1. Weighing Net Present Value and Other Capital Budgeting Criteria
Chapter 13
Fin 325, Section 04 - Spring 2010
Washington State University

2. Introduction In previous chapters we learned how to
Calculate the firm’s cost of capital
Estimate a project’s cash flows
Now, we need to finish the analysis of the project to determine whether the firm should proceed with a potential project.

3. Capital Budgeting Techniques
Most commonly-used methods to evaluate projects:
Net Present Value (NPV)
Payback (PB)
Discounted Payback (DPB)
Internal Rate of Return (IRR)
Modified Internal Rate of Return (MIRR)
Profitability Index (PI)
NPV is generally the preferred technique for most project evaluations
There are situations where you may want to use one of the other techniques in conjunction with NPV

4. Net Present Value
NPV represents the “purest” of the capital budgeting rules
It measures the amount of value created by the project
NPV is completely consistent with the overall goal of the firm: to maximize firm value

5. NPV is the sum of the present value of every project cash flow (including the initial investment)

6. NPV Benchmark
NPV includes all of the project’s cash flows, both inflows and outflows
Since it involves finding the present values of every cash flow using the appropriate cost of capital as the discount rate, anything greater than zero represents the amount of value added above and beyond the required return
Accept project if NPV > 0
Reject project if NPV < 0

7. Example
A project has a cost of $25,000, and annual cash flows as shown. Calculate the NPV of the project if the discount rate is 12 percent
i=12%
(25,000)
8,500
12,000
13,500
15,000

8. Financial Calculator solution:
CF0 = (25,000)
CF1 = 8,500
CF2 = 12,000
CF3 = 13,500
CF4 = 15,000
I = 12 percent
NPV = 11,297.42

9. Interpretation: Do we like this project? Yes – it has a positive NPV
If the market agrees with our analysis, the value of our firm will increase by $11,297 due to this project
When will the value-added occur? When the
project is complete?
NO – it will occur immediately upon the announcement that we are taking the project

11. NPV Strengths and Weaknesses
NPV not only provides a go/no-go decision, but it
also quantifies the dollar amount of the value added
NPV is not a ratio
It works equally well for independent projects and
for choosing between mutually-exclusive projects
Accept the project with the highest positive NPV
Weakness
Misinterpretation
Comparing NPV to the cost of the project is wrong!
Not understanding that the cost is already incorporated into the NPV

12. Payback
Answers the question: How long will it take us to recoup our costs?
Has intuitive appeal
Remains popular because it is easy to compute
Built-in assumptions:
Cash flows are normal
Assumes cash flows occur smoothly throughout the year

13. Example Refer to the problem we worked earlier. Compute the payback.
(25,000)
8,500
12,000
13,500
15,000
Cumulative
(25,000)
(16,500)
(4,500)
Payback will occur during the 3rd year
Payback = 2 + 4,500/13,500
= years

14. Payback Benchmark Firms set some maximum allowable payback
Often set arbitrarily – one of payback’s greatest weaknesses
Accept project if calculated payback < Maximum allowable payback
Reject project if calculated payback > Maximum allowable payback

15. Discounted Payback
One of the major problems with payback is that it ignores the time value of money
It treats all cash flows equally regardless of when they occur
Discounted payback fixes this particular problem
We convert the raw cash flows to their present values, and then calculate payback like before using these discounted cash flows

16. Example i=12% Discounted Payback will occur during the 3rd year
(25,000)
8,500
12,000
13,500
15,000
CF present values
(25,000)
7,589
9,566
9,609
9,533
Cumulative
(25,000)
(17,411)
(7,845)
Discounted Payback will occur during the 3rd year
Discounted Payback = 2 + 7,845/9,609
= years

17. Discounted Payback benchmark
Like payback, management will likely set an arbitrary benchmark
Notice that for normal projects DPB will be larger than PB
The cash flows that are “chipping away” at the initial cost are the smaller discounted cash flows, so it takes longer
Hopefully, the arbitrary benchmark would at least take that effect into account

