T9.1 Chapter Outline
C1 Outline
Capital Budgeting - Decision CriteriaNet Present ValueThe
Payback RuleThe Discounted PaybackThe Average Accounting ReturnThe
Internal Rate of ReturnThe Profitability IndexThe Practice of
Capital BudgetingPage #C2 Outline (continued)Project Cash Flows: A
First LookIncremental Cash FlowsPro Forma Financial Statements and
Project Cash FlowsMore on Project Cash FlowsAlternative Definitions
of Operating Cash FlowSome Special Cases of Discounted Cash Flow
AnalysisSummary and ConclusionsC3 NPV IllustratedAssume you have
the following information on Project X:Initial outlay
-$1,100Required return = 10%Annual cash revenues and expenses are
as follows: Year Revenues Expenses 1 $1,000 $500 2 2,000 1,000
Draw a time line and compute the NPV of project X.
C4 NPV Illustrated (concluded)012Initial
outlay($1,100)Revenues$1,000Expenses500Cash
flow$500Revenues$2,000Expenses1,000Cash flow$1,000
$1,100.00+454.55+826.45+$181.00 1$500 x 1.10 1$1,000 x 1.10 2NPVC5
Underpinnings of the NPV RuleWhy does the NPV rule work? And what
does work mean? Look at it this way:A firm is created when
securityholders supply the funds to acquire assets that will be
used to produce and sell a good or a service;The market value of
the firm is based on the present value of the cash flows it is
expected to generate;Additional investments are good if the present
value of the incremental expected cash flows exceeds their
cost;Thus, good projects are those which increase firm value - or,
put another way, good projects are those projects that have
positive NPVs!Moral of the story: Invest only in projects with
positive NPVs. C6 Payback Rule IllustratedInitial outlay -$1,000
YearCash flow 1$200 2400 3600 Accumulated YearCash flow 1$200 2600
31,200Payback period = 2 2/3 yearsC7 Discounted Payback
IllustratedInitial outlay -$1,000R = 10% PV of Year Cash flow Cash
flow 1$ 200$ 182 2400331 3700526 4300205 Accumulated Year
discounted cash flow 1$ 182 2513 31,039 41,244Discounted payback
period is just under 3 years C8 Ordinary and Discounted Payback
Cash Flow Accumulated Cash Flow Year Undiscounted Discounted
Undiscounted Discounted 1$100$89$100$89 210079200168 310070300238
410062400300 510055500355C9 Average Accounting Return
IllustratedAverage net income: Year 1 2
3Sales$440$240$160Costs22012080Gross
profit22012080Depreciation808080Earnings before taxes140400Taxes
(25%)35100Net income$105$30$0Average net income = ($105 + 30 + 0)/3
= $45C10 Average Accounting Return Illustrated (concluded)Average
book value: Initial investment = $240 Average investment = ($240 +
0)/2 = $120 Average accounting return (AAR): Average net income $45
AAR = = = 37.5% Average book value $120C11 Internal Rate of Return
IllustratedInitial outlay = -$200 Year Cash flow 1$ 50 2100
3150Find the IRR such that NPV = 0 50 100 150 0 = -200 + + +
(1+IRR)1 (1+IRR)2 (1+IRR)3 50 100 150 200 = + + (1+IRR)1 (1+IRR)2
(1+IRR)3C12 Internal Rate of Return Illustrated (concluded)Trial
and Error Discount ratesNPV 0%$100 5%68 10%41 15%18 20%-2IRR is
just under 20% -- about 19.44%Year Cash flow 0 $275 1100 2100 3100
4100C13 Net Present Value ProfileDiscount
rate2%6%10%14%18%12010080604020Net present value0 20 4022%IRRAssume
you are considering a project for which the cash flows are as
follows: Year Cash flows 0 -$252 1 1,431 2 -3,035 3 2,850 4
-1,000C14 Multiple Rates of ReturnC15 Multiple Rates of Return
(continued)Whats the IRR? Find the rate at which the computed NPV =
0:
at 25.00%:NPV = _______ at 33.33%:NPV = _______ at 42.86%:NPV =
_______ at 66.67%:NPV = _______
C16 Multiple Rates of Return (continued)Whats the IRR? Find the
rate at which the computed NPV = 0:
at 25.00%:NPV = 0 at 33.33%:NPV = 0 at 42.86%:NPV = 0 at
66.67%:NPV = 0Two questions:1.Whats going on here?2.How many IRRs
can there be?C17 Multiple Rates of Return
(concluded)$0.06$0.04$0.02$0.00($0.02)NPV($0.04)($0.06)($0.08)0.20.280.360.440.520.60.68IRR
= 1/4IRR = 1/3IRR = 3/7IRR = 2/3
Discount rateC18 IRR, NPV, and Mutually Exclusive
ProjectsDiscount rate2%6%10%14%18%6040200 20 40Net present value 60
80 10022% IRR A IRR B014012010080160 Year 0 1 2 3 4Project A:
$35050100150200Project B: $250125100755026%Crossover PointC19
Profitability Index IllustratedNow lets go back to the initial
example - we assumed the following information on Project X:Initial
outlay -$1,100Required return = 10%Annual cash benefits: YearCash
flows 1 $ 500 2 1,000 Whats the Profitability Index (PI)?
