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C1 Outline
Capital Budgeting - Decision Criteria Net Present Value The Payback Rule The Discounted Payback
The Average Accounting Return The Internal Rate of Return The Profitability Index
The Practice of Capital Budgeting
C2 Outline (continued)
Project Cash Flows: A First Look Incremental Cash Flows Pro Forma Financial Statements and Project Cash Flows More on Project Cash Flows Alternative Definitions of Operating Cash Flow
Some Special Cases of Discounted Cash Flow Analysis Summary and Conclusions
C3 NPV Illustrated
Assume you have the following information on Project X:
Initial outlay -$1,100 Required return = 10%Annual cash revenues and expenses are as follows: Year 1 2
Revenues $1,000 2,000
Expenses $500 1,000
Draw a time line and compute the NPV of project X.
C4 NPV Illustrated (concluded)
0 Initial outlay ($1,100) Revenues Expenses Cash flow $1,100.00 $500 x +454.55 +826.45 +$181.00 NPV
1 $1,000 500 $500 Revenues Expenses
2 $2,000 1,000
Cash flow $1,000
11.10 $1,000 x 1 1.10 2
C5 Underpinnings of the NPV Rule
Why 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 Illustrated
Initial outlay -$1,000
Year1 2 3 Year 1 2 3
Cash flow$200 400 600 Accumulated Cash flow $200 600 1,200
Payback period = 2 2/3 years
C7 Discounted Payback Illustrated Initial outlay -$1,000 R = 10% PV of Cash flow Cash flow $ 200 400 700 300 $ 182 331 526 205 Accumulated discounted cash flow
Year 1 2 3 4 Year
1 2 3 4
$ 182 513 1,039 1,244
Discounted payback period is just under 3 years
C8 Ordinary and Discounted Payback
Cash Flow Year 1 2 3 4 Undiscounted Discounted $100 100 100 100 $89 79 70 62
Accumulated Cash Flow Undiscounted $100 200 300 400 Discounted $89 168 238 300
5
100
55
500
355
C9 Average Accounting Return Illustrated
Average net income:
Year 1 2 3
SalesCosts Gross profit
$440220 220
$240120 120
$16080 80
DepreciationEarnings before taxes Taxes (25%) Net income
80140 35 $105
8040 10 $30
800 0 $0
Average net income = ($105 + 30 + 0)/3 = $45
C10 Average Accounting Return Illustrated (concluded)
Average book value:
Initial investment = $240
Average investment = ($240 + 0)/2 = $120
Average accounting return (AAR):
Average net income AAR = 37.5%
Average book value
$45 = $120
=
C11 Internal Rate of Return Illustrated
Initial outlay = -$200
Year1 2 3
Cash flow$ 50 100 150
Find the IRR such that NPV = 0
50
100
150
0 = -200 +
(1+IRR)1 +
+
(1+IRR)2 +
+
(1+IRR)3
50 200 =
100
150
(1+IRR)1
(1+IRR)2
(1+IRR)3
C12 Internal Rate of Return Illustrated (concluded)
Trial and Error
Discount rates0% 5%
NPV$100 68
10%15% 20%
4118 -2
IRR is just under 20% -- about 19.44%
C13 Net Present Value ProfileNet present value 120 100 80 60 40 20 Year 0 1 2 3 4 Cash flow $275 100 100 100 100
0 20 40 2% 6% 10% 14% 18% IRR 22% Discount rate
C14 Multiple Rates of Return
Assume you are considering a project for
which the cash flows are as follows: Year 0 1 2 Cash flows -$252 1,431 -3,035
34
2,850-1,000
C15 Multiple Rates of Return (continued)
Whats the IRR? Find the rate at which
the computed NPV = 0:
at 25.00%: at 33.33%:
NPV = _______ NPV = _______
at 42.86%:at 66.67%:
NPV = _______NPV = _______
C16 Multiple Rates of Return (continued)
Whats the IRR? Find the rate at which
the computed NPV = 0:
at 25.00%: at 33.33%:
NPV = NPV =
0 0
at 42.86%:at 66.67%:
NPV =NPV =
00
Two questions:
1. Whats going on here? 2. How many IRRs can there be?
C17 Multiple Rates of Return (concluded)NPV $0.06 $0.04 IRR = 1/4
$0.02 $0.00
($0.02)
IRR = 1/3
IRR = 2/3 IRR = 3/7
($0.04)
($0.06)
($0.08)
0.2
0.28
0.36 0.44 0.52 Discount rate
0.6
0.68
C18 IRR, NPV, and Mutually Exclusive Projects
Net present value 160 140 120 100 80 60 40 20 0 20 40 60 80 100 0 Project A: Project B: $350 $250 1 50 125
Year 2 100 100 3 150 75 4 200 50
Crossover Point
Discount rate
0
2%
6%
10%
14% IRR A
18% IRR B
22%
26%
C19 Profitability Index Illustrated
Now 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 flows1 $ 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 Criteria
I. Discounted cash flow criteriaA. 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 Quiz 1. 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 period b. Discounted payback period c. Net present value d. Internal rate of return 3. Why might one use several evaluation techniques to assess a given project?
