# In this chapter, you will learn to use net present value analysis in cost and price analysis.

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1 9.0 - Chapter Intrductin In this chapter, yu will learn t use net present value analysis in cst and price analysis. Time Value f Mney. The time value f mney is prbably the single mst imprtant cncept in financial analysis. When we say that mney has time value, we mean that a dllar t be received tday is wrth mre than a dllar t be received at any future time. Mney has a time value because f the pprtunity t earn interest r the cst f paying interest n brrwed capital. Fr example, assume that yu need t buy a new car but d nt have the mney that yu need t pay fr it. Yu must brrw the entire purchase price. Tw dealers ffer t sell yu identical cars fr \$21,000. Dealer #1 requires cash n delivery. Dealer #2 will prvide yu an interest-free lan fr ne year. Where wuld yu buy the car? Prbably frm Dealer #2, because yu will save all the interest fr the first year f wnership. Present Value. In the example abve, Dealer #2 was clearly the lw-cst chice (because f the interest-free lan fr ne year), but what if Dealer #1 ffered the car at a lwer price, say \$20,000? Which wuld be the lw-cst chice then? T make that decisin, yu must be able t determine the present value f each alternative. If yu culd invest \$20,000 at 5.0 percent interest, it wuld be wrth \$21,000 at the end f ne year. Based n that calculatin, we culd say that \$20,000 is the present value f \$21,000 ne year frm nw when the interest rate is 5.0 percent. At that interest rate, yu wuld presumably be indifferent abut where t buy yur car because the present value f the tw chices is the same. Net Present Value. Calculating present value may invlve receipts as well as expenditures. Fr example, the alternatives may have sme salvage value after their useful life has ended. The estimated receipt frm the sale f the item must be cnsidered in yur analysis. The difference between the present value f the receipts and the present value f the expenditures is net present value. The best financial chice is the alternative with the highest net present value. In prcurement, the alternative with the

2 highest net present value is the alternative with the smallest payment net present value. Factrs Affecting Net Present Value. The majr factrs affecting present value are the timing f the expenditure (receipt) and the discunt (interest) rate. The higher the discunt rate, the lwer the present value f an expenditure at a specified time in the future. Fr example, as yu learned abve, \$20,000 is the present value f \$21,000 ne year frm nw when the interest rate is 5.0 percent. If the interest rate were 10.0 percent, \$19,09 wuld be the apprximate present value f \$21,000 ne year frm nw. Nte that the change in the interest rate wuld have a significant affect n yur net present value analysis in the car case. Yur chice is still t pay \$20,000 nw r \$21,000 a year frm nw. At an interest rate f 10 percent yu culd invest \$19, tday t earn the \$21,000 a year frm nw. S it appears that the lw-cst chice is t wait and pay the \$21,000 in ne year. Office f Management and Budget (OMB) Circular A-94Circular A-94, Guidelines and Discunt Rates fr Benefit-Cst Analysis f Federal Prgrams, delineates the rates that yu shuld use in Gvernment net present value analysis. These rates are based n the rate that the Treasury Department pays t brrw mney fr perids frm 91 days t 30 years and they are updated annually at the time f the President's budget submissin t Cngress. These rates can be fund n the internet at r btained by telephning (202) Net Present Value Analysis. Regardless f the applicatin, yu shuld use this 5-step prcess in net present value analysis: Step 1. Select the discunt rate. Step 2. Identify the csts/benefits t be cnsidered in analysis. Step 3. Establish the timing f the csts/benefits. Step 4. Calculate net present value f each alternative.

