Capital Budgeting
One of the basic financial management issues is
which long-term investments the company will
make. The process of making these decisions is
called capital budgeting.
The basic method of doing this is:
 identify a possible investment opportunity or
project
 analyze the relevant cash flows that the
project will generate
 apply one or more decision criteria to those
projected cash flows
 if the proposed project exceeds the decision
criteria, proceed with the project
The decision criteria that we will look at include;
NPV, IRR, MIRR, payback, discounted payback,
AAR and PI.
K. D. Brewer 2008
Page 4-11
Net Present Value
From a finance point of view this is the best of
the decision criteria. The basic idea is that once
we have identified all of the cash flows that are
going to be generated, if we accept a project, we
simply take the present value of those cash
flows. If the total of these discounted cash flows
is positive then the project should increase the
value of the firm. This form of analysis is also
called Discounted Cash Flow valuation (DCF).
The only noticeable problem with NPV is
determining the appropriate discount rate. The
most appropriate discount rate that the firm
should consider is the cost of financing the
investment that is required. If the firm can raise
capital to pay for the investment at 12%, they
should discount the project's cash flows at 12%.
This 12% is called the firm's cost of capital.
K. D. Brewer 2008
Page 4-22
NPV Example
DCF Inc. is considering a capital budgeting
proposal to invest in a small business.
 It would cost $50,000 to start this business.
 The business is expected to generate $5,000
per year for 5 years.
 Five years from now the business can be
sold for $75,000.
 DCF's cost of capital for this venture is 15%.
According to the NPV criteria, should DCF invest
in this project?
 The PV of the cost is -$50,000.
 $5,000 per year for 5 years is an ordinary
annuity with a PV of $16,761
 $75,000 5 years from now is worth $37,288
 The total is $4,049.
Since the NPV is greater than zero, DCF should
invest in this project.
The project should
increase the value of DCF by $4,049.
K. D. Brewer 2008
Page 4-33
IRR
When talking about investment opportunities,
many people like to talk in terms of rates of
return. IRR, the internal rate of return, finds a
single rate of return to summarize the merits of a
project. To do this, we set up a NPV style
calculation and solve for the discount rate that
sets the NPV equal to zero. If the IRR is greater
than the firm's required rate of return the project
should be accepted.
Since we often have a long series of cash flows
for a single project, we can't easily solve for IRR
directly. Therefore we use a spreadsheet tool or
trial and error, like we did for YTM.
This is the rate of return we would have to make
on a deposit to be able to afford the cash flows
of the project.
Note: if the initial investment is negative, IRR is
a cost of funds not a return on investment.
K. D. Brewer 2008
Page 4-44
IRR Example
Using the previous example, solver generates an
IRR of 17.11%. This is higher than DCF's cost of
capital of 15% so IRR suggests that DCF should
accept this investment project since it has a
higher rate of return than their cost.
IRR=
17.11%
Year
Cash Flow
DCF
0
(50,000.00)
(50,000.00)
1
5,000.00
4,269.40
2
5,000.00
3,645.56
3
5,000.00
3,112.87
4
5,000.00
2,658.02
5
80,000.00
36,314.14
NPV=
(0.00)
Note that for year 5, the $5,000 annual cash flow
and the selling price were added together to give
a net cash flow for the year.
K. D. Brewer 2008
Page 4-55
NPV Profile
When using the trial and error approach to
solving for IRR, we can generate a large number
of NPVs. If we plot those we will get the NPV
profile.
NPV Profile
60,000
50,000
40,000
NPV
30,000
20,000
10,000
(10,000)0%
10%
20%
30%
40%
(20,000)
(30,000)
Discount rate
The project that this curve is based on has an
initial investment of $50,000 and net cash flows
of $10,000 per year for ten years with no
salvage value.
K. D. Brewer 2008
Page 4-66
Problems with IRR
1. Changing decision criteria: if the initial cash flow
is negative, IRR becomes a cost of funds
instead of a rate of return, therefore you want to
accept a proposal if it's IRR is less than your
cost of capital.
2. Multiple solutions: whenever a project has nonconventional cash flows, there can be more than
one IRR. Non-conventional cash flows are any
time the sign of the net cash flow changes more
than once.
3. Mutually exclusive projects: if accepting one
project means that you can't do another project,
the two projects are mutually exclusive. IRR can
give the wrong decision for two reasons, scale
and the reinvestment assumption.
K. D. Brewer 2008
Page 4-77
Non-conventional Cash
Flows
Blue Sky Mines is considering starting a new
open-pit mine. The start up costs are $5m, the
mine should generate $1m per year for the next
30 years, after that the environmental cleanup
costs are estimated at $6m per year for 5 years.
What is the IRR of this project?
The project has non-conventional cash flows
because the first cash flow is negative, cash
flows are then positive for 30 years before
turning negative again.
If you use solver and start with an initial guess
IRR of 5% or greater, you will find an IRR of
19.57%. If your initial guess is around 1% then
solver will come back with an IRR of 1.26%.
K. D. Brewer 2008
Page 4-88
What Happened?
We can see what is happening if we plot the
NPV profile.
NPV Profile
6
4
NPV
2
0
0%
5%
10%
15%
20%
25%
30%
-2
-4
-6
Discount Rate
IRR = 1.26% or IRR = 19.57%
Maximum = $4.4m at r = 5.5%
Minimum = -$5m at r = 0% or r infinity
You might notice that if the BSM analyst had
found the IRR of 1.26%, the analyst would
recommend not accepting the project.
