Key Concepts and Skills

9 Net Present Value and Other Investment Criteria
Prepared by Anne Inglis Edited by William Rentz

Key Concepts and Skills
Be able to compute the net present value and understand why it is the best decision criterion Be able to compute payback and discounted payback and understand their shortcomings Understand accounting rates of return and their shortcomings Be able to compute the internal rate of return and understand its strengths and weaknesses Understand the modified internal rate of return Understand the profitability index and its relation to net present value © 2013 McGraw-Hill Ryerson Limited

© 2013 McGraw-Hill Ryerson Limited
Chapter Outline Net Present Value The Payback Rule The Discounted Payback The Average Accounting Return The Internal Rate of Return The Profitability Index The Practice of Capital Budgeting Summary and Conclusions Appendix A – Modified Internal Rate of Return © 2013 McGraw-Hill Ryerson Limited

What Makes a Good Decision Criteria?
All LOs We need to ask ourselves the following questions when evaluating decision criteria Does the decision rule adjust for the time value of money? Does the decision rule adjust for risk? Does the decision rule provide information on whether we are creating value for the firm? © 2013 McGraw-Hill Ryerson Limited

NPV – Decision Rule LO1 If the NPV is positive, accept the project A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal. © 2013 McGraw-Hill Ryerson Limited

Net Present Value 9.1 LO1 The difference between the market value of a project and its cost How much value is created from undertaking an investment? The first step is to estimate the expected future cash flows. The second step is to estimate the required return for projects of this risk level. The third step is to find the present value of the cash flows and subtract the initial investment. We learn how to estimate the cash flows in chapter 10. We learn how to estimate the required return in chapter 13. © 2013 McGraw-Hill Ryerson Limited

Project Example Information
All LOs You are looking at a new project and you have estimated the following cash flows: Year 0: CF = -165,000 Year 1: CF = 63,120; NI = 13,620 Year 2: CF = 70,800; NI = 3,300 Year 3: CF = 91,080; NI = 29,100 Average Book Value = 72,000 Your required return for assets of this risk is 12%. This example will be used for each of the decision rules so that the students can compare the different rules and see that conflicts can arise. This illustrates the importance of recognizing which decision rules provide the best information for making decisions that will increase shareholder wealth. © 2013 McGraw-Hill Ryerson Limited

Computing NPV for the Project
LO1 Using the formulas: NPV = 63,120/(1.12) + 70,800/(1.12)2 + 91,080/(1.12)3 – 165,000 = 12,627.42 Using the calculator: Use the Cash Flow and NPV functions on the TI BAII Plus CF0 = -165,000; C01 = 63,120; F01 = 1; C02 = 70,800; F02 = 1; C03 = 91,080; F03 = 1; NPV; I = 12; CPT NPV = 12,627.41 Do we accept or reject the project? Again, the calculator used for the illustration is the Texas Instruments BA-II plus. The basic procedure is the same, you start with the year 0 cash flow and then enter the cash flows in order. You toggle between the different cash flows by using the up and down arrows in the top row. F01, F02, etc. are used to set the frequency of a cash flow occurrence. Many of the calculators only require you to use that if the frequency is something other than 1. Using the BAII Plus, press CF. The screen displays CFo= If there is already data enterred into the Cash Flow functions memory, you can clear this by pressing 2nd and CE/C. Enter -165,000 and press ENTER. Press the down arrow once until the screen displays CO1. Enter 63,120 and press ENTER. Press the down arrow twice until the screen displays CO2. Enter 70,800 and press ENTER. Press the down arrow twice until the screen displays CO3. Enter 91,080 and press ENTER. Then press NPV – you should see I= Enter 12 and press enter. Then press the up arrow key once – the calculator should display NPV= Press CPT and the calculator should display the answer. © 2013 McGraw-Hill Ryerson Limited

Decision Criteria Test - NPV
LO1 Does the NPV rule account for the time value of money? Does the NPV rule account for the risk of the cash flows? Does the NPV rule provide an indication about the increase in value? Should we consider the NPV rule for our primary decision criteria? The answer to all of these questions is yes. You should point out, however, that if you get a very large NPV that you should go back and look at your cash flow estimation again. In competitive markets, extremely high NPVs should be rare. © 2013 McGraw-Hill Ryerson Limited

