0. Net Present Value and Other Investment Rules
Chapter 6:
Net Present Value and Other Investment Rules By
Group E
(Ursula G. J)
(Dayang Halimah)

1. Key Concepts and Skills
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 (IRR)and understand its strengths and weaknesses
Be able to compute the net present value (NPV) and understand why it is the best decision criterion

2. agenda Capital Budgeting - why we use NPV Value of Money Over Time
Net Present Value (NPV)
The payback period method
The discounted payback period method
The Internal rate of return (IRR)
The profitability index (PI)

3. Capital budgeting Analysis of potential additions to fixed assets.
Long-term decisions, involve large expenditures
NPV is a tool used in capital budgeting, along with IRR.
Types of projects:
Brand new line of business
Expansion of existing line of business
Replacement of existing asset
Independent vs. Mutually Exclusive

4. Good Decision Criteria
We need to ask ourselves the following questions when evaluating capital budgeting decision rules
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. Value of money
Facts:
money wisely invested today will yield a return in the future ( a fact that creates a natural investor desire for cash today)
Present value of money is crucial interest for financial people because it provides them with a basis of comparing the profitability of different projects or investments over a period of years.

6. Value of money
Present value of money is the cash value of future returns or income once a discount (capitalization) rate has been applied to it.
Discount or capitalization rate is an interest rate applied to a series of future payments to adjust for risk and uncertainty of the time factor
E.g. between 2 future incomes, the one with the longer maturity factor should have a higher risk (means higher discount rate)

7. Value of money over time
A different point of view:
An investment promises to yield a RM1M one-time profit, one year from now
How much of today‘s ringgit am I willing to pay today to have RM1M in a year?
p_max = $1M/(1+r)
r is the discount rate
p_max is the Net Present Value (NPV)

8. Net Present Value
The difference between the market value of a project and its cost
Net present value: a project’s net contribution to wealth – present value minus initial investment.
If the present value of a project’s future cash flow is greater than the initial cost, the project is worth undertaking
We learn how to estimate the cash flows in chapter 10.
We learn how to estimate the required return in chapter 13.

9. Why use net present value?
Accepting positive NPV benefits shareholders
NPV uses cash flow
NPV uses all cash flows of project
NPV discount the cash flow properly
Reinvestment assumption: the NPV rule assumes that all cash flows can be reinvested at the discounted rate

10. Net present value (npv) CONT….
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.

11. Net present value (npv)
In other words, the present Value in "today's ringgit" of the future net cash flow of a project
NPV = PV cash inflows - PV cash outflows
……… n t
today C0

12. Net Present Value (NPV)
NPV = PV of inflows – PV of Outflows
PV = FV N
(1 + R)
Where PV = present value of future income
FV = future income
R = interest or discount rate
N = number of years or periods

13. 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;
Year 2: CF = 70,800;
Year 3: CF = 91,080;
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.

14. 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 = 12,627.42
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 calculators only require you to use that if the frequency is something other than 1.
Since we have a positive NPV, we should accept the project.

15. 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.

16. Npv- CONCLUSION NPV rule account for the time value of money
NPV rule account for the risk of the cash flows (the risk of the cash flow is accounted for through the choice of the discount rate)
NPV rule provide an indication about the increase in value
we should consider the NPV rule for our primary decision rule
The answer to all of these questions is yes
The risk of the cash flows is accounted for through the choice of the discount rate.

17. PAYBACK PERIOD
How long does it take the project to “payback” its initial investment
Payback Period = number of years to recover the initial costs
Minimum acceptable criteria – set by the management
Ranking criteria – set by the management

18. Payback Period 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

19. 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 in year 3
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.
Either way, the payback rule would say to reject the project.

20. 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 rule?
The answer to all of these questions is no.

