Chapter
Ten
Making Capital
Investment
Decisions
© 2003 The McGraw-Hill Companies, Inc. All rights reserved.
10.1
Key Concepts and Skills
 Understand how to determine the relevant cash flows for
various types of proposed investments
 Be able to compute the CCA tax shield
 Understand the various methods for computing operating cash
flow
 Understand how to analyze different capital budgeting
decisions
10.2
Relevant Cash Flows 10.1
 The cash flows that should be included in a capital budgeting
analysis are those that will only occur (or not occur) if the
project is accepted
 These cash flows are called incremental cash flows
 The stand-alone principle allows us to analyze each project in
isolation from the firm simply by focusing on incremental
cash flows
10.3
Asking the Right Question
 You should always ask yourself “Will this cash flow occur (or
not occur) ONLY if we accept the project?”
 If the answer is “yes”, it should be included in the analysis
because it is incremental
 If the answer is “no”, it should not be included in the
analysis because it will occur anyway
 If the answer is “part of it”, then we should include the part
that occurs (or does not occur) because of the project
10.4
Common Types of Cash Flows 10.2
 Sunk costs – costs that have been incurred in the past (& thus
must be excluded from the current decision)
 Example: A firm spent $1 million on R & D before
making the decision to proceed with a project. Should the
$1 million be included as part of the cost of the project?
Answer: No – it is a sunk cost
 Opportunity costs – cost of foregone opportunities
 Example – you purchased an asset many years ago for a
nominal sum. You now want to use that asset in a current
project. How much do you charge to the project, since you
already own the asset?
 Answer: You must charge the project with the amount you
could obtain by selling the asset to another user.
10.5
Common Types of Cash Flows 10.2
 Side effects
 Positive side effects – benefits to other projects
 Example: HP printers & the cost of consumables
 Negative side effects – costs to other projects
 Issue of erosion or cannibalism
 Be sure to only include erosion due to the new project. Erosion
can also occur due to competition from other firms.
 Example: Air Canada – Tango versus the mainline fleet
 Changes in net working capital (NWC)
 Increases in NWC are a cost of the project
 Decreases in NWC are a benefit of the project
 NWC often increases initially and then decreases at the end
of the project’s life
10.6
Common Types of Cash Flows 10.2
 Financing costs
 Are never included in the cash flows of the project
 Financing costs are captured in the discount rate
 Inflation
 The nominal interest rate includes an inflation component
(remember the Fisher Equation). Thus the discount rate
captures expected future inflation.
 Therefore, project cash flows should also include the
effects of inflation
 Capital Cost Allowance (CCA)
 CCA (depreciation for tax purposes) creates a beneficial
tax shield
 A tax shield is the amount of tax that would have been paid, had
the project not been undertaken
10.7
More on NWC 10.4
 Why do we have to consider changes in NWC separately?
 An investment in current assets is exactly the same as an investment in a
fixed asset (but it is harder to visualize)
 An increase in NWC requires either:
 An increase in Current Assets (a use of cash)
 A reduction in Current Liabilities (a use of cash)
 What might cause Current Assets to rise?
 GAAP requires that sales be recorded on the income statement when made,
not when cash is received (The sale is recorded as an Account Receivable
on the Balance Sheet)
 What might cause Current Liabilities to fall?
 Current Liabilities will go down when we reduce a Current Liability, such
as an account payable
 Finally, we have to buy inventory to support sales although we haven’t
collected cash yet (Both inventory (C/A) and accounts payable (C/L)
rise)
10.8
Capital Cost Allowance (CCA)
 CCA is depreciation for tax purposes
 The depreciation expense used for capital budgeting should be
calculated according to the CCA schedule dictated by the tax
code (Refer to Slide #40, Chapter 2 for a list of the various
CCA classes and rates)
 Depreciation itself is a non-cash expense. It is only relevant
because it reduces taxes otherwise payable.
 The amount of tax reduction due to depreciation is called a tax
shield
 The depreciation tax shield = DTC
 D = depreciation expense
 TC = corporation’s marginal tax rate
10.9
Computing Depreciation
 Depreciation can be calculated using two basic methods
 Declining Balance Method (Most Common)
 Multiply the undepreciated capital cost (UCC) by the CCA
rate (from the Tax Act or Slide #40, Chapter 2)
 Half-year rule (can only deduct 50% of the usual amount in
the year of acquisition of the asset)
 Can use PV of CCA Tax Shield Formula (see next page)
 Straight-line depreciation
 Very few assets are depreciated straight-line for tax
purposes
 Depreciation = (Initial cost – salvage) / number of years
10.10
PV of Tax Shield from CCA
PV
Tax Shield
from CCA
 dTc  1  0.5k 
 UCC