Calculating NPVs with a Spreadsheet
LO1 Spreadsheets are an excellent way to compute NPVs, especially when you have to compute the cash flows as well. Using the NPV function The first component is the required return entered as a decimal The second component is the range of cash flows beginning with year 1 Subtract the initial investment after computing the NPV Click on the Excel icon to go to an embedded Excel worksheet that has the cash flows along with the right and wrong way to compute NPV. Click on the cell with the solution to show the students the difference in the formulas. You can also click on the fx icon and show them how to enter the formula initially. © 2013 McGraw-Hill Ryerson Limited

Payback Period 9.2 LO2 How long does it take to get the initial cost back in a nominal sense? Computation Estimate the cash flows Subtract the future cash flows from the initial cost until the initial investment has been recovered Decision Rule – Accept if the payback period is less than some preset limit © 2013 McGraw-Hill Ryerson Limited

Computing Payback For The Project
LO2 Assume we will accept the project if it pays back within two years. Year 1: 165,000 – 63,120 = 101,880 still to recover Year 2: 101,880 – 70,800 = 31,080 still to recover Year 3: 31,080 – 91,080 = - 60,000 project pays back in under 3 years but more than 2 If the preset limit is 2 years, do we accept or reject the project? The payback period is year 3 if you assume that the cash flows occur at the end of the year as we do with all of the other decision rules. If we assume that the cash flows occur evenly throughout the year, then the project pays back in 2.34 years. © 2013 McGraw-Hill Ryerson Limited

Decision Criteria Test - Payback
LO2 Does the payback rule account for the time value of money? Does the payback rule account for the risk of the cash flows? Does the payback rule provide an indication about the increase in value? Should we consider the payback rule for our primary decision criteria? The answer to all of these questions is no. © 2013 McGraw-Hill Ryerson Limited

Advantages and Disadvantages of Payback
LO2 Advantages Easy to understand Adjusts for uncertainty of later cash flows, albeit in a draconian fashion Biased towards liquidity Disadvantages Ignores the time value of money Requires an arbitrary cutoff point Ignores cash flows beyond the cutoff date Biased against long-term projects, such as research and development, and new projects © 2013 McGraw-Hill Ryerson Limited

Discounted Payback Period
LO3 Compute the present value of each cash flow and then determine how long it takes to payback on a discounted basis Compare to a specified required payback period Decision Rule - Accept the project if it pays back on a discounted basis within the specified time © 2013 McGraw-Hill Ryerson Limited

Computing Discounted Payback for the Project
LO3 Assume we will accept the project if it pays back on a discounted basis in 2 years. Compute the PV for each cash flow and determine the payback period using discounted cash flows Year 1: 165,000 – 63,120/1.121 = 108,643 Year 2: 108,643 – 70,800/1.122 = 52,202 Year 3: 52,202 – 91,080/1.123 = -12,627 project pays back in under 3 years Do we accept or reject the project? © 2013 McGraw-Hill Ryerson Limited

Decision Criteria Test – Discounted Payback
LO3 Does the discounted payback rule account for the time value of money? Does the discounted payback rule account for the risk of the cash flows? Does the discounted payback rule provide an indication about the increase in value? Should we consider the discounted payback rule for our primary decision criteria? © 2013 McGraw-Hill Ryerson Limited

Advantages and Disadvantages of Discounted Payback
LO3 Advantages Includes time value of money Easy to understand Does NOT accept NEGATIVE estimated NPV investments Biased towards liquidity Disadvantages MAY reject positive NPV investments Requires an arbitrary cutoff point Ignores cash flows beyond the cutoff date Biased against long-term projects, such as R&D, and new projects © 2013 McGraw-Hill Ryerson Limited

Average Accounting Return 9.3
LO4 There are many different definitions for average accounting return The one used in the book is: Average net income / Average book value Note that the average book value depends on how the asset is depreciated Need to have a target cutoff rate Decision Rule: Accept the project if the AAR is greater than a preset rate. © 2013 McGraw-Hill Ryerson Limited

Computing AAR For The Project
LO4 Assume we require an average accounting return of 25% Average Net Income: (13, , ,100) / 3 = 15,340 AAR = 15,340 / 72,000 = .213 = 21.3% Do we accept or reject the project? Students may ask where you came up with the 25%, point out that this is one of the drawbacks of this rule. There is no good theory for determining what the return should be. We generally just use some rule of thumb. © 2013 McGraw-Hill Ryerson Limited

