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Net Present Value and Capital Budgeting(Text reference: Chapter 7)Topicswhat to discountthe CCA systemtotal project cash flow vs. tax shield approachdetailed CCA calculations and examplesproject interactionsAFM 271 - NPV and Capital BudgetingSlide 1What to Discountsome general principles:1. Only cash flow is relevantthe NPV rule is stated in terms of cash flowscash flow is a simple idea: dollars in - dollars outdon’t confuse cash flow with accounting income(note that accounting income is needed in somecases to calculate taxes)2. Always estimate cash flows on an incremental basisincremental cash flows are the additional cashflows generated by the project. To identify them,ask two questions:What is the cash flow if the project is taken?What is the cash flow if the project is not taken?If the answers differ, then the cash flow isincremental.AFM 271 - NPV and Capital BudgetingSlide 2
Cont’dsome things to watch for:exclude sunk costs: it is incorrect to include costswhich have already been incurred and cannot berecoveredinclude opportunity costs: e.g. a firm owns some landworth 25 million which it is considering using as anew factory site. If the firm builds the factory, it isgiving up the 25 million it could have received byselling the land.incorporate side effects: it is important to ensure thatall effects on the remainder of a firm’s operations aretaken into account (e.g. a new product line may reducesales of existing products)AFM 271 - NPV and Capital BudgetingSlide 3Cont’dinclude working capital requirements: most projectswill require an additional investment in working capital(e.g. due to increased inventories, accountsreceivable, etc.); such investments are typicallyrecovered later onallocated overhead costs: ensure that only thosecharges which are actually due to a project areallocated to itinterest expense: ignore this for nowAFM 271 - NPV and Capital BudgetingSlide 4
Cont’d3. Treat inflation consistentlynominal interest rate inotation:inflation rateπreal interest raterrecall the “Fisher relation”1 i (1 r) (1 π ) r 1 i 11 πexample: if i 10% and π 3.5%, what is the FVafter 2 years of 10,000 in real and nominalterms? (assume the money is invested at i 10%)AFM 271 - NPV and Capital BudgetingSlide 5Cont’dconsistency requires that nominal cash flows bediscounted at a nominal discount rate and realcash flows be discounted at a real discount rate.For example, suppose that i 8% and π 3% andthat we have the following real cash flows:C0C1C2-1000 750 900NPV in real terms:NPV in nominal terms:AFM 271 - NPV and Capital BudgetingSlide 6
Cont’dwhy does this work? Let C0 ,C1 ,C2 , . . . be real cash flows,so:PVnominal C0 C0 C1 (1 π ) C2 (1 π )2 .1 i(1 i)2C1 (1 π )C2 (1 π )2 .(1 r)(1 π ) (1 r)2 (1 π )2it is important to understand how to use both real andnominal discounting since you sometimes have to useboth approaches. This is because some cash flowforecasts (e.g. sales revenue) are often made in realterms, whereas others (e.g. depreciation tax shields) arecalculated in nominal terms.AFM 271 - NPV and Capital BudgetingSlide 7Cont’dfor a single cash flow received at period n:Cnominal Creal (1 π )nfor a series of cash flows, the growth rate must also bechanged (e.g. a perpetuity which is constant in nominalterms is actually decreasing in real terms due to inflation).The relationship between real and nominal growth rates is:(1 gnominal ) (1 greal ) (1 π )e.g. a perpetuity of 1,000 per year (nominal), with r 10%and π 3%:AFM 271 - NPV and Capital BudgetingSlide 8
