Capital Budgeting

1. C1 Outline
Capital Budgeting - Decision Criteria
 Net Present Value
 The Payback Rule
 The Discounted Payback
 The Average Accounting Return
 The Internal Rate of Return
 The Profitability Index
 The Practice of Capital Budgeting

2. C2 Outline (continued)
 Project Cash Flows: A First Look
 Incremental Cash Flows
 Pro Forma Financial Statements and Project Cash Flows
 More on Project Cash Flows
 Alternative Definitions of Operating Cash Flow
 Some Special Cases of Discounted Cash Flow Analysis
 Summary and Conclusions

3. C3 NPV Illustrated
 Assume you have the following information on Project X:
Initial outlay -$1,100 Required return = 10%
Annual cash revenues and expenses are as follows:
Year Revenues Expenses
1 $1,000 $500
2 2,000 1,000
 Draw a time line and compute the NPV of project X.

4. C4 NPV Illustrated (concluded)
0 1 2
Initial outlay
($1,100)
Revenues $1,000
Expenses 500
Cash flow $500
Revenues $2,000
Expenses 1,000
Cash flow $1,000
– $1,100.00
+454.55
+826.45
+$181.00
1
$500 x
1.10
1
$1,000 x
1.102
NPV

5. C5 Underpinnings of the NPV Rule
 Why does the NPV rule work? And what does “work” mean?
Look at it this way:
A “firm” is created when securityholders supply the funds to acquire
assets that will be used to produce and sell a good or a service;
The market value of the firm is based on the present value of the
cash flows it is expected to generate;
Additional investments are “good” if the present value of the
incremental expected cash flows exceeds their cost;
Thus, “good” projects are those which increase firm value - or, put
another way, good projects are those projects that have positive
NPVs!
Moral of the story: Invest only in projects with positive NPVs.

6. C6 Payback Rule Illustrated
Initial outlay -$1,000
Year Cash flow
1 $200
2 400
3 600
Accumulated
1 $200
2 600
3 1,200
Payback period = 2 2/3 years

7. C7 Discounted Payback Illustrated
Initial outlay -$1,000
R = 10%
PV of
Year Cash flow Cash flow
1 $ 200 $ 182
2 400 331
3 700 526
4 300 205
Accumulated
Year discounted cash flow
1 $ 182
2 513
3 1,039
4 1,244
Discounted payback period is just under 3 years

8. C8 Ordinary and Discounted Payback
Cash Flow Accumulated Cash Flow
Year Undiscounted Discounted Undiscounted Discounted
1 $100 $89 $100 $89
2 100 79 200 168
3 100 70 300 238
4 100 62 400 300
5 100 55 500 355

9. C9 Average Accounting Return Illustrated
 Average net income:
Year
1 2 3
Sales $440 $240 $160
Costs 220 120 80
Gross profit 220 120 80
Depreciation 80 80 80
Earnings before taxes 140 40 0
Taxes (25%) 35 10 0
Net income $105 $30 $0
Average net income = ($105 + 30 + 0)/3 = $45

10. C10 Average Accounting Return Illustrated (concluded)
 Average book value:
Initial investment = $240
Average investment = ($240 + 0)/2 = $120
 Average accounting return (AAR):
Average net income $45

11. C11 Internal Rate of Return Illustrated
Initial outlay = -$200
Year Cash flow
1 $ 50
2 100
3 150
 Find the IRR such that NPV = 0
50 100 150
50 100 150

12. C12 Internal Rate of Return Illustrated (concluded)
 Trial and Error
Discount rates NPV
0% $100
5% 68
10% 41
15% 18
20% -2
IRR is just under 20% -- about 19.44%

13. Year Cash flow
0 – $275
1 100
2 100
3 100
4 100
C13 Net Present Value Profile
Discount rate
2% 6% 10% 14% 18%
120
100
80
60
40
20
Net present value
0
– 20
– 40
22%
IRR

14.  Assume you are considering a project for
which the cash flows are as follows:
Year Cash flows
0 -$252
1 1,431
2 -3,035
3 2,850
4 -1,000
C14 Multiple Rates of Return

