3 4 5 PMT PMT PMT PMT PMT(rate, nper, pv, fv, type) PMT(10%, 5, 142908) $37,699 Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 180 Part II • Planning Model B: 0 1 2 3 4 PMT PMT PMT PMT 10% $(123,397) PMT(10%, 4, 123397) $38,928 Thus, adjusted for their relative lifetimes, including both the acquisition and annual outlays, Model A is less expensive per year than Model B ($37,699 versus $38,928).6 Net Present Value The NPC and annualized cost methods discussed previously involve assuming that the capital assets would cost money to acquire. However, it does not assume that the capital asset would have a direct effect onS revenues or support. Often, one of the major reasons to acquire a capital asset is to use it Mto earn more revenues or generate additional financial support. In such cases, we need to consider both the revenues and costs as measured by the present value of their cashI inflows and outflows. The net present value (NPV) method is one of the most common T approaches for making calculations of the present value of inflows and outflows. The NPV approach calculatesHthe PV of inflows and outflows and compares them. If the PV of the inflows exceeds the, PV of the outflows, then the NPV is positive, and the project is considered to be a good investment from a financial perspective: NPV PV A Inflows PV Outflows and if NPV 0, the project is economically viable. D For example, assume that HOS is contemplating opening a new type of lab. The A equipment for the lab will cost $5 million. Each year there will be costs of running the lab and revenues from the lab. As a result M of general financial constraints, the hospital wants to make this investment only if it is financially attractive. The hospital’s cost of money is 8 percent. In addition, since the hospital feels that often projected revenues are not achieved by new projects, it wants 2 to build in an extra 2 percent margin for safety. It has decided to do the project only if it 0 earns at least 10 percent. That 10 percent rate is considered to be a hurdle rate, or a required rate of return. 0 this rate will it be accepted. Therefore, the NPV Only if the project can do better than must be calculated using a 10 percent 8 discount rate. If the project has a positive NPV, that means that it earns more than 10 percent and will be acceptable. T cash flows from the project: Assume the following projected S New Investment Proposed (Capital Equipment Has a Four-Year Life) Start Cash In Cash Out $ 5,000,000 Total $(5,000,000) Year 1 Year 2 Year 3 Year 4 Total $2,700,000 1,000,000 $1,700,000 $2,800,000 1,300,000 $1,500,000 $2,900,000 1,400,000 $1,500,000 $3,000,000 1,600,000 $1,400,000 $11,400,000 10,300,000 $ 1,100,000 6 In the case of annuities, an alternative annualization approach would be to find the annuity payment equivalent to the initial outlay and add that amount to the annual payments. That will provide an annualized cost. However, that will work only in cases in which the payments after the initial outlay are an annuity. Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 Although we are just assuming these cash flows, it should be noted that estimating future cash flows is often a difficult task that requires a careful budgeting effort. In total, the Chapter 5 • Capital Budgeting 181 project shows a $1,100,000 profit. However, that profit does not account for the timing of the cash flows. The hospital will be spending the full $5,000,000 at the start. However, the cash receipts available to repay the cost of the investment and to pay for the cost of capital used are spread out in the future. To determine whether the investment is worthwhile, we will have to find the NPV. This can be accomplished by finding the PV of each cash inflow and then finding the total PV of the inflows. Then the same procedure can be done for the outflows. The PV of the inflows and the PV of the outflows can be compared to determine the NPV. Alternatively, we can simply find the PV of the net flows for each year. That is, we can take the PV of the $5,000,000 net cash outflow at the start plus the PV of the $1,700,000 net cash inflow from the end of the first year plus the PV of the $1,500,000 net cash inflow from the second year and so on. In Excel this would appear as: C10 A 1 2 3 4 5 6 7 8 9 Rate Pmt Nper fx =PV(B1,C3,B2,–C8) B C 10% 0 0 3 4 $ 5,000,000 $(5,000,000) Year 1 $2,700,000 1,000,000 $1,700,000 SD M 2 I T Year 2 $2,800,000 H 1,300,000 , $1,500,000 Year 3 $2,900,000 1,400,000 $1,500,000 Year 4 $3,000,000 1,600,000 $1,400,000 $(5,000,000) $1,545,455 $1,239,669 $1,126,972 $ 956,219 Start Cash In Cash Out Net Cash Flow 10 Present Value 11 12 Net Present Vaue 1 E F ISBN 1-323-02300-3 A $ (131,685) D A Notice that the present values in Row 10 in the above Excel spreadsheet are the values of each combined cash inflow and outflow. For M example, in column C, the inflows were $2,700,000 in Cell C6 and the outflows were $1,000,000 in Cell C7. Cell C8 shows that the net cash flows for Year 1 were $1,700,000, found by subtracting the outflows for 2 present value of the net Year 1 that year from the inflows for that year. In Cell C10, the cash flow is found. Looking to the right of the fx at the 0 