Cont’dsome examples (assume i 10% and π 5%):1. perpetuity Cnominal 100, 1st payment at t 1, gnominal 2%2. perpetuity Cnominal 100, 1st payment at t 4, greal 2%3. 10 period annuity Creal 500, 1st payment at t 1, greal 4%AFM 271 - NPV and Capital BudgetingSlide 9The CCA Systemdepreciation or capital cost allowance (CCA) is not a cash flow,but it has cash flow consequences because it is deductiblefrom taxable incomesince CCA reduces taxable income, it increases cash flowassets such as land or securities cannot be depreciated.Others are assigned to various classes, with varyingdepreciation rates. Table 7A.1 (text p. 219) provides somecommon classes: e.g. manufacturing and processingequipment is in Class 8 with a 20% rate, brick buildings arein Class 1 with a 4% rate. The depreciation rate d reflectsthe economic life of the asset.note that all assets of a firm within a particular class are treatedas if they are a single asset (a “pool”)AFM 271 - NPV and Capital BudgetingSlide 10
Cont’dhow to calculate CCA:CCA is calculated on a declining balanceallows for faster depreciation than straight linereceive cash flows from CCA tax shield fasterincreases NPV of investmentsthe half year rule: in the first year of its life, an assetis depreciated at half the normal rate, i.e. d/2example: a firm purchases some Class 8 (d 20%)equipment for 150,000. What CCA can be claimedfor the first four years?AFM 271 - NPV and Capital BudgetingSlide 11Cont’dhow to calculate PV of CCA tax shield:assume for now that you keep the asset forever, and ignorethe half year rule. We have:YearBeginning UCCCCAEnding UCC1CCdC(1 d)2C(1 d)Cd(1 d)C(1 d)23C(1 d)2Cd(1 d)2C(1 d)3.nC(1 d)n 1Cd(1 d)n 1C(1 d)n.the tax shields are just CCA multiplied by the corporate taxrate Tc , so (using k as the discount rate):PV AFM 271 - NPV and Capital BudgetingCdTcCdTc CdTc (1 d) CdTc (1 d)2 ··· 1 k(1 k)2(1 k)3k dSlide 12
Cont’dnow incorporate the half year rule. We have twoperpetuities, decreasing at rate d, one with firstpayment after one year, the other after two years:12 CdTc12 CdTc1 k dk d1 k"#1CdTc 1 2k d 2 1 k"#11CdTc 2 (1 k) 2 k d1 k"#k1 CdTc2 k d 1 kPV AFM 271 - NPV and Capital BudgetingSlide 13Cont’dnow assume that the asset is sold for an amount S atthe end of year n. If the firm has other assets in thisCCA class, this might reduce the PV of the CCA taxshield as follows:"#kCdTc 1 21min(C, S)dTcPV k d 1 kk d(1 k)nnote that the above formula is only an example: itand the similar equation (7.6) from p. 203 of the textare not always applicable!AFM 271 - NPV and Capital BudgetingSlide 14
Cont’din general, the following steps apply when a firm sells a CCAeligible asset:1. The UCC in the asset class is reduced by the lesser of the sale price or the initialcost.2. If step 1 leaves a negative balance, this amount is added to taxable income(recaptured depreciation), and the UCC of the asset class is reset to zero.3. If step 1 leaves a positive balance and there are no other assets in the assetclass, this amount is deducted from taxable income (terminal loss), and the UCCof the asset class is reset to zero.4. If step 1 leaves a positive balance and there are assets left in the class, thebalance becomes the new UCC for the class.5. If the asset is sold for more than its initial cost, the difference is a capital gain(50% inclusion rate).6. Suppose there is a new acquisition in the same year as an asset is sold. Definenet acquisitions as acquisitions less disposals. If net acquisitions are 0, applythe half year rule to net acquisitions; if net acquisitions are 0, do not apply thehalf year rule.AFM 271 - NPV and Capital BudgetingSlide 15Cont’dexample: Atlantic Trucking Co. is starting up business and hasjust purchased its first truck for 25,000. The truck is in Class10 with a CCA rate of 30%. Calculate applicable CCA for years1, 2, and 3:YearBeginning UCCCCAEnding UCC123now suppose that the firm buys a second truck for 35,000 inyear 2 and that it sells the first truck for 7,000 in year 3:AFM 271 - NPV and Capital BudgetingSlide 16
