McGraw-HillIrwin Copyright © 2013 by The McGraw-Hi.docx

McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc.
All rights reserved.
Making Capital Investment Decisions
Chapter 6
*
6-*
Key Concepts and SkillsUnderstand how to determine the
relevant cash flows for various types of capital investmentsBe
able to compute depreciation expense for tax
purposesIncorporate inflation into capital budgetingUnderstand
the various methods for computing operating cash flowEvaluate
special cases of discounted cash flow analysis
*
6-*
Chapter Outline
6.1 Incremental Cash Flows
6.2 The Baldwin Company: An Example

6.3 Inflation and Capital Budgeting
6.4 Alternative Definitions of Operating Cash Flow
6.5 Some Special Cases of Discounted Cash Flow Analysis
*
6-*
6.1 Incremental Cash FlowsCash flows matter—not accounting
earnings.Sunk costs do not matter.Incremental cash flows
matter.Opportunity costs matter.Side effects like cannibalism
and erosion matter.Taxes matter: we want incremental after-tax
cash flows. Inflation matters.
*
6-*
Cash Flows—Not Accounting IncomeConsider depreciation
expense. You never write a check made out to
“depreciation.”Much of the work in evaluating a project lies in
taking accounting numbers and generating cash flows.
*
6-*

Incremental Cash FlowsSunk costs are not relevantJust 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, that does not mean that it
should also have automatic acceptance. Specifically, if another
project with a higher NPV would have to be passed up, then we
should not proceed.
*
I heard a story about an undergrad at the University of
Missouri-Rolla. A student named Louis abandoned college three
credit hours shy of graduation. Really. Entreaties from his
friends and parents regarding how far he had come and how
hard he had worked could not change Louis’ mind. That was all
a sunk cost to Louis. He already had a job and didn’t value the
degree as much as the incremental work of an easy three-hour
required class called ET-10 Engineering Drafting. Fifteen years
later, he still has a good job, a great wife and two charming
daughters. Louis taught us a lot about sunk costs.
6-*
Incremental Cash FlowsSide effects matter.Erosion is a “bad”
thing. If our new product causes existing customers to demand
less of our current products, we need to recognize that.If,
however, synergies result that create increased demand of
existing products, we also need to recognize that.
*
6-*

Estimating Cash FlowsCash Flow from OperationsRecall that:
OCF = EBIT – Taxes + DepreciationNet Capital
SpendingDo not forget salvage value (after tax, of
course).Changes in Net Working CapitalRecall that when the
project winds down, we enjoy a return of net working capital.
*
Of course, amortization could be included as well; however, the
formula as presented is the typical statement.
6-*
Interest ExpenseLater 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, it is enough to assume that the firm’s level
of debt (and, hence, interest expense) is independent of the
project at hand.
*
It may be beneficial to note the separation theorem, i.e.,
financing and investment decisions are separate activities.
Further, you can note that the discount rate captures these
related issues.
6-*
6.2 The Baldwin Company
Costs of test marketing (already spent): $250,000
Current market value of proposed factory site (which we own):
$150,000
Cost of bowling ball machine: $100,000 (depreciated according

to MACRS 5-year)
Increase in net working capital: $10,000
Production (in units) by year during 5-year life of the machine:
5,000, 8,000, 12,000, 10,000, 6,000
*
See the text for the details of the case.
6-*
The Baldwin Company
Price during first year is $20; price increases 2% per year
thereafter.
Production costs during first year are $10 per unit and increase
10% per year thereafter.
Annual inflation rate: 5%
Working Capital: initial $10,000 changes with sales
*
6-*
The Baldwin Company
Year 0 Year 1 Year 2 Year 3
Year 4 Year 5
Investments:
(1) Bowling ball machine –100.00
21.76*
(2) Accumulated 20.00 52.00 71.20
82.72 94.24 depreciation
(3) Adjusted basis of 80.00 48.00 28.80

17.28 5.76 machine after
depreciation (end of year)
(4) Opportunity cost –150.00
150.00
(warehouse)
(5) Net working capital 10.00 10.00 16.32 24.97
21.22 0 (end of year)
(6) Change in net –10.00 –6.32 –8.65
3.75 21.22 working capital
(7) Total cash flow of –260.00 –6.32 –8.65
3.75 192.98 investment
[(1) + (4) + (6)]
($ thousands) (All cash flows occur at the end of the year.)
*
* We assume that the ending market value of the capital
investment at year 5 is $30,000. Capital gain is the difference
between ending market value and adjusted basis of the machine.
The adjusted basis is the original purchase price of the machine
less depreciation. The capital gain is $24,240 (= $30,000 –
$5,760). We will assume the incremental corporate tax for
Baldwin on this project is 34 percent. Capital gains are now
taxed at the ordinary income rate, so the capital gains tax due is
$8,242 = [0.34 * ($30,000 – $5,760)]. The after-tax salvage
value is $30,000 – 8,242 = $21,758.
6-*
The Baldwin Company
At the end of the project, the warehouse is unencumbered, so we

can sell it if we want to.
Year 4 Year 5
Investments:
(1) Bowling ball machine –100.00
21.76
(2) Accumulated 20.00 52.00 71.20
82.72 94.24 depreciation
(3) Adjusted basis of 80.00 48.00 28.80
17.28 5.76 machine after
depreciation (end of year)
(4) Opportunity cost –150.00
150.00
(warehouse)
(5) Net working capital 10.00 10.00 16.32 24.97
21.22 0
(end of year)
(6) Change in net –10.00 –6.32 –8.65
3.75 21.22 working capital
(7) Total cash flow of –260.00 –6.32 –8.65
3.75 192.98 investment
[(1) + (4) + (6)]
*
In practice, we would want to forecast the market value of the
warehouse at the time the project ends. In this case, the implicit
assumption is that there is no price inflation or deflation over
the period.
6-*