K. D. Brewer 2008
Page 4-99
Dealing with NCF
There are a few ways of dealing with nonconventional cash flows.
1. You could assume that the company is going to
set up a reserve to pay for the cleanup costs.
This could either be a lump sum added to the
initial investment or a regular amount every
year, reducing the cash flows. Assume that this
money earns the company's cost of capital and
that the FV is equal to the PV of the cleanup
costs at year 30.
2. Plot the NPV profile and note that the project is
recommended between the two IRRs.
3. Just use the NPV for the company's cost of
capital.
K. D. Brewer 2008
Page 4-10
10
Mutually Exclusive
Some projects will compete for the same
resources. For example a property development
company owns a plot of land and is evaluating
two proposals. One is to develop the land as a
mall, the other is to build a sub-division on the
property. Obviously only one of the projects can
be accepted. How do you decide which one?
With NPV the choice is obvious, the one with the
higher NPV adds the most value to the
company. With IRR the one with the higher IRR
may not be as good as the lower IRR for
reasons of scale or reinvestment assumptions.
The scale problem is easily demonstrated.
Which one period investment is worth more, a
100% rate of return on $10, or a 30% return on
$1,000? The 100% return gets a profit of $10
while the 30% earns $300, 30 times the return of
the other project!!!
K. D. Brewer 2008
Page 4-11
11
Reinvestment Assumption
IRR implicitly assumes that you can reinvest any
early cash flows at the IRR. Therefore you can
use them in present value calculations but not in
future value calculations because the value of
the investment that is earning the IRR changes
over time.
You are trying to choose between two projects,
both cost $1m and have a life of 5 years.
Project A has a net cash flow of $1.3m in year 1
and breaks even in the other years. Project B
breaks even in all years except year 5, which
has a net cash flow of $3m. What are the IRRs?
Which is the better project if your cost of capital
is 15%?
Project A has an IRR of 30% and a NPV of
$130,435. Project B has an IRR of 24.6% and a
NPV of $491,530. Project B is better.
K. D. Brewer 2008
Page 4-12
12
Why is IRR Used?
 When talking about investment opportunities,
many people like to talk in terms of rates of
return. IRR is expressed as a rate of return;
NPV is a dollar value.
 If you aren't sure of the exact rate of return that
you require on a project, IRR can be used. If
you are entering a new industry or market you
may not know exactly how much it is going to
cost to raise the necessary capital for the
investment.
 For conventional investment projects that are
not mutually exclusive, IRR is well behaved and
comes to the same conclusion as NPV. Most
projects fall into that category.
 The trial and error needed to find the IRR is
simple to do on a computer.
K. D. Brewer 2008
Page 4-13
13
MIRR
The modified internal rate of return addresses one
of the problems of IRR. MIRR removes the
implied reinvestment assumption from IRR but
adds the requirement that you know the cost of
capital as you do with NPV.
What MIRR does is to find the discount rate that
sets the initial cost of the project equal to the
present value of the future value of the project's
cash flows, reinvested at the company's cost of
capital.
Each cash flow is future valued to the end of the
project's life at the cost of capital. This future
value is then treated as a lump sum and
compared to the initial investment. You can
them solve for MIRR.
FVCF  I 0  1  MIRR 
t
K. D. Brewer 2008
Page 4-14
14
MIRR Example
Under "reinvestment assumption" we compared
two projects, A and B. Both projects cost $1m,
and last for 5 years. Project A has a cash flow of
$1.3m in one year. Project B has a cash flow of
$3m in five years. All other net cash flows were
zero. The cost of capital was 15%.
Project A's cash flow is future valued to the end
of year 5.
$1.3m x (1 + 0.15) 4 = $2.27m
We then set the present value equal to the initial
investment of $1m and solve for IRR.
$2.27 = $1 x (1 + MIRR) 5
MIRR = 17.8%
Project B's cash flow occurs at the end of year 5
so the IRR of 24.6% calculated earlier is fine.
MIRR comes to the same conclusions as NPV.
K. D. Brewer 2008
Page 4-15
15
Payback
This simple decision criteria measures how long
a project takes to generate cash flows equal to
the initial investment. If this period is shorter
than an arbitrary value, the project is acceptable.
All cash flows after the payback period are
ignored. A project that costs $50,000 and
generates net cash flows $20,000 per year will
have a payback period of 2.5 years. This
payback period will not change if the project
ends at that point or continues indefinitely.
Payback is easy to understand, doesn't require
forecasting of distant cash flows, and is biased
towards liquidity.
Payback ignores the time value of money, has a
cutoff value that is arbitrary, ignores all cash
flows after the payback period (positive or
negative) and is biased against long term
projects.
K. D. Brewer 2008
Page 4-16
16
Discounted Payback
This rule discounts the future cash flows before
applying the payback criteria. As such it does
not ignore the time value of money, but all of the
other problems of payback remain.
Consider a project that costs $500 and earns
$200 per year for 4 years. What is the payback
period and discounted payback period if the firm
has a cost of capital of 10%?
Year
0
1
2
3
4
CF
-500
200
200
200
200
net
-500
-300
-100
100
300
DCF
-500
182
165
150
137
net
-500
-318
-153
-3
134
This project has a payback period of 2.5 years
and a discounted payback of 3.02 years (3/137).
Note: A $500 shutdown cost in year 5 wouldn't
affect the payback decision.
