Eight:
Net 8-1
Chapter Present Value and Capital
Budgeting
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Chapter Outline
8.1 Incremental Cash Flows
8.2 The Majestic Mulch and Compost Company:
An Example
8.3 The Boeing 777: A Real-World Example
8.4 Inflation and Capital Budgeting
8.5 A Capital Budgeting Simplification
8.6 Investments of Unequal Lives: The Equivalent
Annual Cost Method
8.7 Summary and Conclusions
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8.1 Incremental Cash Flows
Cash flows matternot accounting earnings.
Sunk costs dont matter.
Incremental cash flows matter.
Opportunity costs matter.
Side effects like erosion and synergy matter.
Taxes matter: we want incremental after-tax cash
flows.
Inflation matters.
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Cash FlowsNot Accounting Earnings
Consider depreciation expense.
You never write a cheque made out to
depreciation.
Much of the work in evaluating a project lies in
taking accounting numbers and generating cash
flows.
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8-5
Incremental Cash Flows
Sunk costs are not relevant
Just because we have come this far does not mean that
we should continue to throw good money after bad.
Opportunity costs do matter. Just because a project has a
positive NPV does not mean that it should also have
automatic acceptance. Specifically if another project with a
higher NPV would have to be passed up we should not
proceed.
Side effects matter.
If our new product causes existing customers to demand
less of current products, we need to recognize that fact
(erosion).
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Estimating Cash Flows
Cash Flows from Operations
Recall that:
Operating Cash Flow = EBIT Taxes +
Depreciation
Net Capital Spending
Dont forget salvage value (after tax, of course).
Changes in Net Working Capital
Recall that when the project winds down, we
enjoy a return of net working capital.
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Interest Expense
Later chapters will deal with the impact that the
amount of debt that a firm has in its capital structure
has on firm value.
For now, its enough to assume that the firms level
of debt (hence interest expense) is independent of
the project at hand.
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8.2 The Majestic Mulch and Compost
Company (MMCC): An Example
Costs of test marketing (already spent): $250,000.
The proposed factory site (which we own) has no resale value.
Cost of the tool making machine: $800,000 (CCA calculations are
based on a class 8, 20-percent rate).
Production (in units) by year during 8-year life of the machine:
6,000, 9,000, 12,000, 13,000, 12,000, 10,000, 8,000, and 6,000.
Price during first year is $100; price increases 2-percent per year
thereafter.
Production costs during first year are $64 per unit and increase at
the annual inflation rate of 5-percent per year thereafter.
Fixed production costs are $50,000 each year.
Working capital: initially $40,000, then 15-percent of sales at the
end of each year. Falls to $0 by the projects end.
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The Worksheet for Cash Flows of the
MMCC
(All cash flows occur at the end of the year.)
Year 0
Income:
(1) Sales revenues
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
$600,000 $918,000 $1,248,480 $1,379,570 $1,298,919 $1,104,081 $900,930 $689,211
Recall that production (in units) by year during 8-year life of the machine is
given by: (6,000, 9,000, 12,000, 13,000, 12,000, 10,000, 8,000, 6,000).
Price during first year is $100 and increases 2% per year thereafter.
Sales revenue in year 5 = 12,000[$100(1.02)4] = $1,298,919.
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The Worksheet for Cash Flows of the
MMCC (continued)
(All cash flows occur at the end of the year.)
Year 0
Income:
(1) Sales revenues
(2) Operating costs
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
$600,000 $918,000 $1,248,480 $1,379,570 $1,298,919 $1,104,081 $900,930 $689,211
434,000 654,800
896,720 1,013,144
983,509
866,820 736,129 590,327
Again, production (in units) by year during 8-year life of the machine is
given by: (6,000, 9,000, 12,000, 13,000, 12,000, 10,000, 8,000, 6,000).
Variable costs during first year (per unit) are $64 and (increase 5% per
year thereafter). Fixed costs are $50,000 each year.