The Baldwin Company
Year 4 Year 5
Income:
(8) Sales Revenues 100.00 163.20 249.70 212.24
129.89
Recall that production (in units) by year during the 5-year life
of the machine is given by:
(5,000, 8,000, 12,000, 10,000, 6,000).
Price during the first year is $20 and increases 2% per year
thereafter.
Sales revenue in year 2 = 8,000×[$20×(1.02)1] = 8,000×$20.40
= $163,200.
*
6-*
The Baldwin Company
Year 4 Year 5
Income:
(8) Sales Revenues 100.00 163.20 249.70 212.24
129.89
(9) Operating costs 50.00 88.00 145.20 133.10
87.85

Again, production (in units) by year during 5-year life of the
machine is given by:
(5,000, 8,000, 12,000, 10,000, 6,000).
Production costs during the first year (per unit) are $10, and
they increase 10% per year thereafter.
Production costs in year 2 = 8,000×[$10×(1.10)1] = $88,000
*
6-*
The Baldwin Company
Year 4 Year 5
Income:
(8) Sales Revenues 100.00 163.20 249.70 212.24
129.89
(9) Operating costs 50.00 88.00 145.20 133.10
87.85
(10) Depreciation 20.00 32.00 19.20
11.52 11.52
Depreciation is calculated using the Modified Accelerated Cost
Recovery System (shown at right).
Our cost basis is $100,000.
Depreciation charge in year 4
= $100,000×(.1152) = $11,520.
Year ACRS %
1 20.00%
2 32.00%
3 19.20%
4 11.52%

5 11.52%
6 5.76%
Total 100.00%
*
6-*
The Baldwin Company
Year 4 Year 5
Income:
(8) Sales Revenues 100.00 163.20 249.70 212.24
129.89
(9) Operating costs 50.00 88.00 145.20 133.10
87.85
(10) Depreciation 20.00 32.00 19.20
11.52 11.52
(11) Income before taxes 30.00 43.20 85.30
67.62 30.53
[(8) – (9) - (10)]
(12) Tax at 34 percent 10.20 14.69 29.00
22.99 10.38
(13) Net Income 19.80 28.51 56.30
44.63 20.15
*

6-*
Incremental After Tax Cash Flows
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
(1) Sales Revenues
$100.00
$163.20
$249.70
$212.24
$129.89
(2) Operating costs

-50.00
-88.00
-145.20
-133.10
-87.85
(3) Taxes
-10.20
-14.69
-29.00
-22.99
-10.38
(4) OCF
(1) – (2) – (3)
39.80
60.51
75.50

56.15
31.67
(5) Total CF of Investment
–260.
–6.32
–8.65
3.75
192.98
(6) IATCF
[(4) + (5)]
–260.
39.80
54.19
66.85
59.90
224.65

*
6-*
NPV of Baldwin Company
1
39.80
51.59
–260
CF1
F1
CF0
I
NPV
10
1
54.19
CF2
F2
1
66.85
CF3
F3
1
59.90
CF4
F4
1
224.65
CF5
F5

*
6-*
7.3 Inflation and Capital BudgetingInflation 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 equation:
(1 + Nominal Rate) = (1 + Real Rate) × (1 + Inflation
Rate)
*
6-*
Inflation and Capital BudgetingFor low rates of inflation, this is
l Rate – Inflation
RateWhile the nominal rate in the U.S. has fluctuated with
inflation, the real rate has generally exhibited far less variance
than the nominal rate.In capital budgeting, one must compare
real cash flows discounted at real rates or nominal cash flows
discounted at nominal rates.
*
6-*
6.4 Other Methods for Computing OCFBottom-Up

ApproachWorks only when there is no interest expenseOCF =
NI + depreciationTop-Down ApproachOCF = Sales – Costs –
TaxesDo not subtract non-cash deductionsTax Shield
ApproachOCF = (Sales – Costs)(1 – T) + Depreciation*T
*
6-*
6.5 Some Special Cases of Discounted Cash Flow AnalysisCost-
Cutting ProposalsSetting the Bid PriceInvestments of Unequal
Lives
6-*
Cost-Cutting ProposalsCost savings will increase pretax
incomeBut, we have to pay taxes on this amountDepreciation
will reduce our tax liabilityDoes the present value of the cash
flow associated with the cost savings exceed the cost?If yes,
then proceed.
6-*
Setting the Bid PriceFind the sales price that makes NPV =
0Step 1: Use known changes in NWC and capital to estimate
“preliminary” NPVStep 2: Determine what yearly OCF is
needed to make NPV = 0Step 3: Determine what NI is required
to generate the OCF OCF = NI + DepreciationStep 4: Identify
what sales (and price) are necessary to create the required NINI
= (Sales – Costs – Depreciation)*(1 – T)

It might be helpful to point out that we are essentially working
backwards through the process.
*
6-*
Investments of Unequal LivesThere are times when application
of the NPV rule can lead to the wrong decision. Consider a
factory that must have an air cleaner that is mandated by law.
There are two choices:The “Cadillac cleaner” costs $4,000
today, has annual operating costs of $100, and lasts 10
years.The “Cheapskate cleaner” costs $1,000 today, has annual
operating costs of $500, and lasts 5 years.Assuming a 10%
discount rate, which one should we choose?
*
6-*
Investments of Unequal Lives
At first glance, the Cheapskate cleaner has a higher NPV.
10
–100
–4,614.46
– 4,000
10
5
–500
–2,895.39
–1,000
10

CF1
F1
CF0
I
NPV
CF1
F1
CF0
I
NPV
Cadillac Air Cleaner
Cheapskate Air Cleaner
*
6-*
Investments of Unequal LivesThis overlooks the fact that the
Cadillac cleaner lasts twice as long.When we incorporate the
difference in lives, the Cadillac cleaner is actually cheaper (i.e.,
has a higher NPV).
*
6-*
Equivalent Annual Cost (EAC)The EAC is the value of the level
payment annuity that has the same PV as our original set of
cash flows.For example, the EAC for the Cadillac air cleaner is

$750.98.The EAC for the Cheapskate air cleaner is $763.80,
thus we should reject it.
*
6-*
Cadillac EAC with a Calculator
10
–100
–4,614.46
–4,000
10
750.98
10
–4,614.46
10
CF1
F1
CF0
I
NPV
PMT
I/Y
FV
PV
N
PV
*

