CAPITAL PROJECT SCREENING AND SELECTION

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Harold Sanders
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1 CAPITAL PROJECT SCREEIG AD SELECTIO Before studyig the three measures of ivestmet attractiveess, we will review a simple method that is commoly used to scree capital ivestmets. Oe of the primary cocers of most busiess people is whether, ad whe, the moey ivested i a project ca be recovered. The payback method screes projects o the basis of how log it takes for et receipts to equal ivestmet outlays: The payback period is determied by addig the expected cash flows for each year util the sum is equal to, or greater tha, zero. The sigificace of this procedure ca be easily explaied. The cumulative cash flow equals zero at the poit where cash iflows exactly match or pay back the cash outflows: thus, the project has reached the payback poit. Oce the cumulative cash flows exceed zero, cash iflows exceed cash outflows, ad the project has begu to geerate a profit, thus exceedig its payback poit. This calculatio ca take oe of two forms by either igorig time-value-of moey cosideratios or icludig them. The former case is usually desigated as the covetioal-payback method while the latter case is kow as the discouted-payback method. A commo stadard used to determie whether to pursue a project is that a project does ot merit cosideratio uless it s payback period is shorter tha some specified period of time. (This time limit is largely determied by maagemet policy.) For example, a high-tech firm, such as a computer-chip maufacturer, would set a short time limit for ay ew ivestmet, because high-tech products rapidly become obsolete. If the payback period is withi the acceptable rage, a formal project evaluatio (such as a preset-worth aalysis, which is the subject of this chapter) may begi. It is importat to remember that payback screeig is ot a ed i itself, but rather a method of screeig out certai obviously uacceptable ivestmet alteratives before progressig to a aalysis of potetially acceptable oes. (I) Covetioal-Payback Period with Salvage Value (igores time value of moey) Example : Ashlad Compay has just bought a ew spidle machie at a cost of 5. to replace oe that had a salvage value of,. The projected aual after-tax savigs due to improved efficiecy are as follows: Give: Iitial cost = 85,; cash flow series as show below. Fid: Covetioal-payback period. Period Cash flow () Cumulative cash flow () -5,+ -85, 5, -7, 5, -45, 3 35, -, 4 45, 35, 5 45, 8, 6 35, 5, The salvage value of retired equipmet becomes a major cosideratio i most justificatio aalyses. (I this example, the salvage value of the old machie should be take ito accout, as the compay already decided to replace the old machie.) Whe used, the salvage value of the retired equipmet is subtracted from the purchase price of the ew equipmet, revealig a closer true cost of the ivestmet. As we see from the cumulative cash flow series i table above, the total ivestmet is recovered at the ed of year 4. If the firm's stated maximum payback period is three years, the project would ot pass the iitial screeig stage. I this example, we assumed that cash flows occur oly i discrete lumps at the eds of years. If cash flows occur cotiuously throughout the year, our calculatio of the payback period eeds adjustmet. A egative balace of, remais at the start of year 4. If the 45, is expected to be received as a more or less cotiuous flow durig year 4, the the total ivestmet will be recovered two-teths (,/45.) of the way through the fourth year. I this situatio, the prorated payback period is thus 3. years.

2 Beefits ad Flaws of Payback Screeig The simplicity of the payback method is oe of its most appealig qualities. Iitial project screeig by the payback method reduces the iformatio search by focusig o that time at which the firm expects to recover the iitial ivestmet. The method may also elimiate some alteratives. Thus reducig a firm's eed to make further aalysis efforts o those alteratives. But the much-used payback method of ivestmet screeig has a umber of serious drawbacks as well: The pricipal objectio to the payback method is that it fails to measure profitability; that is, it assumes that o profit is made durig the payback period. Simply measurig how log it will take to recover the iitial ivestmet outlay cotributes little to gaugig the earig power of a project. (For istace, if you kow that the moey you borrowed for the drill press is costig you % per year, the payback method will ot be able to tell you how much your ivested moey is cotributig toward your iterest expese.) Because payback-period aalysis igores differeces i the timig of cash flows, it fails to recogize the differece betwee the preset ad future value of moey. By way of illustratio, cosider two ivestmet projects: Period (yrs) Project () Project () -, -,, 9, 9,, 3,, Payback years years Although the payback period for both ivestmets ca be the same i terms of umbers of years, project is better, because most ivestmet beig recovered at the ed of year is worth more tha that to be gaied later. Because payback screeig also igores all proceeds after the payback period, it does ot allow for the possible advatages of a project with a loger ecoomic life. Discouted-Payback Period (cosiders time value of moey) Oe of the major disadvatages of simple payback period is that it igores the time value of moey. To couter this limitatio, a alterative procedure called discouted payback period may be followed, which accouts for time value of moey by discoutig the cash iflows of the project. Formulas ad Calculatio Procedure I discouted payback period we have to calculate the preset value of each cash iflow takig the start of the first period as zero poit. For this purpose the maagemet has to set a suitable discout rate. The discouted cash iflow for each period is to be calculated usig the formula: Discouted Cash Iflow = Actual Cash Iflow ( + i) Where, i is the discout rate; is the period to which the cash iflow relates. Usually the above formula is split ito two compoets which are actual cash iflow ad preset value factor ( i.e. / ( + i) ). Thus discouted cash flow is the product of actual cash flow ad preset value factor.

