© 2003 The McGraw-Hill Companies, Inc. All rights reserved.

10.1

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

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
 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

Sunk costs
– costs that have been incurred in the past (& thus must be excluded from the current decision)

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?

You must charge the project with the amount you could obtain by selling the asset to another user.

10.5

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

Financing costs

Are never included in the cash flows of the project
 Financing costs are captured in the discount rate

Inflation
 Nominal interest rates include an inflation component
(remember the Fisher Equation). Thus the discount rate captures expected future inflation.

Project cash flows should also include the effect 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
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

10.8
Step #1: PV
Initial Cost
= Purchase Cost + Installation – Trade-in
Step #2:
Step #3:
PV
After tax
Cash Flows
 t
N 

1

Rev t
–
Exp t

1
 k
 t

1

T c

PV
Tax from
Shield
CCA

UCC d dT c
 k

 
1

0 .
5 k
1
 k
Step #4:
Step #5:
Step #6:
PV
Salvage

Salvage

1
 k

N
PV
Tax Shield
Lost due to
Salvage

Salvage d dT c
 k

 
1

1 k

N


PV

NWC
  

1
NWC
 k

N
 

1
NWC
 k

N

10.9

Where:
 Rev t
= Incremental revenue in period t
 Exp t

T c
= Incremental expense in period t
= 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)

10.10

Capital budgeting relies heavily on pro forma accounting statements, particularly income statements

Computing cash flows – (refer back to Chapter 2)

Cash Flow From Assets (CFFA) = Operating Cash Flow – net capital spending (NCS) – Change (increase) in NWC

Operating Cash Flow (OCF) = EBIT + depreciation – taxes
 Net Capital Spending = Net Fixed Assets
End of Period
Fixed Assets
Start of Period
+ Depreciation

Change in NWC = NWC
End of Period
– Net
– NWC
Start of Period

10.11
Sales (50,000 units at $4.00/unit)
Variable Costs ($2.50/unit)
Gross profit
Fixed costs
Depreciation ($90,000 / 3)
EBIT
Taxes (34%)
Net Income
$200,000
125,000
$ 75,000
12,000
30,000
$ 33,000
11,220
$ 21,780

10.12
NWC
Net Fixed Assets
0
↑$20,000
$90,000
1
Year
2 3
↓$20,000

10.13
Op Cash Flow
Change in
NWC
Capital
Spending
CFFA
0
↑$20,000
↑$90,000
-$110,000
Year
1
$51,780
2
$51,780
3
$51,780
↓$20,000
$51,780 $51,780 $71,780

10.14

Given the cash flows, we can apply the techniques from
Chapter 9

Assume the required return is 20%

Enter the cash flows into the calculator and compute NPV and
IRR
110,000 +/-
51,780
51780
71,780
CF
0
CF
1
CF
2
I
CF
3
20
2 nd NPV $10,648
2 nd IRR 25.8%

Should we accept or reject the project?

10.15
Step #1: PV
Initial Cost
= - 90,000
Step #2: PV
After tax
Cash Flows


51,780

1 .
20





51,780
1 .
20

2




51,780
1 .
20

3

Step #3: PV
Tax Shield from CCA

0
Step #4:
Step #5:
PV
Tax Shield
Lost due to
Salvage

0
PV
Tax Shield
Lost due to
Salvage

0
Step #6:
PV

NWC
 
20 , 000

20 , 000

1 .
20

3
Note:
This is not a good example for use with the Six Steps, since CCA (depreciation) is calculated straight-line over three years. This is then captured in the cash flows in
Step Two.