6-*
Cheapskate EAC with a Calculator
5
–500
–2,895.39
–1,000
10
763.80
10
-2,895.39
5
CF1
F1
CF0
I
NPV
PMT
I/Y
FV
PV
N
PV
*
6-*
Quick QuizHow do we determine if cash flows are relevant to
the capital budgeting decision?What are the different methods
for computing operating cash flow, and when are they
important?How should cash flows and discount rates be matched

when inflation is present?What is equivalent annual cost, and
when should it be used?
*
59
.
51
$
)
10
.
1
(
65
.
224
$
)
10
.
1
(
90
.
59
$
)
10
.
1
(
85
.
66

$
)
10
.
1
(
19
.
54
$
)
10
.
1
(
80
.
39
$
260
$
5
4
3
2
=
+
+
+
+
+
-
=
NPV
NPV

Presented below are an organization’s (Company-A) opening
financial position and a series of transactions that take place
over a year. You should determine the appropriate manner in
which to record these transactions and then produce three
financial statements for the organization at the end of the year.
COMPANY-A offers its clients security systems and alarm
monitoring services on a retail basis. COMPANY-A specializes
in offering the most up-to-date services with the most
technologically advanced equipment. For example, the high-end
alarm system, called DAS59, is widely recognized as an
industry leader. All of the balance sheet items from December
31, 2012, are shown below along with the events that occurred
during 2013. Please ignore all taxes (income and sales) in
preparing your answer.
Part 1: Opening Balances
Company-A, Inc. Balance Sheet Items
As of December 31, 2012
Accounts payable $380,000
Accounts receivable $611,000
Accumulated depreciation $1,245,000
Cash $267,000
Common shares $1,152,000
Short-term bank loan $125,000
Plant, property, and equipment $2,111,000
Interest payable $37,000
Inventory $850,000
Licenses (net) $180,000
Long-term bank loan $525,000
Goodwill $80,000
Retained earnings $304,000
Advances from customers $340,000
Salaries payable $180,000
Short-term investments (trading securities) $180,000

Office supplies $9,000
The following events occurred during 2013:
(Part 2: Transactions A-N)
A. New credit sales for the year were $1,910,000.
B. New cash sales for the year were $333,000.
C. COMPANY-A acquired office supplies on credit for $32,000.
D. Cash collections from credit sales were $1,720,000.
E. Cash payments for items purchased on credit during the year
were $344,000.
F. Paid $363,000 for administrative expenses during the year.
G. COMPANY-A acquired $212,000 of inventory on credit.
H. At the end of the year, COMPANY-A owed the bank $19,000
in interest.
I. COMPANY-A collected $327,000 of cash advances from
customers.
J. COMPANY-A offers a “satisfaction guarantee” to its clients
for security services. If clients are unhappy with the services
they purchased, they are eligible for free additional security
services (i.e., this is a form of “after sales warranty” service).
The company estimates that future expenditures of
approximately $67,000 will be required to perform these “after
sales warranty” activities to keep clients satisfied for services
originally rendered to clients in 2013.
K. COMPANY-A spent $125,000 during 2013 on research and
development activities related to new services the company
could offer clients. It is expected that some of these products
would be marketable within one or two years, but nobody is
sure which products will be successful.
L. On the last day of business in 2013, COMPANY-A declared
an $80,000 dividend, which will be paid sometime in the next
year.
M. At the end of the year, COMPANY-A owed its employees a
total of $66,000 in wages.
N. COMPANY-A paid down the long-term loan by $140,000.

(Part 3: Transactions O-Z)
O. Sales of $272,000 were earned from prior period cash
advances from customers.
P. At the end of the year, the market value of the short-term
investments was $157,000.
Q. A total of $3,000 in office supplies remained on hand at the
end of the year.
R. COMPANY-A’s policy is to write off all intangible assets
over 3 years using straight-line amortization. 2013 is the second
year for amortizing licenses.
S. At the end of the year, it was determined that $513,000 of
inventory remained on-hand.
T. At the end of the year, it was determined that the carrying
value of goodwill had declined by $28,000.
U. Old equipment, which had originally cost $147,000 and was
fully depreciated, was scrapped on the first day of business of
the year.
V. COMPANY-A acquired all of the assets and liabilities of
Smith Alarms, LLC for $555,000 cash. The assets included
equipment valued at $425,000 (this equipment was carried on
the books of Smith Alarms, LLC at $300,000 net), accounts
receivable of $230,000, accounts payable of $250,000, and a
demand loan of $52,000. There were no intangible assets.
W. COMPANY-A paid salaries to employees of $390,000 in
cash.
X. Paid the bank $58,000 cash towards interest payments during
the year.
Y. Depreciation on plant, property, and equipment for 2013 was
determined to be $123,000.
Z. At the end of the year, the accountant estimated that $22,000
of accounts receivable owed to the firm would not likely be
collected.
Part 4: Financial Statements

Create the three financial statements on an Excel spreadsheet.
Use standard financial statement heading and formatting
conventions.
· A Balance Sheet for Company-A as of December 31, 2013.
· An Income Statement for Company-A for the year ending
December 31, 2013.
· A Statement of Cash Flows for Company-A for the year
ending December 31, 2013
Sample Transaction Recording – Classification needed of
opening balances.
Company-A.
Balance Sheet Items
As of December 31, 2012
Transaction
Amount

Asset, ContraAsset, Liability, Stockholders’ Equity
Debit (Left)
Credit (Right)
Accounts payable
$380,000
Accounts receivable
$611,000
Accumulated depreciation
$1,245,000
Cash
$267,000
Common shares
$1,152,000
Short-term bank loan
$125,000
Plant, property, and equipment
$2,111,000
Interest payable
$37,000

Inventory
$850,000
Licenses (net)
$180,000
Long-term bank loan
$525,000
Goodwill
$80,000
Retained earnings
$304,000
Advances from customers
$340,000
Salaries payable
$180,000
Short-term investments (trading securities)
$180,000
Office supplies
$9,000

