Transcript Chapter 6

Chapter 6: Capital
Budgeting: The Basics
Objective
Explain Capital Budgeting
Develop Criteria
1
Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley
Chapter 6 Contents
• 1 The Nature of Project
Analysis
• 7 Analyzing Cost-Reducing
Projects
• 2 Where do Investment
Ideas come from?
• 8 Projects with Different
Lives
• 3 The NPV Investment Rule
• 9 Ranking Mutually
Exclusive Projects
• 4 Estimating a Project’s
Cash Flows
• 5 Cost of Capital
• 10 Inflation & Capital
Budgeting
• 6 Sensitivity Analysis
2
Objectives
• To show how to use discounted cash flow
analysis to make decisions such as:
– Whether to enter a new line of business
– Whether to invest in equipment to reduce
costs
3
Introduction
• Recall the objective of a firm
– Maximization of the market value of
shareholders’ equity
• The theory of how to do this was provided in
the prior two chapters
– Compute the net present value of the
project’s expected cash flows, and undertake
only those with positive NPV
4
6.1 The Nature of Project
Analysis
• Basic unit of analysis
– the individual investment project
5
Procedural Outline
• Form ideas on how to increase
shareholders’ equity
• Plan how to implement the ideas
• Gather information on timing and
magnitude of costs and benefits
• Apply NPV criterion
6
Generating a forecast
• Information is often biased towards its
provider’s goal (agency problem)
• There are many ways to implement a
goal
• Some information is not fully quantifiable
• Impact on shareholder wealth difficult to
evaluate when cash flows are risky
7
The Nature of Project Analysis
• We will postpone discussion of risky cash
flows to avoid the complex issue of how
they affect shareholder wealth
• The criterion used
– find the present value of all future cash
flows, and subtract the initial investment to
obtain the net present value (NPV)
8
6.2 Where do Investment
Ideas Come From?
– monitor existing & potential customers needs
– monitor existing & potential technological
capacity of the firm
– monitor the competition’s marketing,
investment, patents, and technical recruiting
– monitor production & distribution functions
for revenue enhancement / cost savings
– reward employees for innovative ideas
9
6.3 Net Present Value Rule
• A project’s net present value is
– the amount by which the project is expected
to increase the wealth of the firm’s current
shareholders
• As a criterion
– Invest in proposed projects with positive NPV
10
Illustration
• The following tables show the
computation of NPV
– To show the affect of the discount rate, three
tables are shown based on different rates
11
NPV of a Project
Discout
10%
Year
0
1
2
3
4
5
DCF Payback
Flow
PV
Cum_PV
-1000
-1000
-1000
450
409
-591
350
289
-302
250
188
-114
150
102
-11
50
31
20
NPV
20
12
Do Project
NPV of a Project
Discout
15%
Year
0
1
2
3
4
5
Flow
PV
Cum_PV
-1000
-1000
-1000
450
391
-609
350
265
-344
250
164
-180
150
86
-94
50
25
-69
NPV
-69
13
Don’t Do Project
Internal Rate of Return
NPV of a Project
Discout
11.04%
Year
0
1
2
3
4
5
Flow
PV
Cum_PV
-1000
-1000
-1000
450
405
-595
350
284
-311
250
183
-128
150
99
-30
50
30
0
NPV
0
14
Indifferent
Common Error
• It is a common mistake to start the
investment in year 1 rather than year 0
(when this was not intended)
– Now is time 0
– Like a child, a project is not one-year old
until a year has passed
15
Summary
• The discount rate
– in the first scenario it was assumed to be
10%, and the resulting NPV was $20
– In the second scenario it was assumed to be
15%, and the NPV was -$69
– In the third scenario, the discount rate that
resulted in a zero NPV was found
16
NPV as a Function of Discount Rate
250
200
150
NPV
100
50
0
-50
0%
5%
10%
15%
-100
-150
-200
17
Discount Rate
20%
6.4 Depreciation and Cash
Flows