15. C15 Multiple Rates of Return (continued)
 What’s the IRR? Find the rate at which
the computed NPV = 0:
at 25.00%: NPV = _______
at 33.33%: NPV = _______
at 42.86%: NPV = _______
at 66.67%: NPV = _______

16. C16 Multiple Rates of Return (continued)
 What’s the IRR? Find the rate at which
the computed NPV = 0:
at 25.00%: NPV = 0
at 33.33%: NPV = 0
at 42.86%: NPV = 0
at 66.67%: NPV = 0
 Two questions:
 1. What’s going on here?
 2. How many IRRs can there be?

17. C17 Multiple Rates of Return (concluded)
$0.06
$0.04
$0.02
$0.00
($0.02)
NPV
($0.04)
($0.06)
($0.08)
0.2 0.28 0.36 0.44 0.52 0.6 0.68
IRR = 1/4
IRR = 1/3
IRR = 3/7
IRR = 2/3
Discount rate

18. C18 IRR, NPV, and Mutually Exclusive Projects
Discount rate
2% 6% 10% 14% 18%
60
40
20
0
– 20
– 40
Net present value
– 60
– 80
– 100
22%
IRRA IRRB
0
140
120
100
80
160
Year
0 1 2 3 4
Project A: – $350 50 100 150 200
Project B: – $250 125 100 75 50
26%
Crossover Point

19. C19 Profitability Index Illustrated
 Now let’s go back to the initial example - we assumed the
following information on Project X:
Initial outlay -$1,100Required return = 10%
Annual cash benefits:
Year Cash flows
1 $ 500
2 1,000
 What’s the Profitability Index (PI)?

20. C20 Profitability Index Illustrated (concluded)
 Previously we found that the NPV of Project X is equal to:
($454.55 + 826.45) - 1,100 = $1,281.00 - 1,100 = $181.00.
 The PI = PV inflows/PV outlay = $1,281.00/1,100 = 1.1645.
 This is a good project according to the PI rule. Can you explain
why?
It’s a good project because the present value of the inflows
exceeds the outlay.

21. C21 Summary of Investment Criteria
 I. Discounted cash flow criteria
A. Net present value (NPV). The NPV of an investment is the
difference between its market value and its cost. The NPV
rule is to take a project if its NPV is positive. NPV has no
serious flaws; it is the preferred decision criterion.
B. Internal rate of return (IRR). The IRR is the discount rate that
makes the estimated NPV of an investment equal to zero. The IRR rule is
to take a project when its IRR exceeds the required return. When project
cash flows are not conventional, there may be no IRR or there may be
more than one.
C. Profitability index (PI). The PI, also called the benefit-cost ratio, is
the ratio of present value to cost. The profitability index rule is to
take an investment if the index exceeds 1.0. The PI
measures the present value per dollar invested.

22. C22 Summary of Investment Criteria (concluded)
 II. Payback criteria
A. Payback period. The payback period is the length of time until the
sum of an investment’s cash flows equals its cost. The payback period
rule is to take a project if its payback period is less than some
prespecified cutoff.
B. Discounted payback period. The discounted payback period is the
length of time until the sum of an investment’s discounted cash flows
equals its cost. The discounted payback period rule is to take an
investment if the discounted payback is less than some prespecified
cutoff.
 III. Accounting criterion
A. Average accounting return (AAR). The AAR is a measure of
accounting profit relative to book value. The AAR rule is to take an
investment if its AAR exceeds a benchmark.

23. C23 A Quick Quiz
1. Which of the capital budgeting techniques do account for both the time
value of money and risk?
2. The change in firm value associated with investment in a project is
measured by the project’s _____________ .
a. Payback period
b. Discounted payback period
c. Net present value
d. Internal rate of return
3. Why might one use several evaluation techniques to assess a given
project?

