Chapter 8 Investment Decision Rules

Chapter Outline 8.1 The NPV Decision Rule 8.2 Using the NPV Rule 8.3 Alternative Decision Rules 8.4 Choosing Between Projects 8.5 Evaluating Projects with Different Lives 8.6 Choosing Among Projects When Resources Are Limited 8.7 Putting it All Together

Learning Objectives Calculate a Net Present Value Use the NPV rule to make investment decisions Understand alternative decision rules and their drawbacks Choose between mutually exclusive alternatives

Learning Objectives Evaluate projects with different lives Rank projects when a company’s resources are limited so that it cannot take all positive- NPV projects

NPV = PV (Benefits) – PV (Costs) 8.1 The NPV Decision Rule Most firms measure values in terms of Net Present Value–that is, in terms of cash today. NPV = PV (Benefits) – PV (Costs) (Eq. 8.1)

8.1 The NPV Decision Rule Logic of the decision rule: When making an investment decision, take the alternative with the highest NPV, which is equivalent to receiving its NPV in cash today.

8.1 The NPV Decision Rule A simple example: In exchange for $500 today, your firm will receive $550 in one year. If the interest rate is 8% per year: PV(Benefit)= ($550 in one year) ÷ ($1.08 $ in one year/$ today) = $509.26 today This is the amount you would need to put in the bank today to generate $550 in one year. NPV= $509.26 - $500 = $9.26 today

8.1 The NPV Decision Rule You should be able to borrow $509.26 and use the $550 in one year to repay the loan. This transaction leaves you with $509.26 - $500 = $9.26 today. As long as NPV is positive, the decision increases the value of the firm regardless of current cash needs or preferences.

8.1 The NPV Decision Rule The NPV decision rule implies that we should: Accept positive-NPV projects; accepting them is equivalent to receiving their NPV in cash today, and Reject negative-NPV projects; accepting them would reduce the value of the firm, whereas rejecting them has no cost (NPV = 0).

Example 8.1 The NPV Is Equivalent to Cash Today Problem: After saving $1,500 waiting tables, you are about to buy a 42-inch plasma TV. You notice that the store is offering “one-year same as cash” deal. You can take the TV home today and pay nothing until one year from now, when you will owe the store the $1,500 purchase price. If your savings account earns 5% per year, what is the NPV of this offer? Show that its NPV represents cash in your pocket.

Example 8.1 The NPV Is Equivalent to Cash Today Solution: Plan: You are getting something (the TV) worth $1,500 today and in exchange will need to pay $1,500 in one year. Think of it as getting back the $1,500 you thought you would have to spend today to get the TV. We treat it as a positive cash flow. Today In one year Cash flows: $ 1,500 –$ 1,500 The discount rate for calculating the present value of the payment in one year is your interest rate of 5%. You need to compare the present value of the cost ($1,500 in one year) to the benefit today (a $1,500 TV).

Example 8.1 The NPV Is Equivalent to Cash Today Execute: You could take $1,428.57 of the $1,500 you had saved for the TV and put it in your savings account. With interest, in one year it would grow to $1,428.57  (1.05) = $1,500, enough to pay the store. The extra $71.43 is money in your pocket to spend as you like (or put toward the speaker system for your new media room).

Example 8.1 The NPV Is Equivalent to Cash Today Evaluate: By taking the delayed payment offer, we have extra net cash flows of $71.43 today. If we put $1,428.57 in the bank, it will be just enough to offset our $1,500 obligation in the future. Therefore, this offer is equivalent to receiving $71.43 today, without any future net obligations.

Example 8.1a The NPV Is Equivalent to Cash Today Problem: After saving $2,500 waiting tables, you are about to buy a 50-inch LCD TV. You notice that the store is offering “one-year same as cash” deal. You can take the TV home today and pay nothing until one year from now, when you will owe the store the $2,500 purchase price. If your savings account earns 4% per year, what is the NPV of this offer? Show that its NPV represents cash in your pocket.