C20 Profitability Index Illustrated (concluded)Previously we
found that the NPV of Project X is equal to:
($454.55 + 826.45) - 1,100 = $1,281.00 - 1,100 = $181.00.
The PI = PV inflows/PV outlay = $1,281.00/1,100 = 1.1645.
This is a good project according to the PI rule. Can you explain
why?Its a good project because the present value of the inflows
exceeds the outlay. C21 Summary of Investment CriteriaI. Discounted
cash flow criteria A. Net present value (NPV). The NPV of an
investment is the difference between its market value and its cost.
The NPV rule is to take a project if its NPV is positive. NPV has
no serious flaws; it is the preferred decision criterion.B.
Internal rate of return (IRR). The IRR is the discount rate that
makes the estimated NPV of an investment equal to zero. The IRR
rule is to take a project when its IRR exceeds the required return.
When project cash flows are not conventional, there may be no IRR
or there may be more than one.C. Profitability index (PI). The PI,
also called the benefit-cost ratio, is the ratio of present value
to cost. The profitability index rule is to take an investment if
the index exceeds 1.0. The PI measures the present value per dollar
invested.
C22 Summary of Investment Criteria (concluded)II. Payback
criteriaA. Payback period. The payback period is the length of time
until the sum of an investments cash flows equals its cost. The
payback period rule is to take a project if its payback period is
less than some prespecified cutoff.B. Discounted payback period.
The discounted payback period is the length of time until the sum
of an investments discounted cash flows equals its cost. The
discounted payback period rule is to take an investment if the
discounted payback is less than some prespecified cutoff.III.
Accounting criterionA. Average accounting return (AAR). The AAR is
a measure of accounting profit relative to book value. The AAR rule
is to take an investment if its AAR exceeds a benchmark. C23 A
Quick Quiz1. Which of the capital budgeting techniques do account
for both the time value of money and risk?
2. The change in firm value associated with investment in a
project is measured by the projects _____________ .a. Payback
periodb. Discounted payback periodc. Net present valued. Internal
rate of return3. Why might one use several evaluation techniques to
assess a given project?
C24 A Quick Quiz1. Which of the capital budgeting techniques do
account for both the time value of money and risk? Discounted
payback period, NPV, IRR, and PI2. The change in firm value
associated with investment in a project is measured by the projects
Net present value.
3. Why might one use several evaluation techniques to assess a
given project?To measure different aspects of the project; e.g.,
the payback period measures liquidity, the NPV measures the change
in firm value, and the IRR measures the rate of return on the
initial outlay.C25 ProblemOffshore Drilling Products, Inc. imposes
a payback cutoff of 3 years for its international investment
projects. If the company has the following two projects available,
should they accept either of them? YearCash Flows ACash Flows B
0-$30,000-$45,000 1 15,000 5,000 2 10,000 10,000 3 10,000 20,000 4
5,000 250,000C26 Solution to Problem (concluded)Project A: Payback
period = 1 + 1 + ($30,000 - 25,000)/10,000 =2.50 yearsProject B:
Payback period = 1 + 1 + 1 + ($45,000 - 35,000)/$250,000 = 3.04
yearsProject As payback period is 2.50 years and project Bs payback
period is 3.04 years. Since the maximum acceptable payback period
is 3 years, the firm should accept project A and reject project
B.C27 Another ProblemA firm evaluates all of its projects by
applying the IRR rule. If the required return is 18 percent, should
the firm accept the following project? YearCash Flow 0-$30,000 1
25,000 2 0 3 15,000C28 Another Problem (continued)To find the IRR,
set the NPV equal to 0 and solve for the discount rate: NPV = 0 =
-$30,000 + $25,000/(1 + IRR)1 + $0/(1 + IRR) 2 +$15,000/(1 +
IRR)3At 18 percent, the computed NPV is ____.So the IRR must be
(greater/less) than 18 percent. How did you know?C29 Another
Problem (concluded)To find the IRR, set the NPV equal to 0 and
solve for the discount rate: NPV = 0 = -$30,000 + $25,000/(1 +
IRR)1 + $0/(1 + IRR)2 +$15,000/(1 + IRR)3At 18 percent, the
computed NPV is $316.So the IRR must be greater than 18 percent. We
know this because the computed NPV is positive.By trial-and-error,
we find that the IRR is 18.78 percent.T30 Fundamental Principles of
Project EvaluationFundamental Principles of Project Evaluation:
Project evaluation - the application of one or more capital
budgeting decision rules to estimated relevant project cash flows
in order to make the investment decision.