3 Step 5. Select the ffer with the best net present value. Lease-Purchase Analysis Examples (OMB Circular A-94, Paragraph 13). In this chapter, we will demnstrate the applicatin f net present value analysis cncepts using lease-purchase examples. Our use f these examples is nt meant t ignre ther uses f net present value analysis in Gvernment cntracting. We selected the lease-purchase decisin because f the emphasis in OMB Circular A-94 and because f the grwing Gvernment interest in leasing as a viable alternative t purchase Identifying Situatins Fr Use OMB Suggested Use (FAR and OMB Circular A-94, Paragraph 4). Unless precluded by agency prcedures, OMB suggests the use f net present value analysis in any analysis t supprt Gvernment decisins t initiate, renew, r expand prgrams r prjects which wuld result in a series f measurable benefits r csts extending fr three r mre years int the future. Examples f acquisitin decisins that invlve such analyses include: Lease-purchase analyses; Analyses f different lease alternatives; Life-cycle cst analyses; and Trade-ff analyses cnsidering acquisitin csts and energy-utilizatin csts f peratin. Required Lease-Purchase Analysis (OMB Circular A-94, Paragraph 13). In additin t the suggested applicatin t any benefit-cst analysis, OMB Circular A-94 requires that any decisin t lease a capital asset be justified as preferable t direct Gvernment purchase and wnership in situatins where bth the fllwing are true: The lease-purchase analysis cncerns a capital asset r a grup f related assets whse ttal fair market value exceeds \$1 millin. The lease-purchase analysis cncerns a capital asset (including durable gds, equipment, buildings, facilities, installatins, r land) which is: Leased t the Gvernment fr a term f three r mre years;

4 New, with an ecnmic life f less than three years, and leased t the Gvernment fr a term f 75 percent r mre f the ecnmic life f the asset; Built fr the express purpse f being leased t the Gvernment; r Leased t the Gvernment and clearly has n alternative cmmercial use (e.g., a specialpurpse Gvernment installatin). The analysis cnducted in supprt f that justificatin shuld invlve net present value analysis and can be perfrmed in ne f three ways, as delineated in the table belw: Methds f Lease-Purchase Analysis Cnduct a separate leasepurchase analysis fr each acquisitin. Use... Only fr majr acquisitins. A lease is a majr acquisitin when ne f the fllwing is true: Cnduct peridic lease-purchase analysis f the recurring acquisitin f assets fr the same general purpse. Adpting a plicy fr smaller leases and submitting the plicy t OMB fr apprval. Acquisitin is a separate line item in the Agency's budget. The agency r the OMB determines that the acquisitin is a majr ne. The ttal purchase price f the asset r grup f assets will exceed \$500,000. Fr an entire class f assets. Nrmally after the agency demnstrates that: The leases in questin wuld generally result in substantial savings t the Gvernment. The leases in questin are s small r s shrt as t

5 make separate analyses impractical. Leases f different types are scred cnsistent with the requirements f OMB Circular A-11, Preparatin and Submissin f Annual Budget Estimates Selecting A Discunt Rate OMB Discunt Rate Guidance (OMB Circular A-94, Appendix C). Unless precluded by agency practice, yu shuld use the current discunt rates cntained in OMB Circular A-94, Appendix C. Nminal Treasury Rates (OMB Circular A-94, Appendix A & Appendix C). Fr mst benefit-cst analysis yu shuld use nminal discunt rates (i.e., discunt rates that include the effect f actual r expected inflatin/deflatin). The fllwing rates are the actual rates cntained in OMB Circular A-94, Appendix C fr use thrugh January 1999: Nminal Discunt Rates Maturity in Discunt Rate Years 3 years 5.6% 5-year 5.7% 7-year 5.8% 10-year 5.9% 30 years 6.1% Real Treasury Rate (OMB Circular A-94, Appendix A & Appendix C). Fr sme prjects (e.g., lng-term real estate leases), yu may find it mre reasnable t state payments in terms f stable purchasing pwer (that is, cnstant dllars) and adjust them separately using a predetermined price index. In such situatins, cash flws shuld be discunted using the real Treasury brrwing rate fr debt f cmparable maturity. The real Treasury rate is the nminal Treasury rate adjusted t eliminate the effect f anticipated inflatin/deflatin. These rates are als

