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Ihe payback decision model has
been regarded as being a con-ceptually unsound method formaking capital expenditure de-
ThehimelValued ProflPaybackDecisionModelMore than aCapitalExpenditureModel
BY RON BRATHWAITE
RON BRATHWAITE, MBA, CMA, teachesaccounting and computer applications in thehospitality industry at the Center for Hotel andTourism Management, University of the West Indies,Nassau, Bahamas
22 . IAHAApril/May 1991
cisions for two primary reasons: (1) itdoesnotconsiderthecashflowstheprojectgenerates after the payback period, and(2) it ignores the time value of the cashflows it does consider.
We're going to look at a modifiedpayback decision model-the time-val-ued-profit payback model (TVP)-thataddresses the two shortcomings of thepayback decision model. 1'11 explain fea-tures of the model that ( 1 ) offer an alter-native for computing NPV, (2) generateinformationthatsupportsaathree-criteriadecision rule for evaluating capital ex-penditureproposals,and(3)providefeed-backasyear-to-yeartargetstocontinuallymonitor and control a projects' liquidity,risk, and profitability performance overits estimated economic life.
i:ap|j:a[ti[#eT%tcmhenT{SuesHotels make capital expenditures to ac-quire fixed or long-lived assets that theyanticipate will generate streams of futurecash benefits. These decisions involveallocating limited funds to competingprojects. To help make these decisions,hospitality operations rely on one or morecriteria. Some are purely financial andquantitative; others non-financial andqualitative.
Quantitativedecisioncriteriausedare:• Netpresentvalue (NPV)
• Internal RateofRetum (IRR)
• Paybackperiod
• TheDiscountedpaybackperiod, and
• Average RateofRetum (ARR).
The NPV criterion is the amount bywhichaproject'sdiscountedcashinflowsexceed its discounted cash outflows. Gen-erally, this amount works out to be posi-tive or negative. The NPV decision ruleis: if the project's expected NPV is posi-tive, accept the project on economicgrounds, otherwise reject it. The ratio-nale:apositiveNPvmeansthatthepresentvalue of the project's cash inflows is ex-pected to be greater than the present valueof the cash outflows. When this occurs,the anticipated financial returns on theproject are expected to be greater than theminimum rate stipulated by the company.The NPV decision model computes theNPV decision criterion. This model usesapredeterminedminimumacceptablerateof return to discount all the cash flowsassociatedwiththeproject,bringingthemto their present values. It then adds the
present value of the positive cash inflowsand negative cash inflows to obtain theNPV decision criterion.
The IRR decision criterion is a rate ofreturn the project is expected to earn overits economic life. The IRR decision ruleis: if the project' s expected IRR is greaterthan the company's cost of capital, theprojectisacceptabieoneconomicgrounds,otherwise it is not acceptable. 2 The basisofthisdecisionrule-whenlRRisgreaterthan the company's capital cost, the fi-nancial returns generated are expected tobe greater than the minimum rate thecompany stipulated. The IRR decisionmodel calculates the IRR decision crite-rion. By using this model, you can findthat rate at which all the cash flows as-sociated with the project must be dis-counted to make the NPV equal zero. Atzero NPV, the project would have earnedthe minimum rate the company requires.
The payback decision criterion is anestimate of the time it will take the projectto generate the cash inflows equal to theinitial cash outlays. Because the paybackcriterion is hardly ever used to make de-cisions about whether to accept/rejectcapital expenditure proposals, its deci-sion rule is less precise than the NPV'sand IRR's. The most common decisionrule: projects with shorter payback peri-ods are preferred to projects with longerpayback periods. The basis of this rule is:the shorter the payback period the higherthe project's liquidity and the lower itsrisk. The payback decision model calcu-lates the payback decision criterion. Thismodel adds the project's positive cashinflows to the negative cash outflowsidentified, producing a cumulative cashbalance. When this cumulative cash bal-ance is zero, the corresponding time isdetermined. It is the estimated paybackperiod or the payback decision criterion.
An improvement on the traditionalpayback decision criterion is the dis-counted payback criterion.3 Like thepaybackdecisioncriterion,thediscountedpayback criterion is an estimate of thetime it will take for the project' s expectedcash inflows to equal its initial cash out-lay. The difference is that we discount thecash inflows using a predeterminedminimum acceptable rate of return. Dis-counting allows the project to earn therequired rate of investment as well astime-values generated by the cash flowswithin the payback period. The model'sdecision rule and the basis of the rule aresimilar to those of the payback perioddecision model' s described above.
The ARR decision criterion is an ac-counting-incomerateofretumtheprojectis expected to earn over its economic life.
The ARR decision rule is: if project ex-pectedARRisgreaterthanthecompany'srequired rate of return, the project is ac-ceptable on economic grounds. The justi-fication of this decision rule is that whenARR is greater than the company' s capi-tal cost, the project's expected financialreturns is presumed to be greater than theminimum rate stipulated by the company.The ARR decision model computes theARR decision criterion used. This modelfinds the average net income the project isexpected to generate over its estimatedeconomic life and divides it by the aver-age investment in the project.