C24 A Quick Quiz
1. Which of the capital budgeting techniques do account for both the time value of money and risk?Discounted payback period, NPV, IRR, and PI 2. 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 Problem
Offshore 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? Year 0 1 Cash Flows A -$30,000 15,000 Cash Flows B -$45,000 5,000
23 4
10,00010,000 5,000
10,00020,000 250,000
C26 Solution to Problem (concluded)
Project A:
Payback period
= 1 + 1 + ($30,000 - 25,000)/10,000 = 2.50 years
Project B:
Payback period
= 1 + 1 + 1 + ($45,000 - 35,000)/$250,000 = 3.04 years
Project 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 Problem
A 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?
Year0 1 2 3
Cash Flow-$30,000 25,000 0 15,000
C28 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)3 At 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)3 At 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 Evaluation
Fundamental 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 Flows
Incremental Cash Flows Key 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 issues
T32 Example: Preparing Pro Forma Statements
Suppose 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 Statements Projected Income Statements Sales $______
Var. costsFixed costs Depreciation EBIT Taxes (34%) Net income
______$20,000 5,000 7,000 $______ 2,720 $______
T34 Example: Preparing Pro Forma Statements (continued)
Pro Forma Financial Statements Projected Income Statements Sales $50,000
Var. costsFixed costs Depreciation EBIT Taxes (34%) Net income
30,000$20,000 5,000 7,000 $ 8,000 2,720 $ 5,280
T35 Example: Preparing Pro Forma Statements (concluded)
Projected Balance Sheets0 NWC NFA Total $______ 21,000 $31,000 1 $10,000 ______ $24,000 2 $10,000 ______ $17,000 3 $10,000 0 $10,000
T36 Example: Preparing Pro Forma Statements (concluded)
Projected Balance Sheets0 NWC NFA Total $10,000 21,000 $31,000 1 $10,000 14,000 $24,000 2 $10,000 7,000 $17,000 3 $10,000 0 $10,000
T37 Example: Using Pro Formas for Project Evaluation
Now lets use the information from the previous example to
do a capital budgeting analysis. Project operating cash flow (OCF):
EBITDepreciation Taxes OCF
$8,000+7,000 -2,720 $12,280
T38 Example: Using Pro Formas for Project Evaluation (continued)
Project Cash Flows
0 OCF Chg. NWC Cap. Sp. Total ______ -21,000 ______
1 $12,280
2 $12,280
3 $12,280 ______
$12,280
$12,280
$______
T39 Example: Using Pro Formas for Project Evaluation (continued)
Project Cash Flows
0 OCF Chg. NWC Cap. Sp. Total -10,000 -21,000 -31,000
1 $12,280
2 $12,280
3 $12,280 10,000
$12,280
$12,280
$22,280
T40 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 21% 2.3 years
IRR PBP
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 return
T41 Example: Estimating Changes in Net Working Capital In 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. 2. Fixed asset spending is zero. The change in net working capital spending is $200:
0 A/R INV -A/P NWC $100 100 100 $100
1 $200 150 50 $300
Change +100 +50 (50)
S/U ___ ___ ___
Chg. NWC = $_____
T42 Example: Estimating Changes in Net Working Capital In 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. 2. Fixed asset spending is zero. The change in net working capital spending is $200:
0 A/R INV -A/P NWC $100 100 100 $100
1 $200 150 50 $300
Change +100 +50 (50)
S/U U U U
Chg. NWC = $200
T43 Example: Estimating Changes in Net Working Capital (continued)
Now, estimate operating and total cash flow:
SalesCosts Depreciation
$300200 0
EBITTax Net Income
$1000 $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:
SalesCosts Depreciation
$300200 0
EBITTax Net Income
$1000 $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 Cash costs
= $300 - ____
= $200 (collections)
= $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 Cash costs Cash flow out)
= $300 - 100
= $200 (collections)
= $200 + 50 + 50 = $300 (disbursements) = $200 - 300 = - $100 (= cash in cash
T47 Modified ACRS Property Classes
Class 3-year 5-year 7-year
Examples Equipment used in research Autos, computers Most industrial equipment
T48 Modified ACRS Depreciation Allowances
Property ClassYear 1 3-Year 33.33% 5-Year 20.00% 7-Year 14.29%
23 4
44.4414.82 7.41
32.0019.20 11.52
24.4917.49 12.49
56 7
11.525.76
8.938.93 8.93
8
4.45
T49 MACRS Depreciation: An Example