In addition to the A-Z transactions, other events were posted to
the General Ledger.
Use the General Ledger's ending balances (shown below in
alphabetical order) to
prepare the company's Income Statement and Balance Sheet for
fiscal year 2014.
Company-A, Inc.
Trial Balance
December 31, 2014
Accounts Payable 555,000
Accounts receivable (net) 1,125,000
Accum.Depreciation 1,273,000
Administrative Expenses 380,000
Advances from Customers 450,000
Bad Debt Expense 27,000
Cash 695,000
Common Stock 1,291,000
Cost of Goods Sold 600,000
Decline in ST Investments 25,000
Demand Loan Payable 225,000
Depreciation Expense 145,000
Dividends Payable 80,000
Dividends, declared 100,000
Equipment & Buildings 2,533,000
Goodwill (net) 325,000
Goodwill Impairment 30,000
Interest Expense 50,000
Interest Payable 33,000
Inventory 535,000
Licenses (net) 140,000
Licenses, Amortization 110,000
Long-term Loan Payable 415,000
Research & Development Expense 140,000
Retained Earnings, Beg.Balance 304,000

Salaries Expense 325,000
Salaries Payable 97,000
Sales Revenue 2,750,000
Short-term Investments (net) 164,000
Supplies 6,000
Supplies Expense 43,000
Warranties Expense 75,000
Warranty Payable 100,000
Statement of Cash Flows
The following information was obtained from the company's
General Ledger's Cash account. Use these events to create a
Statement of Cash Flows for the current fiscal year.
NOTE: The cash amounts in this listing are NOT meant to
correlate to the Income Statement or various non-Cash accounts
on the Balance Sheet!
267,000 Cash, beginning balance
695,000 Cash, ending balance
Cash Generated/Used by the company:
a
500,000
Accounts Payable
b
1,825,000
Accounts Receivable collections
c
400,000
Administrative Expenses
d
600,000
Buying a competitor’s business
e

375,000
Customer Advances
f
25,000
Dividends to Investors
g
15,000
Furniture & Equipment purchases
h
60,000
Interest Expense
i
3,000
Interest Revenue
j
100,000
Issued additional shares of CommonStock
k
150,000
Research and Development
l
475,000
Salaries and Wages
m
350,000
Sales Revenue
McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc.
All rights reserved.

Net Present Value and Other Investment Rules
Chapter 5
*
5-*
Key Concepts and SkillsBe able to compute payback and
discounted payback and understand their shortcomingsBe able
to compute the internal rate of return and profitability index,
understanding the strengths and weaknesses of both
approachesBe able to compute net present value and understand
why it is the best decision criterion
*
5-*
Chapter Outline
5.1 Why Use Net Present Value?
5.2 The Payback Period Method
5.3 The Discounted Payback Period Method
5.4 The Internal Rate of Return
5.5 Problems with the IRR Approach
5.6 The Profitability Index
5.7 The Practice of Capital Budgeting
*

5-*
5.1 Why Use Net Present Value?Accepting positive NPV
projects benefits shareholders.
NPV uses cash flows
NPV uses all the cash flows of the project
NPV discounts the cash flows properly
*
Note that the NPV recognizes the magnitude, risk, and timing of
cash flows, which was an important description of why stock
price maximization should be the primary corporate goal.
5-*
The Net Present Value (NPV) RuleNet Present Value (NPV) =
Total PV of future CF’s + Initial InvestmentEstimating NPV:
1. Estimate future cash flows: how much? and when?
2. Estimate discount rate
3. Estimate initial costsMinimum Acceptance Criteria: Accept if
NPV > 0Ranking Criteria: Choose the highest NPV
*
Note that although we add the initial investment, this value is a
negative number.
5-*
Calculating NPV with SpreadsheetsSpreadsheets are an
excellent way to compute NPVs, especially when you have to

compute the cash flows as well.Using the NPV function:The
first component is the required return entered as a decimal.The
second component is the range of cash flows beginning with
year 1.Add the initial investment after computing the NPV.
*
Click on the Excel icon to go to an embedded Excel worksheet
that has example cash flows, along with the correct and
incorrect ways to compute NPV. Click on the cell with the
solution to show the students the difference in the formulas.
Again, note that when we add the initial investment, this is a
negative number.
Sheet1Year0123Cash Flows-165000631207080091080Required
Return0.12NPV - Incorrect$11,274.48NPV - Correct$12,627.41
Sheet2
Sheet3
Return0.12NPV - Incorrect$11,274.48NPV - Correct$12,627.41
Sheet2
Sheet3
5-*
5.2 The Payback Period MethodHow long does it take the
project to “pay back” its initial investment?Payback Period =
number of years to recover initial costsMinimum Acceptance
Criteria: Set by managementRanking Criteria: Set by
management
*

5-*
The Payback Period MethodDisadvantages:Ignores the time
value of moneyIgnores cash flows after the payback
periodBiased against long-term projectsRequires an arbitrary
acceptance criteriaA project accepted based on the payback
criteria may not have a positive NPVAdvantages:Easy to
understandBiased toward liquidity
*
Cash flows prior to the cutoff are implicitly discounted at a rate
of zero, and cash flows after the cutoff are discounted using an
infinite discount rate.
5-*
5.3 The Discounted Payback PeriodHow long does it take the
project to “pay back” its initial investment, taking the time
value of money into account?Decision rule: Accept the project
if it pays back on a discounted basis within the specified
time.By the time you have discounted the cash flows, you might
as well calculate the NPV.
*
Similar advantages and disadvantages as standard payback
method, with the exception that cash flows prior to the cutoff
are not discounted at zero.
5-*

5.4 The Internal Rate of ReturnIRR: the discount rate that sets
NPV to zero Minimum Acceptance Criteria: Accept if the IRR
exceeds the required returnRanking Criteria: Select alternative
with the highest IRRReinvestment assumption: All future cash
flows are assumed to be reinvested at the IRR
*
5-*
Internal Rate of Return (IRR)Disadvantages:Does not
distinguish between investing and borrowingIRR may not exist,
or there may be multiple IRRs Problems with mutually
exclusive investments
Advantages:Easy to understand and communicate
*
5-*
IRR: Example
Consider the following project:
The internal rate of return for this project is 19.44%
0