top of the spreadsheet, we see the formula used to find the present value is PV(B1, C3, B2, C8). Cell B1 contains the 0 Cell B2 gives the PMT, which discount rate, Cell C3 contains the nper for the computation, is 0, since there is no PMT in this computation, and Cell 8 C8 contains the net cash flow for Year 1. There is a minus sign in front of C8 in the formula, which forces Excel to display T since Excel requires that cash the present value for Year 1 cash flows as a positive number, inflows and outflows have opposite signs. S The NPV is the PV of the inflows less the present value of the outflows. If we total the results of the individual present value computations shown in summary form in the above Excel spreadsheet, we find that the NPV is $131,685. Since the NPV is negative, the investment is earning less than the 10 percent required rate of return. It is therefore not an acceptable project. Spreadsheets typically have an NPV function to solve this more directly. In Excel, the formula to solve an NPV problem is, NPV(rate, value1, value2, …). The values refer to each of the future values in the problem. For the earlier proposed investment, the $5,000,000 outlay occurs in the present and is not included in the formula. So value 1 would be $1,700,000, value 2 would be $1,500,000, and so on. Once the NPV is found for the future values, however, the initial $5,000,000 outlay needs to be subtracted to find the answer. This can be combined into one formula as follows: NPV(rate, value1, value2, . . .) Initial Outlay Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 182 Part II • Planning This can then be solved in Excel as seen below: B9 A 1 2 3 4 5 6 7 8 9 Rate fx =NPV(B1,C6:F6) B C 10% Start Cash In Cash Out Net Cash Flow Present Value of Net Cash Flows 10 Less: Initial Outlay 11 Net Present Value Year 1 $2,700,000 $ 5,000,000 1,000,000 $(5,000,000) $1,700,000 D Year 2 $2,800,000 1,300,000 $1,500,000 E Year 3 $2,900,000 1,400,000 $1,500,000 F Year 4 $3,000,000 1,600,000 $1,400,000 NPV Computation $ 4,868,315 $(5,000,000) $ (131,685) S Note the formula for Cell B9, M which can be seen on the formula bar above columns A and B. The NPV formula requires the rate, 10 percent from Cell B1, and the range I where the future cash flows are located in the spreadsheet, C6:F6, or Cell C6 to Cell F6. T if you enter the individual future cash flow values Excel will generate an error message into the formula rather than providing the cell range in a format such as C6:F6. The initial H cash outflow from Cell B6 is shown in Cell B10 and is then subtracted to finish the NPV , calculation. Organizations are often faced with multiple investment opportunities. Because resources are limited, they cannot do everything and must choose which projects to undertake. To do that, managers will sortA projects based on their net present values. If decisions are made on a purely financial basis, D they will reject all projects with NPVs less than zero and rank projects with NPVs greater than zero based on the size of their returns—choosing investments with higher NPVs beforeAthose with lower projected returns. However, public service organizations may not always follow these conventions. If M they feel some projects advance the organization’s mission and they have sufficient funds to subsidize any anticipated NPV shortfalls, management might choose to undertake projects with negative NPVs. Similarly, 2 managers might choose investments with lower NPVs over those with higher expected returns if they feel those projects are more important to 0 the organization’s social goals. The NPV should be computed in any case, however, so if a project is selected for other than 0 its financial contribution, the organization’s managers will be aware of the extent to which it falls short on the financial merits. Since losses on 8 one project will have to be made up elsewhere, the manager needs to know the size of T is committing to accept. the potential loss that the organization Internal Rate of Return S Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 The NPV approach indicates whether a project does better than a specific hurdle rate. However, it does not indicate the rate of return that the project actually earns. The internal rate of return (IRR) is the rate of return earned by an investment. Many managers are more comfortable ranking projects of different sizes by their rates of return rather than by the NPV. Suppose that we evaluate two projects using a 10 percent hurdle rate. A small project with a 35 percent rate of return might have a lower NPV than a much larger project with a 12 percent rate of return. Both projects have a positive NPV. However, because of the relatively modest magnitude of the smaller project, its exceptional profitability may go unnoticed when compared with another project with a very large NPV. Some managers, therefore, like to use a method that assesses the project’s rate of return, in addition to using the NPV approach. The IRR method can be used to generate that information. Chapter 5 • Capital Budgeting 183 The IRR method is derived from the NPV approach. Assume we start with the following equation: NPV PV Inflows PV Outflows Then if NPV 0, the project earns more than the discount rate, and if NPV 0, the project earns less than the discount rate. Therefore, if NPV 0, the project earns exactly the discount rate. So, if we want to know the rate of return that a project earns, we simply need to determine the discount rate at which the NPV is equal to zero. And, since NPV PV Inflows PV Outflows S M 0 PV Inflows PV Outflows I or T PV Outflows PV Inflows. H So we need to set the PV of the outflows equal to the PV of the inflows and find the , discount rate at which that is true. Suppose we invest $6,700 today to get a cash flow for NPV to be equal to zero, of $1,000 a year for 10 years (i.e., invest $6,700 to get back a total of $10,000 in the future). What is the IRR for this investment? 