Relevant cash flows - the incremental cash flows associated with
the decision to invest in a project. The incremental cash flows for
project evaluation consist of any and all changes in the firms
future cash flows that are a direct consequence of taking the
project. Stand-alone principle - evaluation of a project based on
the projects incremental cash flows.T31 Incremental Cash
FlowsIncremental Cash FlowsKey issues:When is a cash flow
incremental?Terminology A.Sunk costs B.Opportunity costs C.Side
effects D.Net working capital E.Financing costs F.Other issuesT32
Example: Preparing Pro Forma StatementsSuppose we want to prepare a
set of pro forma financial statements for a project for Norma
Desmond Enterprises. In order to do so, we must have some
background information. In this case, assume:1.Sales of 10,000
units/year @ $5/unit. 2.Variable cost per unit is $3. Fixed costs
are $5,000 per year. The project has no salvage value. Project life
is 3 years.3.Project cost is $21,000. Depreciation is $7,000/year.
4.Additional net working capital is $10,000. 5. The firms required
return is 20%. The tax rate is 34%.T33 Example: Preparing Pro Forma
Statements (continued)Pro Forma Financial StatementsProjected
Income Statements Sales$______ Var. costs______ $20,000 Fixed
costs5,000 Depreciation7,000 EBIT$______ Taxes (34%)2,720 Net
income$______T34 Example: Preparing Pro Forma Statements
(continued)Pro Forma Financial StatementsProjected Income
Statements Sales$50,000 Var. costs30,000 $20,000 Fixed costs5,000
Depreciation7,000 EBIT$ 8,000 Taxes (34%)2,720 Net income$ 5,280T35
Example: Preparing Pro Forma Statements (concluded) Projected
Balance Sheets
0123NWC$______$10,000$10,000$10,000NFA21,000____________0Total$31,000$24,000$17,000$10,000T36
Example: Preparing Pro Forma Statements (concluded) Projected
Balance Sheets
0123NWC$10,000$10,000$10,000$10,000NFA21,00014,0007,0000Total$31,000$24,000$17,000$10,000T37
Example: Using Pro Formas for Project EvaluationNow lets use the
information from the previous example to do a capital budgeting
analysis.Project operating cash flow (OCF): EBIT$8,000
Depreciation+7,000 Taxes-2,720 OCF$12,280T38 Example: Using Pro
Formas for Project Evaluation (continued)Project Cash Flows
0123OCF$12,280$12,280$12,280Chg. NWC____________Cap.
Sp.-21,000Total______$12,280$12,280$______T39 Example: Using Pro
Formas for Project Evaluation (continued)Project Cash Flows
0123OCF$12,280$12,280$12,280Chg. NWC-10,00010,000Cap.
Sp.-21,000Total-31,000$12,280$12,280$22,280T40 Example: Using Pro
Formas for Project Evaluation (concluded)Capital Budgeting
Evaluation: NPV = -$31,000 + $12,280/1.201 + $12,280/1.20 2 +
$22,280/1.20 3= $655 IRR = 21% PBP = 2.3 years AAR = $5280/{(31,000
+ 24,000 + 17,000 + 10,000)/4} = 25.76%Should the firm invest in
this project? Why or why not?Yes -- the NPV > 0, and the IRR
> required returnT41 Example: Estimating Changes in Net Working
CapitalIn estimating cash flows we must account for the fact that
some of the incremental sales associated with a project will be on
credit, and that some costs wont be paid at the time of investment.