6 cntained in OMB Circular A-94, Appendix C f and are updated annually. The fllwing real rates are t be used fr discunting dllar cash flws thrugh January Real Discunt Rates Maturity in Discunt Rate Years < 3 years 3.4% 5 year 3.5% 7 year 3.5% 10 year 3.6% > 30 years 3.8% Selecting the Rate fr Analysis. Whether yu are using nminal r real treasury rates, match the rate t the analysis perid (e.g., use 5.6 percent t discunt all expenditures/ receipts fr a 3-year lease analysis). T analyze a prject requiring analysis fr a perid different frm thse presented abve, use linear interplatin t determine the apprpriate discunt rate. Step 1. Estimate the change in the discunt rate fr each year between the next lwer and next higher maturity perid with identified discunt rates. Where: R C = Change in the discunt rate fr each year difference in the prject maturity perid M 1 = Next lwer maturity perid with an identified discunt rate M 2 = Next higher maturity perid with an identified discunt rate R 1 = Discunt rate fr maturity perid M 1 R 2 = Discunt rate fr maturity perid M 2

7 Step 2. Calculate the interplated rate using the rate fr the next lwer maturity perid with an identified rate and the estimated change in the discunt rate fr each year difference in the maturity perid. Where: R I = Interplated discunt rate fr the prject maturity perid M P = Maturity perid fr the prject All ther symbls are as defined abve Linear Rate Interplatin Example. The fllwing example demnstrates the steps invlved in interplating a nminal interest rate fr evaluating an 8-year lease: Step 1. Estimate the change in the discunt rate fr each year between the next lwer and next higher maturity perid with identified discunt rates. Step 2. Calculate the interplated rate using the rate fr the next lwer maturity perid with an identified rate and the estimated change in the discunt rate fr each year difference in the maturity perid.

8 9.3 - Identifying Cash Flws T Cnsider Cash Flw. A cash flw is a receipt r expenditure related t the prpsed lease r purchase. Guidance n the csts/benefits that yu shuld cnsider in lease-purchase analysis is prvided in bth FAR and OMB Circular A-94. The slicitatin shuld require each fferr t identify relevant cash flws assciated with its prpsal. Remember, the purpse f the Gvernment evaluatin is t identify the best net present value. Analysis Perid (OMB Circular A-94, Paragraph 13c8). In lease-purchase analysis, the prper perid fr analysis is the lease perid including all renewal ptins. The perid f the prjected lease must be defined in the slicitatin t assure identificatin and analysis f all relevant cash flws. Pints t Cnsider in Identifying Csts and Benefits fr Analysis (OMB Circular A-94, Para 6a1 & 13c1). Lease-purchase analysis shuld cmpare the net present value f the incremental csts related t leasing the asset with the incremental csts related t purchasing (r cnstructing) and wning the asset. Yu shuld cnsider incremental csts assciated with acquisitin as well as the ancillary csts related t acquisitin and wnership. Use the fllwing general guidelines as yu identify incremental benefits and csts t include in yur analysis: Analysis shuld cnsider csts r benefits assciated with ne alternative in the evaluatin f ther alternatives. Fr example, if the lease payments include maintenance, the purchase alternative shuld als include the cst f maintenance. Analysis shuld cnsider csts r benefits that will be different fr different alternatives. Fr example, if different alternatives will use substantially different amunts f electricity, the cst f electricity shuld be cnsidered. Analysis shuld nt cnsider sunk csts r benefits. Past experience is relevant nly in helping t estimate future csts r benefits. Fr example, if the Gvernment has decided t replace existing equipment, the value f that equipment is nt relevant. Analysis shuld nt cnsider csts which will be identical fr all alternatives. Fr example, if the