Cont’dYearBeginning UCCCCAEnding UCC112,5003,7508,75023instead suppose that the firm buys a second truck for 35,000in year 2 and that it sells the first truck for 7,000 in year 2:YearBeginning UCCCCAEnding UCC112,5003,7508,75023AFM 271 - NPV and Capital BudgetingSlide 17Cont’dto illustrate some asset disposition cases, consider the following four scenarios. Herea firm purchased a number of assets in a single class some time ago for 117,000,and at the beginning of the current year, this pool of assets had a UCC of 82,500.Scenario1234 82,500 82,500 82,500 82,500assets sold 35,000 117,000 85,000 117,000Sale proceeds 12,000 100,000 90,000 50,000Beginning UCCCapital cost ofCapital gainsUCC after saleTerminal lossRecaptureEnding UCCAFM 271 - NPV and Capital BudgetingSlide 18
Total Project Cash Flow vs. Tax Shield Approachto illustrate, we will consider in detail the MMCCexample from the text (pp. 188-193, 200-204). Theinformation provided includes:Expected life of machineCosts of test marketingCurrent market value of factory siteCost of machineSalvage value after 8 yearsProduction in thousands of units (by year)Unit price in first yearGrowth rate in unit price after first yearUnit production costs in first yearGrowth rate in production costs after first yearCorporate tax rateWorking capital: initialWorking capital: endWorking capital: duringInflation:Fixed costs:8 years 250,000 0 800,000 150,0006, 9, 12, 13, 12, 10, 8, 6 1002% 645%40% 40,000 015% of sales5% 50,000 per yearAFM 271 - NPV and Capital BudgetingSlide 19Cont’dthe total project cash flow approach:the basic idea is to determine the project cash flowsyear by year, add them up, and discount to obtainNPVsome notes:in general, cannot use convenient PV formulas(annuities, perpetuities)requires that all cash flows (for a given year) mustbe either in real terms or in nominal termsrequires that all cash flows be discounted at thesame ratemust use this approach if we want to calculateIRR, payback, or AARsee spreadsheet handouts for MMCC exampleAFM 271 - NPV and Capital BudgetingSlide 20
Cont’dthe tax shield approach:a “divide and conquer” methodrecall that after tax operating cash flow revenues expenses - taxessince taxable income revenues - expenses - CCA, wehavetaxes Tc ( revenues expenses CCA )this impliesafter tax operating cash flow revenues (1 Tc ) expenses (1 Tc ) Tc CCAsee spreadsheet handout for MMCC exampleAFM 271 - NPV and Capital BudgetingSlide 21Detailed CCA Calculations and Examplesassume that salvage takes place at the end of year n,and consider the following formula for the PV of CCAtax shields:"#kCdTc 1 2 UCCdTcPV of CCA (1 k) nk d 1 kk d UCC depends on circumstances. Let theundepreciated capital cost of the asset class just beforethe asset is disposed of be UCCn .if the firm only ever has one asset in the class, thenUCCn C(1 d/2)(1 d)n 1AFM 271 - NPV and Capital BudgetingSlide 22
Cont’dCalculate the value X UCCn min(C, S). Then:1. If X 0 recaptured depreciationadd X to taxable income in year n:PV of recapture XTc(1 k)nset UCC of asset class to zero (so UCC UCCn ):"#kCdTc 1 2UCCn dTcPV of CCA (1 k) nk d 1 kk dAFM 271 - NPV and Capital BudgetingSlide 23Cont’d2. If X 0 and there are no other assets in the class terminal losssubtract X from taxable income in year n:PV of terminal loss XTc(1 k)nset UCC of asset class to zero (so UCC UCCn ):"#kUCCn dTcCdTc 1 2 (1 k) nPV of CCA k d 1 kk dAFM 271 - NPV and Capital BudgetingSlide 24