Decision Criteria Test - AAR
LO4 Does the AAR rule account for the time value of money? Does the AAR rule account for the risk of the cash flows? Does the AAR rule provide an indication about the increase in value? Should we consider the AAR rule for our primary decision criteria? The answer to all of these questions is no. In fact, this rule is even worse than the payback rule in that it doesn’t even use cash flows for the analysis. It uses net income and book value. © 2013 McGraw-Hill Ryerson Limited

Advantages and Disadvantages of AAR
LO4 Advantages Easy to calculate Needed information is usually available Disadvantages Not a true rate of return; time value of money is ignored Uses an arbitrary benchmark cutoff rate Based on accounting net income and book values, NOT cash flows and market values © 2013 McGraw-Hill Ryerson Limited

Internal Rate of Return 9.4
LO5 This is the most important alternative to NPV It is often used in practice and is intuitively appealing It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere The IRR rule is very important. Management, and individuals in general, often have a much better feel for percent returns and the value that is created, than they do for dollar increases. A dollar increase doesn’t seem to provide as much information if we don’t know what the initial expenditure was. © 2013 McGraw-Hill Ryerson Limited

IRR – Definition and Decision Rule
LO5 Definition: IRR is the return that makes the NPV = 0 Decision Rule: Accept the project if the IRR is greater than the required return © 2013 McGraw-Hill Ryerson Limited

Computing IRR For The Project
LO5 If you do NOT have a financial calculator, then this becomes a trial and error process Financial calculator Enter the cash flows as you did with NPV Press IRR and then CPT IRR = 16.13% > 12% required return Do we accept or reject the project? Many of the financial calculators will compute the IRR as soon as it is pressed; others require that you press compute. The instructions above are again using the Texas Instruments BAII Plus. Enter the cash flows as described in the notes for the NPV example. Press IRR and then press CPT. The answer of should display on the calculator’s screen. © 2013 McGraw-Hill Ryerson Limited

NPV Profile For The Project
LO5 IRR = 16.13% © 2013 McGraw-Hill Ryerson Limited

Calculating IRRs With A Spreadsheet
LO5 You start with the cash flows the same as you did for the NPV You use the IRR function You first enter your range of cash flows, beginning with the initial cash flow You can enter a guess, but it is not necessary The default format is a whole percent – you will normally want to increase the decimal places to at least two © 2013 McGraw-Hill Ryerson Limited

Decision Criteria Test - IRR
LO5 Does the IRR rule account for the time value of money? Does the IRR rule account for the risk of the cash flows? Does the IRR rule provide an indication about the increase in value? Should we consider the IRR rule for our primary decision criteria? The answer to all of these questions is yes, although it is not always as obvious. The IRR rule accounts for time value because it is finding the rate of return that equates all of the cash flows on a time value basis. The IRR rule accounts for the risk of the cash flows because you compare it to the required return, which is determined by the risk of the project. The IRR rule provides an indication of value because we will always increase value if we can earn a return greater than our required return. We should consider the IRR rule as our primary decision criteria, but as we will see, it has some problems that the NPV does not have. That is why we end up choosing the NPV as our ultimate decision rule. © 2013 McGraw-Hill Ryerson Limited

Advantages of IRR LO5 Knowing a return is intuitively appealing It is a simple way to communicate the value of a project to someone who does NOT know all the estimation details If the IRR is HIGH enough, you may NOT need to estimate a required return, which is often a difficult task Generally leads to the same answers as the NPV method You should point out, however, that if you get a very large IRR that you should go back and look at your cash flow estimation again. In competitive markets, extremely high IRRs should be rare. © 2013 McGraw-Hill Ryerson Limited

Disadvantages of IRR LO5 NPV and IRR will generally give us the same decision EXCEPTIONS: MAY result in MULTIPLE answers or NO answer with NON-NORMAL cash flows MAY lead to INCORRECT decisions in comparisons of MUTUALLY EXCLUSIVE investments © 2013 McGraw-Hill Ryerson Limited

Non-Normal or Non-Conventional Cash Flows
A normal or conventional project has one or more cash outlays followed by one or more cash inflows When the cash flows change sign more than once, there is potentially more than one positive IRR © 2013 McGraw-Hill Ryerson Limited