0 1 2 $1000 , $1,000 ?? % ($6,700) A D … A M 9 10 $1,000 $1,000 Rate(nper, pmt, pv, fv, type, guess) = Rate(10, 1000, -6700) 2 = 8% 0 It turns out that the IRR for this investment would be 8 percent. 0 If the cash flows are different Note that the preceding problem assumes an annuity. each year, it is mathematically harder to determine the8IRR. Suppose, for instance, that the preceding example does not provide payments of T then increases by $100 in each $1,000 per year, but rather $1,000 in the first year and subsequent year as follows: S 0 1 2 ?? % ($6,700) 9 10 $1,800 $1900 , … $1,000 $1,100 Using Excel, this problem can be solved using the IRR function. The Excel formula for internal rate of return is: ISBN 1-323-02300-3 IRR(values, guess) The values represent all of the cash inflows and outflows, including the initial time 0 payments or receipts. The guess is the user’s best guess of the rate of return. The computer uses this as a starting point as it cycles in on the actual rate. Assume that the user guesses 5 percent. If a numeric value formula is used, the values must be provided Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 184 Part II • Planning to Excel within curly brackets, so that the spreadsheet program can distinguish the values from the guess, as follows: IRR({ 6700, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900}, 5%) 15% Note that the IRR function also will not work unless there is at least one inflow or positive number and at least one outflow or negative number in the series of values. However, it is generally not necessary to enter a guess value for the rate of return. A step-by-step Excel solution for an IRR problem is provided in Appendix 5-B. Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 LIMITATIONS OF IRR Managers should be aware of three important limitations of IRR. First of all, it assumes that cash inflows during the project are reinvested at the same rate that the project earns. Second, sometimes it will cause managers to choose incorrectly S from two mutually exclusive projects. Finally, it can create erroneous results if the investM ment does not have a conventional pattern of cash flows. Implicit in the NPV technique Iis an assumption that all money coming from a project during its lifetime is reinvested at the hurdle rate. That is reasonable since the hurdle rate T in some way measures the organization’s other alternative opportunities. We may want Hbecause we have other opportunities that can earn a project to earn at least 10 percent 10 percent. , By contrast, the IRR method assumes that as cash flows are received, they are reinvested at the same rate as the project earns (i.e., the IRR). Suppose that a project has an IRR of 25 percent. Suppose Afurther that this represents an unusually high rate of return for any of the organization’s investments. It may be unrealistic to expect to be able to reinvest cash as it isDreceived from the project in additional projects at 25 percent. In effect, then, the IRR A method may overstate the true rate that will be earned on the project. M one is evaluating two mutually exclusive projAnother problem may arise when ects. It is possible that a small project may have a very high rate of return, whereas a larger project has a very good, but somewhat smaller, rate of return. For example, 2 suppose that the golf course in Millbridge is trying to decide whether to put up a “19th Hole” restaurant and bar on a piece 0 of land or to pave it over for additional parking. Only one piece of land is available on the golf course property to use for any kind of 0 development. Assume that the parking lot8will cost $50,000 and will earn an annual net return of $20,000 per year for 20 years. T The IRR for that investment is 39.95 percent. Alternatively, the 19th Hole will cost $500,000 to build and will earn an annual profit S in an IRR of 29.84 percent. Normally the town of $150,000 for 20 years. This results and the golf course do not have any investments that earn a higher rate of return than 15 percent. Both projects are very attractive, but we cannot do both since they both use the same piece of land. Often, when IRR is used to evaluate investments, managers rank the projects in order of IRR, first selecting those with the highest IRR. If that were done in Millbridge, it would be a mistake. Although a 39.95 percent return may appear better than a 29.84 percent return, overall the town would be better off with the 