How? Answer: Estimate changes in NWC. Assume:1.Fixed asset spending
is zero.2.The change in net working capital spending is $200:
01ChangeS/U A/R$100$200+100 ___ INV100150+50 ___ -A/P10050 (50)___
NWC$100$300 Chg. NWC = $_____T42 Example: Estimating Changes in Net
Working CapitalIn estimating cash flows we must account for the
fact that some of the incremental sales associated with a project
will be on credit, and that some costs wont be paid at the time of
investment. How? Answer: Estimate changes in NWC. Assume:1.Fixed
asset spending is zero.2.The change in net working capital spending
is $200: 01ChangeS/U A/R$100$200+100 U INV100150+50 U -A/P10050
(50)U NWC$100$300 Chg. NWC = $200T43 Example: Estimating Changes in
Net Working Capital (continued)Now, estimate operating and total
cash flow: Sales$300 Costs200 Depreciation0 EBIT$100 Tax0 Net
Income$100 OCF = EBIT + Dep. Taxes = $100Total Cash flow = OCF
Change in NWC Capital Spending = $100 ______ ______ = ______
T44 Example: Estimating Changes in Net Working Capital
(continued)Now, estimate operating and total cash flow: Sales$300
Costs200 Depreciation0 EBIT$100 Tax0 Net Income$100 OCF = EBIT +
Dep. Taxes = $100Total Cash flow = OCF Change in NWC Capital
Spending = $100 200 0 = $100
T45 Example: Estimating Changes in Net Working Capital
(concluded)Where did the - $100 in total cash flow come from? What
really happened: Cash sales = $300 - ____ = $200 (collections) Cash
costs = $200 + ____ + ____ = $300 (disbursements) T46 Example:
Estimating Changes in Net Working Capital (concluded)Where did the
- $100 in total cash flow come from? What really happened: Cash
sales = $300 - 100 = $200 (collections) Cash costs = $200 + 50 + 50
= $300 (disbursements) Cash flow = $200 - 300= - $100 (= cash in
cash out)T47Modified ACRS Property
ClassesClassExamples3-yearEquipment used in research5-yearAutos,
computers7-yearMost industrial equipmentT48 Modified ACRS
Depreciation Allowances Property ClassYear 3-Year 5-Year 7-Year
133.33%20.00%14.29% 244.4432.0024.49 314.8219.2017.49
47.4111.5212.49 511.528.93 65.768.93 78.93 84.45T49 MACRS
Depreciation: An ExampleCalculate the depreciation deductions on an
asset which costs $30,000 and is in the 5-year property class:
YearMACRS %Depreciation 120%$_____ 232% _____ 319.20% 5,760 411.52%
3,456 511.52% 3,456 65.76% 1,728 100%$ _____ T50 MACRS
Depreciation: An ExampleCalculate the depreciation deductions on an
asset which costs $30,000 and is in the 5-year property class:
YearMACRS %Depreciation 120%$6,000 232% 9,600 319.20% 5,760 411.52%
3,456 511.52% 3,456 65.76% 1,728 100% $30,000 T51 Example: Fairways
Equipment and Operating Costs Two golfing buddies are considering
opening a new driving range, the Fairways Driving Range (motto: We
always treat you fairly at Fairways). Because of the growing
popularity of golf, they estimate the range will generate rentals
of 20,000 buckets of balls at $3 a bucket the first year, and that
rentals will grow by 750 buckets a year thereafter. The price will
remain $3 per bucket.Capital spending requirements include: Ball
dispensing machine $ 2,000 Ball pick-up vehicle 8,000 Tractor and
accessories 8,000$18,000 All the equipment is 5-year ACRS property,
and is expected to have a salvage value of 10% of cost after 6
years.