• It is important to remember that when
making financial decisions only timed
cash flows are used
– depreciation is an expense, but is not a cash
expense, and must be excluded
– the tax benefit of depreciation, however, is a
cash flow, and must be included
18
Working Capital & Cash Flows
• Some cash flows do not occur on the
income statement, but involve timing
– working capital additions and reductions are
cash flows
– at the end of a project, the sum of the
nominal changes in working capital is zero
19
Accruals & Deferrals
• Take extra care if you are provided with
net income information by an accountant
– the flows forming net income may include
• accruals
• deferrals
– these are typically small, and may sometimes be ignored
20
Incremental Cash Flows
• Only the incremental cash flows should
form part of an investment decision
– Evaluate the projected cash flows, by
(category and) timing, both with and without
the project, and find the difference
– This difference is a collection of timed cash
flows, and this is what affects the wealth of
the shareholders
21
Illustration: Cannibalism
• A proposed project will generate $10,000
in revenue, but will causes another
product line to lose $3,000 in revenues
• The incremental cash flow is only $7,000
22
Illustration: Prior Expenses
• R&D expenses are $10,000 to-date for
your project, and you plan to spend
another $20,000, making $30,000 in all
– The $10,000 is a sunk cost. The decision
whether to undertake the project will not
change this expenditure
– Only the $20,000 is an incremental cost, and
the $10,000 should be excluded
23
Sunk Costs
• Shareholders are interested in the timing
and magnitude of cash flows
– From an investor’s vantage, a project gives
rise to an alternative cash flow
– If (alternative cash flows) - (original cash
flows) is valuable to shareholders, do project
– A sunk cost has no impact on future cash
flows: it is irrelevant to shareholders
24
Illustration: Underutilized
Resources
• A project uses an existing (non-cancelable)
leased warehouse with a remaining life of 20
years, and total annual rent of $100,000
• The warehouse is projected to remain 50%
utilized, unless your project is undertaken
• The lease prohibits sub-leasing
• The current project is making a loss
• Your project will use 25% of the warehouse
• What should the project be charged?
25
Proposed Solution 1
• The original project currently using the
warehouse is making a loss:
– “Charge the full $100,000 /year so the
company can recover the very real
warehousing costs.”
26
Proposed Solution 2
• Half the warehouse is available:
– “The project should be charged the full
$50,000 /year if it needs to use it. A portion
of the warehousing costs will not be
charged-out otherwise.”
27
Proposed Solution 3
• The project should be charged for its
share of the used space:
– “Charge $33,333 /year.”
28
Proposed Solution 4
• The project is going to use only 25% of
the space.
– “Charge $25,000 /year.”
29
Proposed Solution 5
• The charge should be proportioned
according to revenues generated by each
project--that is fair, isn’t it?
– “The old project’s revenues = $9,000,000,
and the new project has projected revenues
= $1,000,000, so the charge is 10%, or
$10,000/year.”
30
Proposed Solution 6
• There is a suitable new (smaller)
warehouse available on the market for
$27,000 /year.
– “Charge the project the market rate of the
space, $27,000.”
31
Proposed Solution 7
• The original lease was entered into when
warehouse space was cheap, but now
space is twice what it was:
– “The market value of the leased warehouse
is now $200,000, and the project should take
its proper share of that amount.”
32
Proposed Solution 8
• This is a new project, so give it a
sporting chance:
– “The project should be charged nothing.”
