1. Capital Budgeting and the Estimation of Cash Flows

2. WHAT IS CAPITAL BUDGETING?
Analysis of potential additions to fixed assets, whose benefits last for many years.
Long-term decisions; involve large expenditures.
Will affect firm’s performance for many years, so is very important to firm’s future.
Conceptually, capital budget process is identical to decision process used by individuals’ making investment decisions

3. Independent Projects vs Mutually Exclusive Projects

4. Steps: 1. Estimate CFs (inflows & outflows).
2. Assess riskiness of CFs (Cash Flows).
3. Determine R = WACC (adj.). determine appropriate
discount rate, based on riskiness of Cash Flows & general level int.rates
4. Find NPV of the expected cash flows and/or IRR.
5. Accept if NPV > 0 and/or IRR > WACC.

5. Good Decision Criteria for Capital Budgeting Process
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 utilize all relevant information? (such as all cash flows)
Does the decision rule provide information on whether we are creating value for the firm?

6. Project Example Information: You are looking at a new project and you have estimated the following cash flows:
Year CF NI
-165,000 1
63,120
13,620 2
70,800
3,300 3
91,080
29,100
Average Book Value = 72,000
Your required return for assets of this risk is 12%.

7. 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

8. Year CF Cumulative CF -165,000 1 63,120 -101, 880 2 70,800 -31,080 3
Computing Payback For The Project Assume we will accept the project if it pays back within two years.
Year CF
Cumulative CF
-165,000 1
63,120
-101, 880 2
70,800
-31,080 3
91,080
60,000
Payback Period: 2+ (31,080/91,080)=2.34 years
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.

9. 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?
Does the decision rule utilize all relevant information? (such as all cash flows)
Should we consider the payback rule for our primary decision criteria?
The answer to all of these questions is no.

10. 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

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

12. Computing Discounted Payback For The Project Assume we will accept the project if it pays back within two years.
Year CF
PV (CF)
Cum PV(CF)
-165,000 1
63,120
56,357
-108,463 2
70,800
56,441
-52,022 3
91,080
64,829
12,807
The Discounted Payback 2+(52,022/64,829)=2.80 years
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.

13. 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?
Does the decision rule utilize all relevant information? (such as all cash flows)
Should we consider the discounted payback rule for our primary decision criteria?

14. Advantages and Disadvantages of Discounted Payback
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 point
Biased against long-term projects, such as R&D and new products

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 utilize all relevant information? (such as all 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
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

19. 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 future 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.

20. 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.

21. 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 = 12,627.42
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.

22. 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. You can also click on the fx icon and show them how to enter the formula initially.

23. 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?
Does the decision rule utilize all relevant information? (such as all cash flows)
Should we consider the NPV rule for our primary decision criteria?
The answer to all of these questions is yes

24. 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 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.

25. 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
NPV: Enter R, solve for NPV.
IRR: Enter NPV = 0, solve for IRR.

26. 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.

27. 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.

28. NPV Profile For The Project
IRR = 16.13%

29. 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 decision rule utilize all relevant information? (such as all 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.

30. Advantages of IRR 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
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.

31. Profitability Index
Measures the benefit versus 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

32. Define Profitability Index

33. 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

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

35. NPV Vs. IRR
NPV and IRR will generally give us the same decision. (exactly the same decision if evaluating independent projects)
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

36. IRR and Non-conventional Cash Flows
When the cash flows change signs more than once, there may be more than one IRR
When you solve for IRR you are solving for the roots of an equation and when you cross the x-axis more than once, there will be more than one roots that solve the equation
If you have more than one IRR, which one do you use to make your decision?

37. Example – Non-conventional 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.

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

39. IRR and Mutually Exclusive Projects
If you choose one project, 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

40. Example With Mutually Exclusive Projects
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.

41. 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

42. 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

43. Managers like rates--prefer IRR to NPV comparisons
Managers like rates--prefer IRR to NPV comparisons. Can we give them a better IRR?
Yes, MIRR is the discount rate which
causes the PV of a project’s terminal
value (TV) to equal the PV of costs.
TV is found by compounding inflows
at WACC.
Thus, MIRR assumes cash inflows
are reinvested at WACC.

44. IRR – the reinvestment hypothesis
30.0
130.0 1 2 3
-100.0
30%
39.0
50.7
PV outflows
30%
219.7
-100.0
FV inflows

45. IRR – the reinvestment hypothesis
30.0
130.0 1 2 3
-100.0
10%
33.0
36.3
PV outflows
10%
199.3
-100.0
FV inflows

46. Why use MIRR versus IRR?
MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs.
Managers like rate of return comparisons, and MIRR is better for this than IRR.