9 Gvernment has decided t replace existing equipment, the cst f remving that equipment is nt relevant because it must be accmplished fr all alternatives. Examples f Lease-Purchase Csts and Benefits Cmmnly Cnsidered (FAR and OMB Circular A-94 Paragraph 13c). Lease-purchase analysis is ne area where yu might be required t use net present value analysis. The csts and benefits identified belw fr lease-purchase analysis demnstrate the type f cash flws that yu shuld cnsider in a net present value analysis. Net Purchase Price. Any net present value analysis f a decisin t purchase an asset must cnsider the purchase price. OMB defines the purchase price f the asset as the price a willing buyer culd reasnably expect t pay a willing seller in a cmpetitive market t acquire the asset. Nrmally, lease-purchase decisins d nt cnsider trade-ins f existing equipment. Dispsal f existing equipment shuld be handled fllwing agency prperty dispsal prcedures and cnsidered as part f dispsal csts and salvage value as presented belw. Lease Payments. Any decisin t lease prperty using net present value analysis must cnsider the amunt and timing f lease payments. Ancillary Services. If ancillary csts differ between alternatives, they shuld be cnsidered. (If csts and timing are the same fr all alternatives, they need nt be cnsidered.) Bth OMB Circular A-94 and the FAR prvide guidance n the ancillary csts and benefits that yu shuld cnsider in lease-purchase analysis. The fllwing pints cmbine the recmmendatins frm bth surces: All csts assciated with acquiring the prperty and preparing it fr use including: Csts; Transprtatin; Installatin; Site preparatin; Design; and Management. Repair and imprvement csts, including: Estimated unplanned service calls; and

10 Imprvements prjected t be required during the lease perid t assure cntinued peratin. Operatin and maintenance csts, including: Operating labr and supply requirements; and Ruting maintenance. Dispsal csts and salvage value, including the: Cst f mdificatins required t return related equipment t its riginal cnfiguratin; Cst r mdificatins required t return related facilities t their riginal cnfiguratin; and Equipment value t the Gvernment at the end f the lease perid (e.g., salvage value) Determining Cash Flw Timing The timing f cash flws is a vital element f any net present value analysis. This sectin presents tw methds fr cnsidering that timing Discunt Factrs fr End-f-Year Payment Discunt Factrs fr Mid-Year Payment General Equatin fr Present Value Calculatin. Yu can cmpute the present value f any cash flw (expenditure/receipt) in the future, by multiplying the amunt by the apprpriate discunt rate: PV = DF(CF) Where: PV = Present value DF = Discunt factr CF = Cash flw Discunt Factrs. The discunt factr that yu use in net present value analysis will depend n the discunt rate that yu use and the timing f the cash flw. In defining the timing f the cash flw, yu must identify the year and

11 the timing during the year. There are tw cmmnly used assumptins abut when during the year the payment ccurs: End-f-year payment -- use this assumptin when a single payment is made at the end f the year r the beginning f the year. A payment that is due immediately is nt discunted. A payment that is due at the beginning f Year t is evaluated as a payment due at the end f Year t-1. Fr example, payments due at the beginning f Year 2 and Year 3 will be treated as if they are due at the end f Year 1 and Year 2. Mid-year payment -- use this assumptin when a single payment will be made mid-year r payments will be made at regular intervals thrughut the year. Offer-Identified Cash Flws. Slicitatins must require all fferrs t clearly define the amunt and timing f each cash flw (expenditure/receipt) unique t the prpsal. The prpsal shuld als include a ratinale t supprt the timing f any cash flw unless the timing is set frth in the cntract. Fr example: The timing f lease payments des nt require any additinal supprt because the timing (e.g., mnthly, quarterly, r annually) is defined in the lease agreement. Hwever, the lease agreement may include additinal charges (e.g., n-call equipment repair). Fr such charges, the ratinale fr bth the estimated expenditure and its timing shuld be clearly defined in the prpsal. Gvernment-Identified Cash Flws. Gvernment technical persnnel must identify cash flws related t different prpsals that are beynd the cntrl f the fferrs. Fr example: The amunt and timing f expenditures related t Gvernment wnership must als be identified prir t prpsal evaluatin. Nrmally, Gvernment persnnel will be respnsible fr preparing these estimates based n available infrmatin. Hwever, each fferr may be required t prvide infrmatin required t develp these estimates (e.g., csts t mdify equipment t meet anticipated changes in Gvernment requirements).