3 The rest of the procedure is similar to the calculatio of simple payback period except that we have to use the discouted cash flows as calculated above istead of actual cash flows. The cumulative cash flow will be replaced by cumulative discouted cash flow. Discouted Payback Period = A + B C Where, A = Last period with a egative discouted cumulative cash flow; B = Absolute value of discouted cumulative cash flow at the ed of the period A; C = Discouted cash flow durig the period after A. ote: I the calculatio of simple payback period, we could use a alterative formula for situatios where all the cash iflows were eve. That formula wo't be applicable here sice it is extremely ulikely that discouted cash iflows will be eve. The calculatio method is illustrated i the example below. Decisio Rule If the discouted payback period is less that the target period, accept the project. Otherwise reject. Example A iitial ivestmet of $,34, is expected to geerate $6, per year for 6 years. Calculate the discouted payback period of the ivestmet if the discout rate is %. Solutio Step : Prepare a table to calculate discouted cash flow of each period by multiplyig the actual cash flows by preset value factor. Create a cumulative discouted cash flow colum. Year Cash Flow Preset Value Factor Discouted Cash Flow Cumulative Discouted CF PV$=/(+i) CF PV$ Cash Flow $,34,. $,34, $,34, 6,.99 54,54,783,459 6, ,973,96, , ,75 857,77 4 6, ,39 46, , ,7 6,46 6 6, ,785 4,33 3

4 Step : Discouted Payback Period = ,46 / 3, years Advatages ad Disadvatages Advatage: Discouted payback period is more reliable tha simple payback period sice it accouts for time value of moey. It is iterestig to ote that if a project has egative et preset value it wo't pay back the iitial ivestmet. Disadvatage: It igores the cash iflows from project after the payback period. et-preset-worth Criterio Equivalet preset value of the cash flows geerated by the ivestmet over a specified time iterval, with discoutig at a specified iterest rate, i. PV CF CF CF CF CF i)... (, where CF is et cash flow. The discout rate, i is the miimum attractive rate of retur. That is, the rate of retur that could be expected if the fud ivested i the proposed project was to be ivested elsewhere. We will first summarize the basic procedure for applyig the et-preset-worth criterio to a typical ivestmet project, as well as for comparig alterative projects. Evaluatio of a Sigle Project Step : Determie the iterest rate that the firm wishes to ear o its ivestmets. The iterest rate you determie represets the rate at which the firm ca always ivest the moey i its ivestmet pool. This iterest rate is ofte referred to as either a required rate of retur or a miimum attractive rate of retur (MARR). Usually this selectio is a policy decisio made by top maagemet. It is possible for the MARR to chage over the life of a project, but for ow we will use a sigle rate of iterest whe calculatig PW. Step : Estimate the service life of the project. Step 3: Estimate the cash iflow for each period over the service life. Step 4: Estimate the cash outflow for each period over the service life. Step 5: Determie the et cash flows for each period (et cash flow = cash iflow - cash outflow). Step 6: Fid the preset worth of each et cash flow (CF) at the MARR. Add up these preset-worth figures; their sum is defied as the project's PW. That is, CF, will be positive if the correspodig period has a et cash iflow ad egative if the period has a et cash outflow. PW CF CF CF CF... i CF = A ( P / F, i, ) Where, PW(i) = PW calculated at i, A = et cash flow at the ed of period, i = MARR (or cost of capital), ad = service life of the project. Step 7: I this cotext, a positive PW meas that the equivalet worth of the iflows is greater tha the equivalet worth of the outflows, so the project makes a profit. Therefore, if the PW is positive for a sigle project, the project should be accepted; if it is egative, the project should be rejected. The process of applyig the PW measure is implemeted with the followig decisio rule: If PW >, accept the ivestmet. 4

5 If PW =, remai idifferet. If PW <, reject the ivestmet. Comparig More Tha Oe Alterative ote that the foregoig decisio rule is for evaluatio of a sigle project for which you ca estimate the reveues as well as the costs. The followig guidelies should be used for evaluatig ad comparig more tha oe project:. If you eed to select the best alterative, based o the et-preset-worth criterio, select the oe with the highest PW, as log as all the alteratives have the same service lives. Compariso of alteratives with uequal service lives requires special assumptios.. Compariso of mutually exclusive alteratives with the same reveues is performed o a cost-oly basis. I this situatio, you should accept the project that results i the smallest PW of costs, or the least egative PW (because you are miimizig costs, rather tha maximizig profits). some projects caot be avoided-e.g., the istallatio of pollutio-cotrol equipmet to comply with govermet regulatios. I such a case, the project would be accepted eve though its PW <. Example: Use the data i the table below to select a choice out of the two machies. Use the criterio of PV, auity ad future worth. S/ Machie A Machie B First cost 5, 5, Aual cost 6,5 4,3 3 Useful life years years 4 Salvage value Miimum attractive rate of retur before icome tax is stipulated to be % ASWER: PV (Machie A) = 59,9; Auity (Machie A) = 8,7 PV (Machie B) = 54,3; Auity (Machie B) = 7,969 Select machie B 5

Subject CT1 Financial Mathematics Core Technical Syllabus

Subject CT1 Financial Mathematics Core Technical Syllabus Subject CT1 Fiacial Mathematics Core Techical Syllabus for the 2018 exams 1 Jue 2017 Subject CT1 Fiacial Mathematics Core Techical Aim The aim of the Fiacial Mathematics subject is to provide a groudig