19th Hole. Why? Because if it invests in the parking lot, the town will earn 39.95 percent on an investment of $50,000 but will then invest the remainder of the money at 15 percent. If the managers decide to invest $500,000 for the year, they can put the entire amount into the 19th Hole and earn a 29.84 percent return on the total amount versus investing $50,000 at 39.95 percent and $450,000 at 15 percent. Chapter 5 • Capital Budgeting 185 Consider the following annual returns: $20,000 for the parking lot (given previously) 71, 893 for other projects (PV $450,000; N 20; i 15%; PMT $71,893) $91,893 total annual return versus $150,000 for the 19th Hole (given previously) Clearly, the returns are better by investing in the 19th Hole. We would fail to see that we simply chose the project with the highest IRR first. By contrast, the NPV method gives the correct information. The NPV for the 19th Hole evaluated at a hurdle rate of 15 percent is $438,900, whereas the NPV for the parking lot and other projects is $75,187. Finally, many investment projects consist of anSinitial cash outflow followed by a series of cash inflows. This is referred to as a conventional pattern of cash flows. M However, it is possible that some of the subsequent cash flows will be negative. In that case, the method can produce multiple answers, and Ithe actual rate of return becomes ambiguous. In such cases, one is better off relying on T the NPV technique. A modified IRR method addresses some of these concerns. The interested reader H listed at the end of this chapter. should consult an advanced text such as several of those , Selecting an Appropriate Discount Rate ISBN 1-323-02300-3 The rate used for PV calculations is often called the hurdle A rate or required rate of return, or simply the discount rate. The discount or hurdle or required rate should be based on D the organization’s cost of capital. Often not-for-profit organizations receive donations A that can be used for capital investments. This complicates the measurement of the cost of capital. For projects that are M specifically funded by donations, it may not be necessary to calculate the NPV. However, that involves assuming that all costs are covered by the donation. To the extent that the organization must bear other costs, it should employ TVM techniques with a hurdle rate 2 based on its overall cost of capital. Selection of an appropriate discount rate for 0governments to use is difficult. According to Mikesell, “There is . . . no single discount0rate that is immediately obvious as the appropriate rate for analysis.”7 The two methods he proposes are the interest 8 rate that the funds could earn rate the government must pay to borrow funds and the if they were employed in the private sector. The problem with the former approach T is that the government may be able to borrow money at a substantially lower interest rate than could be earned on money invested in the S private sector. This might unduly siphon money out of the private sector. The latter approach (the rate the funds could earn in the private sector) may be more appropriate, but is likely to be much harder to determine. In practice, there is little consistency in the discount rate used across governments and even within different branches of the same government. Yet, despite these difficulties in agreeing on the most appropriate rate for a government to use, there appears to be agreement that taking into account the TVM is clearly appropriate for all types of organizations. 7 John Mikesell. Fiscal Administration: Analysis and Applications for the Public Sector, 6th ed. Belmont, Ca.: Thomson/Wadsworth, 2003, p. 259. Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 186 Part II • Planning In calculating the TVM, the question often arises regarding how to treat inflation. One approach would be to include the anticipated inflation rate in the discount rate. However, the weakness of that approach is that not all cash inflows and outflows will necessarily be affected by inflation to the same extent. When we hear that the inflation rate in society is a certain percentage, that really represents an average impact of inflation rather than one consistent inflation rate for all things. A preferred method is to try to anticipate the impact of inflation on the various cash inflows and outflows and adjust each individual flow before calculating the PV or FV. In that case, inflation would not be included in the discount rate itself. For example, suppose that we think that it will cost $1,000 to operate a machine each year, but that does not take into account inflation. Then we may want to adjust the cash flows for the succeeding years to $1,030, and then $1,061, and so on, multiplying the cash flow each year by 103 percent, if we think the cost will rise 3 percent per year due to inflation (be careful to compound the impact of inflation—note that the third-year expected cost is $1,061 rather thanS$1,060). Other cash inflows and outflows might be expected to rise faster or slower, depending on how inflation affects them. INFLATION M I management can totally predict future cash inUNCERTAINTY There is no way that flows and outflows in many capital T budgeting