pinvestment
Capital Budgeting
MGFB Principles of Finance
Jincheng Tong
University of Toronto
March 23, 2025
1 / 34
Why Is This Important?
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cost
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- Capital budgeting is one of the most important decisions a company can make
- A measurable way for a business to decide whether to take on an investment project or
not, how to choose between alternative investment projects
- Investment choices determine the future destiny of the company
- Investment decisions of the business sector result in the employment opportunities and
economic growth
2 / 34
Capital Budgeting
- Capital budgeting is the process of analyzing investment opportunities and deciding which
ones to accept.
- Basic principles of capital budgeting:
- Decisions are based on cash flows, not accounting income.
- The timing of cash flows matters – time value of money is important.
- Cash flows are incremental – those cash flows that change as a direct consequence of
accepting a project.
- Cash flows are on an after-tax basis.
deductdepreciation interests
- Fundamental steps of capital budgeting:
- Estimate the expected future cash flows
- Estimate the required return for projects of this risk level
- Apply capital budgeting decision rules
3 / 34
Investment Decision Rules
- We will start by evaluating popular capital budgeting methods
- NPV positive addvaluetoshareholder
- Payback period
givedifferentfromNPV
- Internal rate of return relevant
- Profitability index
- We need to ask ourselves the following questions when evaluating decision criteria
- Does the decision rule adjust for the time value of money?
- Does the decision rule adjust for risk?
- Does the decision rule provide information on whether we are creating value for the firm
(shareholders)?
4 / 34
Investment Decision Rules: Example
- Consider two mutually exclusive new product launch projects that Nike Golf is
considering. Assume that the discount rate for Nike Golf is 15%. ermyrttprike.cckM1rt
karate
- Project A. Nike NP-30. Professional clubs that will take an initial investment of $550,000 at
time 0. Next five years (years 1-5) of sales will generate a consistent cash flow of $185,000
per year. Introduction of new product at year 6 will terminate further cash flows from this
project. constantanvity
- Project B. Nike NX-20. High-end amateur clubs that will take an initial investment of
$350,000 at time 0. Cash flow at year 1 is $100,000. In each subsequent year until year 5,
cash flow will grow at 10% per year. Introduction of new product at year 6 will terminate
further cash flows from this project.
growing
annuity
5 / 34
The Net Present Value (NPV) Rule
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addedto
Net Present Value (NPV)
= Total PV of future CF’s → Initial Investment
- Estimating NPV:
now
tospend
earnings
Internal
1. Estimate future cash flows: how much? and when?
2. Estimate discount rate
3. Estimate initial costs
These
In
so
up
price
capital
gainstock
- Minimum Acceptance Criteria: Accept if NPV > 0
- Ranking Criteria: Choose the highest NPV
- Good attributes of the NPV rule:
- Uses all cash flows of the project
- Discounts all cash flows properly
6 / 34
The NPV Rule: Example
- Based on the NPV rule, which project should Nike Golf choose?
Year
0
1
2
3
4
5
The NPV of each project is:
NP-30
→$550, 000
185,000
185,000
185,000
185,000
185,000
a
NX-20
→$350, 000
100,000
110,000
121,000
133,100
146,410
!
isbetter
"
4th's
$185, 000
1
NPVNP-30 = →$550, 000 +
1→
= $70, 148.69
0.15
1.155
!
"
amityofrmula fowipannvilyfor
5
$100, 000
1.10
NPVNX-20 = →$350, 000 +
1→
= $48, 583.79
0.15 → 0.10
1.155
The NPV criteria implies accepting the NP-30
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7 / 34
Alternatives to The NPV Rule
- In practice, other investment rules are also used
1. Payback Period Quicklyrecoverfrominitialcost
2. Internal Rate of Return (IRR)
3. Profitability Index (PI)
- Firms use these rules because they were used historically and they may have worked (in
combination with common sense)
- These rules sometimes give the same answer as NPV, but in general they do not
- You should be aware of their shortcomings and use NPV whenever possible
- The NPV rule dominates these alternatives
8 / 34
The Payback Period Rule
- How long does it take the project to “pay back” its initial investment?