12 Discunt Factrs Fr End-Of-Year Payment When t Use End-f-Year Discunt Factrs. Use end-f-year discunt factrs when payments are due at the end f the year r the beginning f the year. Remember, that a payment due at the beginning f Year 3 is the same as a payment due at the end f Year 2. End-f-Year Discunt Factr Calculatin. The discunt factr frmula fr each end-f-year cash flw (payment/ receipt) is written: Where: DF = End-f-year discunt factr i = Discunt rate t = Number f years until the payment (receipt is due) Fr Example: Determine the present value (PV) f a payment f \$1,000 due at the end f 1 year using the nminal discunt rate fr three years r less, 5.6 percent. Discunt Factr Calculatin: Present Value Calculatin:

13 Sum Factrs fr Repetitive End-f-Year Cash Flws. When there is a repetitive cash flw such as a lease payment, yu can use a sum factr t speed the calculatin prcess. Where: PV = Present value SF = End-f-year sum factr CF = Cash flw Fr example: Determine the present value f a series f three payments f \$1,000 each due at the end f each f the next three years, when the discunt rate is 5.6 percent. Discunt Factr (DF) Present Value (PV) Year Payment Frmula Calculatin 1 \$1,000 1/(1.056) 1 1/ a \$ 947 b 2 1,000 1/(1.056) 2 1/ \$ ,000 1/(1.056) 3 1/ \$ 849 Ttal \$2,693 a Factrs are runded t the fur decimal places. b Amunts are runded t the nearest dllar. The present value f a series f three \$1,000 end-fyear payments is \$2,693 when the discunt rate is 5.6 percent. The sum f the three factrs is Using the sum factr and the equatin abve: Nte: The answer calculated using the sum factr is the same as the answer calculated using individual discunt factrs. Hwever, answers may vary slightly because f differences in runding. End-f-Year Nminal Discunt Tables. Appendix A-1, Discunt Factrs -- Nminal Rates, End-f-Year Payments,

14 cntains factrs fr the 3-year, 5-year, 7-year, 10-year, and 30-year discunt rates. End-f-Year Real Discunt Tables. Appendix A-3, Discunt Factrs -- Real Rates, End-f-Year Payments, cntains factrs fr the 3-year, 5-year, 7-year, 10-year, and 30- year discunt rates Discunt Factrs Fr Mid-Year Payment When t Use Mid-Year Discunt Factrs. Use mid-year discunt factrs when a single payment will be made midyear r payments will be made at regular intervals (e.g., mnthly r quarterly) thrughut the year. Mid-Year Discunt Factr Calculatin. The discunt factr frmula fr mid-year cash flw (payment/receipt) is written: Where: MYDF = Mid-year discunt factr i = Discunt rate t = Number f years until the payment (receipt) is due Fr example: Determine the present value f a series f 12 mnthly payments f \$1,000 each due at the beginning f each mnth fr 1 year. The ttal amunt fr the year is \$12,000. These payments are spaced evenly ver the year; hence the use f a MYDF wuld be apprpriate. Discunt Factr Calculatin:

15 Present Value Calculatin: Sum Factrs fr Repetitive Mid-Year Cash Flws. When there is a repetitive cash flw such as a lease payment, yu can use sum factrs t speed the calculatin prcess. Where: PV = Present value MYSF = Mid-year sum factr CF = Cash flw Fr example: Determine the present value f a series f 36 mnthly payments f \$1,000 each due at the beginning f each mnth fr the next three years; that is, \$12,000 per year fr three years. These payments are spaced evenly ver the year; hence the use f a MYDF wuld be apprpriate. Discunt Factr (MYDF) Present Value (PV) Year Payment Frmula Calculatin 1 \$12,000 1/(1.056).5 1/ a \$11,677 b 2 \$12,000 1/(1.056) 1.5 1/ \$11,058 3 \$12,000 1/(1.056) 2.5 1/ \$10,472 Ttal \$33,207