Calculate the depreciation deductions on an asset which costs
$30,000 and is in the 5-year property class:Year 1 MACRS % 20% Depreciation $_____
23 4
32%19.20% 11.52%
_____5,760 3,456
56
11.52%5.76% 100%
3,4561,728 $ _____
T50 MACRS Depreciation: An Example
Calculate the depreciation deductions on an asset which costs
$30,000 and is in the 5-year property class:Year 1 MACRS % 20% Depreciation $6,000
23 4
32%19.20% 11.52%
9,6005,760 3,456
56
11.52%5.76% 100%
3,4561,728 $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 Ball pick-up vehicle Tractor and accessories $ 2,000 8,000 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)
Working CapitalInitial requirement = $3,000 Working capital requirements are expected to grow at 5% per year for the life of the project
Land leaseWater Electricity
$ 12,0001,500 3,000
LaborSeed & fertilizer Gasoline
30,0002,000 1,500
MaintenanceInsurance Misc. Expenses
1,0001,000 1,000
$53,000
T53 Example: Fairways Revenues, Depreciation, and Other Costs
Projected Revenues
Year1 2 3 4 5 6
Buckets20,000 20,750 21,500 22,250 23,000 23,750
Revenues$60,000 62,250 64,500 66,750 69,000 71,250
T54 Example: Fairways Revenues, Depreciation, and Other Costs (continued)
Cost of balls and buckets Year 1 2 Cost $3,000 3,150
34 5 6
3,3083,473 3,647 3,829
T55 Example: Fairways Revenues, Depreciation, and Other Costs (concluded)
Depreciation on $18,000 of 5-year equipmentYear 1 ACRS % 20.00 Depreciation $3,600 Book value $14,400
23 4 5 6
32.0019.20 11.52 11.52 5.76
5,7603,456 2,074 2,074 1,036
8,6405,184 3,110 1,036 0
T56 Example: Fairways Pro Forma Income Statement
Year 1 Revenues $60,000 2 $62,250 3 $64,500 4 $66,750 5 $69,000 6 $71,250
Variable costsFixed costs Depreciation EBIT Taxes Net income $ $
3,00053,000 3,600 400 60 340 $ $
3,15053,000 5,760 340 51 289
3,30853,000 3,456 $ 4,736 710 $ 4,026
3,47353,000 2,074 $ 8,203 1,230 $ 6,973
3,64753,000 2,074 $10,279 1,542 $ 8,737
3,82953,000 1,036 $13,385 2,008 $11,377
T57 Example: Fairways Projected Changes in NWC
Projected increases in net working capital
Year 0 1 2
Net working capital $ 3,000 3,150 3,308
Change in NWC $ 3,000 150 158
34 5 6
3,4733,647 3,829 4,020
165174 182 - 3,829
T58 Example: Fairways Cash Flows
Operating cash flows:
Year 0 $
EBIT 0
+ Depreciation $ 0
Taxes $ 0
Operating = cash flow$ 0
12 3
400340 4,736
3,6005,760 3,456
6051 710
3,9406,049 7,482
45 6
8,20310,279 13,385
2,0742,074 1,036
1,2301,542 2,008
9,04710,811 12,413
T59 Example: Fairways Cash Flows (concluded)
Total cash flow from assets:
Year0 1 2 3 $
OCF0 3,940 6,049 7,482
Chg. in NWC Cap. Sp. = Cash flow$ 3,000 150 158 165 $18,000 0 0 0 $21,000 3,790 5,891 7,317
45 6
9,04710,811 12,413
174182 3,829
00 1,530
8,87310,629 17,772
T60 Alternative Definitions of OCF
Let:
OCF = operating cash flowS = sales
CD T
= operating costs= depreciation = corporate tax rate
T61 Alternative Definitions of OCF (concluded) The Tax-Shield ApproachOCF == =
(S - C - D) + D - (S - C - D) T(S - C) (1 - T) + (D T) (S - C) (1 - T) + Depreciation x T
The Bottom-Up ApproachOCF = = (S - C - D) + D - (S - C - D) T (S - C - D) (1 - T) + D
=
Net income + Depreciation
The Top-Down ApproachOCF = = = (S - C - D) + D - (S - C - D) T (S - C) - (S - C - D) T Sales - Costs - Taxes
T62 Quick Quiz -- Part 1 of 3 Now 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 life Annual sales = $100; annual costs = $50; straight line depreciation to $0 Tax rate = 34%, required return = 12%
Step 1: Calculate the projects OCF
OCF = (S - C)(1 - T) + Dep TOCF = (___ - __)(1 - .34) + (____)(.34) = $_____
T63 Quick Quiz -- Part 1 of 3 Now 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 life Annual sales = $100; annual costs = $50; straight line depreciation to $0 Tax rate = 34%, required return = 12%
Step 1: Calculate the projects OCF
OCF = (S - C)(1 - T) + Dep TOCF = (100 - 50)(1 - .34) + (60/3)(.34) = $39.80
T64 Quick Quiz -- Part 1 of 3 (concluded)
Project cash flows are thus:
0 OCF
1 $39.8
2 $39.8
3 $39.8
Chg. in NWCCap. Sp.
-40-60 -$100 $39.8 $39.8
40
$79.8
Payback period = ___________ NPV = ____________
T65 Quick Quiz -- Part 1 of 3 (concluded)
Project cash flows are thus:
0 OCF
1 $39.8
2 $39.8
3 $39.8
Chg. in NWCCap. Sp.
40 60 100 $39.8 $39.8
40
$79.8
Payback period = 1 + 1 + (100 79.6)/79.8 = 2.26 years NPV = $39.8/(1.12) + $39.8/(1.12)2 + 79.8 /(1.12)3 - 100 = $24.06