K. D. Brewer 2008
Page 4-17
17
AAR
The average accounting return is another possible
capital budgeting decision criteria. AAR takes
the average net income of the project and
divides that by the average book value of the
project's assets. A project costs $40,000 with no
salvage value that generates a net income of
$5,000 per year for 5 years, has an AAR of 25%
AAR 
average NI
5,000

 25%
average book value 40,000  2
Note: the net income used in the calculation
includes depreciation of the initial investment.
This looks like a rate of return, but it isn't. The
calculation ignores the time value of money. If
the net income was variable, the AAR would not
change.
Also, AAR looks at accounting numbers rather
than cash flows.
K. D. Brewer 2008
Page 4-18
18
Profitability Index
Also known as the benefit/cost ratio, the PI takes
the present value of the project's cash flows and
divides that by the initial investment. If the
profitability ratio is greater than 1, the project is
acceptable. This is very similar to NPV. NPV
subtracts the initial investment, PI divides by it.
If the initial investment is less than the present
value of the project's cash flows, both NPV and
PI will find the project to be acceptable.
The profitability index (minus 1) can be thought
of as the rate of return in excess of the required
rate of return, similar to the real rate of return
adjustment for inflation. This rate of return can
be used to rank projects on a "bang for the
buck" basis.
Since the PI is a ratio, it has the same problem
with scale as IRR when dealing with mutually
exclusive projects.
K. D. Brewer 2008
Page 4-19
19
PI Example
DCF Inc. is considering a capital budgeting
proposal to invest in a small business.
 It would cost $50,000 to start this business.
 The business is expected to generate $5,000
per year for 5 years.
 Five years from now the business can be
sold for $75,000.
 DCF's cost of capital for this venture is 15%.
What is the profitability index for this project?
 $5,000 per year for 5 years is an ordinary
annuity with a PV of $16,761
 $75,000 5 years from now is worth $37,288
 dividing by $50,000 gives a PI of 1.081
The profitability index is 1.081, which is greater
than one so the project should be accepted. If
we subtract one we can see that DCF would
earn 8.1% above their cost of capital with this
project.
K. D. Brewer 2008
Page 4-20
20
CB in Practice
So, what is generally used in practice?
The results of a survey of 392 CFO’s appears in
table 9.5.
IRR and NPV are used the most, followed by
payback period. Discounted payback and ARR
are still used by a minority, while PI is used by
less than 12%.
Most use multiple methods; NPV, IRR, and
payback add up to over 200%.
Previous editions had an older survey that had a
breakdown by types of project. IRR was used
more often in conventional not mutually
exclusive investment proposals, while NPV
dominated dis-investment proposals and leasing
proposals. No decision criteria was used for
social proposals.
K. D. Brewer 2008
Page 4-21
21
Multiple Methods
Why would a firm use multiple decision criteria?
Why is payback so widely used?
The answers to these questions are related.
 The cash flows of the investment opportunity
are based on estimates of sales or possible
cost reductions.
 Sales estimates especially have a tendency
of being overly optimistic.
 If several decision criteria recommend the
project it is probably a good idea.
 If the criteria disagree, the project should be
examined more closely.
 Payback is biased towards liquidity and it is
often used for small projects that can't justify
the cost of a more in depth analysis.
K. D. Brewer 2008
Page 4-22
22
Relevant Cash Flows
So far the cash flows relevant to the project
have been clearly specified.
How do we decide which cash flows to include?
The basic rule is that if a cash flow would occur
if the firm does not accept the project, that cash
flow is not relevant to the project. Only changes
in cash flows that occur if the firm accepts the
project should be considered. This is known as
incremental cash flows.
Cash flows can include: new revenue streams
generated by the project (+ve), expenses that
were avoided by accepting the project (+ve),
new expenses caused by the project (-ve), and
any revenues that the firm would have received
if the project was rejected (-ve).
K. D. Brewer 2008
Page 4-23
23
Sunk Costs
Any cost that has already been incurred and can
not be reversed if the firm chooses not to
proceed with the project is a sunk cost and is not
a relevant cash flow for the project, even if that
cost is directly tied to the project.
An example of this is a market research study
that was commissioned to forecast the cash
flows of the proposed project is a cost that is
going to have to be paid even if the firm decides
not to go ahead with the project.
A sunk cost need not to have been paid before
the start of the project if the liability for that cost
has been incurred and will not be changed by
the project. This can include the allocation of
overhead to the project for cost accounting
purposes where those costs are not affected by
the acceptance of the project.
K. D. Brewer 2008
Page 4-24
24
Opportunity Costs
If the firm bought a property several years ago
for $20,000 and is now considering a proposal
that would use that piece of land there will be no
cash flow to purchase the land. The land has a
current market value of $35,000. How should
the land be valued for capital budgeting
purposes?
From an accounting stand point, the $20,000
historical cost is what would get charged to the
project for the book value calculations. However
from a finance stand point the $20,000 is a sunk
cost and therefore not a relevant cash flow for
the project.
If the firm does not proceed with the project they
can sell it for $35,000 (less costs). Accepting
the project precludes this possibility. $35,000
(less costs) is referred to as an opportunity cost.
The firm loses the opportunity to sell the land so
this is a lost cash flow.
K. D. Brewer 2008
Page 4-25
25
Side Effects
ADC Inc. currently has three products with a
combined market share of 60% in a certain
category. A proposed new product in that same
category is forecast to gain a 50% market share.
Obviously some of those sales are going to
come at the expense of ADC's other product
lines. This effect on other cash flows of the
company is referred to as erosion, piracy or
cannibalism. This effect on the other product
lines should be included in the estimates of the
cash flows that are relevant to the proposal.