Production costs in year 2 = 12,000[$64(1.05)4] + 50,000= $983,509.
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The Worksheet for Cash Flows of the
MMCC (continued)
(All cash flows occur at the end of the year.)
Year 0
Income:
(1) Sales revenues
(2) Operating costs
(3) CCA
Year 1
Year 2
Year 3
Year 5
Year 6
Year 7
Year 8
$600,000 $918,000 $1,248,480 $1,379,570 $1,298,919 $1,104,081 $900,930 $689,211
434,000 654,800
896,720 1,013,144
983,509
866,820 736,129 590,327
80,000 144,000
115,200
92,160
73,728
58,982 47,186 37,749
CCA calculations are based on
a class 8, 20% rate (shown at
right)
The machine cost $800,000.
CCA charge in year 5
=$368,640(.20) = $73,728.
McGraw-Hill Ryerson
Year 4
Annual CCA
Beginning
Ending
Year
UCC
CCA
UCC
1
$400,000 $80,000 $320,000
2
720,000 144,000 576,000
3
576,000 115,200 460,800
4
460,800 92,160 368,640
5
368,640 73,728 294,912
6
294,912 58,982 235,930
7
235,930 47,186 188,744
8
188,744 37,749 150,995
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The Worksheet for Cash Flows of the
MMCC (continued)
(All cash flows occur at the end of the year.)
Year 0
Income:
(1) Sales revenues
(2) Operating costs
(3) CCA
(4) EBIT
[(1) (2) - (3)]
(5) Taxes at 40%
(6) Net Income
McGraw-Hill Ryerson
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
$600,000 $918,000 $1,248,480 $1,379,570 $1,298,919 $1,104,081 $900,930 $689,211
434,000 654,800
896,720 1,013,144
983,509
866,820 736,129 590,327
80,000 144,000
115,200
92,160
73,728
58,982
47,186
37,749
86,000 119,200
236,560
274,266
241,682
178,278 117,615
61,136
34,400
51,600
47,680
71,520
94,624
141,936
109,707
164,560
96,673
145,009
71,311
106,967
47,046
70,569
24,454
36,682
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The Worksheet for Cash Flows of the
MMCC (continued)
(All cash flows occur at the end of the year.)
Investments:
(7) NWC (year end) $
40,000 90000.00 137700.00 187272.00 206935.56 194837.79 165612.12 135139.49 $
0
(8) Change in NWC
(40,000) (50,000) (47,700) (49,572) (19,664) 12,098
29,226
30,473
135139.49
(9) Equipment
-800000.00
(10) Salvage
150000.00
(11) Total cash flow
-840000.00 (50,000) (47,700) (49,572) (19,664) 12,098
29,226
30,473
285139.49
of investment
[(8) + (9) + (10)]
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Incremental After Tax Cash Flows
(IATCF) of the MMCC
(All cash flows occur at the end of the year.)
Year 0
(1) Sales
revenues
(2) Operating
costs
(3) Taxes
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
$600,000 $918,000 $1,248,480 $1,379,570 $1,298,919 $1,104,081 $900,930 $689,211
$434,000 $654,800 $ 896,720 $1,013,144 $ 983,509 $ 866,820 $736,129 $590,327
34,400
47,680
94,624
109,707
96,673
71,311
47,046
24,454
(4) OCF
131,600
[(1) - (2) - (3)]
(5) Total CF of (840,000) (50,000)
Investment
(6) IATCF
(840,000) 81,600
[(4) + (5)]
215,520
257,136
256,720
218,737
165,949
117,755
74,430
(47,700)
(49,572)
(19,664)
12,098
29,226
30,473
285,139
167,820
207,564
237,056
230,835
195,175
148,228
359,570
NPV@4%
$500,135
NPV@10%
$188,042
NPV@15%
$2,280
NPV@20%
($137,896)
IRR
15.07%
McGraw-Hill Ryerson
If the projects
discounting rate is
above 15.07%,
it should not be
accepted (since
NPV > 0).