Cont’d3. If X 0 and there are other assets in the classX becomes the new UCC of the asset class (so UCC min(C, S)):"#CdTc 1 2kmin(C, S)dTcPV of CCA (1 k) nk d 1 kk dthree further points:1. If S C, there is a capital gain:PV of tax liability (S C)Tc /2 (1 k) n2. Formulas for CCA tax shields are always given innominal terms.AFM 271 - NPV and Capital BudgetingSlide 25Cont’d3. The formulas given on the preceding slides have a half year rule adjustmentapplied to the first term but not the second term. This may not always be thecase: the half year rule may instead be applied to both terms, neither term, or thesecond term but not the first, depending on circumstances. In particular, the netacquisitions rule works as follows. Recall that all assets of a given firm within asingle CCA class are treated as part of a common pool. In practice, firms oftenbuy and sell many assets in a single class within a year. Define net acquisitionsfor an asset class as the total capital cost of all acquisitions (in a year) less thetotal adjusted cost of all disposals within that class and in that year. If netacquisitions is positive, apply the half year rule. If net acquisitions is negative,there is no adjustment for the half year rule.AFM 271 - NPV and Capital BudgetingSlide 26
Cont’dillustrative problem: you are considering whether to undertake a project that willgenerate revenues of 50,000 per year for 8 years and expenses of 20,000 per yearfor 8 years. The project requires an investment of 150,000 today in class 8 machinery(d 25%). Assume k 12%, Tc 40%, and all cash flows are nominal, and calculateproject NPV under the following scenarios:1. You always have many other class 8 assets and a positive UCC in that class andyou can salvage the machinery at the end of the 9th year for (i) 10,000; and (ii) 200,000. (Assume there are no other acquisitions or disposals of class 8 assetsin either the current year or in the 9th year.)2. The machinery will always be in its own class and it can be salvaged in 9 years for(i) 10,000; (ii) 20,000; and (iii) 200,000.3. From this point on, the machinery will be in its own class and it can be salvaged in9 years for 10,000. However, you purchased one other class 8 asset 5 years agofor 200,000 which you have just sold for (i) 100,000; and (ii) 175,000.AFM 271 - NPV and Capital BudgetingSlide 27Cont’d1. (i)Cost of machine:- 150,000.00PV after-tax operating revenues: 149,029.19PV after-tax operating expenses:- 59,611.68PV salvage:PV perpetual tax shield on 150,000:PV lost tax shield:NPV:AFM 271 - NPV and Capital Budgeting 3,606.10 38,368.73- 974.62- 19,582.28Slide 28
Cont’d1. (ii)Cost of machine:- 150,000.00PV after-tax operating revenues: 149,029.19PV after-tax operating expenses:- 59,611.68PV salvage: 72,122.00PV capital gain tax:- 3,606.10PV perpetual tax shield on 150,000: 38,368.73PV lost tax shield:- 14,619.33NPV: 31,682.81AFM 271 - NPV and Capital BudgetingSlide 29Cont’d2. (i)Cost of machine:- 150,000.00PV after-tax operating revenues: 149,029.19PV after-tax operating expenses:- 59,611.68PV salvage: 3,606.10PV perpetual tax shield on 150,000: 38,368.73PV lost tax shield:- 1,280.64PV terminal loss:NPV:AFM 271 - NPV and Capital Budgeting 452.90- 19,435.40Slide 30
Cont’d2. (ii)Cost of machine:- 150,000.00PV after-tax operating revenues: 149,029.19PV after-tax operating expenses:- 59,611.68PV salvage: 7,212.20PV perpetual tax shield on 150,000: 38,368.73PV lost tax shield:- 1,280.64PV recapture:- 989.54NPV:- 17,271.74AFM 271 - NPV and Capital BudgetingSlide 31Cont’d2. (iii)Cost of machine:- 150,000.00PV after-tax operating revenues: 149,029.19PV after-tax operating expenses:- 59,611.68PV salvage: 72,122.10PV capital gain tax:- 3,606.10PV perpetual tax shield on 150,000: 38,368.73PV lost tax shield:- 1,280.64PV recapture:NPV:AFM 271 - NPV and Capital Budgeting- 19,741.26 25,280.24Slide 32