The side effects of a project don't have to be
negative. If a new product would increase
demand for an existing product, that beneficial
effect should be included. For example a
company that makes lawn tractors may see
beneficial side effects for adding a snow blower
attachment for their machines.
K. D. Brewer 2008
Page 4-26
26
Working Capital
If the company launches a new product line,
there is likely to be a new category of inventory
created. Some of this inventory will have been
received before they have to make payment
(accounts payable). It is also likely that some of
the goods that they have sold were sold on
credit and the company has not yet received
payment (accounts receivable). The inventory +
receivables - payables = net working capital.
This commitment of assets is a requirement of
proceeding with the project, so it is a relevant
cash flow. If the project is of a limited duration,
then the net working capital will be freed up as
the project winds down and would become a
positive terminal cash flow.
Net working capital can be negative in the case
of a new inventory management system.
K. D. Brewer 2008
Page 4-27
27
Financing Costs
How the money to finance the project is raised is
not relevant to the project in terms of cash flows.
Therefore, any interest, principal or dividend
payments that are related to the financing of the
project are not relevant cash flows for capital
budgeting purposes.
The major reason for this is that the cost of
financing the project is already reflected in the
discount rate used in NPV, MIRR, DPB and PI,
and is also the benchmark rate used for IRR. If
we included the cost of financing in the cash
flows as well, we would be counting that cost
twice.
What if the company can get a no interest loan
from the government for the project? In that
case the difference between the amount
received and the amount that would have been
received with alternative financing is a positive
cash flow for the company.
K. D. Brewer 2008
Page 4-28
28
Inflation
When we were looking at bonds, we noted that
the rate of inflation had an impact on the rate of
return that potential investors demanded before
they would invest in a security. This was called
the Fisher effect.
The discount rate is that we are using is based
upon the rate of return the company has to
promise to convince investors to invest in the
company. Therefore the effect of inflation has
been incorporated the discount rate. As a result,
we should adjust the projected cash flows for the
expected rate of inflation as well. If we don't do
that then we will bias the decision making
process against long term projects.
K. D. Brewer 2008
Page 4-29
29
Government Intervention
The various levels of government can have an
impact on the cash flows of a project.
This impact can be quite noticeable and direct in
the case of grants and tax credits. The benefits
associated with subsidized loans and favorable
tax treatment can also be calculated. In the
case of grants, the grant is a positive cash flow.
An investment tax credit is also a positive cash
flow since it negates a negative cash flow,
though it may reduce future tax deductions
which would have to be accounted for as well. A
subsidized loan can also be seen as a cash
inflow, being the difference between how much
we can borrow vs. how much we could borrow
without the subsidy if we made the required
payments.
Government intervention can be negative as
well, with specific taxes and regulations that
make a project more expensive.
K. D. Brewer 2008
Page 4-30
30
Pro Forma Statements
One method of evaluating a project is to take the
forecasted revenues and costs and plug those
into projected or pro forma financial statements. If
you are very comfortable with accounting or are
planning to calculate AAR, these pro forma
statements are very useful. From a finance
point of view, I find them of somewhat limited
use. A major reason that I find them of limited
use is that they add accounting items such as
depreciation and then have to back them out to
get the project cash flows. I find it easier to just
calculate the cash flows directly.
With a pro forma statement, you would construct
an income statement using: sales - COGS other costs - depreciation - taxes = net income.
You would also construct a depreciation
schedule for the assets in use. To get the cash
flows you add back depreciation.
K. D. Brewer 2008
Page 4-31
31
Accounting Difficulties
There are several other problems with using
accounting numbers in capital budgeting, and
many of them revolve around a central concept
of accounting, the matching principal. With the
matching principal, accounting tries to match the
timing of the revenue with the expense, ignoring
the time value of money. A firm selling washing
machines that come with a 7-year warrantee will
declare a warrantee expense in the year of sale
that is an estimate of how much the firm will
spend on covered repairs even though they will
not actually spend all of that money for 7 years.
Accounting numbers are not even that useful for
estimating the taxes payable, the warrantee
expense above is not allowed for tax purposes.
Also depreciation is calculated differently for tax
and financial reporting.
Further the accounting numbers often include
sunk costs and exclude opportunity costs.
K. D. Brewer 2008
Page 4-32
32
Taxes
One thing that is inevitable when a company is
considering a profitable investment opportunity
is taxes. For this reason the cash flows of the
project must be stated on an after tax basis. To
do this we assume that almost all cash flows are
taxable income if positive and tax deductible if
negative. These cash flows are then reduced by
the amount of tax paid or saved. The method of
doing this is to multiply all cash flows that are
taxable by (1 - t) where t is the firm's marginal
rate of tax. (See chapter 2.4)
Several forms of income are treated differently.
Dividends are not taxable for corporations. Also
capital gains are treated differently. Only one
half of the capital gain has to be included in the
firm's income for tax purposes. Previously the
inclusion rate had been 75% or 2/3 depending
on the year since tax laws change over time.
K. D. Brewer 2008
Page 4-33
33
Taxable Losses
In some cases a company will report a taxable
capital or operating loss in given year. The tax
laws allow such losses to be carried back up to
3 years and carried forward up to 7 years for an
operating loss and indefinitely for a capital loss.
Capital losses can only be applied against
capital gains.
The carry back provision allows a company to
offset previous taxable gains and recover some
of the taxes that were paid on those gains. If
there are not enough previous earnings in the
carry back period, the firm does not have to pay
taxes on future gains until those profits have
exceeded the losses reported, or until those
losses expire.