 d  k  1  k 
Calculates
basic CCA
Adjusts for the
½ year rule
 Where:
 UCC = Initial cost of asset, including installation costs less any
trade-in value received for an existing asset
 d = CCA rate
 Tc = Corporate Tax Rate
 k = discount rate (corporation’s cost of capital)
10.11
PV of the Tax Shield from CCA Lost due to Salvage
PV
Tax Shield
Lost due to
Salvage
 dTc  1
 Salvage 

N
d

k


1

k





 Where
 S = Salvage value
 n = number of periods until the salvage value is realized
10.12
Example: Depreciation and Salvage
 You purchase equipment for $100,000 plus it costs $10,000 to
have it delivered and installed. Based on past information, you
believe that the equipment will have a salvage value of
$17,000 in 6 years. The company’s marginal tax rate is 40%.
If the applicable CCA rate is 20% and the required return on
this project is 10%, what is the present value of the tax shield
from CCA less the present value of the tax shield lost from
salvage?
10.13
Example: Depreciation and Salvage continued
 The delivery and installation costs must be added to the initial cost of
the asset and then depreciated
PV
PV
Tax Shield
from CCA
Tax Shield
Lost due to
Salvage
 dT  1  0.5k 
 UCC c 

d

k
1

k



 0.200.40   1  0.50.10 
 110,000


 0.20  0.10  1  .10 
 28,000
 dTc  1
 Salvage 

N
 d  k  1  k 



 0.20 0.40   1 
 17,000

6
0
.
20

0.10

 1.10  
 $2,558.95
10.14
The Six Steps of Capital Budgeting
Step #1: Calculate the PV of the initial cost plus any delivery &
installation expenses minus any trade-in received
Step #2: Calculate the PV of the after-tax incremental operating
cash flows from undertaking the project
Step #3: Calculate the PV of the tax shield from CCA
Step #4: Calculate the PV of salvage
Step #5: Calculate the PV of the tax shield from CCA lost due to
salvage
Step #6: Calculate the PV of the change in NWC
10.15
The Six Steps of Capital Budgeting
Step #1: PVInitial Cost= Purchase Cost + Installation – Trade-in
N
Step #2:
PVAfter -tax 
 Rev
t 1
Cash Flows
t
– Exp t 1  Tc 
1  k t
 dTc  1  0.5k 
 UCC


d

k
1

k



Step #3:
PV
Step #4:
PV Salvage 
Salvage
1  k N
Step #5:
PV
 dTc  1
 Salvage 

N
 d  k  1  k 
Step #6:
PV
Tax Shield
from CCA
Tax Shield
Lost due to
Salvage
NWC   
NWC
NWC


1  k N
1  k N



10.16
Defining the Terms
 Where:
 Revt = Incremental revenue in period t
 Expt = Incremental expense in period t
 Tc = Corporate Tax Rate
 UCC = Undepreciated capital cost
 d = CCA tax rate
 k = discount rate (the firm’s cost of capital)
 Salvage = the value received at the end of the asset’s
expected useful life
 N = number of periods until the salvage value is realized
 NWC = Net working capital (Current assets – current
liabilities)
10.17
Example #1: Cost Cutting
 Your company is considering a new production system that will initially
cost $1 million. It will save $300,000 a year in inventory and receivables
management costs. The system is expected to last for five years and will be
depreciated at a CCA rate of 20%. The system is expected to have a salvage
value of $50,000 at the end of year 5. There is no impact on net working
capital. The marginal tax rate is 40%. The required return is 8%.
10.18
Example #1: Cost Cutting
Step #1: PVInitial Cost= 1,000,000
Step #2:
PVAfter-tax

Cash Savings
  Rev-Exp 1  Tc  



t
1

k
t 1 




5
 300,000 1  .40 
N

t 1

1.08
t
180, 000 180, 000 180, 000 180, 000 180, 000




2
3
4
5
1.08
1.08 1.08 1.08 1.08
 $718, 688
Step #3:
PV
Tax Shield
from CCA
 dT  1  0.5k 
 UCC c 

d

k
1

k



 0.200.40  1  0.50.08 
 1,000,000


 0.20  0.08  1  .08 
 275,132
10.19
Example #1: Cost Cutting
Step #4:
Step #5:
Salvage
1  k N
50,000