33
Warehouse Illustration
• The solution in this case is proposed
solution # 8, (but for another reason):
The project should be charged nothing
– The warehouse expenditure will occur
whether the project is done or not. It is
therefore not an incremental cash flow
– With different facts (alternative usage or
lease re-negotiation) the answer would be
different
34
6.5 The Cost of Capital
• When determining the cost of capital
– the risk of the project is, in general, different
from the risk of existing projects
– only the market-related risk is relevant
– only the risk from a project’s cash flows is
relevant (not that of financing instruments)
35
Computing the Average Cost
of Capital of a Corporation
• Determine the return to security holders
of each class of security issued
• Determine the market value of each class
of the company’s securities, and compute
the weight of each
• After adjusting for tax, compute the
weighted sum of returns
36
Average Cost of Capital:
Example with 3-Securities
• Let
• ke be the return on equity
• kd be the return on debt
• kp be the return on preferred
• Ve be the market value of issued equity
• Vd be the Market value of issued bonds
• Vp be the market value of issued preferred
• t be the tax rate
37
Average Cost of Capital:
Example with 3-Securities
• k = ke * Ve + kp * Vp + kd * Vd* (1 - t)
• The average cost of capital is also the
cost of capital for each of the firms
business divisions weighted according to
their market value
38
6.6 Sensitivity Analysis Using
Spreadsheets
• Will the project still be economical if
some of the underlying variables are
inaccurate?
– Spreadsheets are an excellent tool for
exploring the influence of estimation errors
on financial decisions
39
Base Case
• The following is an embedded Excel
worksheet for the cash flow of a firm
– It is generally a good practice to divide the
worksheet into two segments, one
containing only data, and the other
containing only formulae
– This practice increases flexibility & reduces
the chance of error
– It is also a good practice to name variables
using Insert:Name:Create in Excel
40
Tax rate
Unit sales in year 1
Sales growth rate
Unit price
Unit Price Growth
Fixed Start
Fixed Growth
Variable pcent
Depreciation schedule
Start working capt
Investment schedule
Capital movements sch
Dividend
Working Cap Sch
Year
CF Forecast
Sales revenue
Expenses
Fixed Costs (cash)
Variable costs
Depreciation
Operating Profit
Taxes
Net Profit
Operating CF
Working cap move
Investment in P&E
Invest CF
Net CF
PV(NCF)
40.00%
$4,000
0.00%
$5,000
0.00%
3,100,000
0.00%
75.00%
400,000
2,200,000
2,800,000
0
1,000,000
2,200,000
0
2200
2,800
5,000
-5,000
-5000
NPV =
1236
1
2
3
4
5
6
7
20,000
20,000
20,000
20,000
20,000
20,000
20,000
3,100
15,000
400
1,500
600
900
1,300
3,100
15,000
400
1,500
600
900
1,300
3,100
15,000
400
1,500
600
900
1,300
3,100
15,000
400
1,500
600
900
1,300
3,100
15,000
400
1,500
600
900
1,300
3,100
15,000
400
1,500
600
900
1,300
0
1,300
1130
0
0
1,300
983
0
0
1,300
855
0
0
1,300
743
0
0
1,300
646
0
0
1,300
562
3,100
15,000
400
1,500
600
900
1,300
-2,200
0
-2,200
3,500
1316
41
A Modified Scenario
– In this case the cash is piling up (Watch out
for IRS penalties in this case!)
– The assumption is now made that sales units
grow by +2%, unit prices by -3%, and fixed
costs by +8% (No, Victor: Fixed costs may
vary with time. Yes, Valerie: Fixed costs do
not vary with sales.)