decisions. Things do not always go as planned. To protect against unexpectedly poor results, many organizations increase their required discount rate. The greaterH the chance of unexpected negative events, the more the discount rate would be adjusted. , For example, in buying a new refrigeration unit, the chances of problems may be small. However, in opening an entire new soup kitchen location, the potential for unexpected problems may be substantially higher. Thus, the hurdle rate is adjusted upward based A on the riskiness of the project. The greater the risk, the higher the hurdle rate is raised. D Cost-Benefit Analysis A Cost-benefit analysis (CBA) is another M technique widely used by governments for evaluating capital budget decisions. CBA compares the costs and benefits of an action or program. The method takes into account not only private costs and benefits but public ones as well. Cost-benefit analysis has been defined 2 as being an 0 analytical technique that compares the social costs and benefits of proposed programs or policy actions. All losses and gains . . . are included and measured in 0 dollar terms. The net benefits . . . are calculated by subtracting the losses incurred 8 the gains that accrue to others. Alternative actions by some sectors of society from are compared, so as to choose T (ones) that yield the greatest net benefits, or ratio of benefits to costs. The inclusion of all gains and losses to society in cost-benefit analysis distinguishes it fromScost effectiveness analysis, which is a more limited view of costs and benefits.8 Many people think that cost-benefit analysis is associated with large-scale public projects, such as the building of a dam. However, the technique can be extremely useful even for evaluating small purchases such as a personal computer. Any organization attempts to determine if the benefits from spending money will exceed the cost. If the benefits do outweigh the costs, it makes sense to spend the money; otherwise it does not. In the case of the government, the benefits and costs must be evaluated broadly to include their full impact on society. In the political arena that John L. Mikesell. Fiscal Administration: Analysis and Applications for the Public Sector, 4th ed. Fort Worth, Tex.: Harcourt Brace College Publishers, 1995, pp. 559–60. Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 8 Chapter 5 • Capital Budgeting 187 government managers find themselves in, the careful measurement of costs and benefits provides the information needed to support a spending decision. There are several key elements in performing a cost-benefit analysis: • determining project goals, • estimating project benefits, • estimating project costs, • discounting cost and benefit flows at an appropriate rate, and • completing the decision analysis. To determine the benefits, it is first necessary to understand what the organization hopes the project will accomplish. So identification of goals and objectives is essential. Suppose that Millbridge’s town manager, Dwight Ives, is considering buying a new garbage truck. The first question is why he feels that the town would be better off with a new garbage truck. The goals may be few or numerous, S depending on the specific situation. Perhaps the old truck breaks down frequently and has high annual repair costs. One goal will be to lowerM repair costs. Perhaps the old truck is much smaller than newer ones. As a result, it has to make frequent trips to unload. A I second goal may be to save labor costs related to the frequent unloading trips. A third T goal may relate to reduction of the costs of hauling recyclables. If the new truck is appropriate for multiple uses, it may eliminate the need toHpay for an outside service to haul recyclable materials such as paper or bottles. DETERMINING PROJECT GOALS , Once the goals have been identified, the specific amount of the benefits must be estimated. The benefits should include only the increA the manager would not include mental benefits that result from the project. For instance, the benefit to citizens of having their garbage collected, D since that will be accomplished (in this example) whether the town uses the old truck or the new truck.9 However, all additional benefits should be considered, estimated,Aand included in the cost-benefit calculation. M In the Millbridge example, it is likely that the town manager or one of his assistants will be able to calculate the benefits fairly directly. For example, the town knows how many trips the current truck makes to unload its garbage. 