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
$1,000
$500
2
2,000
1,000
Draw a time line and compute the NPV of project X.
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
1.10
2
NPV
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
Initial outlay

$1,000
Year
Cash flow
1
$200
2
400
3
600
Accumulated
Year
Cash flow
1
$200
2
600
3
1,200
Payback period =
2
2/3
years
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
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
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
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
AAR =
=
= 37.5%
Average book value
$120
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
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%
$100
5%
68
10%
41
15%
18
20%

2
IRR is just under 20%

about
19.44
%
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
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
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)
$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
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%
IRR
A
IRR
B
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
C19 Profitability Index Illustrated
Now let’s go back to the initial example

we assumed the
following information on Project X:
Initial outlay

$1,100
Required return = 10%
Annual cash benefits:
Year
Cash flows
1
$ 500
2
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
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
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
Cash Flow
0

$30,000
1
25,000
2
0
3
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
______
$20,000
Fixed costs
5,000
Depreciation
7,000
EBIT
$______
Taxes (34%)
2,720
Net income
$______
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
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
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
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
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
$______
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
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
$100
$200
+100
___
INV
100
150
+50
___

A/P
100
50
(
50)
___
NWC
$100
$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
$100
$200
+100
U
INV
100
150
+50
U

A/P
100
50
(50)
U
NWC
$100
$300
Chg. NWC = $
200
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
______
______ = ______
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
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
Examples
3

year
Equipment used in research
5

year
Autos, computers
7

year
Most industrial equipment
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
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%
$ _____
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
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
:
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
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
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
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
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
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
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
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
T60 Alternative Definitions of OCF
Let:
OCF
=
operating cash flow
S
=
sales
C
=
operating costs
D
=
depreciation
T
=
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
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 =
____________
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
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