Assume a $4,000 investment and the following cash flows fortwo alternatives. Yea

Question

Assume a $4,000 investment and the following cash flows fortwo alternatives. Year      InvestmentX          Investment Y 1             $1,000                     $1,300 2                 800                       2800 3                 700                        100 4                 1900                     5             2000 Under the payback method, which investment should be chosen?Show work/anyalysis/calculations. WHy do other methods allow for a better anaylysis? Assume a $4,000 investment and the following cash flows fortwo alternatives. Year      InvestmentX          Investment Y 1             $1,000                     $1,300 2                 800                       2800 3                 700                        100 4                 1900                     5             2000 Under the payback method, which investment should be chosen?Show work/anyalysis/calculations. WHy do other methods allow for a better anaylysis?

Explanation / Answer

Pl see Payback period below. The payback period, defined asthe expected number of years required to recover the originalinvestment, was the ?rst formal method used to evaluate capitalbudgeting projects. Payback period = Year before full recovery + (Unrecovered costat start of year/Cash flow during year)
Investment X: So in present question, We see that by the end of Year 3the cumulative inflows have recovered 1300 of the initial outflow of 4000. Thus, the payback occurred during the 2nd year. Ifthe balance 2700 of inflow come in evenly during Year 2, then the exact payback period can be found as follows: Payback period = Year before full recovery + (Unrecovered costat start of year/Cash flow during year) = 1 + (4000-1300)/2800 = 1+2700/2800 = 1.96 years. So payback period is 3.79 years or 3.79*12 = 45.5months.
Investment Y: So in present question, We see that by the end of Year 1the cumulative inflows have recovered (1000+800+700 = 2500) of the initial outflow of 4000. Thus, the payback occurred during the 4rd year. Ifthe balance 1500 of inflow come in evenly during Year 4, then the exact payback period can be found as follows: Payback period = Year before full recovery + (Unrecovered costat start of year/Cash flow during year) = 3 + (4000-2500)/1900 = 3+1500/1900 = 3.79 years. So payback period is 1.96 years or 1.96*12 = 23.6months.
Thus Using Payback method, Inv 'Y should be choses as it givesfaster payback. However Payback method doesn't take into account the cost ofcapital.
Other methods are NPV & IRR. Investment Y: So in present question, We see that by the end of Year 1the cumulative inflows have recovered (1000+800+700 = 2500) of the initial outflow of 4000. Thus, the payback occurred during the 4rd year. Ifthe balance 1500 of inflow come in evenly during Year 4, then the exact payback period can be found as follows: Payback period = Year before full recovery + (Unrecovered costat start of year/Cash flow during year) = 3 + (4000-2500)/1900 = 3+1500/1900 = 3.79 years. So payback period is 1.96 years or 1.96*12 = 23.6months.
Thus Using Payback method, Inv 'Y should be choses as it givesfaster payback. However Payback method doesn't take into account the cost ofcapital.
Other methods are NPV & IRR. Payback and discounted payback provide an indication of boththe risk and the liquidity of a project—a long payback means(1) that the investment dollars will be locked up for many years,hence the project is relatively illiquid, and (2) that theproject’s cash flows must be forecasted far out into thefuture, hence the project is probably quite risky. A goodanalogy for this is the bond valuation process. An investor shouldnever compare the yields to maturity on two bonds without alsoconsidering their terms to maturity, because a bond’sriskiness is  significantly influenced by itsmaturity.
NPV is important because it gives a direct measure of thedollar benefit of the project to shareholders, so we regard NPV asthe best single measure of profitability. IRR also measuresprofitability, but here it is expressed as a percentage rate ofreturn, which many decision makers prefer. Further, IRRcontains information concerning a project’s“safety margin.” To illustrate, consider the followingtwo projects: Project S (for small) costs $10,000 and is expectedto return $16,500 at the end of one year, while Project L (forlarge) costs  $100,000 and has an expected payoff of$115,500 after one year. At a 10 percent cost of capital, bothprojects have an NPV of $5,000, so by the NPV rule we should beindifferent between them. However, Project S has a muchlarger margin for error. Even if its realized cash inflow were39 percent below the $16,500 forecast, the firm would still recoverits $10,000 investment. On the other hand, if Project L’sinflows fell by only 13 percent from the forecasted $115,500,the firm would not recover its investment. Further, if no inflowswere generated at all, the firm would lose only $10,000 withProject S, but $100,000 if it took on Project L. The NPV providesno information about either of these factors—the“safety margin” inherent in the cash flow forecasts orthe amount of capital at risk. However, the IRR does provide “safetymargin” information—Project S’s IRR is a whopping65.0 percent, while Project L’s IRR is only 15.5 percent. Asa result, the realized return could fall substantially for ProjectS, and it would   still make money. Finally, the modified IRR has all thevirtues of the IRR, but (1) it incorporates a better reinvestmentrate assumption, and (2) it avoids the multiple rate of returnproblem.
In summary, the different measures provide different types ofinformation to decision makers. Since it is easy to calculate allof them, all should be considered in the decision process. For mostdecisions, the greatest weight should be given to the NPV, but itwould be foolish to ignore the information provided by any ofthe methods.
Payback and discounted payback provide an indication of boththe risk and the liquidity of a project—a long payback means(1) that the investment dollars will be locked up for many years,hence the project is relatively illiquid, and (2) that theproject’s cash flows must be forecasted far out into thefuture, hence the project is probably quite risky. A goodanalogy for this is the bond valuation process. An investor shouldnever compare the yields to maturity on two bonds without alsoconsidering their terms to maturity, because a bond’sriskiness is  significantly influenced by itsmaturity.
NPV is important because it gives a direct measure of thedollar benefit of the project to shareholders, so we regard NPV asthe best single measure of profitability. IRR also measuresprofitability, but here it is expressed as a percentage rate ofreturn, which many decision makers prefer. Further, IRRcontains information concerning a project’s“safety margin.” To illustrate, consider the followingtwo projects: Project S (for small) costs $10,000 and is expectedto return $16,500 at the end of one year, while Project L (forlarge) costs  $100,000 and has an expected payoff of$115,500 after one year. At a 10 percent cost of capital, bothprojects have an NPV of $5,000, so by the NPV rule we should beindifferent between them. However, Project S has a muchlarger margin for error. Even if its realized cash inflow were39 percent below the $16,500 forecast, the firm would still recoverits $10,000 investment. On the other hand, if Project L’sinflows fell by only 13 percent from the forecasted $115,500,the firm would not recover its investment. Further, if no inflowswere generated at all, the firm would lose only $10,000 withProject S, but $100,000 if it took on Project L. The NPV providesno information about either of these factors—the“safety margin” inherent in the cash flow forecasts orthe amount of capital at risk. However, the IRR does provide “safetymargin” information—Project S’s IRR is a whopping65.0 percent, while Project L’s IRR is only 15.5 percent. Asa result, the realized return could fall substantially for ProjectS, and it would   still make money. Finally, the modified IRR has all thevirtues of the IRR, but (1) it incorporates a better reinvestmentrate assumption, and (2) it avoids the multiple rate of returnproblem.
In summary, the different measures provide different types ofinformation to decision makers. Since it is easy to calculate allof them, all should be considered in the decision process. For mostdecisions, the greatest weight should be given to the NPV, but itwould be foolish to ignore the information provided by any ofthe methods.

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