Example 8.1a The NPV Is Equivalent to Cash Today Solution: Plan: You are getting something (the TV) worth $2,500 today and in exchange will need to pay $2,500 in one year. Think of it as getting back the $2,500 you thought you would have to spend today to get the TV. We treat it as a positive cash flow. Today In one year Cash flows: $ 2,500 –$ 2,500 The discount rate for calculating the present value of the payment in one year is your interest rate of 4%. You need to compare the present value of the cost ($2,500 in one year) to the benefit today (a $2,500 TV).

Example 8.1a The NPV Is Equivalent to Cash Today Execute: You could take $2,403.85 of the $2,500 you had saved for the TV and put it in your savings account. With interest, in one year it would grow to $2,403.85  (1.04) = $2,500, enough to pay the store. The extra $96.15 is money in your pocket to spend as you like.

Example 8.1a The NPV Is Equivalent to Cash Today Evaluate: By taking the delayed payment offer, we have extra net cash flows of $96.15 today. If we put $2,403.85 in the bank, it will be just enough to offset our $2,500 obligation in the future. Therefore, this offer is equivalent to receiving $96.15 today, without any future net obligations.

8.2 Using the NPV Rule A take-it-or-leave-it decision: A fertilizer company can create a new environmentally friendly fertilizer at a large savings over the company’s existing fertilizer. The fertilizer will require a new factory that can be built at a cost of $81.6 million. Estimated return on the new fertilizer will be $28 million after the first year, and last four years.

8.2 Using the NPV Rule Computing NPV The following timeline shows the estimated return:

8.2 Using the NPV Rule Given a discount rate r, the NPV is: We can also use the annuity formula: (Eq. 8.2) (Eq. 8.3)

8.2 Using the NPV Rule If the company’s cost of capital is 10%, the NPV is $7.2 million and they should undertake the investment.

8.2 Using the NPV Rule NPV of Fredrick’s project The NPV depends on cost of capital. NPV profile graphs the NPV over a range of discount rates. Based on this data the NPV is positive only when the discount rates are less than 14%.

8.2 Using the NPV Rule FIGURE 8.1 NPV of Fredrick’s New Project

8.3 Alternative Decision Rules FIGURE 8.2 The Most Popular Decision Rules Used by CFOs

8.3 Alternative Decision Rules The Payback Rule Based on the notion that an opportunity that pays back the initial investment quickly is the best idea. Calculate the amount of time it takes to pay back the initial investment, called the payback period. Accept if the payback period is less than required Reject if the payback period is greater than required

Example 8.2 Using the Payback Rule Problem: Assume the fertilizer company requires all projects to have a payback period of two years or less. In this case would the firm undertake the project under this rule?

Example 8.2 Using the Payback Rule Solution: Plan: In order to implement the payback rule, we need to know whether the sum of the inflows from the project will exceed the initial investment before the end of 2 years. The project has inflows of $28 million per year and an initial investment of $81.6 million.

Example 8.2 Using the Payback Rule Execute: The sum of the cash flows from year 1 to year 2 is $28m x 2 = $56 million, this will not cover the initial investment of $81.6 million. Because the payback is > 2 years (3 years required $28 x 3 = $84 million) the project will be rejected.

Example 8.2 Using the Payback Rule Evaluate: While simple to compute, the payback rule requires us to use an arbitrary cutoff period in summing the cash flows. Further, also note that the payback rule does not discount future cash flows. Instead it simply sums the cash flows and compares them to a cash outflow in the present. In this case, Fredrick’s would have rejected a project that would have increased the value of the firm.

Example 8.2a Using the Payback Rule Problem: Assume a company requires all projects to have a payback period of three years or less. For the project below, would the firm undertake the project under this rule? Year Expected Net Cash Flow -$10,000 1 $1,000 2 3 $12,000

Example 8.2a Using the Payback Rule Solution: Plan: In order to implement the payback rule, we need to know whether the sum of the inflows from the project will exceed the initial investment before the end of 3 years. The project has inflows of $1,000 for two years, an inflow of $12,000 in year three, and an initial investment of $10,000.