1
2
3
$50
$100
$150
-$200
*
5-*
NPV Payoff Profile
If we graph NPV versus the discount rate, we can see the IRR as
the x-axis intercept.
IRR = 19.44%
*
Sheet10123-2005010015019.44%Discount
RateNPV0%$100.001%$92.202%$84.793%$77.744%$71.045%$
64.666%$58.607%$52.828%$47.329%$42.0810%$37.0911%$32
.3312%$27.7913%$23.4714%$19.3415%$15.4116%$11.6517%$
8.0718%$4.6519%$1.3820%($1.74)21%($4.72)22%($7.56)23%(
$10.28)24%($12.88)25%($15.36)26%($17.73)27%($20.00)28%(
$22.17)29%($24.24)30%($26.22)31%($28.12)32%($29.93)33%(
$31.67)34%($33.32)35%($34.91)36%($36.43)37%($37.88)38%(
$39.26)39%($40.59)40%($41.86)Discount
RateNPV0%$100.004%$73.888%$51.1112%$31.1316%$13.522

0%($2.08)24%($15.97)28%($28.38)32%($39.51)36%($49.54)40
%($58.60)44%($66.82)48%($50.20)52%($53.36)56%($55.99)60
%($58.17)64%($59.95)17%$8.0718%$4.6519%$1.3820%($1.74
)21%($4.72)22%($7.56)23%($10.28)24%($12.88)25%($15.36)2
6%($17.73)27%($20.00)28%($22.17)29%($24.24)30%($26.22)3
1%($28.12)32%($29.93)33%($31.67)34%($33.32)35%($34.91)3
6%($36.43)37%($37.88)38%($39.26)39%($40.59)40%($41.86)
Sheet100000000000000000000000000000000000000000
NPV
Discount rate
NPV
Sheet2
Sheet3
Chart500.010.020.030.040.050.060.070.080.090.10.110.120.130
.140.150.160.170.180.190.20.210.220.230.240.250.260.270.280.
290.30.310.320.330.340.350.360.370.380.390.4
NPV
Discount rate
NPV
100
93.1230776249
86.484836149
80.0745291367
73.8819981793
67.8976352446
62.112347777
56.5175263236
51.1050144795
45.8670809688
40.796393689
35.8859955646
31.12928207
26.5199802897
22.0521294001
17.720062464

13.5183894379
9.4419813026
5.485955234
1.6456607359
-2.0833333333
-5.7052509058
-9.2241200805
-12.6437837847
-15.9679097714
-19.2
-22.3433994409
-25.4013043459
-28.3767700195
-31.2727181254
-34.0919435594
-36.8371209173
-39.5108105852
-42.1154644767
-44.6534314394
-47.1269623533
-49.53821494
-51.889258301
-54.1820772034
-56.4185761271
-58.6005830904
Sheet10123-2005010015019.44%Discount
RateNPV0%$100.001%$93.122%$86.483%$80.074%$73.885%$
67.906%$62.117%$56.528%$51.119%$45.8710%$40.8011%$35
.8912%$31.1313%$26.5214%$22.0515%$17.7216%$13.5217%$
9.4418%$5.4919%$1.6520%($2.08)21%($5.71)22%($9.22)23%(
$12.64)24%($15.97)25%($19.20)26%($22.34)27%($25.40)28%(
$28.38)29%($31.27)30%($34.09)31%($36.84)32%($39.51)33%(
$42.12)34%($44.65)35%($47.13)36%($49.54)37%($51.89)38%(
$54.18)39%($56.42)40%($58.60)Discount
RateNPV0%$100.004%$73.888%$51.1112%$31.1316%$13.522
0%($2.08)24%($15.97)28%($28.38)32%($39.51)36%($49.54)40

%($58.60)44%($66.82)48%($74.29)52%($81.11)56%($87.35)60
%($93.07)64%($98.33)17%$9.4418%$5.4919%$1.6520%($2.08
)21%($5.71)22%($9.22)23%($12.64)24%($15.97)25%($19.20)2
6%($22.34)27%($25.40)28%($28.38)29%($31.27)30%($34.09)3
1%($36.84)32%($39.51)33%($42.12)34%($44.65)35%($47.13)3
6%($49.54)37%($51.89)38%($54.18)39%($56.42)40%($58.60)
Sheet100000000000000000000000000000000000000000
NPV
Discount rate
NPV
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Sheet2
Sheet3
5-*
Calculating IRR with SpreadsheetsYou start with the same cash
flows as you did for the NPV.You use the IRR function:You
first enter your range of cash flows, beginning with the initial
cash flow.You can enter a guess, but it is not necessary.The
default format is a whole percent – you will normally want to
increase the decimal places to at least two.
*
Click on the Excel icon to go to an embedded spreadsheet so
that you can illustrate how to compute IRR on a spreadsheet.
Return0.12NPV - Incorrect$11,274.48NPV -
Correct$12,627.41IRR16%16.13%Default Format

Sheet2
Sheet3
5-*
5.5 Problems with IRR
Multiple IRRsAre We Borrowing or LendingThe Scale
ProblemThe Timing Problem
*
5-*
Mutually Exclusive vs. IndependentMutually Exclusive
Projects: only ONE of several potential projects can be chosen,
e.g., acquiring an accounting system. RANK all alternatives,
and select the best one.
Independent Projects: accepting or rejecting one project does
not affect the decision of the other projects.Must exceed a
MINIMUM acceptance criteria
*
5-*
Multiple IRRs
There are two IRRs for this project:

Which one should we use?
0 1 2 3
$200 $800
-$200
- $800
100% = IRR2
0% = IRR1
*
It is good to mention that the number of IRRs is equivalent to
the number of sign changes in the cash flows.
Chart4-0.1-
0.0500.050.10.150.20.250.30.350.40.450.50.550.60.650.70.750.
80.850.90.9511.051.11.151.21.251.31.351.41.451.51.551.61.651
.71.751.81.851.9
NPV
Discount rate
NPV
-87.5171467764
-36.1277154104
0
25.0296944174
41.9233658903
52.8149913701
59.2592592593
62.4
63.0860263996

61.9519382208
59.4752186589
56.0170568699
51.8518518519
47.1887482797
42.1875
36.9702534992
31.6303684103
26.2390670554
20.8504801097
15.5054981936
10.2347280945
5.0607731081
0
-4.9360862437
-9.7397689234
-14.4062786924
-18.9331329827
-23.3196159122
-27.5663680447
-31.6750623658
-35.6481481481
-39.4886484373
-43.2
-46.7859269813
-50.2503413746
-53.5972648562
-56.8307676675
-59.9549211119
-62.9737609329
-65.8912593889
-68.7113042765
Sheet10123-200200800-800-0.00%Discount RateNPV-
10%($87.52)-
5%($36.13)0%$0.005%$25.0310%$41.9215%$52.8120%$59.26
25%$62.4030%$63.0935%$61.9540%$59.4845%$56.0250%$51.