2 Based on the capacity of the new truck, the number of trips the new truck would need to make can be calculated. The 0 estimated number of trips saved can then be calculated. The town can measure how long 0 and use that information along it takes for the driver to make trips to unload the truck with the driver’s pay rate to estimate labor savings. This 8 assumes that the driver is an hourly employee and that there really would be reduced labor payments. If the driver is T of work are required, then there to be paid the same amount no matter how many hours would be no labor benefit. S The labor savings is one component of the benefits. The town manager will also have to estimate the repair cost savings, the savings from not using an outside service to haul recyclables, and so on. All impacts of the change, as well as future circumstances, must be considered. For example, if the town is growing in population, it is likely to have more garbage in the future. That could mean the new truck would result in saving even more trips in the future. However, the estimation of benefits is a potentially difficult process. Many times the benefits cannot be measured by simply evaluating saved costs. In such situations, it is ISBN 1-323-02300-3 ESTIMATING PROJECT BENEFITS 9 The example assumes that the old truck is reliable enough to remove garbage on schedule. If collections are occasionally delayed by several days because of the unreliability of the old truck, then the benefit of prompt collection would also need to be measured. Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 188 Part II • Planning helpful to determine the value of benefits in a private market situation, if possible. If the benefits have a comparable value in the private sector, that can be used as an estimate. However, a private sector comparison is not always available. Suppose that there is a proposal for Millbridge to convert a wooded area into a park with a baseball field. Many people will enjoy playing ball on the field. How much is that benefit worth? What would people be willing to pay for the benefit? Mikesell notes that When the product or service is of this type . . . a different approach is used . . . the estimation of consumers’ surplus—the difference between the maximum price consumers would willingly pay for . . . a commodity and the price that the market demands . . . The underlying logic . . . is relatively simple . . . Points along an individual’s demand curve . . . represent the value the person places on particular amounts of the product . . . . Consumer surplus (is) the difference between the (total) maximum price the individual would have paid less the price he or she actually pays.10 S it will be necessary to estimate consumer surplus. As part of the cost-benefit analysis, An in-depth discussion of demand M curves and estimation of consumer surplus is beyond the scope of this book. More complexity is added if the project either is lifesaving or may cost lives. The reader is referred toIthe Suggested Readings at the end of this chapter for further discussion of these and other T advanced cost-benefit issues. H have costs as well as benefits, and these costs Projects must also be estimated as part of ,the cost-benefit analysis. In the case of the garbage truck, the primary cost relates to the acquisition of the truck. The truck has a market price, so this estimation is fairly straightforward. But how about the park and baseball field? Certainly, we can assign market-based prices to the cost of clearing the woods A and preparing the field. However, in cost-benefit analysis it is also critical to consider D opportunity costs. Opportunity cost refers to the fact that when a decision is made to do something, other alternatives A are sacrificed. In the case of converting a wooded area for use as a park and baseball field, Millbridge and its residents will have to M sacrifice other possible uses for the land, including preservation of the wooded area. The opportunity cost of the wooded area in its next best use to being a park should be estimated. 2 Suppose that several houses currently look out on woods and, after the park is 0 lots of people in it. The homeowners might view made, will look out on a park with the ready accessibility of the park0to be a benefit. It is possible, however, that since they chose to live near woods, they will be made unhappy by their loss. This is a cost 8 that must be included in the analysis. This can be to society and therefore is something done in the same way as benefits are T estimated. While some users of the park will have a consumer surplus, those who prefer the wooded area will have a negative consumer surplus if the project is carried out.S ESTIMATING PROJECT COSTS DISCOUNTING COST AND BENEFIT FLOWS Often projects evaluated using CBA require flows of benefits and costs that occur over a period of years. The time value of money techniques discussed earlier in the chapter would have to be applied to these cash flows to find their present value. Once all of the relevant costs and benefits of a project have been estimated and adjusted in a discounting process, they can be compared to each other in the form of a ratio. Generally, benefits are divided by costs. If the result COMPLETING THE DECISION ANALYSIS Mikesell, pp. 240–41. Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 10 Chapter 5 • Capital Budgeting 189 is greater than 1, it means that the benefits exceed the costs, and the project is desirable. The greater the benefit to cost ratio, the more desirable the project is. Other Techniques of Capital Budgeting In addition to the techniques for evaluating capital acquisitions that have been discussed previously, there are two other widely known techniques, both of which have serious flaws. Although we do not recommend use of these techniques by themselves, the reader should be aware of their existence and limitations. These two methods are the payback approach and the accounting rate of return (ARR) approach. The payback approach argues that the sooner we get back our money, the better the project will be. This is a risk-averse method. Essentially, it focuses on recovery of the initial investment as soon as possible. Then any additional flows are viewed as being profits. The investor is safe at that point, having recovered all the money invested. However, consider the following three projects: Investment A ($) Start Year 1 Year 2 Year 3 Year 4 (100,000) 90,000 10,000 20,000 0 S Investment M B ($) (100,000) I 10,000 T 90,000 20,000H 0 , Investment C ($) (100,000) 80,000 10,000 150,000 150,000 The payback technique argues that A and B are equally good and are better than C. In both A and B, the $100,000 initial investment is recovered by the end of the second A year. In C, the investment is not recovered until sometime during the third year. The D objection to the payback method is that it ignores everything that happens after the payback period. It also does not consider the TVM. WeAwould argue that A is better than B because of the TVM. Further, C is better than A or B. For project B, getting $90,000 in the second year instead of the first will result in a M lower NPV than that of Project A. Further, the NPV of C is better than A or B because of the large returns in the fourth and fifth years. 2 Some organizations employ payback together with one of the TVM techniques discussed earlier. They argue that TVM techniques are 0good for evaluating profitability, accounting for the timing of cash flows. However, payback adds information about risk. 0 Among differing projects with similar NPVs or IRRs, the one with the shortest payback 8 into the future, the greater the period involves the least risk. Since the further we project uncertainties, employing payback as an additional toolTfor capital budgeting rather than the primary tool is a potentially useful approach. S is the ARR approach. In this The other capital budgeting method not yet discussed approach, the profits that are expected to be earned from a project are divided by the total investment, as follows: Profit Return on Investment Investment ISBN 1-323-02300-3 For example, suppose that we invest $100,000 today in a project that will have revenues of $50,000 and expenses of $40,000 each year.11 The project therefore earns 11 Assume that each year the expenses include a pro-rata (proportional) share of the cost of the capital investment. Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. 190 Part II • Planning annual profits of $10,000 per year for five years. The total profit is $50,000 and the calculation of the accounting rate of return would then be as follows: $50, 000 100% 50% $100, 000 This is clearly unrealistic for a number of reasons. First, it is a return for the entire project life. This is sometimes corrected by dividing the return by the number of years in the project’s life, as follows: 50% 10% 5 However, this still does not resolve the problems related to the failure to account for the TVM. The failure to account for the fact that the investment is made today and the profits are earned in future time periods will typically cause the ARR to be overstated. S all cash flows, they do not account for the TVM, These methods do not consider and they do not rank the projects in Mterms of their ability to make the organization better off financially. As such, they violate a number of the conditions for a good capital investI ment analysis tool. Summary T H , Assets with lifetimes of more than one year are often referred to as capital assets. The process of planning for their purchase is often referred to as capital budgeting. A capital budget is prepared as a separate document, which becomes part of the organization’s master budget. Capital assets are considered separately from the operating budget, because it is not appropriate to charge the entire cost of a resource that will last more than one year to the operating budget of the year it is acquired. Who could ever justify buying a new building if the entire cost of the building were included as an operating expense in the year it was acquired? Capital items also require special attention because (1) the initial cost is large, making a poor choice costly; (2) the items are generally kept a long time, so the organization often lives with any poor choices for a long time; (3) we A can only understand the financial impact if we evaluate the D entire lifetime of the assets; and (4) since we often pay for the asset early and receive payments as we use A it later, the time value of money must be considered M Consideration of the time value of money requires careful attention to the principles of compounding and discounting. Present values and future values must 2 determined where appropriate to allow managbe ers 0 to make informed decisions. Often it is necessary to employ TVM techniques such as net present cost, 0 annualized cost, net present value, and internal rate of return when assessing potential capital investments. 