1. Net Present Value and Other Investment Criteria
Chapter 8
Net Present Value and Other Investment Criteria

2. Key Concepts and Skills
Understand the payback rule and its shortcomings
Understand accounting rates of return and their problems
Understand the internal rate of return and its strengths and weaknesses
Understand the net present value rule and why it is the best decision criteria

3. Chapter Outline Net Present Value The Payback Rule
The Average Accounting Return
The Internal Rate of Return
The Profitability Index
The Practice of Capital Budgeting

4. Good Decision Criteria
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?

5. Project Example Information
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 owner wealth.

6. Net Present Value
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 9.
We learn how to estimate the required return in chapter 12.

7. NPV Decision Rule 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.

8. Computing NPV for the Project
Using the formulas:
NPV = 63,120/(1.12) + 70,800/(1.12)2 + 91,080/(1.12)3 – 165,000 = $12,627.41
Using the calculator:
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 TI- 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. 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.

9. Decision Criteria Test - NPV
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

10. Calculating NPVs with a Spreadsheet
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.

11. Payback Period
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

12. Computing Payback For the Project
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 during year 3
Payback = 2 years + 31,080/91,080 = 2.34 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, which 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.

13. Decision Criteria Test - Payback
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.

14. Advantages and Disadvantages of Payback
Easy to understand
Adjusts for uncertainty of later cash flows
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

15. Average Accounting Return
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.
The example in the book uses straight line depreciation to a zero salvage; that is why you can take the initial investment and divide by 2. If you use MACRS, you need to compute the BV in each period and take the average in the standard way.

16. Computing AAR For the Project
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.

17. Decision Criteria Test - AAR
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.

18. Advantages and Disadvantages of AAR
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
Advantages
Easy to calculate
Needed information will usually be available

19. Internal Rate of Return
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 has 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.

20. IRR – Definition and Decision Rule
Definition: IRR is the return that makes the NPV = 0
Decision Rule: Accept the project if the IRR is greater than the required return

21. Computing IRR For the Project
If you do not have a financial calculator, then this becomes a trial-and-error process
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.

22. NPV Profile For the Project
IRR = 16.13%

23. Decision Criteria Test - IRR
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.

24. Advantages of IRR Knowing a return is intuitively appealing
It is a simple way to communicate the value of a project to someone who doesn’t 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
You should point out, however, that if you get a very large IRR, you should go back and look at your cash flow estimation again. In competitive markets, extremely high IRRs should be rare.

25. Summary of Decisions For the Project
Net Present Value
Accept
Payback Period
Reject
Average Accounting Return
Internal Rate of Return
So, what should we do – we have two rules that indicate to accept and two that indicate to reject.

26. Calculating IRRs With a Spreadsheet
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
Click on the Excel icon to go to an embedded spreadsheet so that you can illustrate how to compute IRR on the spreadsheet.

27. NPV vs. IRR NPV and IRR will generally give us the same decision
Exceptions
Nonconventional cash flows – cash flow signs change more than once
Mutually exclusive projects
Initial investments are substantially different
Timing of cash flows is substantially different

28. IRR and Nonconventional Cash Flows
When the cash flows change signs more than once, there is more than one IRR
When you solve for IRR, you are solving for the root of an equation and 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 IRR, which one do you use to make your decision?

29. Another Example – Nonconventional 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 = 1,769.54
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.

30. NPV Profile
IRR = 10.11% and 42.66%
You should accept the project if the required return is between 10.11% and 42.66%

31. Summary of Decision Rules
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 nonconventional cash flows, and that you need to look at the NPV profile

32. IRR and 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 Harvard or Stanford, 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

33. Example With Mutually Exclusive Projects
Period
Project A
Project B
-500
-400 1
325 2
200
IRR
19.43%
22.17%
NPV
64.05
60.74
The required return for both projects is 10%.
Which project should you accept and why?
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 which combination of projects with project A provides the highest NPV and which combination of projects with project B provides 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.

34. NPV Profiles 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%, and doesn’t exceed B’s IRR of 22.17%, then you should choose B

35. Conflicts Between NPV and IRR
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
IRR is unreliable in the following situations
Non-conventional cash flows
Mutually exclusive projects

36. Modified Internal Rate of Return (MIRR)
Compute IRR of modified cash flows
Controls for some problems with IRR
Discounting Approach – Discount future outflows to present and add to CF0
Reinvestment Approach - Compound all CFs except the first one forward to end
Combination Approach – Discount outflows to present; compound inflows to end
MIRR will be a unique number for each method, but is difficult to interpret; discount/compound rate is externally supplied

37. Example: MIRR Project cash flows:
Time 0: -$500 today; Time 1: + $1,000; Time 2: -$100
Use combined method and RRR = 11%
PV (outflows) = -$ $100/(1.11)2 = $581.16
FV (inflow) = $1,000 x 1.11 = $1,110
MIRR: N=2; PV= ; FV=1,110; CPT I/Y = MIRR = 38.2%

38. Profitability Index
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 receive $1.10 worth of benefits, so we create an additional $0.10 in value
This measure can be very useful in situations in which we have limited capital

39. Advantages and Disadvantages of Profitability Index
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

40. Capital Budgeting In Practice
We should consider several investment criteria when making decisions
NPV and IRR are the most commonly used primary investment criteria
Payback is a commonly used secondary investment criteria
Even though payback and AAR should not be used to make the final decision, we should consider the project very carefully if they suggest rejection. 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

41. 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 the required payback is 4 years.
What is the payback period?
What is the NPV?
What is the IRR?
Should we accept the project?
What should be the primary decision method?
When is the IRR rule unreliable?
Payback period = 4 years
NPV = -2,758.72
IRR = 7.93%

42. Comprehensive Problem
An investment project has the following cash flows: CF0 = -1,000,000; C01 – C08 = 200,000 each
If the required rate of return is 12%, what decision should be made using NPV?
How would the IRR decision rule be used for this project, and what decision would be reached?
How are the above two decisions related?
NPV = -$6,472; reject the project since it would lower the value of the firm.
IRR = 11.81%, so reject the project since it would tie up investable funds in a project that will provide insufficient return.
The NPV and IRR decision rules will provide the same decision for all independent projects with conventional/normal cash flow patterns. If a project adds value to the firm (i.e., has a positive NPV), then it must be expected to provide a return above that which is required. Both of those justifications are good for shareholders; sadly, neither is the case for this project.
Other questions to pose:
Payback of the project? 5 years
PI of the project? (benefits are below the costs)
MIRR of the project? All three methods are the same for this conventional project, and it’s basically a moot point, but MIRR = 11.91% (higher than the IRR due to the negative NPV of the project; the reinvestment rate is above the discount rate in this case).