Payback Period = number of years to recover initial costs
- Minimum Acceptance Criteria: set by management
- Ranking Criteria: set by management typicallyASAPbreakeven
- Disadvantages:
- Ignores the time value of money
- Ignores cash flows after the payback period
- Biased against long-term projects
- Requires an arbitrary acceptance criteria
- A project accepted based on the payback criteria may not have a positive NPV
9 / 34
The Payback Period: Example
- Based on the Payback Period rule, which project should Nike Golf choose?
(i) Project A (NP-30):
A 550,000
Cumulative CF Year 1 = $185, 000
Cumulative CF Year 2 = $185, 000 + $185, 000 = $370, 000msn.toiiinm.mars
Cumulative CF Year 3 = $370, 000 + $185, 000 = $555, 000
EEisiiiaiae
Project
Payback period = 2 + ($180, 000/$185, 000) = 2.97 years
(ii) Project B (NX-20):
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term
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ignores
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Cumulative CF Year 1 = $100, 000
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the
425
year
invest
Cumulative CF Year 2 = $100, 000 + $110, 000 = $210, 000
Cumulative CF Year 3 = $210, 000 + $121, 000 = $331, 000
Cumulative CF Year 4 = $331, 000 + $133, 100 = $464, 100
inbetween
yrs y
Payback period = 3 + ($19, 000/$133, 100) = 3.14 years
↑ If the company accepts only projects that payback in under 3 years, Project B would be
rejected.
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10 / 34
The Internal Rate of Return (IRR) Rule
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IRR = the discount that sets NPV to zero
- Minimum Acceptance Criteria:
- Accept if the IRR exceeds the required return
- Ranking Criteria:
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- Select alternative with the highest IRR
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- Disadvantages:
- IRR may not exist or there may be multiple IRRsjlgaeo don'tallvsNPVis
- Incorrect rankings for loans and other projects with negative cashflows in future periods
- Problems with mutually exclusive projects if
- Initial investments are substantially di!erent
- Timing of cash flows is substantially di!erent
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11 / 34
The IRR Rule: Example Yn
p1
were
If
IRR
- Based on the IRR rule, which project should Nike Golf choose?
(i) Project A (NP-30):
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Bond
mar
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pvo
9st
$185, 000
1
→$550, 000 +
1→
=0
IRR
(1 + IRR)5
Using Excel, financial calculator, or trial and error to find the root of the equation, we find
that:
IRRNP-30 = 20.27%
(ii) Project B (NX-20):
!
"
$100, 000
(1 + 0.1)5
→$350, 000 +
1→
=0
IRR → 0.1
(1 + IRR)5
Using Excel, financial calculator, or trial and error to find the root of the equation, we find
that:
Yaformulawontwork
IRRNX-20 = 20.34%
The IRR criteria implies accepting the NX-20
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effective
mostcost
12 / 34
The Profitability Index (PI) Rule
iifm.at
Benefit
PI =
NPV PV Investment
Total PV of Future Cash Flows
Initial Investment
- Minimum Acceptance Criteria:
- Accept if PI > 1
- Ranking Criteria: Iroyerthereturnbetterthe
investment
project
- Select alternative with highest PI
- Disadvantages:
- PI scales projects by their initial investments. The scaling can lead to wrong answers in
comparing mutually exclusive projects
13 / 34
The PI Rule: Example
- Based on the PI rule, which project should Nike Golf choose?
#
!
"$
$185, 000
1
PINP-30 =
1→
/$550, 000
5
0.15
1.15
return
12.8 net
PINP-30 = 1.128
#
!
$100, 000
1→
0.15 → 0.10
1.155
PINX-20 = 1.139 13.9 netreturn
PINX-20 =
1.105
"$
/$350, 000
The PI criteria implies accepting the NX-20
14 / 34
Interest Rates and Inflation
- Quoted interest rates are nominal interest rates: growth rate of money
- The real interest rate indicates the rate of growth of one’s purchasing power after
adjusting for inflation.
- From the relationship between interest rates and inflation, often referred to as the Fisher
relationship:
Fisherequation
we have
(1 + Nominal Rate) = (1 + Real Rate) ↓ (1 + Inflation Rate)
Real Rate =
Nominal Rate → Inflation Rate
1 + Inflation Rate
- For low rates of inflation, this is often approximated as
increase
forworkers
inflationwage
core
fixen
para
21
more
Real Rate ↔ Nominal Rate → Inflation Rate
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workers
bankloanaaiiihiiir.ie
15 / 34
Interest Rates and Inflation
- Key Definitions:
- Nominal Interest Rate: The stated rate of return (e.g., 10%).
