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

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

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
2
$1,000
2,000
$500
1,000
 Draw a time line and compute the NPV of project X.

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

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.

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

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

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

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

C10 Average Accounting Return Illustrated (concluded)
 Average book value:
Initial investment = $240
Average investment = ($240 + 0)/2 = $120
 Average accounting return (AAR):
AAR =
Average net income
Average book value
=
$45
$120
= 37.5%

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

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

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

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

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 = _______

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?

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

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

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
1
2
Cash flows
$ 500
1,000
 What’s the Profitability Index (PI)?

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.

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.

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.

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?

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.

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
2
3
0
1
4
-$30,000
15,000
10,000
10,000
5,000
-$45,000
5,000
10,000
20,000
250,000

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.

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
0
1
2
3
Cash Flow
-$30,000
25,000
0
15,000

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?

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.

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.

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

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%.

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

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

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

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

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
Depreciation
Taxes
OCF
$8,000
+7,000
-2,720
$12,280

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

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

T40 Example: Using Pro Formas for Project Evaluation (concluded)
 Capital Budgeting Evaluation:
NPV = -$31,000 + $12,280/1.20
1 + $12,280/1.20
2 + $22,280/1.20
3
= $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

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
INV
-A/P
NWC
$100
100
100
$100
$200
150
+100 ___
+50 ___
50 (50) ___
$300 Chg. NWC = $_____

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
INV
-A/P
NWC
$100
100
100
$100
$200
150
+100
+50
U
U
50 (50) U
$300 Chg. NWC = $ 200

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

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

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)

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)

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

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

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
4
5
2
3
6
20%
32%
19.20%
11.52%
11.52%
5.76%
100%
$_____
_____
5,760
3,456
3,456
1,728
$ _____

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
4
5
2
3
6
20%
32%
19.20%
11.52%
11.52%
5.76%
100%
$ 6,000
9,600
5,760
3,456
3,456
1,728
$ 30,000

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
Ball pick-up vehicle
Tractor and accessories
$ 2,000
8,000
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:

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

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

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

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
3
32.00
19.20
5,760
3,456
8,640
5,184
4
5
6
11.52
11.52
5.76
2,074
2,074
1,036
3,110
1,036
0

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

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

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

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

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

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

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) = $_____

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

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

T65 Quick Quiz -- Part 1 of 3 (concluded)
 Project cash flows are thus:
0 1
$39.8
OCF
Chg. in NWC
Cap. Sp.
– 40
– 60
2
$39.8
3
$39.8
40
– 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