Example 8.2a Using the Payback Rule Execute: The sum of the cash flows from years 1 through 3 is $14,000. This will cover the initial investment of $10,000. Because the payback is less than 3 years the project will be accepted.

Example 8.2a Using the Payback Rule Evaluate: While simple to compute, the payback rule requires us to use an arbitrary cutoff period in summing the cash flows. Further, also note that the payback rule does not discount future cash flows. Instead it simply sums the cash flows and compares them to a cash outflow in the present.

Example 8.2b Using the Payback Rule Problem: Assume a company requires all projects to have a payback period of three years or less. For the project below, would the firm undertake the project under this rule? Year Expected Net Cash Flow -$10,000 1 $1,000 2 3 4 $1,000,000

Example 8.2b Using the Payback Rule Solution: Plan: In order to implement the payback rule, we need to know whether the sum of the inflows from the project will exceed the initial investment before the end of 3 years. The project has inflows of $1,000 for three years, an inflow of $1,000,000 in year four, and an initial investment of $10,000.

Example 8.2b Using the Payback Rule Execute: The sum of the cash flows from years 1 through 3 is $3,000. This will not cover the initial investment of $10,000. Because the payback is more than 3 years the project will not be accepted, even though the 4th cash flow is very high!

Example 8.2b Using the Payback Rule Evaluate: While simple to compute, the payback rule requires us to use an arbitrary cutoff period in summing the cash flows. Further, also note that the payback rule does not discount future cash flows – in this case, a huge mistake! Instead it simply sums the cash flows and compares them to a cash outflow in the present.

8.3 Alternative Decision Rules Weakness of the Payback Rule Ignores the time value of money. Ignores cash-flows after the payback period. Lacks a decision criterion grounded in economics

8.3 Alternative Decision Rules The Internal Rate of Return Rule Take any investment opportunity where IRR exceeds the opportunity cost of capital.

Table 8.1 Summary of NPV, IRR, and Payback for Fredrick’s New Project

8.3 Alternative Decision Rules Weakness in IRR In most cases IRR rule agrees with NPV for stand- alone projects if all negative cash flows precede positive cash flows. In other cases the IRR may disagree with NPV.

8.3 Alternative Decision Rules Delayed Investments Two competing endorsements: Offer A: single payment of $1million upfront Offer B: $500,000 per year at the end of the next three years Estimated cost of capital is 10% Opportunity timeline:

8.3 Alternative Decision Rules The NPV is: Set NPV to zero and solve for r to get IRR. Given: 3 1,000,000 -500,000 Solve for: 23.38 Excel Formula: =RATE(NPER,PMT,PV,FV) = RATE(3,-500000,1000000,0)

8.3 Alternative Decision Rules 23.38% > the 10% opportunity cost of capital, so according to IRR, Option A best. However, NPV shows that Option B is best To resolve the conflict we can show a NPV Profile

8.3 Alternative Decision Rules FIGURE 8.3 NPV of Cole’s $1 Million QuenchIt Deal For most investments expenses are upfront and cash is received in the future. In these cases a low rate is best. When cash is upfront a high interest rate is best.

8.3 Alternative Decision Rules Multiple IRRs Suppose the cash flows in the previous example change. The company has agreed to make an additional payment of $600,000 in 10 years.

8.3 Alternative Decision Rules The new timeline: The NPV of the new investment opportunity is: If we plot the NPV profile, we see that it has two IRRs!

8.3 Alternative Decision Rules FIGURE 8.4 NPV of Evan’s Sports Drink Deal with Additional Deferred Payments

8.3 Alternative Decision Rules Modified Internal Rate of Return (MIRR) Used to overcome problem of multiple IRRs Computes the discount rate that sets the NPV of modified cash flows to zero Possible modifications Bring all negative cash flows to the present and incorporate into the initial cash outflow Leave the initial cash flow alone and compound all of the remaining cash flows to the final period of the project.