1.085
 34,029
PV Salvage 
PV
Tax Shield
Lost due to
Salvage
 dTc  1
 Salvage 

N
d

k

 1  k 



 0.20 0.40   1 
 50,000

5
 0.20  0.08  1.08 
 $9,723
Step #6:
PV
NWC   
0
NWC
NWC


1  k N
1  k N
10.20
Summary of Cash Flows: Cost Cutting
Step #1
Step #2
Step #3
Step #4
Step #5
Step #6
NPV
-1,000,000
718,688
275,132
34,029
- 9,723
0
$18,126
Since the NPV is positive,
the firm should proceed
with the cost cutting
initiative. If the NPV were
negative, the firm should not
proceed.
10.21
Example #2: Repair versus Replace
 Original Machine
 Initial cost = 100,000
 Purchased 5 years ago
 Salvage today = 65,000
 Salvage in 5 years = 10,000
 New Machine
 Initial cost = 150,000
 5-year life
 Salvage in 5 years = 0
 Cost savings = 50,000 per
year
Required return = 10%
CCA Rate = 20%
Tax rate = 40%
10.22
Example #2: Repair versus Replace
Step #1: PV of Initial Cost less trade-in = $150,000 - 65,000 = 85,000
 1  1  k  t
Step #2: PVAftertax  Annual Cost Savings1  Tc 
k
cos t savings

 1  1.10 5 

 50,0001  0.40 

 0.10 
 $113,724
Step #3:
PV
Tax Shield
from CCA
 dTc   1  0.5k 
 UCC 


 d  k  1 k 
  0.20  0.40    1  0.5  0.10  
 85, 000 


0.20

0.10
1

.10



 $21,636




10.23
Example #2: Repair versus Replace
Step #4:
Step #5:
Salvage
1  k N
10,000

1.105
 $6,209
PV Salvage 
PV
Tax Shield
Lost due to
Salvage
 dTc  1
 Salvage 

N
 d  k  1  k 



 0.20 0.40   1 
 10,000

5
 0.20  0.10  1.10  
 $1,656
Step #6:
PV
NWC   
0
NWC
NWC


1  k N
1  k N
10.24
Summary of Cash Flows: Repair vs Replace
Step #1
Step #2
Step #3
Step #4
Step #5
Step #6
NPV
-85,000
+113,724
+21,636
- 6,209
+1,656
0
$45,806
Since the NPV is positive,
the firm should proceed
with acquiring the new
machine. If the NPV were
negative, the firm should
keep the old machine.
10.25
Example #3: Equivalent Annual Cost Analysis
 Machine A
 Initial Cost = $150,000
 Pre-tax operating cost =
$65,000
 Expected life is 8 years
 Machine B
 Initial Cost = $100,000
 Pre-tax operating cost =
$57,500
 Expected life is 6 years
• The machine chosen will be replaced indefinitely
• Neither machine will impact revenue
• No change in NWC is required
• The required return is 10%
• CCA rate is 20%
• Tax rate is 40%.
Which machine should you buy?
10.26
Example #3: Equivalent Annual Cost Analysis
 To perform an equivalent annual cost calculation, first
calculate the NPV of each alternative, using the 6 steps.
 Then divide the NPV by the annuity factor to obtain an
equivalent annual cost/benefit
 Choose the alternative with the higher annual benefit or lower
annual cost
10.27
Example #3: Equivalent Annual Cost Analysis
Machine A
Step #1:
$150,000
Step #2:
PVAfter tax
cos ts
Step #3:
PV
 1  1  k t
 Annual Cost 1  Tc  

k

 1  1.10 8 
 65, 000 1  0.40  

 0.10 


 $208, 062
Tax Shield
from CCA




 dT  1  0.5k 
 UCC c 

 d  k  1  k 
 0.200.40   1  0.50.10 
 150,000


0
.
20

0.10
1

.
10



 $38,182
10.28
Example #3: Equivalent Annual Cost Analysis
Step #4:
Step #5:
0
1  k N
0
PV Salvage 
PV
Tax Shield
Lost due to
Salvage
 dTc  1
 Salvage 