Deficiencies of MethodsCapital expenditure proposals are evalu-ated on the basis of their value-addingpotential. Value is measured by matchingtheproject'sexpectedtime-valued,futurecash inflows and outflows with one other,and making provisions for the risk inher-ent in these cash flows. When the time-valued cash inflows exceed the time-valued cash outflows, value is added tothe firm. The only two decision criteriacurrently in use that are time-valued,profitability-oriented and capable of pro-viding for risk, are the NPV and the IRRdecision criteria. The traditional payback
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decision criterion emphasizes liquidityand risk rather than time-valued profit-ability. The discounted payback criterionaddresses the time-value of the cash flows,but only focuses on the cash flows occur-ring within the payback period. Becauseof this, it is not profitability oriented. TheARR decision criterion emphasizes ac-counting income rather than value-add-ing cash flows.
The Time-Valued-Profit (TVP)Payback Decision ModelThe TVP payback decision model gener-ates a payback decision criterion, a NPVprofit decision criterion, and a profitabil-ity index (PI) decision criterion. It there-fore supports a decision rule that consid-ers these three criteria. Table 1 illustratesthis model.
The assumptions section of the modelshowstheexpectedcostoftheprojectandits discount rate. Other assumptions: theproject'sestimatedeconomiclifeandcashflows have been placed in the model itselffor convenience.
Column 1 lists the years during whichthe project's estimated cash flows occur.Theinitialcashoutlaywasmadeinyearo,the present time. Column 2 shows theestimated yearly cash outflows and in-
flows. Column 3 lists the present valueinterest factor (PVIF) for year zero andeach of the ensuing ten years. Column 4records the present values (PV) of all thecash flows in column 3. These are thetime-valuedordiscountedcashflows,andare obtained by multiplying each year'scash flow by the corresponding PVIF.Column 5 shows the cumulative dis-counted cash flows. These cash flowsresult from adding the yearly cash inflowsin column 4 to the cumulative balance inthe prior year shown in column 5. Forexample, $25,000 in year 1 , (column 4), isadded to $ 100,000 in year o (column 5) toobtain the balance of $75 ,000 at the end ofyear 1. Column 6 lists the profitabilityindex (PI) for the years when cumulativecash flows are positive. During year 8, theproject is expected to generate enoughcash flows to recover the initial $ 100,000investment and earn the stipulated mini-mum 12 percent interest required. It isduring this year that profits are expectedto begin accruing to the project. The prof-itabilityindicesincolumn6measuretheseprofits in relation to the initial investment.Foryears8,9andlo,thepI'sareexpectedto be 2.6 percent, 2.5 percent and 1.6
percent respectively. These yearly PI'stotal 6.7 percent, which is the project's
The Bottomline . 23
llll!l]ll!l]ll!l]llill llllllillll!llllillllllll 1111111
estimated PI over its expected ten-yearlife.
Thepaybackperiodliesbetweenyears7 and 8, where the cumulative discountedcash flows change from negative topositive. To obtain the fraction of a year,you divide the cumulative balance at theend of year 7 by the discounted cash flowinyear8,ignoringthemathematicalsigns.The 7.46 years estimated payback periodis the time during which the project isexpected to recoup the $100,000 cashoutlayinvestedandalsoearntheminimum12percentrequiredrateofinvestment.Asexplained earlier, it is also the point whentheprojectisexpectedtobegingeneratingprofits measured in time-valued cashflows.Forexample,duringapproximatelythe last six months of year 8, the valueadded by the project in terms of time-valued cash flows is $2,603. This amountconverts to a PI of 2.6 percent shown incolumn 6.
The table also shows what the NPV ofthe project is estimated to be if the NPVdecision model were used. At the end ofyear 10, the estimated life of the project,
the cumulative discounted cash flow is$6,737. When the project' s NPv is calcu-lated using the NPV decision model(NPvlinTablel)theresultisalso$6,737.Changes in any one assumption or in anycombination of the assumptions, producethe same equality condition between thecumulative discounted cash flow at theend of year 10 and NPV1 (the NPV cal-culated using the NPV decision model).The conclusion: the NPV and the cumu-lative discounted cash flow at the end ofthe project's estimated life are alwaysidentical, which means that the TVPpayback decision model also computesthe NPV.
The TVP payback graph shown inFigure I displays the properties in Table1. The discounted cumulative cash flowsare plotted against the Y-axis and thepayback period are plotted against the X-axis. The cumulative cash flow line iszero at a point that lies between years 7and 8. The time on the X-axis corre-spondingtothiszeropointisthediscountedpayback period. The project starts togenerate profits when the line rises above
the zero cumulative cash flow line. Be-yond this zero point, the line representsthe NPV of the project. The NPV of theproject at the end of year 9, for instance,is $5,127. The project's NPV is the cu-mulative cash flow line at year 10, itsestimated life.