21. PAYBACK METHOD Table: Expected cash flows for Project A through C ($)
YEAR A B C
________________________________________________________________
0 -$100 -$100 -$100
,000
PAYBACK PERIOD (YEARS)

22. Payback method 3 problems
Timing of cash flow within the payback period is not considered (NPV discounts the cash flows properly)
It ignores the cash flows occurring after the payback period (NPV uses all cash flows of the project)
Arbitrary standard for payback period

23. Advantages and Disadvantages of Payback
Easy to understand
Adjusts for uncertainty of later cash flows
Biased toward liquidity
Disadvantages
Ignores the time value of money
Requires an arbitrary cutoff point
Ignores cash flows beyond the cutoff date
(not serve as measure of profitability)
Biased against long-term projects, such as research and development, and new projects

24. Discounted Payback Period
Compute the present value of each cash flow and then determine how long it takes to pay back on a discounted basis
taking the time value of money into account
Compare to a specified required period
Decision Rule - Accept the project if it pays back on a discounted basis within the specified time

25. Computing Discounted Payback for the Project
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 year 3
Do we accept or reject the project?
No – it doesn’t pay back on a discounted basis within the required 2-year period

26. Decision Criteria Test – Discounted Payback
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 rule?
The answer to the first two questions is yes.
The answer to the third question is no because of the arbitrary cut-off date.
Since the rule does not indicate whether or not we are creating value for the firm, it should not be the primary decision rule.

27. Advantages and Disadvantages of Discounted Payback
Includes time value of money
Easy to understand
Does not accept negative estimated NPV investments when all future cash flows are positive
Biased towards liquidity
Disadvantages
May reject positive NPV investments
Requires an arbitrary cutoff point
Ignores cash flows beyond the cutoff point
Biased against long-term projects, such as R&D and new products

28. Other methods for investment decision
Average Accounting Return Method (AAR)
Internal Rate of Return (IRR)
Profitability Index (PI)
(the above will be presented by Puan Dayang Halimah in the next class)
Thank you.

29. Average Accounting Return (AAR)
AAR is the average project earnings after taxes and depreciation, divided by the average book value of the investment during its life
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.

30. 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.
This rule would indicate that we reject the project.

31. 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 rule?
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.

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

33. Internal Rate of Return (IRR)
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 percentage returns and the value that is created, than they do for dollar increases. A dollar increase doesn’t appear to provide as much information if we don’t know what the initial expenditure was. Whether or not the additional information is relevant is another issue.

34. IRR – Definition and Decision Rule
Definition: IRR is the discount rate that sets the NPV = 0
Decision Rule: Accept the project if the IRR is greater than the required return
Ranking criteria: select alternative with highest IRR
Reinvestment assumption: all future cash flow assumed re-invested in at the IRR

35. 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.

36. IRR: Example Consider the following project:1 2 3
$50
$100
$150
-$200
The internal rate of return for this project is 19.44%

37. NPV Payoff Profile
If we graph NPV versus the discount rate, we can see the IRR as the x-axis intercept.
IRR = 19.44%

38. Calculating IRR with Spreadsheets
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 a spreadsheet.

39. 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.

40. 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 that you should go back and look at your cash flow estimation again. In competitive markets, extremely high IRRs should be rare.
Also, since the IRR calculation assumes that you can reinvest future cash flows at the IRR, a high IRR may be unrealistic.

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

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

43. IRR and Non-conventional Cash Flows
When the cash flows change sign 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?

44. IRR and Mutually Exclusive Projects
If you choose one, you can’t choose the other
Example: You can choose to attend graduate school 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

45. 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 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.

46. 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%, then you should choose B

47. 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

48. Modified Internal Rate of Return
Method 1: Discounting Approach
Discount all negative cash flows back to the present and add them to the initial investment.
There is no rule regarding the discount rate, but the book uses the required rate.

49. Modified Internal Rate of Return
Method 2: Reinvestment approach
Compound all future cash flows to the end of the project.
There is no rule regarding the compounding rate, but the book uses the required rate.

50. 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 create an additional $0.10 in value
This measure can be very useful in situations in which we have limited capital

51. Modified Internal Rate of Return
Method 3: Combination Approach
Discount negative cash flows back to the present.
Compound positive cash flows to the end of the project
Different discounting and compounding rates may be used, but the book uses the required rate for both.

52. 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

53. Summary – Discounted Cash Flow Criteria
Net present value
Difference between market value and cost
Take the project if the NPV is positive
Has no serious problems
Preferred decision criterion
Internal rate of return
Discount rate that makes NPV = 0
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
Benefit-cost ratio
Take investment if PI > 1
Cannot be used to rank mutually exclusive projects
May be used to rank projects in the presence of capital rationing

54. Summary – Payback Criteria
Payback period
Length of time until initial investment is recovered
Take the project if it pays back within some specified period
Doesn’t 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
Take the project if it pays back in some specified period
There is an arbitrary cutoff period

55. 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

56. End of Chapter Thank you