2005 McGrawHill Ryerson Limited
8-15
8.3 The Boeing 777: A Real-World Example
In late 1990, the Boeing Company announced its intention to
build the Boeing 777, a commercial airplane that could carry
up to 390 passengers and fly 7,600 miles.
Analysts expected the up-front investment and R&D costs
would be as much as $8 billion.
Delivery of the planes was expected to begin in 1995 and
continue for at least 35 years.
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Table 8.5 Incremental Cash Flows: Boeing 777
Sales Operating
Year Units Revenue Costs Dep.
1991
$865.00
1992
1993
1,340.00 96.00
1,240.00 116.40
1994
1995 14 $1,847.55
1996 145 19,418.96
1997 140 19,244.23
Taxes
Capital Invest- Net Cash
NWC Spending ment
Flow
$40.00 $(307.70)
840.00 124.76
1,976.69 112.28
17,865.45 101.06
16,550.04 90.95
$400.00 $400.00 $(957.30)
(488.24)
(461.18)
600.00
300.00
600.00 (1,451.76)
300.00 (1,078.82)
(328.02)
(82.08) 1 8 1 .0 6
493.83 1 ,7 2 2 .0
0
885.10 ( 1 7 .1 2 )
200.00 200.00 (711.98)
1.85 182.91 (229.97)
19.42 1,741.42
681.74
19.42
2.30 1,806.79
Net Cash Flow can be determined in three steps:
Taxes ($19,244.23 $16,550.04 $90.95)0.34 = $885.10
Investment
NCF
$17.12 + $19.42 = $2.30
$19,244.23 $16,550.04 $885.10 $2.30 = $1,806.79
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Year
NCF
1991 $
Year
NCF
Year NCF
(957.30)
2002 $ 1,717.26
2013 $ 2,213.18
1992 $ (1,451.76)
2003 $ 1,590.01
2014 $ 2,104.73
1993 $ (1,078.82)
2004 $ 1,798.97
2015 $ 2,285.77
1994 $
(711.98)
2005 $
616.79
2016 $ 2,353.81
1995 $
(229.97)
2006 $ 1,484.73
2017 $ 2,423.89
1996 $
681.74
2007 $ 2,173.59
2018 $ 2,496.05
1997 $ 1,806.79
2008 $ 1,641.97
2019 $ 2,568.60
1998 $ 1,914.06
2009 $
677.92
2020 $ 2,641.01
1999 $ 1,676.05
2010 $ 1,886.96
2021 $ 2,717.53
2000 $ 1,640.25
2011 $ 2,331.33
2022 $ 2,798.77
2001 $ 1,716.80
2012 $ 2,576.47
2023 $ 2,882.44
2024 $ 2,964.45
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8.3 The Boeing 777: A Real-World Example
Prior to 1990, Boeing had invested several hundred
million dollars in research and development.
Since these cash outflows were incurred prior to the
decision to build the plane, they are sunk costs.
The relevant costs were the at the time the decision
was made were the forecasted Net Cash Flows
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NPV Profile of the Boeing 777 Project
NPV
$60,000
$50,000
$40,000
$30,000
IRR = 21.12%
$20,000
$10,000
$0
($10,000)
0%
10%
20%
30%
40%
50%
Discounting Rate
This graph shows NPV as a function of the discounting rate.
Boeing should accept this project at discounting rates less
than 21 percent and reject the project at higher discount
rates.
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Boeing 777
As it turned out, sales failed to meet expectations.
In fairness to the financial analysts at Boeing, there
is an important distinction between a good decision
and a good outcome.
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8.4 Inflation and Capital Budgeting
Inflation is an important fact of economic life and must be
considered in capital budgeting.