– Assume a dividend of $1,000,000/year
42
Assumptions
Cost of capital
Tax rate
Unit sales in year 1
Sales growth rate
Unit price
Unit Price Growth
Fixed Start
Fixed Growth
Variable pcent
Depreciation schedule
Start working capt
Investment schedule
Capital movements sch
Dividend
Working Cap Sch
Year
CF Forecast
Sales revenue
Expenses
Fixed Costs (cash)
Variable costs
Depreciation
Operating Profit
Taxes
Net Profit
Operating CF
Working cap move
Investment in P&E
Invest CF
Net CF
PV(NCF)
(Table in $'000)
15.00%
40.00%
$4,000
2.00%
$5,000
-3.00%
3,100,000
8.00%
75.00%
400,000
2,200,000
2,800,000
0
1,000,000
2,200,000
0
2200
2,800
5,000
-5,000
-5000
NPV =
-797
1
2
3
4
5
6
7
20,000
19,788
19,578
19,371
19,165
18,962
18,761
3,100
15,000
400
1,500
600
900
1,300
3,348
14,841
400
1,199
480
719
1,119
3,616
14,684
400
879
351
527
927
3,905
14,528
400
538
215
323
723
4,218
14,374
400
174
70
104
504
4,555
14,222
400
-214
-86
-129
271
0
1,300
1130
0
0
1,119
846
0
0
927
610
0
0
723
413
0
0
504
251
0
0
271
117
4,919
14,071
400
-629
-252
-377
23
-2,200
0
-2,200
2,223
836
43
Additional Scenarios
• The following graphs are variations of
from the basic model constructed by
changing one variable at a time:
44
Assumptions
Cost of capital
Tax rate
Unit sales in year 1
Sales growth rate
Unit price
Unit Price Growth
Fixed Start
Fixed Growth
Variable pcent
Depreciation schedule
Start working capt
Investment schedule
Capital movements sch
Dividend
Working Cap Sch
Year
CF Forecast
Sales revenue
Expenses
Fixed Costs (cash)
Variable costs
Depreciation
Operating Profit
Taxes
Net Profit
Operating CF
Working cap move
Investment in P&E
Invest CF
Net CF
PV(NCF)
(Table in $'000)
25.00%
40.00%
$4,000
0.00%
$5,000
0.00%
3,100,000
0.00%
75.00%
400,000
2,200,000
2,800,000
0
1,000,000
2,200,000
0
2200
2,800
5,000
-5,000
-5000
Was 15%
NPV =
-429
1
2
3
4
5
6
7
20,000
20,000
20,000
20,000
20,000
20,000
20,000
3,100
15,000
400
1,500
600
900
1,300
3,100
15,000
400
1,500
600
900
1,300
3,100
15,000
400
1,500
600
900
1,300
3,100
15,000
400
1,500
600
900
1,300
3,100
15,000
400
1,500
600
900
1,300
3,100
15,000
400
1,500
600
900
1,300
0
1,300
1040
0
0
1,300
832
0
0
1,300
532
0
0
1,300
426
0
0
1,300
341
3,100
15,000
400
1,500
600
900
1,300
-2,200
0
-2,200
3,500
734
0
0
1,300
66645
Assumptions
Cost of capital
Tax rate
Unit sales in year 1
Sales growth rate
Unit price
Unit Price Growth
Fixed Start
Fixed Growth
Variable pcent
Depreciation schedule
Start working capt
Investment schedule
Capital movements sch
Dividend
Working Cap Sch
Year
CF Forecast
Sales revenue
Expenses
Fixed Costs (cash)
Variable costs
Depreciation
Operating Profit
Taxes
Net Profit
Operating CF
Working cap move
Investment in P&E
Invest CF
Net CF
PV(NCF)
(Table in $'000)
15.00%
30.00%
$4,000
0.00%
$5,000
0.00%
3,100,000
0.00%
75.00%
400,000
2,200,000
2,800,000
0
1,000,000
2,200,000
0
2200
2,800
5,000
-5,000
-5000
Was 40%
NPV =
1860
1
2
3
4
5
6
7
20,000
20,000
20,000
20,000
20,000
20,000
20,000
3,100
15,000
400
1,500
450
1,050
1,450
3,100
15,000
400
1,500
450
1,050
1,450
3,100
15,000
400
1,500
450
1,050
1,450
3,100
15,000
400
1,500
450
1,050
1,450
3,100
15,000
400
1,500
450
1,050
1,450
3,100
15,000
400
1,500
450
1,050
1,450
0
1,450
1261
0
0
1,450
1096
0
0
1,450
953
0
0
1,450
829
0
0
1,450
721
0
0
1,450
627
3,100
15,000
400
1,500
450
1,050
1,450
-2,200
0
-2,200
3,650
1372
46
Assumptions
Cost of capital
Tax rate
Unit sales in year 1
Sales growth rate
Unit price