47. 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

48. Cash Flows Estimation: Relevant Cash Flows
The cash flows that should be included in a capital budgeting analysis are those that will only occur if the project is accepted
These cash flows are called incremental cash flows
The stand-alone principle allows us to analyze each project in isolation from the firm simply by focusing on incremental cash flows

49. Asking the Right Question
You should always ask yourself “Will this cash flow occur ONLY if we accept the project?”
If the answer is “yes”, it should be included in the analysis because it is incremental
If the answer is “no”, it should not be included in the analysis because it will occur anyway
If the answer is “part of it”, then we should include the part that occurs because of the project

50. Cash flows Estimation – New Project1 2 3
Initial Investment(-)
Operating Cash Flow(+)
Operating Cash Flow(+)
Operating Cash Flow(+) Non-Op Cash Flow(+)

51. Initial Investment
Total cost for project: the cost incurred in order to make the asset readily available to operate. That includes the purchase cost for the asset, shipping and testing costs. The firm needs to impute opportunity cost for asset that is already owned by the firm, and ignore the sunk costs for the project. Side effects should be also included and considered.
The net working capital increased by the implementation for the project.

52. Sunk costs
Sunk costs – costs that have accrued regardless acceptance or rejection of the project, will be irrelevant for the decision making.
Example: the consulting fees for the feasibility analysis.
Impact: To wrongly include sunk costs may lead to wrong decision.
The NPV for a project (including 5 million consulting fees) is -3 million, should the firm accept the project?

53. Opportunity costs
Opportunity costs – costs of lost options, the highest value given up in alternative uses.
Example: A firm uses a currently idled land to build a plant, should the firm impute any cost?
If the idled land was purchased 10 years ago for 1 million dollars, should the cost be 1 million?
The cost should be the highest value given up in alternative uses.

54. Side effects Positive side effects – benefits to other projects
Negative side effects – costs to other projects

55. Accounting Income and Operating Cash Flow
Accrued
Cash Flows
Revenue
$100
Cash Costs 50
Depreciation 20
Earnings Before Taxes 30
Taxes (50%) 15
Earnings After Taxes 35
Operating cash flow – students often have to go back to the income statement to see that the two definitions of operating cash flow are equivalent when there is no interest expense.

56. Non-operating cash flows (NOCF)
Disposal Value
The recovery of NWC

57. New Investment Example:
A toy company is thinking about to expand its production line into stuff toys, in addition to its current plastic toys.
According to the firm, this expansion will not influence the cash flows of its current operations. The purchase price for the new machine is $10,000,000, and additional $2,000,000 is needed for the shipping and handling. The firm will use straight line for its depreciation, the depreciable life is set to be 5 years, and zero salvage value. The manufacturing department thinks the market value for the machine will be $3,000,000 after 5 years.

58. The marketing department thinks the expansion will results an increase of $6,000,000revenue for the first two years, and $8,000,000 for the final three years. The operating costs for the first two years will be $2,000,000, and $3,000,000 for the final three years. The firm needs to invest additional $1,000,000 NWC, which is expected to be recovered in the same amount after 5 years, for the new expansion.
The tax rate is 25%, and after-tax cost of capital for the firm is 7%, should the firm go for the expansion?

59. （t=0） （t=1） （t=2） （t=3） （t=4） （t=5） Purchase price (10,000,000)
Shipping and handling
(2,000,000)
Total Cost
(12,000,000)
NWC investment
(1,000,000)
Initial
Investment
(13,000,000)
Revenue
6,000,000
8,000,000
Cost
(3,000,000)
Depreciation
2,400,000
Operating
cash flow
3,600,000
4,350,000

60. （1）NPV=$5,797,050。 （2）IRR = 20.52% ( 3 ) PI = 1.446 3,000,000
Market value
3,000,000
Book value
Disposal gain
Tax liability
(750,000)
After-tax cash flow from disposal
2,250,000
Recovery of NWC
1,000,000
Non-op CF
3,250,000 CF
(13,000,000)
3,600,000
4,350,000
7,600,000
（1）NPV=$5,797,050。
（2）IRR = 20.52%
( 3 ) PI = 1.446

61. Why we do not consider the cash flows related to the financing?
When you use the after-tax cost of capital to be the discount rate, you basically take in the effect of the financing.
If you discount the project cash flows (without financing) by the after-tax cost of capital, you will get the exact net present value as you use it to discount the total cash flows (project cash flows plus the financing cash flows).
That is, when you use the after-tax cost of capital to discount financing related cash flows, the net present value would be zero.

62. （t=0）
（t=1）
（t=2）
（t=3）
（t=4）
Initial invest.
(total cost)
(8,000,000)
Inc. rev.
6,000,000
Inc. cost
(2,000,000)
Deprec.
2,000,000
OP CF
3,500,000
NOP CF
3,000,000
Project CF
6,500,000
Financing
8,000,000
Interest (AT)
(360,000)
Repay.
Fin. Rel. CF
(8,360,000)
Total CF
3,140,000
(1,860,000)

63. Assuming that financing totally comes from debt, and the before-tax
cost of capital is 6%, tax rate 25%, so the after-tax cost of capital 4.5%.
（t=0）
（t=1）
（t=2）
（t=3）
（t=4）
Project CF
(8,000,000)
3,500,000
6,500,000
NPV (at 4.5%)
7,072,024
（t=0）
（t=1）
（t=2）
（t=3）
（t=4）
Total CF
3,140,000
(1,860,000)
NPV (at 4.5%)
7,072,024
（t=0）
（t=1）
（t=2）
(t=3）
（t=4）
Fin. Rel. CF
8,000,000
(360,000)
(8,360,000)
NPV (at 4.5%)