If two firms merge, the new firm can use taxable
losses from either firm.
K. D. Brewer 2008
Page 4-34
34
Capital Assets
The main cash flow that is treated differently for
tax purposes is the initial investment. In most
cases the initial investment must be capitalized.
This means that although the cost is incurred up
front the investment is deducted over the life of
the project instead of when it is incurred. The
main reason for this is that the investment has
resulted in the acquisition of a fixed asset that
still has most of its value. As such it is seen as
an investment rather than an expense.
This investment however declines in value as it
generates income. For this reason the value of
the investment is expensed over time. Financial
reporting depreciation is quite influenced by
managerial decisions and is not allowed for tax
reporting in Canada or the USA. For tax
purposes the Capital Cost Allowance or CCA is
the only allowable method of depreciation in
Canada. (See chapter 2.5)
K. D. Brewer 2008
Page 4-35
35
CCA
Instead of allowing each firm's management to
decide what depreciation policy to use, the
government specifies that policy. Each asset is
assigned to an asset class based on the tax
code. When an asset is acquired, the value of
the asset is added to the value of that asset
class on the firm's books. In effect, all assets of
a single class are pooled and treated as one
asset for depreciation purposes.
Each year the firm is allowed to deduct from
taxable income a percentage of the value of
each as class specified in the tax code. The
amount that is deducted as an expense is also
subtracted from the balance of the asset class.
For example if the firm has $100,000 in asset
class 9 (electrical equipment), it is allowed to
deduct 25% or $25,000 as an expense. The
pool would also be reduced by this amount
leaving a UCC of $75,000.
K. D. Brewer 2008
Page 4-36
36
Half-Year Rule
If the value of the pool increases over the year,
only half of the net increase is usable in the
calculation of the allowable CCA expense.
If the firm in the previous example added a new
asset to the pool with a cost of $25,000, the
undepreciated capital cost of the pool (UCC)
would be $100,000 but only half of that increase
can be used in the first year. Therefore the firm
can only claim a maximum deduction of 25% of
$87,500 or $21,875. This would leave a UCC of
$78,125.
Year
Starting UCC
CCA Ending UCC
1
100,000
25,000
75,000
2
100,000*
21,875
78,125
3
78,125
19,531
58,594
4
58,594
14,648
43,945
5
43,945
10,986
32,959
K. D. Brewer 2008
Page 4-37
37
Asset Sales
If the firm disposes of an asset, the net proceeds
from disposition (the selling price less any costs)
is deducted from the UCC of the asset class, up
to a maximum of the original cost. Anything
above that is treated as a capital gain.
If the sale of an asset leaves the pool with a
negative balance, the entire amount is added to
the firm's taxable income that year. This is
called recaptured depreciation. In effect the tax
people realize that they have allowed the firm to
deduct too much depreciation and they want it
back.
If the sale leaves no assets in the pool, but a
positive UCC, the firm has a terminal loss and
can deduct the entire UCC that year. If a single
asset remains in the class and the UCC is 100
times the cost of that asset, there is no terminal
loss.
K. D. Brewer 2008
Page 4-38
38
Complications
The above description of CCA applies to most
assets. Some assets are treated differently.
1. Land is not depreciable under CCA.
2. Certain assets are not pooled. Each asset of
that class is treated as a separate class.
3. Leasehold improvements are depreciated on
a straight-line basis over the life of the lease.
4. Intangible assets with a limited life (patents,
licenses, etc.) are depreciated on a straightline basis over the life of the asset.
5. Timber and mining rights are depreciated in
a different manner.
I don't expect students to be tax accountants, if
something is treated differently, I'll specify that in
any questions asked.
K. D. Brewer 2008
Page 4-39
39
CCA Tax Savings
How much tax does a company save due to
CCA? Assume a company with a marginal tax
rate of 35%, and a cost of capital of 15%. What
would the tax savings be over 5 years, on a
class 8 asset (manufacturing machinery, 20%)
that cost $100,000? What is the present value
of those tax savings?
Year
1
2
3
4
5
UCC, start
100,000
90,000
72,000
57,600
46,080
36,864
CCA
10,000*
18,000
14,400
11,520
9,216
Tax Benefit
3,500
6,300
5,040
4,032
3,226
PV
3,043
4,764
3,314
2,305
1,604
15,030
What would be the tax effect of selling that
machine for $50,000 at that point?
1. In most cases there will be no immediate tax
effect, the UCC is reduced by $50,000.
2. If it was the only asset in the class and not
replaced, $13,136 would be recaptured.
K. D. Brewer 2008
Page 4-40
40
PV of Tax Shield
If an asset is added to the pool and never
removed from the pool, the tax savings will
continue forever.
 Each year the amount of the tax savings will
decrease by the CCA rate.
 This is a declining perpetuity.
 This can be considered the same as a
growing perpetuity with a negative growth
rate.
 We already have a formula for a growing
perpetuity under equity, the Gordon Growth
Model.
 If we replace D1 with the tax savings in the
first year (ignoring the half-year rule) we get:
PVtax shield
K. D. Brewer 2008
CdTc

rd
Where:
C = the initial cost of the asset
d = the CCA depreciation rate
Tc = the marginal tax rate
r = the cost of capital
Page 4-41
41
The Half-year Rule
The existence of Revenue Canada's half-year
rule complicates things. The easiest approach
to adjusting for that rule is to split the initial
investment into two pieces, the first of which is
depreciated as above, the second is calculated
the same way, but since it doesn't start until next
year we discount that for one period.