Unit Price Growth
Fixed Start
Fixed Growth
Variable pcent
Depreciation schedule
Start working capt
Investment schedule
Capital movements sch
Dividend
Working Cap Sch
Year
CF Forecast
Sales revenue
Expenses
Fixed Costs (cash)
Variable costs
Depreciation
Operating Profit
Taxes
Net Profit
Operating CF
Working cap move
Investment in P&E
Invest CF
Net CF
PV(NCF)
(Table in $'000)
15.00%
40.00%
$4,000
5.00%
$5,000
0.00%
3,100,000
0.00%
75.00%
400,000
2,200,000
2,800,000
0
1,000,000
2,200,000
0
2200
2,800
5,000
-5,000
-5000
Was 0%
NPV =
2885
1
2
3
4
5
6
7
20,000
21,000
22,050
23,153
24,310
25,526
26,802
3,100
15,000
400
1,500
600
900
1,300
3,100
15,750
400
1,750
700
1,050
1,450
3,100
16,538
400
2,013
805
1,208
1,608
3,100
17,364
400
2,288
915
1,373
1,773
3,100
18,233
400
2,578
1,031
1,547
1,947
3,100
19,144
400
2,881
1,153
1,729
2,129
0
1,300
1130
0
0
1,450
1096
0
0
1,608
1057
0
0
1,773
1014
0
0
1,947
968
0
0
2,129
920
3,100
20,101
400
3,200
1,280
1,920
2,320
-2,200
0
-2,200
4,520
1699
47
Assumptions
Cost of capital
Tax rate
Unit sales in year 1
Sales growth rate
Unit price
Unit Price Growth
Fixed Start
Fixed Growth
Variable pcent
Depreciation schedule
Start working capt
Investment schedule
Capital movements sch
Dividend
Working Cap Sch
Year
CF Forecast
Sales revenue
Expenses
Fixed Costs (cash)
Variable costs
Depreciation
Operating Profit
Taxes
Net Profit
Operating CF
Working cap move
Investment in P&E
Invest CF
Net CF
PV(NCF)
(Table in $'000)
15.00%
40.00%
$4,000
0.00%
$5,000
0.00%
3,100,000
0.00%
85.00%
400,000
2,200,000
2,800,000
0
1,000,000
2,200,000
0
2200
2,800
5,000
-5,000
-5000
Was 75%
NPV =
-3757
1
2
3
4
5
6
7
20,000
20,000
20,000
20,000
20,000
20,000
20,000
3,100
17,000
400
-500
-200
-300
100
3,100
17,000
400
-500
-200
-300
100
3,100
17,000
400
-500
-200
-300
100
3,100
17,000
400
-500
-200
-300
100
3,100
17,000
400
-500
-200
-300
100
3,100
17,000
400
-500
-200
-300
100
0
100
87
0
0
100
76
0
0
100
66
0
0
100
57
0
0
100
50
0
0
100
43
3,100
17,000
400
-500
-200
-300
100
-2,200
0
-2,200
2,300
865
48
Assumptions
Cost of capital
Tax rate
Unit sales in year 1
Sales growth rate
Unit price
Unit Price Growth
Fixed Start
Fixed Growth
Variable pcent
Depreciation schedule
Start working capt
Investment schedule
Capital movements sch
Dividend
Working Cap Sch
Year
CF Forecast
Sales revenue
Expenses
Fixed Costs (cash)
Variable costs
Depreciation
Operating Profit
Taxes
Net Profit
Operating CF
Working cap move
Investment in P&E
Invest CF
Net CF
PV(NCF)
(Table in $'000)
15.00%
40.00%
$4,000
0.00%
$5,000
0.00%
3,500,000
0.00%
75.00%
400,000
2,200,000
2,800,000
0
1,000,000
2,200,000
0
2200
2,800
5,000
-5,000
-5000
Was $3,100,000
NPV =
237
1
2
3
4
5
6
7
20,000
20,000
20,000
20,000
20,000
20,000
20,000
3,500
15,000
400
1,100
440
660
1,060
3,500
15,000
400
1,100
440
660
1,060
3,500
15,000
400
1,100
440
660
1,060
3,500
15,000
400
1,100
440
660
1,060
3,500
15,000
400
1,100
440
660
1,060
3,500
15,000
400
1,100
440
660
1,060
0
1,060
922
0
0
1,060
802
0
0
1,060
697
0
0
1,060
606
0
0
1,060
527
0
0
1,060
458
3,500
15,000
400
1,100
440
660
1,060
-2,200
0
-2,200
3,260
1226
49
Consequences
– Notice that the reduced long-term viability of
the product, together with the dividend for
demands, will cause:
– a cash flow crisis early in year 5,
– negative accounting profits in year 6,
– and a serious negative operating cash flow in
year 8 when the tax benefits of depreciation
are finally consumed.