IRR and Non-Normal Cash Flows
When you solve for the IRR, you are solving for the root of an equation. When you cross the x-axis more than once, there will be more than one return that solves the equation. If you have more than one positive IRR, which one do you use to make your decision? © 2013 McGraw-Hill Ryerson Limited

Example: Non-Normal Cash Flows
Suppose an investment will cost $90,000 initially and will generate the following cash flows: Year 1: + $132,000 Year 2: + $100,000 Year 3: - $150,000 The required return is 15%. Should we accept or reject the project? NPV = 132,000 / ,000 / (1.15)2 – 150,000 / (1.15)3 – 90,000 = 1,769.54 Calculator: CF0 = -90,000; C01 = 132,000; F01 = 1; C02 = 100,000; F02 = 1; C03 = -150,000; F03 = 1; I = 15; CPT NPV = If you compute the IRR on the calculator, you get 10.11% because it is the first one that you come to. So, if you just blindly use the calculator without recognizing the uneven cash flows, NPV would say to accept and IRR would say to reject. © 2013 McGraw-Hill Ryerson Limited

NPV Profile LO5 IRR = 10.11% and 42.66% You should accept the project if the required return is between 10.11% and 42.66% The MIRR (Modified IRR) function in MS Excel addresses the multiple IRR problem. It takes the cash flows, finance rate (interest rate to be paid for negative cash flows), and reinvestment rate (interest rate that would be earned on positive cash flows) as inputs and returns a single value. Modified IRR is covered in Appendix A. © 2013 McGraw-Hill Ryerson Limited

Summary of Decision Rules
LO5 The NPV is positive at a required return of 15%, so you should Accept If you use the financial calculator, you would get an IRR of 10.11% which would tell you to Reject You need to RECOGNIZE that there are NON-NORMAL cash flows and look at the NPV profile © 2013 McGraw-Hill Ryerson Limited

IRR and Mutually Exclusive Projects
LO5 Mutually exclusive projects If you choose one, you can’t choose the other Example: You can choose to attend graduate school next year at either Rotman or Ivey, but NOT both Intuitively you would use the following decision rules: NPV – choose the project with the higher NPV IRR – choose the project with the higher IRR © 2013 McGraw-Hill Ryerson Limited

Example With Mutually Exclusive Projects
LO5 The required return for both projects is 10%. Which project should you accept and why? Period Project A Project B - 500 - 400 1 325 2 200 IRR 19.43% 22.17% NPV 64.05 60.74 As long as we do not have limited capital, we should choose project A. Students will often argue that you should choose B because then you can invest the additional $100 in another good project, say C. The point is that if we do not have limited capital, we can invest in A and C and still be better off. If we have limited capital, then we will need to examine what combinations of projects with A provide the highest NPV and what combinations of projects with B provide the highest NPV. You then go with the set that will create the most value. If you have limited capital and a large number of mutually exclusive projects, then you will want to set up a computer program to determine the best combination of projects within the budget constraints. The important point is that we DO NOT use IRR to choose between projects regardless of whether or not we have limited capital. © 2013 McGraw-Hill Ryerson Limited

NPV Profiles LO5 IRR for A = 19.43% IRR for B = 22.17% Crossover Point = 11.8% If the required return is less than the crossover point of 11.8%, then you should choose A If the required return is greater than the crossover point of 11.8%, then you should choose B © 2013 McGraw-Hill Ryerson Limited

Crossover or Fisher Rate
LO5 The crossover or Fisher rate occurs when NPVA = NPVB or NPVA – NPVB = 0 Construct a Project Δ that is the difference between the cash flows for Project A and B Note that NPVA – NPVB = NPVΔ = 0 Project Δ cash flows are as follows: CF0 = - 100, CF1 = 0, CF2 = 125 © 2013 McGraw-Hill Ryerson Limited

Fisher Rate or Project Δ IRR
LO5 For this problem, the IRR calculation is easily done on a scientific calculator On BAII+, CFo = - 100, C01 = 0, F01 = 1, C02 = 125, F02 =1. Touch IRR followed by CPT to display IRR = 11.80 © 2013 McGraw-Hill Ryerson Limited

Conflicts Between NPV and IRR
LO5 NPV directly measures the increase in value to the firm Whenever there is a conflict between NPV and another decision rule, you should always use NPV unless there is a substantial difference in project scale IRR is NOT reliable in the following cases NON-CONVENTIONAL cash flows MUTUALLY EXCLUSIVE projects © 2013 McGraw-Hill Ryerson Limited