Consider the relationship between interest rates and
inflation, often referred to as the Fisher relationship:
(1 + Nominal Rate) = (1 + Real Rate) (1 + Inflation Rate)
For low rates of inflation, this is often approximated as
Real Rate Nominal Rate Inflation Rate
While the nominal rate in the U.S. has fluctuated with
inflation, most of the time the real rate has exhibited far less
variance than the nominal rate.
When accounting for inflation in capital budgeting, one must
compare real cash flows discounted real at rates or nominal
cash flows discounted at nominal rates.
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Example of Capital Budgeting under Inflation
Canadian Electronics Inc. (CEI) has an investment opportunity to produce a
new stereo colour TV.
The required investment on January 1 of this year is $32 million. CCA
calculations are based on a class 8, 20% rate. The firm is in the 34% tax
bracket.
This investment will have no resale value at the end of the project (in four
years).
The price of the product on January 1 will be $400 per unit. The price will stay
constant in real terms.
Labour costs will be $15 per hour on January 1. The will increase at 2% per
year in real terms.
Energy costs will be $5 per TV; they will increase 3% per year in real terms.
The inflation rate is 5%.
Revenues are received and costs are paid at year-end.
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Example of Capital Budgeting under
Inflation (continued)
Year 1
Year 2
Year 3
Year 4
Physical
Production
(units)
100,000
200,000
200,000
150,000
Labour Input
(hours)
2,000,000
2,000,000
2,000,000
2,000,000
Energy input,
physical units
200,000
200,000
200,000
200,000
The riskless nominal discounting rate is 4%.
The real discounting rate for costs and revenues is 8%. Calculate the
NPV.
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A Capital Budgeting Simplification
Operating Cash Flow After Taxes = Revenues - Expenses - Taxes
Where
Taxes = TC (Revenues - Expenses - CCA)
TC is the tax rate.
CCA is the Capital Cost Allowance (depreciation for tax
purposes).
Operating Cash Flow After Taxes
= Revenues - Expenses - TC (Revenues - Expenses - CCA)
= (1-TC)Revenues - (1-TC)Expenses + TC *CCA
After Tax Revenues After Tax Expenses
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CCA Tax Shield
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8.5 A Capital Budgeting Simplification
Present Value of the Tax Shield on CCA
The PV of CCA tax shield is a perpetuity, with an
adjustment for
the 1st year 50-percent rule
the sale of the asset at the time when the project is terminated
The PV of CCA tax shield is given by:
PVCCA Tax Shield
C d Tc [1 + 0.5k ] S d Tc
1
=
n
k +d
1+ k
k +d
(1 + k )
S = Min[resale value of assets, original price of assets]
C = original price of the assets
d = depreciation rate that applies to the asset class
k= discounting rate
n = the time when assets are sold
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Salvage
Warning: The formula in the text (and on the previous slide)
assumes that S < original cost.
According to Canadian tax law, when an asset is sold for S,
the UCC in its asset class should be reduced by:
Min(S, Original Cost of Asset)
So, that is what should appear in the formula in the general
case.
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Example of Capital Budgeting under
Inflation (continued)
The depreciation tax shield is a risk-free nominal cash flow, and
is therefore discounted at the nominal riskless rate.