24. C24 A Quick Quiz
1. Which of the capital budgeting techniques do account for both the time
value of money and risk?
Discounted payback period, NPV, IRR, and PI
2. The change in firm value associated with investment in a project is
measured by the project’s Net present value.
3. Why might one use several evaluation techniques to assess a given
project?
To measure different aspects of the project; e.g., the payback period
measures liquidity, the NPV measures the change in firm value, and the
IRR measures the rate of return on the initial outlay.

25. C25 Problem
 Offshore Drilling Products, Inc. imposes a payback cutoff of 3
years for its international investment projects. If the company
has the following two projects available, should they accept
either of them?
Year Cash Flows A Cash Flows B
0 -$30,000 -$45,000
1 15,000 5,000
2 10,000 10,000
3 10,000 20,000
4 5,000 250,000

26. C26 Solution to Problem (concluded)
 Project A:
Payback period = 1 + 1 + ($30,000 - 25,000)/10,000
= 2.50 years
 Project B:
Payback period = 1 + 1 + 1 + ($45,000 - 35,000)/$250,000
= 3.04 years
 Project A’s payback period is 2.50 years and project B’s
payback period is 3.04 years. Since the maximum acceptable
payback period is 3 years, the firm should accept project A and
reject project B.

27. C27 Another Problem
 A firm evaluates all of its projects by applying the IRR
rule. If the required return is 18 percent, should the firm
accept the following project?
Year Cash Flow
0 -$30,000
1 25,000
2 0
3 15,000

28. C28 Another Problem (continued)
 To find the IRR, set the NPV equal to 0 and solve for the
discount rate:
NPV = 0 = -$30,000 + $25,000/(1 + IRR)1
+ $0/(1 + IRR)2
+$15,000/(1 + IRR)3
 At 18 percent, the computed NPV is ____.
 So the IRR must be (greater/less) than 18 percent. How did
you know?

29. C29 Another Problem (concluded)
 To find the IRR, set the NPV equal to 0 and solve for the
discount rate:
NPV = 0 = -$30,000 + $25,000/(1 + IRR)1
+ $0/(1 + IRR)2
+$15,000/(1 + IRR)3
 At 18 percent, the computed NPV is $316.
 So the IRR must be greater than 18 percent. We know this
because the computed NPV is positive.
 By trial-and-error, we find that the IRR is 18.78 percent.

30. T30 Fundamental Principles of Project Evaluation
 Fundamental Principles of Project Evaluation:
Project evaluation - the application of one or more capital
budgeting decision rules to estimated relevant project cash
flows in order to make the investment decision.
Relevant cash flows - the incremental cash flows associated with
the decision to invest in a project.
The incremental cash flows for project evaluation consist
of any and all changes in the firm’s future cash flows that
are a direct consequence of taking the project.
Stand-alone principle - evaluation of a project based on the
project’s incremental cash flows.

31. T31 Incremental Cash Flows
Incremental Cash Flows
 Key issues:
 When is a cash flow incremental?
 Terminology
A. Sunk costs
B. Opportunity costs
C. Side effects
D. Net working capital
E. Financing costs
F. Other issues

32. T32 Example: Preparing Pro Forma Statements
 Suppose we want to prepare a set of pro forma financial statements
for a project for Norma Desmond Enterprises. In order to do so, we
must have some background information. In this case, assume:
1. Sales of 10,000 units/year @ $5/unit.
2. Variable cost per unit is $3. Fixed costs are $5,000 per year.
The project has no salvage value. Project life is 3 years.
3. Project cost is $21,000. Depreciation is $7,000/year.
4. Additional net working capital is $10,000.
5. The firm’s required return is 20%. The tax rate is 34%.