Non-normal or Non-conventional Cash Flows
A “project” that has one or more cash inflows followed by one or more cash outlays is a type of non-normal project What happens to the IRR rule when we consider two mutually exclusive “projects” of this type? © 2013 McGraw-Hill Ryerson Limited

Mutually Exclusive Example with Non-normal Cash Flows
“Project A”: Initial inflow of $10,000 at the BEGINNING of the year followed by a cash outlay of $11,000 at year’s END “Project B”: Initial inflow of $10,000 at the BEGINNING of the year followed by a cash outlay of $10,500 at year’s END © 2013 McGraw-Hill Ryerson Limited

IRR Calculations LO5 “Project A”: 0 = + $10,000 - $11,000/(1 + IRR) 0 = + $10,000 x (1 + IRR) - $11,000 0 = 1 + IRR  IRR = 0.1 or 10% “Project B”: 0 = + $10,000 - $10,500/(1 + IRR) 0 = + $10,000 x (1 + IRR) - $10,500 0 = 1 + IRR – 1.05  IRR = 0.05 or 5% © 2013 McGraw-Hill Ryerson Limited

Choosing a “Project” LO5 Which “project” should one choose? Based on the traditional IRR rule, one might be inclined to choose “Project A” because IRRA = 10% > IRRB = 5% However, this would NOT be correct The “projects” are NOT really projects but instead are LOANS One wants to borrow as cheaply as possible. Thus, choose LOAN B! © 2013 McGraw-Hill Ryerson Limited

Profitability Index 9.5 LO7 Measures the benefit per unit cost, based on the time value of money A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value This measure can be very useful in situations where we have limited capital © 2013 McGraw-Hill Ryerson Limited

Advantages and Disadvantages of Profitability Index
LO7 Advantages Closely related to NPV, generally leading to identical decisions Easy to understand and communicate May be useful when available investment funds are limited Disadvantages MAY lead to INCORRECT decisions in comparisons of mutually exclusive investments © 2013 McGraw-Hill Ryerson Limited

The Practice of Capital Budgeting 9.6
All LOs NPV and IRR are the most commonly used primary investment criteria Payback is a commonly used secondary investment criteria Capital budgeting techniques vary with industry. Firms that are better able to estimate cash flows precisely are more likely to use NPV These methods should be used with considerable judgment and thought. There may be more risk than we have considered or we may want to pay additional attention to our cash flow estimations. Sensitivity and scenario analysis can be used to help us evaluate our cash flows. The fact that payback is commonly used as a secondary criteria may be because short paybacks allow firms to have funds sooner to invest in other projects without going to the capital markets © 2013 McGraw-Hill Ryerson Limited

Quick Quiz Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9% and required payback is 4 years. What is the payback period? What is the NPV? What is the IRR? Should we accept the project? What decision rule should be the primary decision method? When is the IRR rule unreliable? © 2013 McGraw-Hill Ryerson Limited

Summary continued Internal Rate of Return Discount rate that makes NPV = 0 Take the project if the IRR is greater than required return Same decision as NPV with conventional cash flows IRR is UNRELIABLE with NON-NORMAL cash flows or MUTUALLY EXCLUSIVE projects © 2013 McGraw-Hill Ryerson Limited

Summary continued Profitability Index Benefit-cost ratio Take investment if PI > 1 Usually NOT used to rank mutually exclusive projects May be used to rank projects in the presence of capital rationing Payback Period Length of time until initial investment is recovered Take the project if it pays back in some specified period Does NOT account for time value of money and there is an arbitrary cutoff period © 2013 McGraw-Hill Ryerson Limited

Summary continued Discounted Payback Period Length of time until initial investment is recovered on a discounted basis Take the project if it pays back in some specified period There is an arbitrary cutoff period Average Accounting Return Measure of accounting profit relative to book value Similar to return on assets measure Take the investment if the AAR exceeds some specified return level Serious problems and should NOT be used © 2013 McGraw-Hill Ryerson Limited

© 2013 Dr. William F. Rentz & Associates
Additions, deletions, and corrections to these transparencies were performed by Dr. William F. Rentz solely for use at the University of Ottawa. The above copyright notice applies to all changes made herein.

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