Cost of investment today: C = $32,000,000
Project life: n = 4 years
Class 8 depreciation rate: d = 20%
Asset resale value: S = 0
Finally: k = 0.04 and TC = 0.34
The PV of CCA tax shield is given by:
PVCCA Tax Shield =
32,000,000 .2 .34 [1 + (.5 .04] 0 .2 .34
1
=
4
.04 + .2
1.04
.04 + .2 (1.04 )
= $8,892,308
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Example of Capital Budgeting under
Inflation (continued)
Risky Real Cash Flows
Price: $400 per unit with zero real price increase
Labour: $15 per hour with 2% real wage increase
Energy: $5 per unit with 3% real energy cost increase
Year 1 After-tax Real Risky Cash Flows:
After-tax revenues =
$400 100,000 (1-.34) = $26,400,000
After-tax labour costs =
$15 2,000,000 1.02 (1-.34) = $20,196,000
After-tax energy costs =
$5 2,00,000 1.03 (1-.34) = $679,800
After-tax net operating CF =
$26,400,000 - $20,196,000 - $679,800 =$5,524,200
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Example of Capital Budgeting under
Inflation (continued)
Year One After-tax revenues = $400 100,000 (1-.34) = $26,400,000
Year One After-tax labour costs = $15 2,000,000 1.02 (1-.34) = $20,196,000
Year One After-tax energy costs = $5 2,00,000 1.03 (1-.34) = $679,800
Year One After-tax net operating CF =$5,524,200
$5,524,200
0
$31,499,886
1
$31,066,882
2
3
$17,425,007
4
$32,000,000
$5,524,200 $31,499,886 $31,066,882 $17,425,007
+
+
+
2
3
(1.08)
(1.08)
(1.08)
(1.08) 4
= $69,590,868
PVrisky CashInflows =
PVrisky CashInflows
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Example of Capital Budgeting under
Inflation (continued)
The project NPV can now be computed as the sum of the PV
of the cost, the PV of the risky cash flows discounted at the
risky rate, and the PV of the risk-free CCA tax shield cash
flows discounted at the risk-free discounting rate.
NPV = -$32,000,000 + $69,590,868 + $8,892,308 = $46,483,176
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Salvage
Observe that CCA tax shield formula uses a riskless nominal
discounting rate in a term involving the salvage value of the
asset:
PVCCA Tax Shield
C d Tc [1 + 0.5k ] S d Tc
1
=
n
k +d
1+ k
k +d
(1 + k )
This is a simplification. The salvage value is probably not
known for sure in advance.
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Salvage and Tax (Ch. 8 Appendix)
Does the firm pay tax on the received salvage value? Is the
appropriate term to add to the NPV:
S/(1+r)N or
(1-TC)S/(1+r)N ?
The answer is more complicated, and depends on the tax
laws. In Canada, the following rule applies when there are
still other assets in the same CCA class:
If S < Original cost, no tax: use S/(1+r)N
If S > Original cost, pay tax on 1/2 of the of the capital
gain: use S/(1+r)N - 0.5(TC)(S-Cost)/(1+r)N
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Salvage and Tax
The general formula for the PV of the salvage payment then
becomes:
S 0.5TC max(S Original Cost,0)
(1 + r ) N
Things are even more complicated when closing out a CCA
pool:
If it ends with a negative balance, the corporation must
pay tax on this amount.
If it ends with a positive balance, a loss is recorded,
which can be used to reduce taxes.
See the chapter appendix for more details.
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8.6 Investments of Unequal Lives: The
Equivalent Annual Cost Method
There are times when application of the NPV rule can lead
to the wrong decision. Consider a factory that must have an
air cleaner. The equipment is mandated by law, so there is
no doing without.
There are two choices:
The Cadillac cleaner costs $4,000 today, has annual
operating costs of $100 (real terms) and lasts for 10
years.
The cheaper cleaner costs $1,000 today, has annual
operating costs of $500 (real terms) and lasts for five
years.
Which one should we choose, given a real interest rate of
10%?
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8.6 Investments of Unequal Lives: The
Equivalent Annual Cost Method (continued)
The Cadillac cleaner time line of cash flows:
$4,000100100100100100100100100100
100
012345678910
10
NPVCadillac = $4,000
t =1
$100
= 4,614.46
t
(1.10)
The cheaper cleaner time line of cash flows over 10 years:
$1,0005005005005001,500500500500500500
012345678910
NPVcheap
$500 $1,000 10 $500
= $1,000
= $4,693.20
t
5
t
(1.10) t =6 (1.10)
t =1 (1.10)
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8.6 Investments of Unequal Lives: The
Equivalent Annual Cost Method (continued)
At first glance, the cheap cleaner has the lower NPV ( r = 10%):
NPVCadillac
NPVcheap
10
$100
= $4,000
= 4,614.46
t
t =1 (1.10)
5
$500
= $1,000
= 2,895.39
t
t =1 (1.10)
This overlooks the fact that the Cadillac cleaner lasts twice as
long.