Figure 8.5 NPV Profile with Multiple IRRs

Figure 8.6 NPV Profile of MIRR

8.4 Choosing Between Projects Mutually exclusive projects. Can’t just pick the project with a positive NPV. The projects must be ranked and the best one chosen. Pick the project with the highest NPV.

Example 8.3 NPV and Mutually Exclusive Projects Problem: You own a small piece of commercial land near a university. You are considering what to do with it. You have been approached recently with an offer to buy it for $220,000. You are also considering three alternative uses yourself: a bar, a coffee shop, and an apparel store. You assume that you would operate your choice indefinitely, eventually leaving the business to your children. You have collected the following information about the uses. What should you do? Initial Investment Cash flow in the First Year Growth rate Cost of capital Bar $400,000 $60,000 3.5% 12% Coffee shop $200,000 $40,000 3% 10% Apparel Store $500,000 $85,000 13%

Example 8.3 NPV and Mutually Exclusive Projects Solution: Plan: Since you can only do one project (you only have one piece of land), these are mutually exclusive projects. In order to decide which project is most valuable, you need to rank them by NPV. Each of these projects (except for selling the land) has cash flows that can be valued as a growing perpetuity, the present value of the inflows is CF1 / (r-g). The NPV of each investment will be

Example 8.3 NPV and Mutually Exclusive Projects Execute: The NPVs are: Based on the rankings the coffee shop should be chosen

Example 8.3 NPV and Mutually Exclusive Projects Evaluate: All of the alternatives have positive NPVs, but you can only take one of them, so you should choose the one that creates the most value. Even though the coffee shop has the lowest cash flows, its lower start-up cost coupled with its lower cost of capital (it is less risky), make it the best choice.

Example 8.3a NPV and Mutually Exclusive Projects Problem: You own a small piece of commercial land near a university. You are considering what to do with it. You have been approached recently with an offer to buy it for $300,000. You are also considering three alternative uses of the land for yourself: a bar, a coffee shop, and an apparel store. You assume that you would operate your choice indefinitely, eventually leaving the business to your children. You have collected the following information about the uses. What should you do? Initial Investment Cash flow in the First Year Growth rate Cost of capital Bar $400,000 $65,000 5.0% 12.0% Coffee shop $250,000 $45,000 5.5% 12.5% Apparel Store $800,000 $90,000 4.5% 13.0%

Example 8.3a NPV and Mutually Exclusive Projects Solution: Plan: Since you can only do one project (you only have one piece of land), these are mutually exclusive projects. In order to decide which project is most valuable, you need to rank them by NPV. Each of these projects (except for selling the land) has cash flows that can be valued as a growing perpetuity, the present value of the inflows is CF1 / (r-g). The NPV of each investment will be

Example 8.3a NPV and Mutually Exclusive Projects Execute: The NPVs are: Based on the rankings the bar should be chosen.

Example 8.3a NPV and Mutually Exclusive Projects Evaluate: All of the alternatives have positive NPVs, but you can only take one of them, so you should choose the one that creates the most value. Even though the coffee shop has the lowest start-up costs, the higher cash flows of the bar, along with its lower cost of capital (it is less risky), makes it the best choice.

8.4 Choosing Between Projects Differences in Scale A 10% IRR can have very different value implications for an initial investment of $1 million vs. an initial investment of $100 million.

8.4 Choosing Between Projects Identical Scale NPV of Javier’s investment in his girlfriend’s business: NPV of Javier’s investment in the Internet café:

8.4 Choosing Between Projects Identical Scale IRR of his girlfriend’s business: Given: 3 -10,000 6,000 Solve for: 36.3 Excel Formula: =RATE(NPER,PMT,PV,FV) = RATE(3,6000,-10000,0)

Figure 8.7 NPV of Javier’s Investment Opportunities

8.4 Choosing Between Projects Change in Scale: Javier realizes he can just as easily install five times as many computers in the Internet café. Setup costs would be $50,000 and annual cash flows would be $25,000.