- Real Interest Rate: Adjusted for inflation, reflects actual purchasing power growth.
- Example:
- Deposit $1,000 at a 10% nominal interest rate:
0
109
1 burger 1000burgerscan
buy
Future Value = 1, 000 ↓ 1.10 = $1, 100
1.06burger
- Inflation = 6% ↗ Prices rise (e.g., hamburger: $1.00 ↗ $1.06).
- Purchasing Power:
$1, 100
Hamburgers Bought =
↔ 1, 038
$1.06
- Actual increase in purchasing power = 3.8%.
by38moreburgers
- This matches the Fisher relationship:
Real Rate =
Nominal Rate → Inflation Rate
10% → 6%
=
= 3.8%
1 + Inflation Rate
1 + 6%
16 / 34
Real vs. Nominal Interest Rates
Date 0
Date 1
Individual invests
$1,000 in bank
Because hamburgers sell for $1
at date 0, $1,000 would have
purchased 1,000 hamburgers.)
10%
Interest rate
Individual receives
$1,100 from bank
Inflation rate has
been 6% over year
3.8%
Because each hamburger sells for $1.06
at date 1, 1,038 (= $1,100/$1.06)
hamburgers can be purchased.
Nominal Rate
1.10
1 + Real Rate = 11+
+Inflation Rate = 1.06 = 1.038
17 / 34
Cash Flows and Inflation
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rate
itaaiusteaforintationc.at
- Like interest rates, cash flows can be expressed in either nominal or real terms.
- A cash flow is expressed in nominal terms if the actual dollars to be received (or paid
out) are given.
- A cash flow is expressed in real terms if the current or date 0 purchasing power of the
cash flow is given.
- Treat inflation consistently!
- Discount real cash flows with real discount rate
- Discount nominal cash flows with nominal discount rate
- Assume cash flows are nominal unless the question says they are real
18 / 34
Detailed calculation of a project’s cash-flow
19 / 34
Incremental Cash Flows
- Will this cash flow change only if we accept the project? If the answer is “yes”, it should
be included in the analysis because it is incremental.
- Incremental cash flows include:
itaontdothisinvestment.wnatanyougingtoi.se
- Opportunity Costs: Benefits forgone in order to accept the project
- Side E!ects: Impacts on other projects from accepting this project.
- Net Working Capital: Increased cash and short-term asset requirements.
cnn.TT
tsmcsmpany- Tax: Corporate income tax and tax implications of asset sales.
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iiitimes
20 / 34
Determining Relevant Cash Flows
- Incremental cash flows exclude:
back
saying
- Sunk Costs: Expenses that must be paid whether or not the project is accepted, including all
past costs, associated with the project or not.
Example: A company is considering a line of chocolate milk. As part of the evaluation, the
company had paid a consulting firm $100,000 to perform a marketing analysis. The
expenditure was made last year. Is this cost relevant for the capital budgeting decision now?
- Financing Costs: Only cash flow from assets, not financing costs such as interest expenses
are considered. The cost of financing is represented in the discount rate.
- Allocated Overhead: Admin. costs that exist regardless of the project.
Example: The company devotes one wing of its o”ces to a library requiring a cash outflow of
$100,000 per a year in upkeep. A new project is expected to generate revenue equal to 5% of
the firm’s overall sales. Should then $5,000 = 5% ↓ 100,000 be viewed as the new project’s
share of the library’s costs?