PVtax shield
1 CdTc 1 CdTc
1
 2
 2

rd
rd
1 r
1 CdTc
1 

 2
 1 
rd
 1  r 
r
CdTc 1  2 



r  d  1 r 


Note: at this point the text changes terminology,
switching from r to k for the discount rate when
the discount rate is the cost of capital. This is
common in financial literature.
K. D. Brewer 2008
Page 4-42
42
Salvage Value
In most cases, the firm will not keep an asset
forever. What happens when the firm disposes
of the asset?
1. If the net salvage value is zero or lower and
there are other assets in the class, there is
no effect on the present value. The portion
of the pool that the asset represented
continues to depreciate forever.
2. If the net salvage value is positive, less than
the UCC and the original cost, and the pool
is not left empty or with a negative UCC, the
net salvage value is deducted from the UCC
and the firm loses the tax shield on the net
salvage value.
PVlost tax shield 
SdTc
1

r  d 1  r t
Although there are quite a few exceptions we
can ignore them during capital budgeting.
K. D. Brewer 2008
Page 4-43
43
An Example
DCF Inc. is considering a capital budgeting
proposal to replace an obsolete machine. The
old machine was purchased 2 years ago for
$200,000. It had an expected life of 7 years with
a salvage value of $22,500. The machine is
being depreciated on a straight-line basis for
financial reporting purposes and is in asset class
8 (20%) for CCA. The old machine would only
net $30,000 for parts if sold today. The new
machine is also asset class 8, costs $25,000 it
has an expected life of 5 years with no salvage
value. The asset class will not be left empty at
that time. The new machine produces less
waste for an after-tax cost saving of $2,000 in
the first year, increasing at the rate of inflation
forecast at 3% annually. It would also reduce
inventory by $200 and A/P by $100.
What are the relevant cash flows and is this
project acceptable if DCF's cost of capital is 17%
and its marginal tax rate it 38%?
K. D. Brewer 2008
Page 4-44
44
Cash Flows
1. The original purchase price and depreciation
can be ignored.
2. The $30,000 for parts is netted against the
investment of $25,000.
Net investment
would be -$5,000, a cash inflow.
3. The UCC for class 8 would decrease by
$5,000. The PV of that loss of tax shield
would be -$1,027 (no half-year rule).
4. The reduction of working capital of $100 is
also a relevant cash inflow at time zero.
5. Cost savings of 2000, 2060, 2122, 2185,
2251 would be relevant over the five years.
6. In Year 5 there is a negative cash flow of
$22,500. If the machine is not replaced they
can sell it for $22,500 in 5 years. Of course
this is reduced by the tax shield lost.
7. The working capital change is likely to be
permanent.
K. D. Brewer 2008
Page 4-45
45
Decision
Net cash flows for the project are:
DCF Inc.
Purchase
Sale of asset
CCA on net investment
Inventory 
Accounts payable 
Cost savings Year 1
Cost savings Year 2
Cost savings Year 3
Cost savings Year 4
Cost savings Year 5
Forgone Salvage Year 5
CCA on lost salvage
Payback = 0
Cash Flow
-25,000.00
30,000.00
-1,027.03
200.00
-100.00
2,000.00
2,060.00
2,121.80
2,185.45
2,251.02
-22,500.00
4,621.62
NPV =
IRR =
PI =
PV @ 17.0%
-25,000.00
30,000.00
-1,027.03
200.00
-100.00
1,709.40
1,504.86
1,324.79
1,166.27
1,026.71
-10,262.50
1,873.75
2,416.26
5.52%
-0.5167
The net present value of the project is positive,
which recommends the project. The IRR is less
than the cost of capital and the PI is negative.
These actually recommend the project since the
decision criteria reverse if the initial investment
is negative.
K. D. Brewer 2008
Page 4-46
46
Project Interdependence
Sometimes when one or more projects are
under consideration, the decision regarding one
of the projects can have an impact on the cash
flows of another project under consideration.
Complementary

Positive interdependence

Independent

Negative interdependence

Mutually exclusive
K. D. Brewer 2008
Page 4-47
47
Interdependence II
With complementary projects, project B can only
be undertaken if project A is accepted. When
analyzing the projects, consider A alone and
A+B as a single project. Whichever of those has
the best NPV is what the firm should do.
Interdependent projects have an overlap, either
positive or negative on the cash flows of the
other projects. In that case find the NPV of all of
the project combinations that are possible. The
combination that has the highest NPV
(assuming that it is positive) is the option that
should be undertaken.
If projects are independent then accepting one
has no bearing on the others. Accept a project if
it has a positive NPV.
Only one of the mutually exclusive projects can
be accepted. Choose the one with the highest
net present value (if positive).
K. D. Brewer 2008
Page 4-48
48
Interdependence III
ADC Limited is considering two proposals for
developments on a remote site. Both projects
can be accommodated on the site. Project A
has a net present value of $5,000 and an initial
cost of $500,000. Project B has an initial cost of
$250,000 and a NPV of -$10,000. Both projects
include a cost of $100,000 to extend power lines
to the site. This cost only needs to be paid by
one of the projects. What should ADC decide?
Project A: NPV = $5.000
Project B: NPV = -$10.000
Project A + B: NPV = $95,000 
In general if the sum of the NPVs is not the
same as the NPV of the combined project then
the projects are interdependent.