33. T33 Example: Preparing Pro Forma Statements (continued)
Pro Forma Financial Statements
Projected Income Statements
Sales $______
Var. costs ______
$20,000
Fixed costs 5,000
Depreciation 7,000
EBIT $______
Taxes (34%) 2,720
Net income $______

34. T34 Example: Preparing Pro Forma Statements (continued)
Pro Forma Financial Statements
Projected Income Statements
Sales $50,000
Var. costs 30,000
$20,000
Fixed costs 5,000
Depreciation 7,000
EBIT $ 8,000
Taxes (34%) 2,720
Net income $ 5,280

35. T35 Example: Preparing Pro Forma Statements (concluded)
Projected Balance Sheets
0 1 2 3
NWC $______ $10,000 $10,000 $10,000
NFA 21,000 ______ ______ 0
Total $31,000 $24,000 $17,000 $10,000

36. T36 Example: Preparing Pro Forma Statements (concluded)
Projected Balance Sheets
0 1 2 3
NWC $10,000 $10,000 $10,000 $10,000
NFA 21,000 14,000 7,000 0
Total $31,000 $24,000 $17,000 $10,000

37. T37 Example: Using Pro Formas for Project Evaluation
 Now let’s use the information from the previous example to do
a capital budgeting analysis.
Project operating cash flow (OCF):
EBIT $8,000
Depreciation +7,000
Taxes -2,720
OCF $12,280

38. T38 Example: Using Pro Formas for Project Evaluation (continued)
 Project Cash Flows
0 1 2 3
OCF $12,280 $12,280 $12,280
Chg. NWC ______ ______
Cap. Sp. -21,000
Total ______ $12,280 $12,280 $______

39. T39 Example: Using Pro Formas for Project Evaluation (continued)
 Project Cash Flows
0 1 2 3
OCF $12,280 $12,280 $12,280
Chg. NWC -10,000 10,000
Cap. Sp. -21,000
Total -31,000 $12,280 $12,280 $22,280

40. T40 Example: Using Pro Formas for Project Evaluation (concluded)
 Capital Budgeting Evaluation:
NPV = -$31,000 + $12,280/1.201
+ $12,280/1.202
+ $22,280/1.203
= $655
IRR = 21%
PBP = 2.3 years
AAR = $5280/{(31,000 + 24,000 + 17,000 + 10,000)/4} = 25.76%
 Should the firm invest in this project? Why or why not?
Yes -- the NPV > 0, and the IRR > required return

41. T41 Example: Estimating Changes in Net Working Capital
 In estimating cash flows we must account for the fact that some of the incremental
sales associated with a project will be on credit, and that some costs won’t be paid
at the time of investment. How?
Answer: Estimate changes in NWC. Assume:
1. Fixed asset spending is zero.
2. The change in net working capital spending is $200:
0 1 Change S/U
A/R $100 $200 +100 ___
INV 100 150 +50 ___
-A/P 100 50 (50) ___
NWC $100 $300 Chg. NWC = $_____

42. T42 Example: Estimating Changes in Net Working Capital
 In estimating cash flows we must account for the fact that some of the incremental
sales associated with a project will be on credit, and that some costs won’t be paid
at the time of investment. How?
Answer: Estimate changes in NWC. Assume:
1. Fixed asset spending is zero.
2. The change in net working capital spending is $200:
0 1 Change S/U
A/R $100 $200 +100 U
INV 100 150 +50 U
-A/P 100 50 (50) U
NWC $100 $300 Chg. NWC = $200

43. T43 Example: Estimating Changes in Net Working Capital (continued)
 Now, estimate operating and total cash flow:
Sales $300
Costs 200
Depreciation 0
EBIT $100
Tax 0
Net Income $100
OCF = EBIT + Dep. − Taxes = $100
Total Cash flow = OCF− Change in NWC − Capital Spending
= $100 − ______ − ______ = ______

44. T44 Example: Estimating Changes in Net Working Capital (continued)
 Now, estimate operating and total cash flow:
Sales $300
Costs 200
Depreciation 0
EBIT $100
Tax 0
Net Income $100
OCF = EBIT + Dep. − Taxes = $100
Total Cash flow = OCF− Change in NWC − Capital Spending
= $100 − 200 − 0 = − $100

45. T45 Example: Estimating Changes in Net Working Capital (concluded)
 Where did the - $100 in total cash flow come from?
 What really happened:
Cash sales = $300 - ____ = $200 (collections)
Cash costs = $200 + ____ + ____ = $300 (disbursements)