N
d

k

 1  k 
0
Step #6:
PV
NWC   
0
NWC
NWC


1  k N
1  k N



10.29
Example #3: Equivalent Annual Cost Analysis
Machine B
Step #1:
$100,000
Step #2:
PVAfter tax
cos ts
Step #3:
PV
 1  1  k t
 Annual Cost 1  Tc  

k

 1  1.10 6 
 57,500 1  0.40  

 0.10 


 $150, 256
Tax Shield
from CCA




 dT  1  0.5k 
 UCC c 

d

k
1

k



 0.200.40   1  0.50.10 
 100,000


0
.
20

0.10
1

.
10



 $25,455
10.30
Example #3: Equivalent Annual Cost Analysis
Step #4:
Step #5:
0
1  k N
0
PV Salvage 
PV
Tax Shield
Lost due to
Salvage
 dTc  1
 Salvage 

N
d

k

 1  k 
0
Step #6:
PV
NWC   
0
NWC
NWC


1  k N
1  k N



10.31
Example #3: Equivalent Annual Cost Analysis
Calculate the NPV for each machine & divide by the annuity factor
Machine A
Machine B
Step #1
-150,000
-100,000
Step #2
-208,062
-150,256
Step #3
+38,182
+25,455
Step #4
0
0
Step #5
0
0
Step #6
0
0
-$319,880
-$224,801
-$59,960
-$51,615
Total NPV
Equivalent Annual Cost
To calculate EAC, divide NPV by the annuity factor (see next page for the annuity factor)
10.32
EAC: Calculating the Annuity Factors
 The formula for the PV of an ordinary annuity looks like this:
 1  1  k t
PVAnnuity  C 
k





 The Annuity Factor is the component contained within the brackets
 1  1  k  t


k





 The Annuity Factors for Machine A & B are thus:
 1  1.108 

Annuity FactorA  

.10


 5.33
 1  1.106 

Annuity FactorB  

.10


 4.36
10.33
Example #4: Setting the Bid Price
 Consider the example in the textbook:
 Need to produce 5 modified trucks per year for 4 years
 We can buy the truck platforms for $10,000 each
 Facilities will be leased for $24,000 per year
 Labor and material costs are $4,000 per truck
 Need $60,000 investment in new equipment, depreciated at
20% (CCA class 8)
 Expect to sell the equipment for $5,000 at the end of 4
years
 Need $40,000 in net working capital
 Tax rate is 43.5%
 Required return is 20%
10.34
Example #4: Setting the Bid Price
Step #1
Step #2
$60,000
PVAfter tax  Annual Cost
cos ts
 1  1  k t
k

1  Tc  




 1  1.20 4 
  5 x10, 000   24, 000   5 x 4, 000   1  0.435 

 0.20 


 $137, 488
Step #3
PV
Tax Shield
from CCA
 dTc  1  0.5k 
 UCC


 d  k  1  k 
 0.200.435  1  0.50.20 
 60,000


 0.20  0.20  1  .20 
 $11,963
10.35
Example #4: Setting the Bid Price
Step #4
PV Salvage 
Step #5
 dT  1
PV Tax Shield  Salvage  c 
N
Lost due to
 d  k  1  k 
Salvage
1  k N
5,000

1.204
 $2,411
Salvage



 0.200.435  1 
 5,000

4
 0.20  0.20  1.20 
 $524
Step #6
PV
NWC
NWC
NWC


1  k N
1  k N
40,000
 40,000 
1.204
 20,710

10.36
Example #4: Setting the Bid Price
Step #1
-$60,000
Step #2
-$137,488
Step #3
+$11,963
Step #4
+$2,411
Step #5
-$524
Step #6
-$20,710
PVCosts
-$204,348
10.37
Example #4: Setting the Bid Price
 To calculate the bid price, must now set the PV of costs equal to the PV
of revenue
PVCost  PVRevenue
 1  1  k t
204,348  5P1  T 
k





 1  1.20 4 

 5P1  0.435

.20


P  $27,942
P is equal to the
required bid price per
truck
10.38
Summary 10.8
 You should know:
 How to determine the relevant incremental cash flows that
should be considered in capital budgeting decisions
 How to calculate the CCA tax shield for a given investment
 How to perform a capital budgeting analysis for:




Replacement problems
Cost cutting problems
Bid setting problems
Projects of different lives