APPLYING THE TVP
E#,buaact¥n3epcrjosjjeocntsMode[The TVP payback model generates threedecision criteria that are invaluable inevaluating capital expenditure propos-als:
1.) a discounted payback period,
2.) the NPV, and
3.) profitability index.
The discounted payback period crite-rion focuses on the assessment of liquid-ity and risk; the NPV criterion on risk anddollar profitability. The profitability in-dexcriterionaddressesriskandalsoprof-itability in relation to investment. These
24 . IAHAApril/May lggl
Figure I
TVP PAYBA€K GRAPHSlo£SOE($10)'ca5::::;'i^i(:i;;ii;1;i;($11q)
//
/0 1 2 3 4 5 6 7 8 9 10
FEARS
threecriteriaarecombinedtoproduceonethree-dimensional decision criterion. Thismay appear complex; however, the envi-ronment in which hospitality managersoperate today is anything but simple. Thecurrent economy is characterized by fast-paced technological changes, rapidproduct and service obsolescence and thefleeting fancies of consumers. In thisvolatile business environment, it is be-coming more and more apparent that aproject' s technological life and product-market life are as important as its physicallife.Thecontinuedabilityoftheprojecttogenerate satisfactory levels of cash flowsor other intangible benefits is the overrid-ing criterion in determining the project'slife. 4 Before you make capital expendi-ture decisions you must consider a num-ber of factors related to risk, liquidity andprofitability.
The decision rule must also incorpo-rate these factors. The TVP payback deci-sion model supports decision rules thatconsider risk, liquidity and profitability.The following is a typical decision rule:
If payback <= 4 years and NPV>O andPI>10 percent, then accept the project,otherwise reject it.
Compare this relatively complex deci-sionrulewiththefollowingNPvdecisionrule:
If NPV>0, then accept the project,otherwise reject it.
Like its decision criterion, the TVPdecision rule is also three-dimensional. Itevaluates each project on the basis of itsexpected risk, liquidity and profitability.The NPV decision rule is one-dimen-sional, focusing mainly on profitability.
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AI8C
45 ASSUMPTIONS:
6 Cost of project $100,000
Discount Rate 12 %
PV PAYBACK M0I]EL:
CashYear Flows
0 (S I oo,000)
1 28,000
27,000
3 20,000
4 18,000
5 18,000
6 16,00
16,000
12,000
7,000
5,000
Table 2
THE TVP PAYBACK DECISION MODEL
1/(1+SE$7)^814
1/(1+SE$7)^815
1/(1+SE$7)^816
1/(1+SE$7)^817
1/(I+SE$7)^Bl8
1/(1+SE$7)^B19
1/(1+SE$7)^820
1/(1+SE$7)^821
1/(1+SE$7)^822
1/(1+SE$7)^823
Cash Flows+D13*C13
+C14*D14
+C15*D15
+C16*D16
+C17*D17
+C18*Dl8
+Cl9*Dl9
+C20*D20
+C2l*D21
+C22*D22
+C23*D23
DCF Indices+E13 @NA
+F13+E14 @NA
+F14+E15 @NA
+F15+E16 @NA
+F16+E 17 @NA
+F17+E18
F18+El9
+F20+E2l
+F21+E22
+F22+E23@SUM(G2l
Discounted Payback Period
7 + (2,243/4,847)
After-Payback Returns
NPV1
Profitability Index
+820+(-F20ffi21)
+F23
@NPV(E7,C14..C23)-E6
the TVP payback decision model. ThePVIF is calculated using the reciprocalsof the compounding formula: 1/(1+r)^n,where r is the discount rate in the assump-tion section and # is the year in column 1.NPV 1, shown in cell E30, has been calcu-lated using Lotus @NPV function. Theamount is always the same as the cumula-tive DCF at the end of year 10 when anyof the assumptions or cash flows in col-umn 1 has been changed.
ConclusionCapital expenditure decisions are becom-ing increasingly complex as the businessenvironment in which hospitality firmsoperate becomes more and more volatile.
26 . IAHAApril/May 1991
Capital expenditure decision rules areevolving from simple one-criterion basedto complex multiple-criteria supported.And the decision model we use must beable to support the decision rules by gen-eratingappropriateinformation.TheTPVpayback decision model is developedalong these lines. It provides informationthat supports a complex decision rule thataddresses elements of risk liquidity andprofitability inherent in a capital expen-diture project. It also corrects the twomajor deficiencies of the traditionalpayback method and offers an alternativeto computing the NPV. Finally, it gener-ates timely, relevant information that pro-vides targets against which projects' per-
formance, measured in terms of liquidity,risk and profitability, can be monitoredand controlled. .
Footnotes1. Capital expenditures decisions are defined asinvestments to acquire fixed assets. Throughout thisarticle, the terms capital expenditures and capitalinvestments are used interchangeably.
2. The cost of capital is the stipulated minimum ratethe company requires the capital expenditure projectto earn. It is the same as the discount rate the NPVdecision model uses to discount the projects' cashflows.
3. The society of Management Accountants ofCanada, "The Capital Investment Decision," Canada,1989, p.11.
