Capabilities
• 1. Discuss the difficulty encountered in finding profitable projects in
competitive markets and the importance of the search.
• 2. Determine whether or not a new project should be accepted or
rejected using the payback period, the net present value, the
profitability index, and the internal rate of return.
• 3. Explain how the capital-budgeting decision process changes when a
dollar limit is placed on the dollar size of the capital budget.
• 4. Discuss the problems encountered in project ranking.
• 5. Explain the importance of ethical considerations in capitalbudgeting decisions.
• 6. Discuss the trends in the use of different capital-budgeting criteria.
●
Finding Profitable Projects
● Capital-Budgeting Decision Criteria
●
●
●
Capital Rationing
Problems in Project Ranking—Capital Rationing, Mutually
Exclusive Projects, and Problems with the IRR
Ethics in Capital Budgeting
A Glance at Actual Capital-Budgeting Practices
• Objective 1
FINDING PROFITABLE
PROJECTS
• to evaluate profitable projects or investments in
fixed assets, a process referred to as capital
budgeting,
•
• Axiom 5: The Curse of Competitive Markets—
Why It’s Hard to Find Exceptionally Profitable
Projects.
• The payback period is the number of years
needed to recover the initial cash outlay.
Objective 2 CAPITAL-BUDGETING
DECISION CRITERIA
•
•
•
•
•
•
•
•
A
Initial cash outlay －$10,000
Annual net cash inflows
Year 1
$ 6,000
2
4,000
3
3,000
4
2,000
5
1,000
B
－$10,000
$ 5,000
5,000
0
0
0
Net Present Value
• The net present value (NPV) of an
investment proposal is equal to the present
value of its annual net cash flows after taxes
less the investment’s initial outlay.
n
NPV =

t 1
ACFt
t
(1  k)
- IO
NPV
• ACFt = the annual after-tax cash flow in
time period t .
•
k = the appropriate discount rate; that is,
the required rate of return or cost of capital
•
IO = the initial cash outlay
•
n = the project’s expected life
Principal
• NPV ≥ 0.0 : accept
• NPV ＜ 0.0 : reject
NPV Illustration of Investment in New
Machinery
AFTER-TAX
CASH FLOW
Inflow year 1
15,000
2
14,000
3 －$40,000
13,000
Initial outlay
4
12,000
5
11,000
Calculation for NPV Illustration of Investment in New Machinery
PRESENT VALUE
AFTER-TAX
FACTOR AT
PRESENT
CASH FLOW 12 PERCENT
VALUE
2
14,000
.797
11,158
3
13,000
.712
9,256
4
12,000
.636
7,632
5
11,000
.567
6,237
Initial
outlay
－40,000
Net present
value
$ 7,678
Inflow year 1
15,000
Present value of cash flows
.893
$13,395
$ 47,678
Profitability Index (BenefitCost Ratio)
• The profitability index (PI), or benefitcost ratio, is the ratio of the present value
of the future net cash flows to the initial
outlay.
n
PI =
ACFt

t
t 1 (1  k )
IO
• ACFt = the annual after-tax cash flow in time
period t (this can take on either positive
or negative values )
•
k = the appropriate discount rate; that is, the
required rate of return or cost of capital
•
IO = the initial cash outlay
•
n = the project’s expected life
Principale
•
• PI ≥ 1.0 : accept
PI ＜ 1.0 : reject
PRESENT VALUE
AFTER-TAX
FACTOR AT
PRESENT
CASH FLOW 10 PERCENT
VALUE
Inflow year 1
15,000
0.909
13,635
2
8,000
0.826
6,608
3
10,000
0.751
7,510
4
12,000
0.683
8,196
5
14,000
0.621
8,694
6
16,000
0.564
9,024
Initial outlay
－$50,000
1.000
－$50,000
n

t 1
ACFt
t
(1  k )
IO
$13,635  $6,608  $7,510  $8,196  8,694  $9,024
$50,000
$53,667
$50,000
= 1.0733
Internal Rate of Return
• The internal rate of return (IRR) the
discount rate that equates the present value
of the project’s future net cash flows with
the project’s initial cash outlay.
n
IO =

t 1
ACFt
t
(1  IRR)
IRR
• ACFt = the annual after-tax cash flow in
time period t (this can take on either
positive or negative values )
•
IO = the initial cash outlay
•
n = the project’s expected life
•
IRR = the project’s internal rate of return
$15,000
$15,000 $15,000 $15,000
$45,555 =
(1  IRR )1 (1  IRR ) 2 (1  IRR ) 3 (1  IRR ) 4
$45,555 =
15,000
4