Anticipated operating expenses are as follows:
T52 Example: Fairways Equipment and Operating Costs
(concluded)Operating Costs (annual) Land lease$ 12,000 Water1,500
Electricity3,000 Labor30,000 Seed & fertilizer2,000
Gasoline1,500 Maintenance1,000 Insurance1,000 Misc. Expenses1,000
$53,000Working CapitalInitial requirement = $3,000 Working capital
requirements are expected to grow at 5% per year for the life of
the project
T53 Example: Fairways Revenues, Depreciation, and Other
CostsProjected Revenues Year Buckets Revenues 120,000$60,000
220,75062,250 321,50064,500 422,25066,750 523,00069,000
623,75071,250T54 Example: Fairways Revenues, Depreciation, and
Other Costs (continued)Cost of balls and buckets Year Cost 1$3,000
23,150 33,308 4 3,473 5 3,647 6 3,829T55 Example: Fairways
Revenues, Depreciation, and Other Costs (concluded) Depreciation on
$18,000 of 5-year equipment Year ACRS % Depreciation Book value
120.00$3,600$14,400 232.005,7608,640 319.203,4565,184
411.522,0743,110 511.522,0741,036 65.761,0360T56 Example: Fairways
Pro Forma Income Statement Year 1 2 3 4 5
6Revenues$60,000$62,250$64,500$66,750$69,000$71,250Variable
costs3,0003,1503,3083,4733,6473,829Fixed
costs53,00053,00053,00053,00053,00053,000Depreciation3,6005,7603,4562,0742,0741,036EBIT$
400$ 340$ 4,736$ 8,203$10,279$13,385Taxes60517101,2301,5422,008Net
income$ 340$ 289$ 4,026$ 6,973$ 8,737$11,377T57 Example: Fairways
Projected Changes in NWCProjected increases in net working capital
Year Net working capital Change in NWC 0$ 3,000$ 3,000 1 3,150150
23,308158 33,473165 43,647174 53,829182 64,020 - 3,829T58 Example:
Fairways Cash FlowsOperating cash flows: OperatingYearEBIT+
Depreciation Taxes= cash flow 0$ 0$ 0$ 0$ 0 14003,600603,940
23405,760516,049 34,7363,4567107,482 48,2032,0741,2309,047
510,2792,0741,54210,811 613,3851,0362,00812,413T59 Example:
Fairways Cash Flows (concluded)Total cash flow from assets: YearOCF
Chg. in NWC Cap. Sp. = Cash flow 0$ 0$ 3,000$18,000 $21,000
13,94015003,790 26,04915805,891 37,48216507,317 49,04717408,873
510,811182010,629 612,413 3,829 1,53017,772T60 Alternative
Definitions of OCFLet:OCF = operating cash flowS= salesC= operating
costsD= depreciationT= corporate tax rateT61 Alternative
Definitions of OCF (concluded)The Tax-Shield Approach OCF = (S - C
- D) + D - (S - C - D) T = (S - C) (1 - T) + (D T) =(S - C) (1 - T)
+ Depreciation x TThe Bottom-Up Approach OCF =(S - C - D) + D - (S
- C - D) T = (S - C - D) (1 - T) + D = Net income + DepreciationThe
Top-Down Approach OCF = (S - C - D) + D - (S - C - D) T = (S - C) -
(S - C - D) T = Sales - Costs - TaxesT62 Quick Quiz -- Part 1 of
3Now lets put our new-found knowledge to work. Assume we have the
following background information for a project being considered by
Gillis, Inc. See if we can calculate the projects NPV and payback
period. Assume:Required NWC investment = $40; project cost = $60; 3
year lifeAnnual sales = $100; annual costs = $50; straight line
depreciation to $0Tax rate = 34%, required return = 12%Step 1:
Calculate the projects OCFOCF = (S - C)(1 - T) + Dep TOCF = (___ -
__)(1 - .34) + (____)(.34) = $_____T63 Quick Quiz -- Part 1 of 3Now
lets put our new-found knowledge to work. Assume we have the
following background information for a project being considered by
Gillis, Inc. See if we can calculate the projects NPV and payback
period. Assume:Required NWC investment = $40; project cost = $60; 3
year lifeAnnual sales = $100; annual costs = $50; straight line
depreciation to $0Tax rate = 34%, required return = 12%Step 1:
Calculate the projects OCFOCF = (S - C)(1 - T) + Dep TOCF = (100 -
50)(1 - .34) + (60/3)(.34) = $39.80T64 Quick Quiz -- Part 1 of 3
(concluded)Project cash flows are thus: 0123 OCF$39.8$39.8$39.8
Chg. in NWC-4040 Cap. Sp.-60 -$100$39.8$39.8$79.8 Payback period =
___________NPV = ____________T65 Quick Quiz -- Part 1 of 3
(concluded)Project cash flows are thus: 0123 OCF$39.8$39.8$39.8
Chg. in NWC 4040 Cap. Sp. 60 100$39.8$39.8$79.8 Payback period = 1
+ 1 + (100 79.6)/79.8 = 2.26 yearsNPV = $39.8/(1.12) +
$39.8/(1.12)2 + 79.8 /(1.12)3 - 100 = $24.06