16 a Factrs are runded t the fur decimal places. b Amunts are runded t the nearest dllar. The present value f a series f three \$12,000 mid-year payments is \$33,207, when the discunt rate is 5.6 percent. The sum f the three mid-year discunt factrs is Using the sum factr and the equatin abve: Nte: The answer calculated using the sum factr is slightly higher than the ne calculated using individual discunt factrs, because f runding differences. Mid-Year Nminal Discunt Tables. Appendix A-2, Discunt Factrs -- Nminal Rates, Mid-Year Payments, cntains factrs fr the 3-year, 5-year, 7-year, 10-year, and 30- year discunt rates. Mid-Year Real Discunt Tables. Appendix A-4, Discunt Factrs -- Real Rates, Mid-Year Payments, cntains factrs fr the 3-year, 5-year, 7-year, 10-year, and 30-year discunt rates Calculating Net Present Value And Selecting The Best Alternative Net Present Value Analysis. Remember frm the Chapter Intrductin that yu shuld use the fllwing 5-step prcess in net present value analysis: Step 1. Select the discunt rate. Step 2. Identify the csts/benefits t be cnsidered in analysis. Step 3. Establish the timing f the csts/benefits. Step 4. Calculate net present value f each alternative. Step 5. Select the ffer with the best net present value.

17 This sectin will demnstrate the use f that 5-step prcess in tw lease-purchase decisin examples using nminal discunt rates. Yu shuld fllw the same steps fr any net present value analysis whether yu are using nminal discunt rates r real discunt rates. Lease-Purchase Decisin Example 1. Assume that yu want t determine which f the fllwing prpsals will result in the lwest ttal cst f acquisitin? Offerr A: Prpses t lease the asset fr 3 years. The annual lease payments are \$10,000 per year. The first payment will be due at the beginning f the lease, the remaining tw payments are due at the beginning f Years 2 and 3. Offerr B: Prpses t sell the asset fr \$29,000. It has a 3-year useful life. Salvage value at the end f the 3-year perid, will be \$2,000. Step 1. Select the discunt rate. The term f the lease analysis is three years, s we will use the nminal discunt rate fr three years, 5.4 percent. Steps 2 and 3. Identify and establish the timing f the csts/benefits t be cnsidered in analysis. The expenditures and receipts assciated with the tw ffers and their timing are delineated in the table belw: (Parentheses indicate a cash utflw.) Offer-Related Expenditures/Receipts t Offer A Offer B 0 (\$10,000) (\$29,000) 1 (\$10,000) -0-2 (\$10,000) \$2,000 Step 4. Calculate net present value. The tables belw summarize the net present value calculatins applied t each alternative. Net present value f Offer A t Cash Flw DF PV 0 (\$10,000) (\$10,000)

18 1 (\$10,000) (\$9,470) 2 (\$10,000) (\$8,968) Net Present Value (\$28,438) Nte the fllwing pints in the net present value calculatins abve: There are n cash inflws assciated with Offer A, nly utflws. Payments due nw are nt discunted. Offerr A payments due at the beginning f Years 2 and 3 are treated as if they are due at the end f Years 1 and 2. Yu culd have calculated the net present value f Offer A using the Sum f Discunt Factrs (Appendix A-1) fr the payments due at the beginning f Years 2 and 3. Remember that payments due nw are nt discunted and payments due at the beginning f Years 2 and 3 are treated as if they are due at the end f Years 1 and 2. The calculatins wuld be: Net present value f Offer B t Cash Flw DF PV 0 (\$29,000) (\$29,000) 3 \$2, \$ 1,698 Net Present Value (\$27,302) Nte the fllwing pints in the net present value calculatins abve: Offer B salvage value is treated as a cash inflw at the end f Year 3. Payments due nw are nt discunted. Step 5. Select the ffer with the best net present value. In this example, we wuld select Offer B, the ffer with the smallest negative net present value.