8.4 Choosing Between Projects Change in Scale IRR is unaffected by scale. IRR of girlfriend’s business is the same. Given: 3 -50,000 25,000 Solve for: 23.4 Excel Formula: =RATE(NPER,PMT,PV,FV) = RATE(3,25000,-50000,0)

Figure 8.8 NPV of Javier’s Investment Opportunities

Example 8.4 Computing the Crossover Point Problem: Solve for the crossover point for Javier from Figure 8.8.

Example 8.4 Computing the Crossover Point Solution: Plan: The crossover point is the discount rate that makes the NPV of the two alternatives equal. We can find the discount rate by setting the equations for the NPV of each project equal to each other and solving for the discount rate. In general, we can always compute the effect of choosing Project A over Project B as the difference of the NPVs. At the crossover point the difference is 0

Example 8.4 Computing the Crossover Point Execute: Setting the difference equal to 0: As you can see, solving for the crossover point is just like solving for the IRR, so we will need to use a financial calculator or spreadsheet:

Example 8.4 Computing the Crossover Point Execute (cont’d): And we find that the crossover occurs at a discount rate of 20% (20.04% to be exact). Given: 3 -40,000 19,000 Solve for: 20.04 Excel Formula: =RATE(NPER, PMT, PV,FV) = RATE(3,19000,‑40000,0)

Example 8.4 Computing the Crossover Point Evaluate: Just as the NPV of a project tells us the value impact of taking the project, so the difference of the NPVs of two alternatives tells us the incremental impact of choosing one project over another. The crossover point is the discount rate at which we would be indifferent between the two projects because the incremental value of choosing one over the other would be zero.

Example 8.4a Computing the Crossover Point Problem: Solve for the crossover point for the following two projects. Year Expected Net Cash Flow Project A Project B -$12,000 -$10,000 1 $5,000 $4,100 2 3

Example 8.4a Computing the Crossover Point Solution: Plan: The crossover point is the discount rate that makes the NPV of the two alternatives equal. We can find the discount rate by setting the equations for the NPV of each project equal to each other and solving for the discount rate. In general, we can always compute the effect of choosing Project A over Project B as the difference of the NPVs. At the crossover point the difference is 0

Example 8.4a Computing the Crossover Point Execute: Setting the difference equal to 0: As you can see, solving for the crossover point is just like solving for the IRR, so we will need to use a financial calculator or spreadsheet:

Example 8.4a Computing the Crossover Point Execute (cont’d): And we find that the crossover occurs at a discount rate of 16.65%. Given: 3 -2,000 900 Solve for: 16.65 Excel Formula: =RATE(NPER, PMT, PV,FV) = RATE(3,900,‑2000,0)

Example 8.4a Computing the Crossover Point Evaluate: Just as the NPV of a project tells us the value impact of taking the project, so the difference of the NPVs of two alternatives tells us the incremental impact of choosing one project over another. The crossover point is the discount rate at which we would be indifferent between the two projects because the incremental value of choosing one over the other would be zero.

Example 8.4b Computing the Crossover Point Problem: Solve for the crossover point for the following two projects. Year Expected Net Cash Flow Project A Project B -$12,000 -$20,000 1 $5,000 $8,100 2 3

Example 8.4b Computing the Crossover Point Solution: Plan: The crossover point is the discount rate that makes the NPV of the two alternatives equal. We can find the discount rate by setting the equations for the NPV of each project equal to each other and solving for the discount rate. In general, we can always compute the effect of choosing Project A over Project B as the difference of the NPVs. At the crossover point the difference is 0

Example 8.4b Computing the Crossover Point Execute: Setting the difference equal to 0: As you can see, solving for the crossover point is just like solving for the IRR, so we will need to use a financial calculator or spreadsheet:

Example 8.4b Computing the Crossover Point Execute (cont’d): And we find that the crossover occurs at a discount rate of 16.65%. Given: 3 8,000 -3,100 Solve for: 7.924% Excel Formula: =RATE(NPER, PMT, PV,FV) = RATE(3,-3100,8000,0)

Example 8.4b Computing the Crossover Point Evaluate: Just as the NPV of a project tells us the value impact of taking the project, so the difference of the NPVs of two alternatives tells us the incremental impact of choosing one project over another. The crossover point is the discount rate at which we would be indifferent between the two projects because the incremental value of choosing one over the other would be zero.

8.4 Choosing Between Projects Timing of the Cash Flows Suppose Javier could sell the Internet café business at the end of the first year for $40,000. Should he plan to sell it?

Figure 8.9 NPV With and Without Selling

8.4 Choosing Between Projects The Bottom Line on IRR Picking the investment opportunity with the largest IRR can lead to a mistake. In general, it is dangerous to use the IRR in choosing between projects. Always rely on NPV.

8.5 Evaluating Projects with Different Lives Often, a company will need to choose between two solutions to the same problem. TABLE 8.2 Cash Flows ($ Thousands) for Network Server Options TABLE 8.3 Cash Flows ($ Thousands) for Network Server Options, Expressed as Equivalent Annual Annuities

Example 8.5 Computing an Equivalent Annual Annuity Problem: You are about to sign the contract for Server A from Table 8.2 when a third vendor approaches you with another option that lasts for 4 years. The cash flows for Server C are given below. Should you choose the new option or stick with Server A?

Example 8.5 Computing an Equivalent Annual Annuity Solution: Plan: In order to compare this new option to Server A, we need to put it an equal footing by computing its annual cost. We can do this Computing its NPV at the 10% discount rate we used above Computing the equivalent 4-year annuity with the same present value.

Example 8.5 Computing an Equivalent Annual Annuity Execute: Its annual cost of 5.62 is greater than the annual cost of Server A (5.02), so we should choose Server A.

Example 8.5 Computing an Equivalent Annual Annuity Evaluate: In this case, the additional cost associated with purchasing and maintaining Server C is not worth the extra year we get from choosing it. By putting all of these costs into an equivalent annuity, the EAA tool allows us to see that.

Example 8.5a Computing an Equivalent Annual Annuity Problem: You considering a maintenance contract from two vendors. Vendor Y charges $100,000 upfront and then $12,000 per year for the three-year life of the contract. Vendor Z charges $85,000 upfront and then $35,000 per year for the two-year life of the contract. Compute the NPV and EAA for each vendor assuming an 8% cost of capital.

Example 8.5a Computing an Equivalent Annual Annuity Solution: Plan: In order to compare the two options, we need to put both on an equal footing by computing its annual cost. We can do this Computing its NPV at the 8% discount rate we used above Computing the equivalent annual annuity with the same present value.

Example 8.5a Computing an Equivalent Annual Annuity Execute:

Example 8.5a Computing an Equivalent Annual Annuity Execute (cont’d): The annual cost of Vendor Z is greater than the annual cost of Vendor Y, so we should choose Vendor Y.

Example 8.5a Computing an Equivalent Annual Annuity Evaluate: In this case, the higher upfront cost associated with Vendor Y is worth the extra year we get from choosing it. By putting all of these costs into an equivalent annuity, the EAA tool allows us to see that.

8.6 Choosing Among Projects when Resources are Limited Sometimes different investment opportunities demand different amounts of a particular resource. If there is a fixed supply of the resource so that you cannot undertake all possible opportunities, simply picking the highest-NPV opportunity might not lead to the best decision.