18. PB and DPB Strengths and Weaknesses
Easy to calculate
Intuitive
Weaknesses:
Both methods have severe weaknesses that make
them unsuitable to be the primary method used to
select projects
PB ignores the time value of money
Both methods rely on arbitrary accept/reject benchmarks
Both methods ignore cash flows that occur after the payback period. This is perhaps the most serious flaw of all

19. Internal Rate of Return
IRR is the most popular technique to analyze projects
Often referred to as “the return on the project”
IRR is generally consistent with Net Present Value
Problems occur if cash flows are not normal
Problems can occur when choosing among mutually exclusive projects

20. IRR is so closely related to NPV that it is actually defined in terms of NPV
IRR is the discount rate that results in a zero NPV

21. Internal Rate of Return benchmark
Once we calculate IRR, we must compare it to the cost of capital (investors’ required return) to see if the project is acceptable
We only want to invest in projects where the rate we expect to get (IRR) exceeds the rate investors require (i)

22. Example
Refer to our previous problem. Calculate the IRR of the project.
i=12%
(25,000)
8,500
12,000
13,500
15,000

23. Financial Calculator solution:
CF0 = (25,000)
CF1 = 8,500
CF2 = 12,000
CF3 = 13,500
CF4 = 15,000
IRR = ?
= 30.08%
Do we like this project?
Yes – the IRR is greater than the required return

24. Problems with IRR IRR will be consistent with NPV as long as:
The project has normal cash flows
Projects are independent
NPV profiles
The NPV profile is a graph of NPV versus different discount rates
It can help us determine if we may encounter a problem with IRR

25. For normal cash flows, the NPV profile slopes downward
IRR can be found where the profile crosses the x-axis (i.e. where NPV = 0, the definition of IRR)

26. For non-normal cash flows there will be multiple IRRs for the same project
IRRs represent the solution to a mathematical series. These solutions are called ‘roots’, and a series will have as many roots as there are sign changes. This is Descartes’ Rule of Signs, discovered in 1637.
For us, this means that there will be as many IRRs as there are sign changes in the cash flows.

27. - + + + + - + + + - - + + - + + Examples:
In our normal project, we have one IRR because we have one sign change
What if a project involves a cleanup at the end? We might have two sign changes (and two IRRs):
What if a project has to shut down in the 3rd year for maintenance, and then starts up again? We might have three sign changes:

28. Here is a sample NPV profile for a project with non-normal cash flows
Here is a sample NPV profile for a project with non-normal cash flows. Notice that the line crosses the x-axis twice:
Fortunately, we can fix the problem of multiple IRRs using a technique called Modified Internal Rate of Return (MIRR)

29. Calculating MIRR Calculating MIRR is a three-step process:
Step 1: Calculate the PV of the cash outflows using the required rate of return.
Step 2: Calculate the FV of the cash inflows at the last year of the project’s time line using the required rate of return.
Step 3: Calculate the MIRR, which is the discount rate that equates the PV of the cash outflows with the PV of the terminal value, ie, that makes PVoutflows = PVinflows

30. Example Calculate the MIRR of the following project: 1 2 3 4 5 i = 9%1 2 3 4 5
i = 9%
-10,000
4,000
6,000
-5,000
12,000
15,000

31. Step 1: PV of outflows = -13,861 Step 2: FV of inflows = 41,497
Step 3: Calculate MIRR
MIRR = 24.52%
Exceeds the required return of 9%, so accept project
INPUT 5
-13,861 N
I/YR PV
PMT FV
OUTPUT
41,497
24.52

32. Profitability Index Based on NPV Measures “bang per buck invested”
PI benchmark:
Accept project if PI > 0
Reject project if PI < 0

33. Example Calculate the PI of our example Recall that the NPV = $11,297
= %
PI indicates that we should accept the project
i=12%
(25,000)
8,500
12,000
13,500
15,000