46. T46 Example: Estimating Changes in Net Working Capital (concluded)
 Where did the - $100 in total cash flow come from?
 What really happened:
Cash sales = $300 - 100 = $200 (collections)
Cash costs = $200 + 50 + 50 = $300 (disbursements)
Cash flow = $200 - 300 = - $100 (= cash in − cash out)

47. T47 Modified ACRS Property Classes
Class Examples
3-year Equipment used in research
5-year Autos, computers
7-year Most industrial equipment

48. T48 Modified ACRS Depreciation Allowances
Property Class
Year 3-Year 5-Year 7-Year
1 33.33% 20.00% 14.29%
2 44.44 32.00 24.49
3 14.82 19.20 17.49
4 7.41 11.52 12.49
5 11.52 8.93
6 5.76 8.93
7 8.93
8 4.45

49. T49 MACRS Depreciation: An Example
 Calculate the depreciation deductions on an asset which costs
$30,000 and is in the 5-year property class:
Year MACRS % Depreciation
1 20% $_____
2 32% _____
3 19.20% 5,760
4 11.52% 3,456
5 11.52% 3,456
6 5.76% 1,728
100% $ _____

50. T50 MACRS Depreciation: An Example
 Calculate the depreciation deductions on an asset which costs
$30,000 and is in the 5-year property class:
Year MACRS % Depreciation
1 20% $6,000
2 32% 9,600
3 19.20% 5,760
4 11.52% 3,456
5 11.52% 3,456
6 5.76% 1,728
100% $30,000

51. T51 Example: Fairways Equipment and Operating Costs
Two golfing buddies are considering opening a new driving
range, the “Fairways Driving Range” (motto: “We always treat
you fairly at Fairways”). Because of the growing popularity of
golf, they estimate the range will generate rentals of 20,000
buckets of balls at $3 a bucket the first year, and that rentals will
grow by 750 buckets a year thereafter. The price will remain $3
per bucket.
Capital spending requirements include:
Ball dispensing machine $ 2,000
Ball pick-up vehicle 8,000
Tractor and accessories 8,000
$18,000
All the equipment is 5-year ACRS property, and is expected to
have a salvage value of 10% of cost after 6 years.
Anticipated operating expenses are as follows:

52. T52 Example: Fairways Equipment and Operating Costs (concluded)
Operating Costs (annual)
Land lease $ 12,000
Water 1,500
Electricity 3,000
Labor 30,000
Seed & fertilizer 2,000
Gasoline 1,500
Maintenance 1,000
Insurance 1,000
Misc. Expenses 1,000
$53,000
Working Capital
Initial requirement = $3,000
Working capital requirements
are expected to grow at 5%
per year for the life of the
project

53. T53 Example: Fairways Revenues, Depreciation, and Other Costs
Projected Revenues
Year Buckets Revenues
1 20,000 $60,000
2 20,750 62,250
3 21,500 64,500
4 22,250 66,750
5 23,000 69,000
6 23,750 71,250

54. T54 Example: Fairways Revenues, Depreciation, and Other Costs (continued)
Cost of balls and buckets
Year Cost
1 $3,000
2 3,150
3 3,308
4 3,473
5 3,647
6 3,829

55. T55 Example: Fairways Revenues, Depreciation, and Other Costs (concluded)
Depreciation on $18,000 of 5-year equipment
Year ACRS % Depreciation Book value
1 20.00 $3,600 $14,400
2 32.00 5,760 8,640
3 19.20 3,456 5,184
4 11.52 2,074 3,110
5 11.52 2,074 1,036
6 5.76 1,036 0

56. T56 Example: Fairways Pro Forma Income Statement
Year
1 2 3 4 5 6
Revenues $60,000 $62,250 $64,500 $66,750 $69,000 $71,250
Variable costs 3,000 3,150 3,308 3,473 3,647 3,829
Fixed costs 53,000 53,000 53,000 53,000 53,000 53,000
Depreciation 3,600 5,760 3,456 2,074 2,074 1,036
EBIT $ 400 $ 340 $ 4,736 $ 8,203 $10,279 $13,385
Taxes 60 51 710 1,230 1,542 2,008
Net income $ 340 $ 289 $ 4,026 $ 6,973 $ 8,737 $11,377