10.16

Step #1: - 90,000
 Step #2: +109,074
 Step #3: 0

Step #4: 0

Step #5: 0

Step #6: - 8,426

NPV = + 10,648

10.17
 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)

GAAP requires that sales be recorded on the income statement when made, not when cash is received (recorded as an Account Receivable on the B/S)
 GAAP also requires that we record cost of goods sold when the corresponding sales are made, regardless of whether we have actually paid our suppliers yet (costs recorded as an Account Payable on the
B/S)
 Finally, we have to buy inventory to support sales although we haven’t collected cash yet (Both inventory and accounts payable rise)

10.18

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

Depreciation itself is a non-cash expense, consequently, it is only relevant because it affects taxes

Depreciation tax shield = DT
C

D = depreciation expense

T
C
= corporation’s marginal tax rate

10.19
 Need to know which asset class for tax purposes

Declining Balance
 Multiply the undepreciated capital cost (UCC) by the CCA rate (from the Tax Act)
 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

10.20
PV
Tax Shield from CCA

UCC d dT c
 k

 
1

0 .
5 k
1
 k
 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)

10.21
PV of the Tax Shield from CCA Lost due to Salvage
PV
Tax Shield
Lost due to
Salvage

Salvage d dT c
 k

 
1

1 k

N



Where

S = Salvage value
 n = number of periods until the salvage value is realized

10.22

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?

10.23
Example: Depreciation and Salvage continued

The delivery and installation costs must be added to the initial cost of the asset and then depreciated
PV
Tax Shield from CCA


UCC

 d
110 , 000 dT c

 k
 
1
 k

0.20

0.40

0 .
20
1


0 .
5 k
0.10

 
1

0 .
5
1


0 .
10

.
10

28 , 000
PV
Tax Shield
Lost due to
Salvage

Salvage d dT c
 k

 
1

1 k

N

17 , 000

0.20

0.40

0 .
20

0.10

$ 2 , 558 .
95





1
1 .
10

6



10.24

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%.

10.25
Step #1: PV
Initial Cost
= - 1,000,000
Step #2: PV
After-tax
Cash Savings

N

  t


1 t
5 

1



1
 k

 t

T c
 


 
1.08
 t

180, 000
1.08

180, 000

1.08

2

180, 000

1.08

3

180, 000

1.08

4

180, 000

1.08

5

$718, 688
Step #3:
PV
Tax Shield from CCA


UCC

 d dT c

1 , 000 , 000

1
 k
 
1
 k

0.20

0.40

0 .
20

0 .
5 k
0.08

 
1

0 .
5
1


0 .
08

.
08

275 , 132

10.26
Step #4:
Step #5:
PV
Salvage

Salvage

1
 k

N

50 , 000

1 .
08

5

34 , 029
PV
Tax Shield
Lost due to
Salvage

Salvage

50 , 000 d dT c
 k

 
1

1 k

N



0.20

0.40

0 .
20

0.08

 
1
1 .
08

5



$ 9 , 723
Step #6:
PV

NWC
  
NWC

1
 k

N

0
 
NWC

1
 k

N

10.27
Step #1 -1,000,000
Step #2 718,688
Step #3 275,132
Step #4 34,029
Step #5 9,723
Step #6 0
NPV $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.

10.28

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%

10.29
Step #1: PV of Initial Cost less trade-in = -$150,000 + 65,000 = -85,000
Step #2: PV
After
 tax cos t savings

Annual Cost

Savings

1

T c



1


1
 k
  t k


50 , 000

1

0 .
40


1 .
10


5
0 .
10



$ 113 , 724
Step #3: PV
Tax Shield from CCA

UCC

85, 000

 d dT c
 k
 k  1
 k
   

 

$21,636



10.30
Step #4:
Step #5:
PV
Salvage

Salvage

1
 k

N

10 , 000

1 .
10

5

$ 6 , 209
PV
Tax Shield
Lost due to
Salvage

Salvage

10 , 000 d dT c
 k

 
1

1 k

N

0.20

0.40

0 .
20

0.10





1
1 .
10

5



$ 1 , 656
Step #6:
PV

NWC
  
NWC

1
 k

N

0
 
NWC

1
 k

N

10.31
Step #1 -85,000
Step #2 +113,724
Step #3 +21,636
Step #4 - 6,209
Step #5 +1,656
Step #6 0
NPV $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.