K. D. Brewer 2008
Page 4-49
49
Unequal Lives
With mutually exclusive projects, a difference in
the length of the project can alter which decision
is correct if the projects are repeatable.
MFM Inc. is considering 2 proposals to replace a
piece of production machinery. Proposal A has
a NPV of $200,000 over its 3-year life. Proposal
B would have a life of 6 years and a NPV of
$300,000. Both proposals can be repeated.
Which proposal should MFM accept if they have
a cost of capital of 15%?
Using the normal NPV rule, MFM would accept
Proposal B. However, if they accept Proposal A,
they can do that project twice in the time that
Proposal B takes. MFM can do a $200,000 NPV
project starting at time 0, and again at time 3.
The second time has an NPV of $131,503
($200,000 3 years from now) for a total of
$331,503 for doing proposal A twice.
K. D. Brewer 2008
Page 4-50
50
EAA
The tactic of finding the NPV of a series of
projects that set the two projects to equal lives is
termed a project chain. If one project is half the
life of the other project, this approach is quite
simple. If you have 2 projects with lives of 7
years and 9 years, you would have to do the first
project 9 times and the second project 7 times.
This is quite clumsy.
A different approach would be to find out how
much NPV is added for each year of the project.
To find the EAA, or Effective Annual Annuity, we
divide the NPV of each project by the PVIFA at
the cost of capital with a number of payments
equal to the life of the project. The firm should
be indifferent to gaining an annuity with those
payments or proceeding with the project.
K. D. Brewer 2008
Page 4-51
51
EAA Example
How much would MFM have to receive each
year to yield the same NPV as the two projects?
$200,000 = EAAA x PVIFA(15%, 3)
EAAA = $87,595
$300,000 = EAAB x PVIFA(15%, 6)
EAAB = $79,721
Using the EAA we see that Proposal A actually
has a higher net present value added per year
than Proposal B.
If the projects cannot be repeated, the straight
NPV is the appropriate decision criterion.
The text calls this EAC or effective annual cost.
They only apply EAC to required expenses.
EAA is useful when considering any mutually
exclusive projects that can be repeated.
K. D. Brewer 2008
Page 4-52
52
Forecasting Risk
If we have a forecast of project cash flows of
$5,000 per year for 5 years, do we actually
expect to have exactly $5,000 in cash flows in
each of the next 5 years?
It is not likely. The project's cash flows are
based on estimates of sales and costs. We do
not know for certain the level of sales in the
future, and even if we did (long term contract)
the level of costs could easily change.
If we take a weighted average of the possible
outcomes, the cash flows should be $5,000. For
example; a 10% chance of $7,500, 20% chance
of $6,000, 50% chance of $5,000 and a 20%
chance that the cash flow would be $2,750
would give the project an expected cash flow of
$5,000.
The chance that our estimated cash flows are
wrong is called forecasting risk.
K. D. Brewer 2008
Page 4-53
53
Dealing with Forecasting
Risk
How would we control for forecasting risk?
There are several options to deal with this risk.
We can construct multiple models of cash flows
and see how much of an impact the various
assumptions that we have made have on the
project's cash flows. Depending on the method
used this type of analysis can be called;
scenario, what-if, sensitivity, simulation, or breakeven analysis.
All of these do similar things. The basic idea is
to find out how much our cash flow projections
can be off and still recommend the project. If a
minor difference in an assumption can make the
project unattractive, we should examine the
project more carefully. This form of analysis is
simple with a well-constructed spreadsheet.
K. D. Brewer 2008
Page 4-54
54
Managerial Options
One implicit assumption that we have made in
our earlier cash flow models is that once the
project has been launched, it will continue to
operate at a certain level throughout it's life.
 How would this change if management has
the ability to alter the operations of the firm
when they get more information about the
actual results of the project?
 What sort of decisions can management
make during the life of the project?
 Can we enhance the value of a project by
considering these managerial options?
 Would it be worthwhile to spend more initially
if we increase the flexibility of operations?
K. D. Brewer 2008
Page 4-55
55
Types of Options
Expansion options: if sales and/or profits are
better than forecast, is the project able to be
expanded to take advantage of this opportunity?
If the project can be expanded, how much is that
going to cost? Is there anything we can do at
the start to enhance this opportunity? Can a
minor increase in startup costs significantly
reduce the cost of expansion?
Contraction options: if sales fall short of our
projections, can we scale back production to
significantly reduce costs? A project that has
low fixed costs and high variable costs (low
operating leverage) will be able to realize more
savings from contraction than a project with high
fixed costs and low variable costs will have less
opportunity to cut costs, but may be better able
to expand production.
K. D. Brewer 2008
Page 4-56
56
More Options
Abandonment options: if things go wrong in a
big way, can the firm get out of this project and
recover much of their investment? Alternatively
can we use the investment that was made for
this project for some other project? The option
to abandon the project if things do not work out
right can be a valuable option.
The option to wait: sometimes, it might be in the
best interests of the firm to wait for more
information before making a decision on an
investment. For example, the firm is considering
an expansion of existing capacity. The firm has
submitted a bid for a major contract. If they are
awarded that contract they will need a major
expansion of capacity, if not, then a minor
increase in capacity is more appropriate. In that
case, it may be in the firm's best interest to wait
for that decision before committing to either
project.
K. D. Brewer 2008
Page 4-57
57
Other Options
Tax options: some flexibility in operations can
have a large impact on the taxes paid by a firm.