19 Lease-Purchase Decisin Example 2. Assume that we want t determine which f the fllwing prpsals will result in the lwest acquisitin cst? Offerr A-Prpses t lease the asset fr 3 years. The mnthly lease payments are \$1,500; that is, the ttal amunt fr each year is \$18,000. These payments are spaced evenly ver the year, s the use f a MYDF wuld be apprpriate. Offerr B-Prpses t sell the asset fr \$56,000. It has a 3-year useful life. At the end f the 3-year perid it will have a \$3,000 salvage value. Step 1. Select the discunt rate. The term f the analysis is three years, s we will use the nminal discunt rate fr three years, 5.6 percent. Steps 2 and 3. Identify and establish the timing f the csts/benefits t be cnsidered in analysis. The expenditures and receipts assciated with the tw ffers and their timing are delineated in the table belw: Offer Expenditures/Receipts t Offer A Offer B 0-0- (\$56,000) 1 (\$18,000) -0-2 (\$18,000) -0-3 (\$18,000) \$3,000 Step 4. Calculate net present value. The tables belw summarize the net present value calculatins applied t each alternative. Net present value f Offer A t Cash Flw DF PV 1 (\$18,000) (\$17,516) 2 (\$18,000) (\$16,587) 3 (\$18,000) (\$15,709) Net Present Value (\$49,812) NOTE the fllwing pints in the net present value calculatins abve:

20 There are n cash inflws assciated with Offer A, nly utflws. Offerr A payments are due mnthly, s we used the nminal rate, mid-year factrs frm Appendix A-2. Yu culd als calculate the net present value f Offer A using the Sum f Discunt Factrs in Appendix A-2. That calculatin wuld prduce a slightly different answer due t runding differences. Net present value f Offer B t Cash Flw DF PV 0 (\$56,000) (\$56,000) 3 \$3, \$2,548 Net Present Value (\$53,452) Nte the fllwing pints in the net present value calculatins abve: Offer B salvage value is treated as a cash inflw at the end f Year 3. Payments due nw are nt discunted. Step 5. Select the ffer with the best net present value. In this example, we wuld select Offer A, the ffer with the smallest negative net present value Identifying Issues And Cncerns Questins t Cnsider in Analysis. As yu perfrm price/cst analysis, cnsider the issues and cncerns identified in this sectin, whenever yu use net present value analysis. Is net present value analysis used when apprpriate? Net present value analysis shuld be used in any analysis supprting Gvernment decisins t initiate, renew, r expand prgrams r prjects which wuld result in a series f measurable benefits r csts extending fr three r mre years int the future.

21 Are the dllar estimates fr expenditures and receipts reasnable? The base fr all present value calculatins is estimated future cash flws. The ratinale fr thse estimates must be dcumented and supprted just like any cst estimate. This includes estimates f csts that will be included in the cntract r lease agreement and estimates f ther cash flws that are nt included. All may be used in present value calculatins. Are the times prjected fr expenditures and receipts reasnable? Discunt factrs depend n the discunt rate and the timing f the cash flw. The timing f any cash flw nt dcumented in the cntract r lease agreement must be clearly supprted. The fferr is respnsible fr estimating and defending cash flw estimates included in the prpsal. Gvernment technical persnnel have that respnsibility fr estimated csts related t item wnership. Are the prper discunt rates used in the net present value calculatins? Unless precluded by agency plicy, discunt rates shuld be taken frm Appendix C f OMB Circular A-94. If they are nt, the ratinale must be dcumented. The rate selected shuld be based n the number f time perids included in the analysis. If the perid f the analysis des nt match any f the discunt rate perids delineated in OMB Circular A-94, linear interplatin shuld be used t estimate a rate fr that perid f time. Nminal discunt rates shuld be used fr any analysis nt based n cnstant year dllars. Real discunt rates shuld be used fr any analysis that is based n cnstant year dllars. Are the prper discunt factrs used in analysis? The discunt factr shuld be calculated cnsidering the timing f the cash flw.

22 End-f-year discunt factrs (Appendices A-1 and A-3) shuld be used fr cash flws at the beginning r end f the year. Mid-year discunt factrs (Appendices A-2 and A- 4) shuld be used fr cash flws in the middle f the year r regularly thrughut the year (e.g., mnthly r quarterly). Are discunt factrs prperly calculated frm the discunt rate? End-f-year r mid-year discunt rates shuld be calculated fllwing the prcedures delineated in Sectin 9.4. Have all cash flws been cnsidered? Net present value analysis must cnsider all relevant cash flws thrughut the decisin life cycle.

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