8555%$47.1960%$42.1965%$36.9770%$31.6375%$26.2480%$
20.8585%$15.5190%$10.2395%$5.06100%$0.00105%($4.94)11
0%($9.74)115%($14.41)120%($18.93)125%($23.32)130%($27.5
7)135%($31.68)140%($35.65)145%($39.49)150%($43.20)155%
($46.79)160%($50.25)165%($53.60)170%($56.83)175%($59.95
)180%($62.97)185%($65.89)190%($68.71)Discount
RateNPV0%$0.004%$20.768%$35.9912%$46.9016%$54.4220%
$59.2624%$61.9928%$63.0632%$62.8236%$61.5540%$59.484
4%$56.7748%$53.5952%$50.0456%$46.2160%$42.1964%$38.0
317%$55.8518%$57.1319%$58.2720%$59.2621%$60.1222%$6
0.8623%$61.4824%$61.9925%$62.4026%$62.7127%$62.9328%
$63.0629%$63.1130%$63.0931%$62.9932%$62.8233%$62.593
4%$62.3035%$61.9536%$61.5537%$61.1038%$60.6039%$60.0
640%$59.48
Sheet100000000000000000000000000000000000000000
NPV
Discount rate
NPV
-87.5171467764
-38.0291741162
0
23.8378042071
38.1121508094
45.9260794523
49.3827160494
49.92
48.5277126151
45.890324608
42.4822990421
38.6324530137
34.5679012346
30.4443537288
26.3671875
22.4062142419
18.6060990649
14.9937526031

11.583600061
8.3813503749
5.3866989971
2.5952682606
0
-2.4078469481
-4.6379852016
-6.7005947407
-8.6059695376
-10.3642737388
-11.9853774107
-13.4787499429
-14.8533950617
-16.1178156887
-17.28
-18.3474223456
-19.3270543748
-20.2253829646
-21.0484324695
-21.8017894953
-22.4906289046
-23.1197401364
-23.6935531988
Sheet2
Sheet3
5-*
Modified IRRCalculate the net present value of all cash
outflows using the borrowing rate.Calculate the net future value
of all cash inflows using the investing rate.Find the rate of
return that equates these values.Benefits: single answer and
specific rates for borrowing and reinvestment

*
The alternative approach discussed in the text is to discount
cash flows over a single period (or subset of time), then
combine them as necessary to eliminate any sign differences.
The approach presented in the slide is more generalized.
5-*
The Scale Problem
Would you rather make 100% or 50% on your investments?
What if the 100% return is on a $1 investment, while the 50%
return is on a $1,000 investment?
*
5-*
The Timing Problem
0 1 2 3
$10,000 $1,000 $1,000
-$10,000

Project A
0 1 2 3
$1,000 $1,000 $12,000
-$10,000
Project B
*
The preferred project in this case depends on the discount rate,
not the IRR.
5-*
The Timing Problem
10.55% = crossover rate
16.04% = IRRA
12.94% = IRRB
*
The cross-over rate is the IRR of project A-B
Chart7000.010.010.020.020.030.030.040.040.050.050.060.060.0
70.070.080.080.090.090.10.10.110.110.120.120.130.130.140.14
0.150.150.160.160.170.170.180.180.190.190.20.20.210.210.220.
220.230.230.240.240.250.250.260.260.270.270.280.280.290.290
.30.30.310.310.320.320.330.330.340.340.350.350.360.360.370.3

70.380.380.390.390.40.4
Project A
Project B
Discount rate
NPV
2000
4000
1851.8762963445
3617.4768344396
1707.4126844125
3249.4289526653
1566.4754325646
2895.1696077794
1428.9371870733
2554.0509786072
1294.676600799
2225.4616132167
1163.5779871975
1908.824062817
1035.5309976874
1603.5926902158
910.4303205812
1309.2516384697
788.1753999331
1025.3129466599
668.6701728024
751.3148009016
551.822823554
486.8199097564
437.5455539359
231.4139941691
325.7543677754
-15.2956170815
216.3688692337
-253.6812946494
109.3120736418

-484.0963261281
4.5102300217
-706.8760506786
-98.1073455323
-922.3389170792
-198.6084263727
-1130.7874709683
-297.0580224181
-1332.5092765727
-393.5185185185
-1527.7777777778
-488.0498046638
-1716.8531029979
-580.709398584
-1899.9828179451
-671.5525612524
-2077.4026300644
-760.6324057601
-2249.3370481018
-848
-2416
-933.7044635609
-2577.5954120625
-1017.7930592082
-2734.3177521001
-1100.3112792969
-2886.3525390625
-1181.3029274385
-3033.8768214678
-1260.8101957214
-3177.0596267638
-1338.8737377624
-3316.0623835957
-1415.5327378468
-3451.0393188079
-1490.8249763988

