1. Net Present Value and Other Investment Rules

2. Percent of CFOs who say they use the following rules to evaluate projects
Graham, Smart, and Megginson (2010) Figure 7.1

3. What Makes for a Good Investment Rule?
Recognize the time value of money
Should rely solely on expected future cash flows and the opportunity cost of capital
-Manager discretion & accounting numbers, are easy to manipulate
Want to be able to rank projects, and evaluate portfolios of projects

4. Potential Investment Criteria
Payback Period
Average Accounting Return
IRR
NPV

5. Payback Period
Definition: The number of years before the project’s cumulative future cash flows equal the initial investment.
How long does it take the project’s to pay for itself?
Decision rule: Accept projects whose payback period is less than a manager determined cut-off

6. Payback Example Assume Payback cut-off is 1 year
Which project do we take
Project
Year 0
Year 1
Year 2 PB
10% A
-10 10
Cum. CF B 15

7. The Payback Period Method
Disadvantages:
Biased against long-term projects
Ignores cash flows after the payback period
Requires an arbitrary acceptance criteria
Ignores the time value of money
A “Good” project may destroy value
Advantages:
Easy to understand
Biased toward liquidity

8. The Discounted Payback Period
Cash flows are discounted before payback period is calculated
Effectively pick positively NPV project
Very conservative → only very valuable projects accepted
STILL ignores cash flows after the payback period

9. Average Accounting Return
Decision Rule: If the calculated value is above a benchmark (Ex. the firm’s current return on book or the industry average) accept the project.
Fatally Flawed because:

10. AAR Example
A project has net income of $1,200, and $1,600 a year over its 2-year life. The initial cost of the project is $5,000, which will be depreciated using straight-line depreciation to a book value of zero over the life of the project. What is the AAR for this project?

11. AAR example AAR = 1 2 Ave NI BV
A project has net income of $1,200, and $1,600 a year over its 2-year life. The initial cost of the project is $5,000, which will be depreciated using straight-line depreciation to a book value of zero over the life of the project. What is the AAR for this project?
AAR = 1 2
Ave NI BV

12. Average Accounting Return
Disadvantages:
Uses accounting numbers instead of cash flows
Ignores the time value of money
The benchmark is arbitrary.
Advantages:
The accounting information is easy to obtain
Easy to calculate

13. Internal Rate of Return (IRR)
Definition: It is the discount rate that makes a project’s NPV equal 0.
Decision Rule: Accept all projects with IRR’s greater than the opportunity cost of capital.

14. IRR’s Underlying Assumptions
All intermediate cash flows can be reinvested at the IRR
Is this reasonable?
That short-term interest rates are equal to long-term interest rates
Does not address which to use if they are not equal

15. IRR Notes
To find the IRR of a project lasting t years, solve the following equation:
C0+C1/(1+IRR)+C2/(1+IRR)2+….+Ct/(1+IRR)t=0 
NPV > 0 implies that IRR > Op Cost
IRR > Op Cost DOES NOT IMPLY that NPV > 0
IRR assumes that causality goes both ways

16. IRR & NPV Investment Example
A firm has a project that requires an initial investment of $10m. In the first year, it will return $12m, what is the IRR?
If r=10% do we accept the project based on IRR and NPV?

17. Internal Rate of Return (IRR)
Disadvantages:
No distinction between investing and borrowing
May have multiple IRR’s, or no IRR
Problems with mutually exclusive investments
Scale Problem
Timing Problem
Advantages:
Easy to understand and communicate

18. Loan Example According to IRR which project do we pick? C0 C1 IRR
10%
Project A
-10 20
100%
Project B 10
-20
According to IRR which project do we pick?

19. No IRR
Example of No IRR

20. Multiple IRR
$ $800
-$200
- $800
If cash flows switch signs more than once then there exists multiple IRR’s
There will be as many IRRs as there are sign changes
Which IRR do we use?

21. The Scale Problem
Would you rather make 100% or 50% on your investments?

22. Mutually Exclusive Projects
Choosing between projects
RANK all alternatives, and select highest IRR
IRR ignore the amount of wealth generated
Which project should we take according to IRR?
Which project do investors prefer? C0 C1
IRR
10%
Project A
-100
150
50%
36.36
Project B
-75
120
34.09

23. Resource constraint The firm has $100 to invest, what should it buy?
IRR:
NPV:
Project C0
IRR
NPV 10% A
-100
300 50
216%
$210 B
-50
200
156%
$160 C
150
130%
$120

24. Otherwise IRR can lead to BAD decisions
Verdict on IRR
Gives the same result as NPV if:
Flat term structure
Conventional cash flows
Independent projects
Otherwise IRR can lead to BAD decisions

25. The Profitability Index (PI)
Minimum Acceptance Criteria:
Accept if PI > 1
Ranking Criteria:
Select alternative with highest PI

26. Selection Example Which projects do we take? C0 C1 C2 NPV @ 10% PI A
-100
300 50
214 B
-50
200
161 C
150
119

27. The Profitability Index
Disadvantages:
Problems when there are additional constraints
Use linear or integer programming
Advantages:
When funds limited (Capital Rationing), provides better rankings than NPV
Easy to understand and communicate

28. The Net Present Value (NPV) Rule
Total PV of future CF’s + Initial Investment
Estimating NPV:
1. Estimate future cash flows: how much? and when?
2. Estimate discount rate
3. Estimate initial costs
Minimum Acceptance Criteria: Accept if NPV > 0
Ranking Criteria: Choose the highest NPV

29. Why We Love NPV NPV recognizes the time value of money
NPV depends only on future cash flows and the opportunity cost of capital
Present value, can be added up, thus allowing us to evaluate “packages of projects” or a single project
Accepting positive NPV projects, increases wealth

30. Capital Budgeting in Practice
Varies by industry
The most frequently used technique for large corporations are: IRR or NPV
However, many companies also consider payback

31. Example of Investment Rules
Compute the Payback Period, NPV, and PI for the following two projects. Assume the required return is 10%.
Year Project A Project B
0 -$200 -$150
1 $200 $50
2 $800 $100
3 -$800 $150

32. Summary – Discounted Cash Flow
Net present value
Accept the project if the NPV is positive
Has no serious problems
Yields the best decision
Internal rate of return
Take the project if the IRR is greater than the required return
Same decision as NPV with conventional cash flows
IRR is unreliable with non-conventional cash flows or mutually exclusive projects
Profitability Index
Take investment if PI > 1
Cannot be used to rank mutually exclusive projects
Should be used to rank projects in the presence of capital rationing

33. Summary – Payback Criteria
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
Discounted payback period
Length of time until initial investment is recovered on a discounted basis
There is an arbitrary cutoff period

34. Summary – Accounting Criterion
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

35. 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 payback cutoff is 4 years.
What is the payback period?
What is the discounted payback period?
What is the NPV?
What is the IRR?
Should we accept the project?
What method should be the primary decision rule?
When is the IRR rule unreliable?

36. Why We Care Help you develop your finance intuition
Showing you common mistakes, so that you won’t make those mistakes