Cont’d3. (i)Cost of machine:- 150,000.00PV after-tax operating revenues: 149,029.19PV after-tax operating expenses:- 59,611.68PV salvage: 3,606.10PV perpetual tax shield on 50,000: 12,789.58PV continuing tax shield on 55,371.09 14,965.16PV lost tax shield:- 832.08PV recapture (year 9):- 210.96PV avoided recapture today:NPV: 17,851.56- 12,413.13AFM 271 - NPV and Capital BudgetingSlide 33Cont’d3. (ii)Cost of machine:- 150,000.00PV after-tax operating revenues: 149,029.19PV after-tax operating expenses:- 59,611.68PV salvage: 3,606.10PV perpetual tax shield on 30,371.09: 8,208.40PV lost tax shield:- 222.25PV recapture (year 9):- 1,113.51PV avoided recapture today: 47,851.56NPV:- 2,252.19AFM 271 - NPV and Capital BudgetingSlide 34
Project Interactionsmany projects have effects on others, e.g. it is important toincorporate effects on other aspects of a firm’s business incapital budgeting analysis (including opportunity costs), andCCA pooling of assets can lead to other interactions betweenprojectsanother aspect of this is choosing between investments ofunequal lives. Suppose that two machines produce the sameoutput but have the following after-tax operating costs per 0-100At a 10% discount rate, which is cheaper to operate?AFM 271 - NPV and Capital BudgetingSlide 35Cont’dthe replacement chain:why not just use NPV and choose the machine withlower discounted costs?assume that machines are needed foreverthe matching cycle approach:run the example for 6 years. A has 3 completecycles, B has 2:PV of costs over 6 years:AFM 271 - NPV and Capital BudgetingSlide 36
Cont’dthe equivalent annual cost (EAC) approach:idea is to convert PV of costs for machine into anappropriate annuity:firm is indifferent between PV of costs and EACsince the project is assumed to continue forever,the EAC lasts forever, so choose the machine withlower EACAFM 271 - NPV and Capital BudgetingSlide 37Cont’dwhen to replace an old machine?1. Calculate EAC for new machine (EACnew )2. Calculate cost of operating old machine for 1 moreyear (Cold )3. Replace just before Cold EACnewexample: a firm has an existing machine, which could be salvaged for 2,800 today, 2,100 after one year, 1,200 after two years, or zero after 3 years (at which point itwould have to be replaced). Maintenance costs on this old machine are 1,175 afterone year, 1,600 after two years, and 1,800 after three years. A new machine isavailable which costs 5,000 and can be salvaged after four years for 1,800. Itsmaintenance costs are 1,000 after one year, 1,250 after two years, 1,500 afterthree years, and 2,000 after four years. The new machine produces the same outputas the old machine. When should the firm replace the old machine? Assume adiscount rate of 10%.AFM 271 - NPV and Capital BudgetingSlide 38
Cont’dthe EAC for the new machine is:should the existing machine be replaced now?AFM 271 - NPV and Capital BudgetingSlide 39Cont’dwhat about replacing it after one year?note that these types of decisions can easily get farmore complicated (e.g. different output levels for themachines, different numbers of machines required,anticipated new technology, etc.)AFM 271 - NPV and Capital BudgetingSlide 40
Total Project Cash Flow vs. Tax Shield Approach to illustrate, we will consider in detail the MMCC example from the text (pp. 188-193, 200-204). The information provided includes: Expected life of machine 8 years Costs of test marketing 250,000 Current market value of factory site 0 Cost of machine 800,000 Salvage value after 8 years 150,000