-3582.1378308681
-1564.7868920047
-3709.4988412804
-1637.4536401971
-3833.2571254382
-1708.859149196
-3953.5416242622
-1779.0361727853
-4070.4757378703
-1848.016340496
-4184.1776024401
-1915.8302052525
-4294.760351338
-1982.5072886297
-4402.332361516
Sheet10123$ (10,000.00)$ 10,000.00$ 1,000.00$
1,000.00A$ (10,000.00)$ 1,000.00$ 1,000.00$
12,000.00B16.04%IRR A12.94%IRR BDiscount RateProject
AProject
B0%$2,000.00$4,000.001%$1,851.88$3,617.482%$1,707.41$3,
249.433%$1,566.48$2,895.174%$1,428.94$2,554.055%$1,294.6
8$2,225.466%$1,163.58$1,908.827%$1,035.53$1,603.598%$91
0.43$1,309.259%$788.18$1,025.3110%$668.67$751.3111%$55
1.82$486.8212%$437.55$231.4113%$325.75($15.30)14%$216.3
7($253.68)15%$109.31($484.10)16%$4.51($706.88)17%($98.11
)($922.34)18%($198.61)($1,130.79)19%($297.06)($1,332.51)20
%($393.52)($1,527.78)21%($488.05)($1,716.85)22%($580.71)(
$1,899.98)23%($671.55)($2,077.40)24%($760.63)($2,249.34)25
%($848.00)($2,416.00)26%($933.70)($2,577.60)27%($1,017.79
)($2,734.32)28%($1,100.31)($2,886.35)29%($1,181.30)($3,033.
88)30%($1,260.81)($3,177.06)31%($1,338.87)($3,316.06)32%(
$1,415.53)($3,451.04)33%($1,490.82)($3,582.14)34%($1,564.7
9)($3,709.50)35%($1,637.45)($3,833.26)36%($1,708.86)($3,95
3.54)37%($1,779.04)($4,070.48)38%($1,848.02)($4,184.18)39
%($1,915.83)($4,294.76)40%($1,982.51)($4,402.33)Discount
RateNPV0%$2,000.004%$1,428.948%$910.4312%$437.5516%$

4.5120%($393.52)24%($760.63)28%($1,100.31)32%($1,415.53)
36%($1,708.86)40%($1,982.51)44%($2,238.40)48%($2,478.23)
52%($2,703.47)56%($2,915.42)60%($3,115.23)64%($3,303.93)
17%($98.11)18%($198.61)19%($297.06)20%($393.52)21%($48
8.05)22%($580.71)23%($671.55)24%($760.63)25%($848.00)26
%($933.70)27%($1,017.79)28%($1,100.31)29%($1,181.30)30%
($1,260.81)31%($1,338.87)32%($1,415.53)33%($1,490.82)34%
($1,564.79)35%($1,637.45)36%($1,708.86)37%($1,779.04)38%
($1,848.02)39%($1,915.83)40%($1,982.51)
Sheet1000.010.010.020.020.030.030.040.040.050.050.060.060.0
70.070.080.080.090.090.10.10.110.110.120.120.130.130.140.14
0.150.150.160.160.170.170.180.180.190.190.20.20.210.210.220.
220.230.230.240.240.250.250.260.260.270.270.280.280.290.290
.30.30.310.310.320.320.330.330.340.340.350.350.360.360.370.3
70.380.380.390.390.40.4
Project A
Project B
Discount rate
NPV
2000
4000
1833.5408874698
3581.6602321185
1673.934004326
3185.7146594758
1520.8499345287
2810.8442793975
1373.9780644935
2455.8182486608
1233.0253340943
2119.4872506826
1097.7150822618
1800.7774177518
967.7859791471
1498.684757211
842.9910375752

1212.2700356201
723.0966971864
940.6540795045
607.8819752749
683.0134553651
497.1376788775
438.576495276
390.665673157
206.619637651
288.2782015711
-13.5359443199
189.7972537138
-222.5274514468
95.0539770798
-420.9533270679
3.8881293291
-609.3759057574
-83.8524320789
-788.3238607515
-168.3122257396
-958.2944669223
-249.6285902673
-1119.7556945989
-327.9320987654
-1273.1481481482
-403.3469460031
-1418.8868619817
-475.9913103148
-1557.3629655288
-545.9776920751
-1688.9452276946
-613.4132304517
-1813.9814904047
-678.4
-1932.8
-741.0352885404

-2045.7106444941
-801.4118576442
-2153.0061040158
-859.6181869507
-2254.9629211426
-915.7387034407
-2351.8424972619
-969.8539967088
-2443.8920205875
-1022.0410211927
-2531.3453309891
-1072.3732862476
-2614.4237263696
-1120.9210348863
-2693.3367149384
-1167.7514119438
-2768.2827173734
-1212.9286223682
-2839.4497225468
-1256.5140802912
-2907.0159001928
-1298.5665494783
-2971.150173628
-1339.1422757217
-3032.0127553914
-1378.2951116924
-3089.7556484446
-1416.0766347355
-3144.5231153686
Sheet2
Sheet3
5-*
Calculating the Crossover Rate

Compute the IRR for either project “A-B” or “B-A”
10.55% = IRR
*
Sheet1YearProject AProject BProject A-BProject B-
A0($10,000)($10,000)$0$01$10,000$1,000$9,000($9,000)2$1,0
00$1,000$0$03$1,000$12,000($11,000)$11,00010.55%Discount
rtaeA-BB-
A0%($2,000.00)1%($1,748.12)2%($1,511.78)3%($1,289.99)4%
($1,081.84)5%($886.46)6%($703.06)7%($530.90)8%($369.28)9
%($217.56)10%($75.13)11%$58.5612%$184.0513%$301.8114
%$412.3215%$516.0116%$613.2617%$704.4718%$789.9819%
$870.1320%$945.22
Sheet1000000000000000000000
A-B
Discount rate
NPV
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
Sheet2
Sheet3
Chart2000.010.010.020.020.030.030.040.040.050.050.060.060.0
70.070.080.080.090.090.10.10.110.110.120.120.130.130.140.14
0.150.150.160.160.170.170.180.180.190.190.20.2
A-B
B-A
Discount rate
NPV
-2000
2000
-1765.6005380952
1765.6005380952
-1542.0162682528
1542.0162682528
-1328.6941752149
1328.6941752149
-1125.1137915339
1125.1137915339
-930.7850124177
930.7850124177
-745.2460756195
745.2460756195
-568.0616925283
568.0616925283
-398.8213178885
398.8213178885
-237.1375467268
237.1375467268