21 / 34
Estimating Total Project Cash Flows
1. Cash flow from investments in plant and equipment
resia
- Initial investments (after-tax)
- Salvage values (after-tax) at end of project
2. Cash flow from investment in net working capital
- Measured by the change, not the level of the net working capital oweothers
to
- Net Working Capital (NWC) = Current Assets – Current Liabilities
instTuria
- We can approximate NWC as Cash + Inventory + Accounts receivable → Accounts payable
3. Cash flow (after-tax) from operations.
inflow
futurecash
before
inause
tunes
earning
- Operating Cash Flow (OCF) = EBIT – Taxes + Depreciation
- EBIT = Sales – Costs – Depreciation
- Taxes = EBIT ↓ τc , where τc is the corporate tax rate
Thrate
oct iTe EBITDepreciation
20
oct ite salescosts to
not
p
Depreciation
sina.ie
22 / 34
Change in Net Working Capital
account
putter
creditsales
later
- An investment in NWC arises whenever:
- Raw materials and other inventory are purchased prior to the sale of finished goods
- Cash is kept in the project as a bu!er against unexpected expenditures
- Credit sales are made, generating accounts receivable rather than cash.
- Only the change in NWC is included in our cash flows:
- An increase in NWC implies a negative cash flow, because cash generated elsewhere in the
firm is tied up in the project.
- A decrease in NWC implies a positive cash flow.
- In the end of the project, NWC is reduced – ultimately to zero. Accounts receivable are
collected, the project’s cash bu!er is returned to the rest of the firm, and remaining
inventory is sold o!.
23 / 34
Capital Cost Allowance
- Capital Cost Allowance (CCA)
depends
rate
on
asset
Starvation
rateauranu
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Itis
- The amount of write-o! on depreciable assets allowed by Canada
Revenue Agency against
taxable income.
- It is calculated by multiplying UCC by the appropriate CCA rate. The CCA rate is assigned
according to an asset class system
- Most asset classes use a declining balance method for computing CCA: apply the CCA rate
to the balance for each year.
- The half-year rule consists in adding only one-half of the purchase cost of the asset to the
asset class and use it to compute CCA in the year of purchase. The remaining half of the
cost will be added next year.
first
year
- Undepreciated Capital Cost (UCC)
- The balance remaining in an asset class that has not yet been depreciated in that year.
- CCA Tax Shield: Tax savings arising from the CCA charge.
24 / 34
CCA Calculation: Example
ABC Corporation purchased $100,000 worth of photocopiers in 2016. Photocopiers fall under
asset class 8 with a CCA rate of 20%. How much CCA will be claimed in 2016, 2017 and
2018?
or no instead
Year
2016
2017
2018
haem
o
Beginning UCC
50, 000
(= 100, 000 ↓ 50%)
90, 000
(= 40, 000 + 50, 000)
72, 000
CCA (Depreciation)
10, 000
(= 50, 000 ↓ 20%)
18, 000
(= 90, 000 ↓ 20%)
14, 400
(= 72, 000 ↓ 20%)
0
FEE.itfartnat
I
Ending UCC
40, 000
(= 50, 000 → 10, 000)
72, 000
(= 90, 000 → 18, 000)
57, 600
(= 72, 000 → 14, 400)
c ashflow
Eoperating
CCATo
25 / 34
Total Project Cash Flow: Example
- Investments
- Equipment investment. The cost of the new product machine is $800,000. The machine has
an estimated market value at the end of eight years of $150,000.
- Investment in net working capital. Required working capital is $40,000 in year 0, stays at 15
percent of sales at the end of each year, and falls to $0 by the project’s end.
- Income, Taxes and Operating Cash Flow
- Sales revenues. Expected production (in units) by year during 8-year life of the machine is
given by: (6000, 9000, 12000, 13000, 12000, 10000, 8000, 6000). The price per unit in the
first year will be $100 and will increase by 2% per year.
- Operating costs. Variable production cash outflows are expected to grow 5% per year.
First-year variable production costs will be $64Mtfaritanchargetoconfms
per unit, and fixed production costs will be
$50,000 each year.
- CCA. The capital investment of $800,000 is CCA class 8, 20% rate.
- Taxes. The tax rate is 40 percent.
- More details in Chapter 8.2 in the textbook
26 / 34
Total Project Cash Flow: Example (cont.) Testwith
missingnumbers
getNPVPV
OCF
1Te x salescosts ToDegregation
Table 1: Operating Revenues and Costs
Ex
variance Total
cost
Ei
Year
1
2
price
p
3
4
5
6
7
8
Production
6,000
9,000
12,000
13,000
12,000
10,000
8,000
6,000
Price
$100
102
104
106
108
110
113
115
Revenue
$600,000
918,000
1,248,480
1,379,570
1,298,919
1,104,081
900,930
689,211
Cost
$64
67
71
74
78
82
86
90
5550
oooounts
Fixed cost
$50,000
50,000
50,000
50,000
50,000
50,000
50,000
50,000
Operating cost
434,000
654,800
896,720
1,013,144
983,509
866,820
736,129
590,327
27 / 34
Total Project Cash Flow: Example (cont.)