8.6 Choosing Among Projects when Resources are Limited TABLE 8.4 Possible Projects for $200 Million Budget

8.6 Choosing Among Projects when Resources are Limited Profitability Index (Eq. 8.4)

Example 8.6 Profitability Index with a Human Resource Constraint Problem: Your division at NetIt, a large networking company, has put together a project proposal to develop a new home networking router. The expected NPV of the project is $18.8 million, and the project will require 50 software engineers. NetIt has a total of 190 engineers available, and is unable to hire additional qualified engineers in the short run. Therefore, the router project must compete with the following other projects for these engineers:

Example 8.6 Profitability Index with a Human Resource Constraint Problem (cont’d): How should NetIt prioritize these projects? Project NPV ($ millions) Engineering Headcount Router 17.7 50 Project A 22.7 47 Project B 8.1 44 Project C 14.0 40 Project D 11.5 61 Project E 20.6 58 Project F 12.9 32 Total 107.5 332

Example 8.6 Profitability Index with a Human Resource Constraint Solution: Plan: The goal is to maximize the total NPV we can create with 190 employees (at most). We can use Eq. 8.4 to determine the profitability index for each project. In this case, since engineers are our limited resource, we will use Engineering Headcount in the denominator. Once we have the profitability index for each project, we can sort them based on the index.

Example 8.6 Profitability Index with a Human Resource Constraint Execute:

Example 8.6 Profitability Index with a Human Resource Constraint Execute (cont’d): We now assign the resource to the projects in descending order according to the profitability index. The final column shows the cumulative use of the resource as each project is taken on until the resource is used up. To maximize NPV within the constraint of 190 employees, NetIt should choose the first four projects on the list.

Example 8.6 Profitability Index with a Human Resource Constraint Evaluate: By ranking projects in terms of their NPV per engineer, we find the most value we can create, given our 190 engineers. There is no other combination of projects that will create more value without using more engineers than we have. This ranking also shows us exactly what the engineering constraint costs us—this resource constraint forces NetIt to forgo three otherwise valuable projects (C, D, and B) with a total NPV of $33.6 million.

Example 8.6a Profitability Index with a Human Resource Constraint Problem: AaronCo is considering several projects to undertake. All of the projects currently under consideration have a positive NPV, but AaronCo has a fixed capital budget of $300 million. The company does not believe they will be able to raise any additional funds. How should AaronCo prioritize the projects (listed on the following slide)?

Example 8.6a Profitability Index with a Human Resource Constraint Problem (cont’d):

Example 8.6a Profitability Index with a Human Resource Constraint Solution: Plan: The goal is to maximize the total NPV we can create with $300 million (at most). We can use Eq. 8.3 to determine the profitability index for each project. In this case, since money is our limited resource, we will use Initial Cost in the denominator. Once we have the profitability index for each project, we can sort them based on the index.

Example 8.6a Profitability Index with a Human Resource Constraint Execute:

Example 8.6a Profitability Index with a Human Resource Constraint Execute (cont’d): We now assign the resource to the projects in descending order according to the profitability index. The final column shows the cumulative use of the resource as each project is taken on until the resource is used up. To maximize NPV within the constraint of $300 million, AaronCo should choose the first four projects on the list.

Example 8.6a Profitability Index with a Human Resource Constraint Evaluate: By ranking projects in terms of their NPV per engineer, we find the most value we can create, given our $300 million budget. There is no other combination of projects that will create more value without using more money than we have. This ranking also shows us exactly what the budget constraint costs us—this resource constraint forces AaronCo to forgo three otherwise valuable projects (B, D, and E) with a total NPV of $110 million.

8.7 Putting It All Together TABLE 8.5 Summary of Decision Rules

8.7 Putting It All Together TABLE 8.5 Summary of Decision Rules (cont.)

Chapter Quiz Explain the NPV rule for stand-alone projects. Under what conditions will the IRR rule lead to the same decision as the NPV rule? What is the most reliable way to choose between mutually exclusive projects? Explain why choosing the option with the highest NPV is not always correct when the options have different lives. What does the profitability index tell you?