1

t 
 t 1 (1  IRR ) 
$45,555 = $15,000 (PVIFA i , 4yr )
Dividing both sides by $15,000, this becomes
3.037 = PVIFA i, 4yr
IRR for Uneven Cash Flows
Present Value
Net Cash Flows
Present Value
Inflow year 1
$1,000
Inflow year 2
2,000
Inflow year 3
3,000
Present value of inflows
Initial outlay
2. TRY i = 20 PERCENT:
Factor at 15 Percent
.870
.756
.658
$ 870
1,512
1,974
$ 4,356
－$ 3,817
•
Net Cash Flows
Present Value
Factor at 20 Percent
Present
Value
•
•
•
•
•
•
Inflow year 1
$1,000
Inflow year 2
2,000
Inflow year 3
3,000
Present value of inflows
Initial outlay
3. TRY i = 22 PERCENT:
.833
.694
.579
$ 833
1,388
1,737
$ 3,958
－$ 3,817
Present Value
Net Cash Flows
Inflow year 1
$1,000
Inflow year 2
2,000
Inflow year 3
3,000
Present value of inflows
Initial outlay
Factor at 22 Percent
.820
.672
.551
Present Value
$ 820
1,344
1,653
$ 3,817
－$ 3,817
Three IRR Investment
A
Initial outlay
－$10,000
Inflow year 1
Inflow year 2
Inflow year 3
Inflow year 4
3,362
3,362
3,362
3,362
B
－$10,000
0
0
0
13,605
C
－$10,000
1,000
3,000
6,000
7,000
15%
Present Value
Net Cash Flows
Inflow year 1
$1,000
Inflow year 2
3,000
Inflow year 3
6,000
Inflow year 4
7,000
Present value of inflows
Initial outlay
Factor at 15 Percent
.870
.756
.658
.572
Present Value
$ 870
2,268
3,948
4,004
$11,090
－$ 10,000
Present Value
•
•
•
•
•
•
•
Net Cash Flows
Factor at 19 Percent
Inflow year 1
$1,000
Inflow year 2
3,000
Inflow year 3
6,000
Inflow year 4
7,000
Present value of inflows
Initial outlay
.840
.706
.593
.499
Present Value
$ 840
2,118
3,558
3,493
$10,009
－$ 10,000
Net present value($)
1,500
1,000
500
0
-500 0
100
200
300
400
-1,000
-1,500
-2,000
Discount rates(%)
500
600
Objective 4
• PROBLEMS IN PROJECT RANKING-CAPITAL
RATIONING, MUTUALLY EXCLUSIVE PROJECTS,
AND PROBLEMS WITH THE IRR.
• 1 Size disparity
• 2 Time disparity
• 3 Unequal live
Capital-Rationing Example of Five Indivisible Projects
Project
Initial Outlay
Profitability Index
Net Present Value
A
$200,000
2.4
$280,000
B
200,000
2.3
260,000
C
800,000
1.7
560,000
D
300,000
1.3
90,000
E
300,000
1.2
60,000
Investment Evaluation
Methods Used:
A Primary
Method
Payback period
Internal rate of return
A Secondary
Method
24%
This Method
59%
88%
Total Using
83%
11%
99%
Net present value
63%
22%
85%
Profitability index
15%
18%
33%
Project Size and Decision-Making Authority
Project Size
Typical Boundaries
Primary Decision Site
Very small
Small
Medium
Large
Up to $100,000
Plant
$100,000 to $1 million
Division
$1 million to $10 million
Corporate
investment committee
Over $10 million
CEO & board
KEY TERMS
Benefit-Cost Ratio (see Profitability Index)
Capital Budgeting
Capital Rationing
Equivalent Annual Annuity (EAA)
Internal Rate of Return (IRR)
Mutually Exclusive Projects
Net Present Value (NPV)
Payback period
Profitability Index (PI or Benefit-Cost Ratio)