Table 2: Capital Cost Allowance
rule
Half
year
machine
toget
sepence
800.000
applies
first rule
yr
400,000
year1to2
20 80,000
Year
1
2
3
pgf.gg
4
5
6
7
8
Beg. UCC
400,000
720,000
576,000
460,800
368,640
294,912
235,930
188,744
CCA
80,000
144,000
115,200
92,160
73,728
58,982
47,186
37,749
Tc CCA
End UCC
320,000
576,000
460,800
368,640
294,912
235,930
188,744
150,995
cashflow
operating
28 / 34
Total Project Cash Flow: Example (cont.)
sales cost Texuce
Oct 1Te
TT
Table 3: Operating Cash Flow (OCF)
Year
1
2
3
4
5
6
7
8
Sales
$600,000
918,000
1,248,480
1,379,570
1,298,919
1,104,081
900,930
689,211
Costs
$434,000
654,800
896,720
1,013,144
983,509
866,820
736,129
590,327
Depreciation
$80,000
144,000
115,200
92,160
73,728
58,982
47,186
37,749
r Taxes
$34,400
47,680
94,624
109,707
96,673
71,311
47,046
24,454
OCF
$131,600
215,520
257,136
256,720
218,737
165,949
117,755
74,430
29 / 34
Total Project Cash Flow: Example (cont.)
fiiiiii.at
Table 3: Investment Cash Flow (ICF)
Year
Equipment
0
1
2
3
4
5
6
7
8
$(800,000)
buying
NWC
∆NWC
$40,000
90,000
137,700
187,272
206,936
194,838
165,612
135,139
0
$(40,000)
(50,000)
(47,700)
(49,572)
(19,664)
12,098
29,226
30,473
135,139
After-tax
salvage
15 of
sales
more
ifeng.ee
a.iiiii.it
$150,000
Sellingmachine
ICF
$(840,000)
(50,000)
(47,700)
(49,572)
(19,664)
12,098
29,226
30,473 notcontributing
285,139
plidaslumpsum
tkyEsfmmiwe
investmentcashflow
30 / 34
Total Project Cash Flow: Example (cont.)
- Project cash flow = Operating cash flow + Investment cash flow
- Net Present Value
sing
Iiii
p p 820 $207, 564
$81, 600 $167,
NPV = →$840, 000 +
+
+
1+r
(1 + r )2
(1 + r )3
$237, 056 $230, 835 $195, 175 $148, 228 $359, 570
+
+
+
+
+
(1 + r )4
(1 + r )5
(1 + r )6
(1 + r )7
(1 + r )8
- Net Present Value at r = 4%: $500,135
- Net Present Value at r = 10%: $188,042
- Net Present Value at r = 15%: $2,280
- Net Present Value at r = 20%: $-137,895
31 / 34
Alternative Definitions of Operating Cash Flows
- Bottom-Up Approach
- OCF = Net Income + Depreciation
- Project Net Income = EBIT – Taxes
- Works only when there is no interest expense subtracted in the calculation of net income
- Top-Down Approach
- OCF = Sales – Costs – Taxes
- Do not subtract non-cash deductions
32 / 34
Summary
- Use the NPV rule for capital budgeting decisions: take all projects with positive NPV, or
take highest-NPV project if mutually exclusive
- Be wary of alternatives to NPV:
- Payback rule, discounted payback rule
- Internal rate of return
- Profitability index
- Capital budgeting must be conducted on an incremental basis. This means that sunk
costs must be ignored, while opportunity costs, side e!ects, and allocated costs need to
be considered.
33 / 34
Summary (cont.)
- Project cash flows are the sum of investment cash flow (PP&E and ∆NWC) and
operating cash flow
- In the total project cash flow example, we computed NPV using the following two steps:
1. Calculate the net cash flow from all sources for each period.
2. Calculate the NPV using the cash flows calculated above.
34 / 34