For example if there are few assets left in an
asset class and a large UCC, disposing of those
assets could trigger a large terminal loss, saving
the company a significant amount of current
taxes payable.
Strategic options: sometimes a company will
accept a project with a negative NPV in order to
explore possible opportunities (McDonald's in
Moscow) or because they expect some of the
expenses to reduce the cost of other projects.
In the positive interdependence example, if only
project B was being considered, its -$10,000
NPV would normally be enough to reject the
project, but accepting the project opens up the
site for other proposals, so it might be accepted
when the strategic options are considered.
K. D. Brewer 2008
Page 4-58
58
Managerial Options
Example
Crispy Corp. has a cost of capital of 12%.
Management is considering a capital budgeting
proposal that would require an initial investment
of $2 million. Annual cash flows are forecast at
$300,000 per year for 10 years with no salvage
value.
The $300,000 annual cash flow is
actually a weighted average of $400,000 and
200,000 (based on market reaction) and the
cash flow for the life of the project will be known
after one year of operation.
What is the net present value of the project?
NPV = -$2 m + 300,000xPVIFA(12%, 10)
NPV = -$304,933
Ignoring options the project has a negative NPV
and is not worth considering.
K. D. Brewer 2008
Page 4-59
59
Option Example cont.
If the project includes an option to double the
cash flows if market reaction is good ($400,000)
for an additional investment of $1 million at the
end of year 1, find the NPV taking into account
this expansion option.
To find the NPV we split the calculation into two
cases, find the NPV of the two cases and
average them.
Year
0
1
2
3
4
5
6
7
8
9
10
High Cash Flow
CF
DCF
-2000
-2,000
-600
-536
800
638
800
569
800
508
800
454
800
405
800
362
800
323
800
288
800
258
1,270
NPV with Option =
Low Cash Flow
CF
DCF
-2,000
-2,000
200
179
200
159
200
142
200
127
200
113
200
101
200
90
200
81
200
72
200
64
-870
200.11
With the option, the project has a positive NPV.
K. D. Brewer 2008
Page 4-60
60
Option Example cont.
Would an option to shut the project down after
one year for a salvage value of $1 million be
useful to Crispy Corp.?
Crispy Corp. would only consider this option if
the low cash flow scenario were realized. The
way to evaluate this is to see if they would use
this option in this case. The option gives Crispy
Corp. the opportunity to get $1 million in
exchange for the remaining cash flows of
$200,000 per year for 9 years. Those cash
flows have a present value of $1.066 million,
which is more than what would be realized if
they shut down the project. Therefore this
abandonment option would not be valuable to
Crispy Corp. If they option would have yielded
more than $1.066 million, that option would have
had value.
K. D. Brewer 2008
Page 4-61
61
Capital Rationing
If the firm has a limited amount of money
available for capital spending and has more
positive NPV projects than this, we have a
situation that is called capital rationing.
If the firm has only allocated a limited amount of
money, but can raise more if necessary this is
called soft rationing. Under soft rationing, if the
available positive NPV projects require more
funds than are allocated, the rational course of
action is to attempt to get more funds. Failing
that we should try to get the maximum NPV by
choosing the projects with the highest PI first.
This can be complicated if the soft rationing is a
one-time event and some of the projects can be
delayed at no reduction in cash flows.
Under hard rationing the firm cannot raise any
more money for capital spending under any
circumstances.
K. D. Brewer 2008
Page 4-62
62
Capital Rationing II
The text argues that capital rationing is not
consistent with the goal of maximizing the value
of the firm and spends very little space on this
issue. There are multiple possible reasons that
capital rationing can occur in real life.
A firm with a market capitalization of $10 million
is not likely to be able to raise $1 billion for a
capital investment project. That $10 million firm
is likely to find that there is a level of capital
spending, above which the cost of raising new
capital starts to increase. In other words, a firm
can only raise a limited amount of funds at their
current cost of capital. If they want to invest
more than that amount, they have to take into
account the increased cost of funds and how
this would affect the value of the company.
Protective covenants in a previous bond issue
may also prevent the company from pursuing all
positive NPV projects.
K. D. Brewer 2008
Page 4-63
63
Capital Rationing Example
HCR Limited has a cap on capital spending of
$5 million due to a bond covenant. Currently
HCR had six positive NPV projects that it would
like to undertake. They are (in $thousands)…
Project
A
B
C
D
E
F
Total
Cost
1,300
1,700
3,000
500
2,200
1,900
10,600
PI
1.10
1.07
1.06
1.20
1.05
1.18
NPV
?
?
?
?
?
?
What are the NPVs of these projects and how
should HCR Limited allocate their spending
assuming that all of the projects can be delayed
with no adverse effects?
K. D. Brewer 2008
Page 4-64
64
Rationing Solution
To find the NPV of each project, simply multiply
the cost by (PI-1). The PI is the present value of
the future cash flows divided by the cost, the
NPV is the present value of the future cash flows
minus the cost.
To decide how to allocate funds, rank the
projects according to the PI.
Project
D
F
A
B
C
E
Cost
PI
NPV
Cost
500
1.20
100
500
1,900
1.18
342
2400
1,300
1.10
130
3700
1,700
1.07
119
5400
3,000
1.06
180
8400
2,200
1.05
110 10,600
10,600
HCR could afford to do projects D, F, and A.
This has a NPV of $572. To do Project B would
require $1,700 and they only have $1,300 left.
They can afford B if they skip D, that would
increase the NPV by $19. The ideal choice of
projects is A, B and F.
K. D. Brewer 2008
Page 4-65
65