10.32
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?

10.33
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

10.34
Example #3: Equivalent Annual Cost Analysis
Machine A
Step #1: $150,000
Step #2:
Step #3:
PV cos ts

Annual Cost
 

1

T c





1

1 k
  t k





1
 
1.10
 
8
0.10









$208, 062
PV
Tax Shield from CCA


UCC

 d dT c
 k
150 , 000

 

0.20

0.40

0 .
20
1


1
0 .
5 k
 k
0.10

 
1

0 .
5

0 .
10

1

.
10

$ 38 , 182

10.35
Example #3: Equivalent Annual Cost Analysis
Step #4: PV
Salvage


0
0

1
 k

N
Step #5: PV
Tax Shield
Lost due to
Salvage

Salvage

0 d dT c
 k

 
1

1 k

N


Step #6: PV

NWC
  
NWC

1
 k

N

0
 
NWC

1
 k

N

10.36
Example #3: Equivalent Annual Cost Analysis
Machine B
Step #1: $100,000
Step #2: PV cos ts

Annual Cost
 

1

T c





1

1 k
  t k





1
 
1.10
 
6
0.10









$150, 256
Step #3:
PV
Tax from
Shield
CCA

UCC



 d dT c
 k
100 , 000



0 .
20
1


1
0 .
5
 k

0.20

0.40

0.10
k

$ 25 , 455



1

0 .
5

0 .
10

1

.
10 



10.37
Example #3: Equivalent Annual Cost Analysis
Step #4: PV
Salvage


0
0

1
 k

N
Step #5: PV
Tax Shield
Lost due to
Salvage

Salvage

0 d dT c
 k

 
1

1 k

N


Step #6: PV

NWC
  
NWC

1
 k

N

0
 
NWC

1
 k

N

10.38
Example #3: Equivalent Annual Cost Analysis
To calculate EAC, divide NPV by the annuity factor (see next page for the annuity factor)

10.39
EAC: Calculating the Annuity Factors

The formula for the PV of an ordinary annuity looks like this:
PV
Annuity

C


1


1
 k
  t 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:
Annuity Factor
A


5 .
33

1 .
10
 
8

.
10
Annuity Factor
B


4 .
36

1 .
10


6
.
10



10.40

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%

10.41
Step #1 $60,000
Step #2
PV cos ts

Annual Cost

1 T c


 
1

1 k
  t k


 
5 10, 000
 
24, 000
  x
  

$137, 488



1
 
1.20
 
4
0.20


Step #3
PV
Tax from
Shield
CCA

UCC




60 , 000


 d dT c
1

0 .
5 k
 k 1
 k

0.20

0.435

0 .
20

0.20

$ 11 , 963



1

0 .
5

0 .
20

1

.
20 



10.42
Step #4
Step #5
PV
Salvage

Salvage

1
 k

N

5 , 000

1 .
20

4

$ 2 , 411
PV
Tax Shield
Lost due to
Salvage

Salvage

5 , 000 d dT c
 k

 
1

1 k

N

0.20

0 .
435

0 .
20

0.20





1
1
.
20

4

$ 524


Step #6
PV

NWC
  
NWC

1
 k

N
 
 
40 , 000

40 , 000

1 .
20

4
 
20 , 710
NWC

1
 k

N

10.43
Step #1
Step #2
Step #3
Step #4
Step #5
Step #6
PV
Costs
-$60,000
-$137,488
+$11,963
+$2,411
-$524
-$20,710
-$204,348

10.44

To calculate the bid price, must now set the PV of costs equal to the PV of revenue
PV
Cost

204 , 348

PV
Revenue
5 P

1

T


1


1
 k
  t k


5 P

1

0 .
435


1 .
20
 
4

.
20
P

$ 27 , 942
P is equal to the required bid price per truck

10.45

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