-82.6446280992
82.6446280992
65.0029137977
-65.0029137977
206.1315597668
-206.1315597668
341.0499848569
-341.0499848569
470.0501638831
-470.0501638831
593.4083997699
-593.4083997699
711.3862807003
-711.3862807003
824.2315715469
-824.2315715469
932.1790445956
-932.1790445956
1035.4512541547
-1035.4512541547
1134.2592592593
-1134.2592592593
Sheet1YearProject AProject BProject A-BProject B-
A0($10,000)($10,000)$0$01$10,000$1,000$9,000($9,000)2$1,0
00$1,000$0$03$1,000$12,000($11,000)$11,00010.55%Discount
rtaeA-BB-
A0%($2,000.00)$2,000.001%($1,765.60)$1,765.602%($1,542.0
2)$1,542.023%($1,328.69)$1,328.694%($1,125.11)$1,125.115%
($930.79)$930.796%($745.25)$745.257%($568.06)$568.068%($
398.82)$398.829%($237.14)$237.1410%($82.64)$82.6411%$65
.00($65.00)12%$206.13($206.13)13%$341.05($341.05)14%$47
0.05($470.05)15%$593.41($593.41)16%$711.39($711.39)17%$
824.23($824.23)18%$932.18($932.18)19%$1,035.45($1,035.45)
20%$1,134.26($1,134.26)
Sheet1
A-B

B-A
Discount rate
NPV
Sheet2
Sheet3
5-*
NPV versus IRRNPV and IRR will generally give the same
decision.Exceptions:Non-conventional cash flows – cash flow
signs change more than onceMutually exclusive projectsInitial
investments are substantially differentTiming of cash flows is
substantially different
*
5-*
5.6 The Profitability Index (PI)Minimum Acceptance Criteria:
Accept if PI > 1
Ranking Criteria: Select alternative with highest PI
*
5-*
The Profitability IndexDisadvantages:Problems with mutually
exclusive investmentsAdvantages:May be useful when available

investment funds are limitedEasy to understand and
communicateCorrect decision when evaluating independent
projects
*
5-*
5.7 The Practice of Capital BudgetingVaries by industry:Some
firms may use payback, while others choose an alternative
approach.The most frequently used technique for large
corporations is either IRR or NPV.
*
5-*
Example of Investment Rules
Compute the IRR, NPV, PI, and payback period for the
following two projects. Assume the required return is 10%.
Year Project A Project B
0 -$200 -$150
1 $200 $50
2 $800 $100
3 -$800 $150
*

5-*
Project A Project B
CF0 -$200.00 -$150.00
PV0 of CF1-3 $241.92 $240.80
NPV = $41.92 $90.80
IRR = 0%, 100% 36.19%
PI = 1.2096 1.6053
*
5-*
Payback Period:
Project A Project B
Time CF Cum. CF CF Cum. CF
0 -200 -200 -150 -150
1 200 0 50 -100
2 800 800 100 0
3 -800 0 150 150
Payback period for project B = 2 years.
Payback period for project A = 1 or 3 years?
*

5-*
NPV and IRR Relationship
Discount rate NPV for A NPV for B
-10% -87.52 234.77
0% 0.00 150.00
20% 59.26 47.92
40% 59.48 -8.60
60% 42.19 -43.07
80% 20.85 -65.64
100% 0.00 -81.25
120% -18.93 -92.52
*
5-*
($200)
($100)
$0
$100
$200
$300
$400
-15%
0%
15%
30%
45%
70%
100%
130%
160%

190%
Discount rates
NPV
NPV Profiles
IRR 2(A)
Cross-over Rate
Project A
Project B
IRR 1(A)
IRR (B)

*
5-*
Summary – Discounted Cash FlowNet present valueDifference
between market value and costAccept the project if the NPV is

positiveHas no serious problemsPreferred decision
criterionInternal rate of returnDiscount rate that makes NPV =
0Take the project if the IRR is greater than the required
returnSame decision as NPV with conventional cash flowsIRR
is unreliable with non-conventional cash flows or mutually
exclusive projectsProfitability IndexBenefit-cost ratioTake
investment if PI > 1Cannot be used to rank mutually exclusive
projectsMay be used to rank projects in the presence of capital
rationing
*
5-*
Summary – Payback CriteriaPayback periodLength of time until
initial investment is recoveredTake the project if it pays back in
some specified periodDoes not account for time value of money,
and there is an arbitrary cutoff periodDiscounted payback
periodLength of time until initial investment is recovered on a
discounted basisTake the project if it pays back in some
specified periodThere is an arbitrary cutoff period
*
5-*
Quick QuizConsider an investment that costs $100,000 and has
a cash inflow of $25,000 every year for 5 years. The required
return is 9%, and payback cutoff is 4 years.What is the payback
period?What is the discounted payback period?What is the

NPV?What is the IRR?Should we accept the project?What
method should be the primary decision rule?When is the IRR
rule unreliable?
*
Payback period = 4 years
The project does not pay back on a discounted basis.
NPV = -2758.72
IRR = 7.93%
32
)1(
150$
)1(
100$
)1(
50$
2000
IRRIRRIRR
NPV
0%$100.00
4%$73.88
8%$51.11
12%$31.13
16%$13.52
20%($2.08)
24%($15.97)
28%($28.38)

32%($39.51)
36%($49.54)
40%($58.60)
44%($66.82)
($100.00)
($50.00)
$0.00
$50.00
$100.00
$150.00
-1%9%19%29%39%
Discount rate
NPV
($100.00)
($50.00)
$0.00
$50.00
$100.00
-50%0%50%100%150%200%
Discount rate
NPV
($5,000.00)
($4,000.00)
($3,000.00)
($2,000.00)
($1,000.00)
$0.00
$1,000.00
$2,000.00
$3,000.00
$4,000.00
$5,000.00
0%10%20%30%40%
Discount rate
NPV

Project A
Project B
YearProject AProject BProject A-B Project B-A
0($10,000)($10,000)$0$0
1$10,000$1,000$9,000($9,000)
2$1,000$1,000$0$0
3$1,000$12,000($11,000)$11,000
($3,000.00)
($2,000.00)
($1,000.00)
$0.00
$1,000.00
$2,000.00
$3,000.00
0%5%10%15%20%
Discount rate
NPV
A-B
B-A
Investent Initial
FlowsCash Future of PV Total

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