57. T57 Example: Fairways Projected Changes in NWC
 Projected increases in net working capital
Year Net working capital Change in NWC
0 $ 3,000 $ 3,000
1 3,150 150
2 3,308 158
3 3,473 165
4 3,647 174
5 3,829 182
6 4,020 - 3,829

58. T58 Example: Fairways Cash Flows
 Operating cash flows:
Operating
Year EBIT + Depreciation – Taxes = cash flow
0 $ 0 $ 0 $ 0 $ 0
1 400 3,600 60 3,940
2 340 5,760 51 6,049
3 4,736 3,456 710 7,482
4 8,203 2,074 1,230 9,047
5 10,279 2,074 1,542 10,811
6 13,385 1,036 2,008 12,413

59. T59 Example: Fairways Cash Flows (concluded)
 Total cash flow from assets:
Year OCF – Chg. in NWC – Cap. Sp. = Cash flow
0 $ 0 $ 3,000 $18,000 – $21,000
1 3,940 150 0 3,790
2 6,049 158 0 5,891
3 7,482 165 0 7,317
4 9,047 174 0 8,873
5 10,811 182 0 10,629
6 12,413 – 3,829 – 1,530 17,772

60. T60 Alternative Definitions of OCF
Let:
OCF = operating cash flow
S = sales
C = operating costs
D = depreciation
T = corporate tax rate

61. T61 Alternative Definitions of OCF (concluded)
 The Tax-Shield Approach
OCF = (S - C - D) + D - (S - C - D) × T
= (S - C) × (1 - T) + (D × T)
= (S - C) × (1 - T) + Depreciation x T
 The Bottom-Up Approach
OCF = (S - C - D) + D - (S - C - D) × T
= (S - C - D) × (1 - T) + D
= Net income + Depreciation
 The Top-Down Approach
OCF = (S - C - D) + D - (S - C - D) × T
= (S - C) - (S - C - D) × T
= Sales - Costs - Taxes

62. T62 Quick Quiz -- Part 1 of 3
 Now let’s put our new-found knowledge to work. Assume we have the
following background information for a project being considered by Gillis, Inc.
 See if we can calculate the project’s NPV and payback period. Assume:
Required NWC investment = $40; project cost = $60; 3 year life
Annual sales = $100; annual costs = $50; straight line
depreciation to $0
Tax rate = 34%, required return = 12%
 Step 1: Calculate the project’s OCF
 OCF = (S - C)(1 - T) + Dep × T
 OCF = (___ - __)(1 - .34) + (____)(.34) = $_____

63. T63 Quick Quiz -- Part 1 of 3
 Now let’s put our new-found knowledge to work. Assume we have the
following background information for a project being considered by Gillis, Inc.
 See if we can calculate the project’s NPV and payback period. Assume:
Required NWC investment = $40; project cost = $60; 3 year life
Annual sales = $100; annual costs = $50; straight line
depreciation to $0
Tax rate = 34%, required return = 12%
 Step 1: Calculate the project’s OCF
 OCF = (S - C)(1 - T) + Dep × T
 OCF = (100 - 50)(1 - .34) + (60/3)(.34) = $39.80

64. T64 Quick Quiz -- Part 1 of 3 (concluded)
 Project cash flows are thus:
0 1 2 3
OCF $39.8 $39.8 $39.8
Chg. in NWC -40 40
Cap. Sp. -60
-$100 $39.8 $39.8 $79.8
Payback period = ___________
NPV = ____________

65. T65 Quick Quiz -- Part 1 of 3 (concluded)
 Project cash flows are thus:
0 1 2 3
OCF $39.8 $39.8 $39.8
Chg. in NWC – 40 40
Cap. Sp. – 60
– 100 $39.8 $39.8 $79.8
Payback period = 1 + 1 + (100 – 79.6)/79.8 = 2.26 years
NPV = $39.8/(1.12) + $39.8/(1.12)2
+ 79.8 /(1.12)3
- 100 = $24.06