50
Graphs
– Graphs are a useful supplement to
spreadsheets as they may illustrate behavior
of the model to continuing changes in a
selected independent variable
– The following graphs explore a model
51
Table 6.4 Project Sensitivity to Sales Volume
Sales Units
2000
3000
3604
4000
5000
6000
Net CF Operations
200000
550000
1003009
1300000
2050000
2800000
52
NPV Project
5005022
1884708
0
1235607
4355922
7476237
NPV v. Discount Rate
$7,000
$6,000
$5,000
NPV $000
$4,000
$3,000
$2,000
$1,000
$0
0%
5%
10%
15%
20%
25%
30%
$1,000
$2,000
$3,000
Rate
53
35%
40%
45%
50%
Sensitivity of Project to Sale Volume
$3,000,000
Net CF from Operations
$2,500,000
$2,000,000
$1,500,000
$1,000,000
$500,000
$0
$2,000
$2,500
$3,000
$3,500
$4,000
$4,500
$500,000
Sales (Units)
54
$5,000
$5,500
$6,000
NPV Project
$10,000,000
$8,000,000
$6,000,000
NPV
$4,000,000
$2,000,000
$0
2000
2500
3000
3500
4000
4500
$2,000,000
$4,000,000
$6,000,000
Sales (Units)
55
5000
5500
6000
Spreadsheet Planning
Conclusions:
• Spreadsheets permit management to
explore perturbations caused by
randomness in the model’s inputs
– This should lead to management correctly
prioritizing time to the variables of the model
– Management will recognize dangers sooner,
and will create contingency plans to avoid
their worst consequences
56
6.7 Break-Even and
Indifference Points
• Break-even point is number of sales
resulting in a NPV = 0
• IRR is discount rate resulting in NPV = 0
• Price B/E is unit price resulting in NPV= 0
• Payback period is the project life
resulting in NPV = 0
57
6.8 Projects with Different
Lives
• When do you replace a sales car?
– As a car ages
• its resale price decreases
• the annual repair bills increase
• sales people become discontented
– people who live in their cars demand reliability
– customers are influenced by sales people’s cars
– a nice car is part of their unofficial remuneration
58
Data Collection
• A car uses about the same amount of oil,
gasoline, cleaning, tire usage, et cetera,
no matter how old it is
– This data need not be collected, because we
are interested only in incremental cash flows
• assume that the degree of tires wear is
compensated by a credit on sale
59
Data Collection
• In order to simplify this example, it will
be assumed that all cash flows are in real
terms
• Assumed that the required rate of return
on cars is a real 10% (Excited already?)
60
Data Collection
• Sales people use the Bdella Sedan.