8 Key Terms from This Chapter net present cost for each alternative is determined and then translated into a periodic payment for each year of the asset’s life to find the cost per year, taking into account the time value of money. annuity. Series of payments or receipts each in the same amount and spaced at even time periods. For example, $127.48 paid monthly for three years. annuity in advance. An annuity with the first payment at the beginning of the first period. annuity in arrears. An annuity with the first payment at the end of the first period. Financial Management for Public, Health, and Not-for-Profit Organizations, Fourth Edition, by Steven A. Finkler, Thad D. Calabrese, Robert M. Purtell, and Daniel L. Smith. Published by Prentice Hall. Copyright © 2013 by Pearson Education, Inc. ISBN 1-323-02300-3 accounting rate of return (ARR). The profitability of an investment calculated by considering the profits it generates, as compared with the amount of money invested. accumulated depreciation. Total amount of depreciation related to a fixed asset that has been taken over all of the years the organization has owned that asset. amortization. Allocation of the cost of an intangible asset over its lifetime. annualized cost method. Approach used to compare capital assets with differing lifetimes. The T S Chapter 5 • Capital Budgeting 191 ISBN 1-323-02300-3 annuity payments (PMT). See annuity. capital acquisitions. See capital assets. capital assets. Buildings or equipment with useful lives extending beyond the year in which they were purchased or put into service; also referred to as long-term investments, capital items, capital investments, or capital acquisitions. capital budget. Plan for the acquisition of buildings and equipment that will be used by the organization in one or more years beyond the year of acquisition. Often a minimum dollar cutoff must be exceeded for an item to be included in the capital budget. capital budgeting. Process of proposing the purchase of capital assets, analyzing the proposed S purchases for economic or other justification, and M encompassing the financial implications of capital items into the master budget. I cash flow. Measure of the amount of cash received T or disbursed at a given point in time, as opposed to H revenues or income, which frequently is recorded at a time other than when the actual cash receipt or , payment occurs. cell reference formula. An Excel formula that uses the cell addresses where the raw data are located. A compound interest. Method of calculating interest D that accrues interest not only on the amount of the original investment, but also on the interest that has A been earned. M cost of capital. The cost to the organization of its money. Often represented by the interest rate that the organization pays on borrowed money. 2 cost-benefit analysis. Measurement of the relative 0 costs and benefits associated with a particular project 0 or task. depletion. The process of allocating a portion of 8 the value of natural resources to expense as units of T the resource are extracted. S depreciation. Allocation of a portion of the cost of a capital asset into each of the years of the asset’s expected useful life. depreciation expense. Amount of the original cost of a capital asset allocated as an expense each year. discounted cash flow. Method that allows comparisons of amounts of money paid at different points of time by discounting all amounts to the present. discounting. Reverse of compound interest; a process in which interest that could be earned over time is deducted from a future payment to determine how much the future payment is worth at the present time. discount rate. Interest rate used in discounting. future value (FV). The amount a present amount of money will grow to be worth at some point in the future. hurdle rate. See required rate of return. internal rate of return (IRR). Discounted cash flow technique that calculates the rate of return earned on a specific project or program. net present cost (NPC). Aggregate present value of a series of payments to be made in the future. …

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- Making our customers happy is an important part of our service. So do not be surprised if you get your paper well before the deadline!
- We pay a lot of attention to ensuring that you get excellent customer service. You can contact our Customer Support Representatives 24/7. When you order from us, you can even track the progress of your paper as it is being written!
- We are attentive to the needs of our customers. Therefore, we follow all your instructions carefully so that you can get the best paper possible.
- It matters to us who writes for you, and we are serious about selecting the best candidates.
- Our writers are always learning something new, so they are familiar with the latest developments in the scientific world and can write papers with updated information and the latest findings.

**Our Guarantees:**

- Quality original papers that follow your instructions carefully.
- On time delivery – you get the paper before the specified deadline.
- Attentive Customer Support Representatives available 24/7.
- Complete confidentiality – we do not share you details or papers with anybody else.