When we incorporate that, the Cadillac cleaner is actually
cheaper.
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Investments of Unequal Lives
Replacement Chain
Repeat the projects forever, find the PV of that
perpetuity.
Assumption: Both projects can and will be
repeated.
Matching Cycle
Repeat projects until they begin and end at the
same timelike we just did with the air
cleaners.
Compute NPV for the repeated projects.
The Equivalent Annual Cost Method
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Investments of Unequal Lives: EAC
The Equivalent Annual Cost Method
Applicable to a much more robust set of circumstances
than replacement chain or matching cycle.
The Equivalent Annual Cost is the value of the level
payment annuity that has the same PV as our original set
of cash flows.
NPV = EAC ArT
For example, the EAC for the Cadillac air cleaner is
$750.98
10
10
$100
$750.98
$4,000
= 4,614.46 =
t
t
t =1 (1.10)
t =1 (1.10)
The EAC for the cheaper air cleaner is $763.80
which confirms our earlier decision to reject it.
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Example of Replacement Projects
Consider a Belgian Dentists office; he needs an autoclave to
sterilize his instruments. He has an old one that is in use, but
the maintenance costs are rising and so he is considering
replacing this indispensable piece of equipment.
New Autoclave
Cost = $3,000 today,
Maintenance cost = $20 per year (real dollars)
Resale value after 6 years = $1,200 (real dollars)
NPV of new autoclave (at real rate r = 10%):
6
$20
$1,200
$2,409.74 = $3,000
+
t
(1.10) (1.10) 6
t =1
EAC of new autoclave = -$553.29
$553.29
$2,409.74 =
(1.10) t
t =1
6
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Example of Replacement Projects
Existing Autoclave
Year
0
Maintenance
0
Resale
900
Total Annual Cost
1
200
850
340
2
275
775
435
3
325
700
478
4
450
600
620
5
500
500
660
Total Cost for year 1 = (900 1.10 850) + 200 = $340
Total Cost for year 2 = (850 1.10 775) + 275 = $435
Total Cost for year 3 = (775 1.10 700) + 325 = $478
Total Cost for year 4 = (700 1.10 600) + 450 = $620
Total Cost for year 5 = (600 1.10 500) + 500 = $660
Note that the total cost of keeping an autoclave for the first year
includes the $200 maintenance cost as well as the opportunity cost of
the foregone future value of the $900 we didnt get from selling it in
year 0 less the $850 we have if we still own it at year 1.
McGraw-Hill Ryerson
2005 McGrawHill Ryerson Limited
8-41
Example of Replacement Projects
New Autoclave
EAC of new autoclave = -$553.29
Existing Autoclave
Year
0
1
2
3
Maintenance
0
200
275
325
Resale
900
850
775
700
435
478
Total Annual Cost
340
4
450
600
620
5
500
500
660
We should keep the old autoclave until its cheaper to buy
a new one.
Replace the autoclave after year 3: at that point the new
one will cost $553.29 for the next years autoclaving and
the old one will cost $620 for one more year.
McGraw-Hill Ryerson
2005 McGrawHill Ryerson Limited
8-42
8.7 Summary and Conclusions
Capital budgeting must be placed on an incremental basis.
Sunk costs are ignored
Opportunity costs and side effects matter
Inflation must be handled consistently
Present value real flows at real rates
Present value nominal flows at nominal rates
When a firm must choose between two machines of unequal
lives:
the firm can apply either the matching cycle approach
or the equivalent annual cost approach
McGraw-Hill Ryerson
2005 McGrawHill Ryerson Limited