• The market prices for new and used
Bdellas is given on the next slide
• The expected annual maintenance
charges by year are also given
• Intangible losses have been listed
61
Schedule of Bdella Price & Maint
Age
0
1
2
3
4
5
6
7
8
9
10
Discount
Price
Maint
Intang
20,000
0
16,000
0
1,000
12,800
1,000
800
10,240
1,100
0
8,192
1,210
-500
4,096
1,331
-600
2,048
1,464
-840
1,024
1,611
-1,176
512
1,772
-1,646
256
1,949
-2,305
128
2,144
-3,227
5.00%
62
Car Replacement
• First compute the NPV of
– purchasing in year 0, and selling in year 1,
– purchasing in year 0, and selling in year 2,
–…
– purchasing in year 0, and selling in year 10
• These figures are shown in col. PV_Proj
63
Schedule of Bdella Price & Maint
Age
0
1
2
3
4
5
6
7
8
9
10
Discount
Price
Maint
Intang
PV_Price PV_Maint PV_Intang PV_Proj
20,000
0
20,000
16,000
0
1,000
15,238
0
952
-3,810
12,800
1,000
800
11,610
907
726
-7,619
10,240
1,100
0
8,846
950
0
-11,334
8,192
1,210
-500
6,740
995
-411
-14,846
4,096
1,331
-600
3,209
1,043
-470
-19,890
2,048
1,464
-840
1,528
1,093
-627
-23,290
1,024
1,611
-1,176
728
1,145
-836
-26,071
512
1,772
-1,646
347
1,199
-1,114
-28,766
256
1,949
-2,305
165
1,256
-1,486
-31,689
128
2,144
-3,227
79
1,316
-1,981
-35,073
5.00%
64
Interpretation
• We see that the incremental cost of
replacing the car every year is $3810,
replacing it every two years is $7,619…
• You are not yet tempted to select
“replace every year” because this option
does not provide a Bdella Sedan after the
1st year, while replace after 2-years does
65
Additional Analysis
• The analysis so far does not provide for a
replacement car.
• The simplest way to do this is to replace
each project with an identical project
forever
• We have the perpetuity equation for this
66
Additional Analysis
• Take the two year problem as an
example
• The NPV is discounted to year 0, the 1st
replacement NPV is discounted to year 2,
the 2nd to year 4, … for ever
• This is a perpetuity due, with interest
(1.05)2 - 1 = 10.25%
67
Schedule of Bdella Price & Maint
Age
0
1
2
3
4
5
6
7
8
9
10
Discount
Price
Maint
Intang
PV_Price PV_Maint PV_Intang PV_Proj Rate
PV_Infinity Ann_Equ
20,000
0
20,000
16,000
0
1,000
15,238
0
952
-3,810
5.00%
-80,000
-3,810
12,800
1,000
800
11,610
907
726
-7,619
10.25%
-81,951
-3,902
10,240
1,100
0
8,846
950
0
-11,334
15.76%
-83,236
-3,964
8,192
1,210
-500
6,740
995
-411
-14,846
21.55%
-83,738
-3,988
4,096
1,331
-600
3,209
1,043
-470
-19,890
27.63%
-91,881
-4,375
2,048
1,464
-840
1,528
1,093
-627
-23,290
34.01%
-91,771
-4,370
1,024
1,611
-1,176
728
1,145
-836
-26,071
40.71%
-90,112
-4,291
512
1,772
-1,646
347
1,199
-1,114
-28,766
47.75%
-89,013
-4,239
256
1,949
-2,305
165
1,256
-1,486
-31,689
55.13%
-89,167
-4,246
128
2,144
-3,227
79
1,316
-1,981
-35,073
62.89%
-90,841
-4,326
5.00%
68
Conclusion
• Replacing the car every year is the best
scenario, but, watch out for an agency
problem. Without the intangibles the
answer is to keep the car as long as
possible
• The Bdella Sedan is like a Volvo on
Geritol: it doesn't know when to die
69
6.9 Ranking Mutually
Exclusive Projects
• Using the NPV method, you are unlikely
to encounter any serious problems
– Some managers, particularly those with an
engineering background, prefer to use the
IRR method
• The IRR method may be made to give the
correct answer, but this requires considerable
skill. Avoid it (unless your boss engineer)
70
6.10 Inflation and Capital
Budgeting
• When computing NPV
– Use the nominal cost of capital to discount
nominal cash flows
• (Nominal cash flows are rarely constant)
– Use the real cost of capital to discount real
cash flows
71