8-2 Capital Budgeting Analysis of potential projects Long-term decisions Large expenditures...
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Transcript of 8-2 Capital Budgeting Analysis of potential projects Long-term decisions Large expenditures...
SESSIONS 3 & 4
8-2
Capital Budgeting
• Analysis of potential projects• Long-term decisions• Large expenditures• Difficult/impossible to reverse• Determines firm’s strategic direction
Keep in mind: VALUE CREATION
8-3
Required
Replacement
Expansion
Diversification
Capital Investment Process
Identification Evaluation Selection Implementation and follow-up
Riskier &
D
ifficult
Type of Investment
8-4
Net Present Value
How much value is created from undertaking an investment?
Step 1: Estimate the expected future cash flows.
Step 2: Estimate the required return for projects of this risk level. (Also called opportunity cost).
Step 3: Find the present value of the cash flows and subtract the initial investment to arrive at the
Net Present Value.
8-5
Net Present Value Sum of the PVs of all cash flows
Initial cost often is CF0 and is an outflow.
NPV = ∑n
t = 0
CFt
(1 + R)t
NPV = ∑n
t = 1
CFt
(1 + R)t- CF0
NOTE: t=0
8-6
NPV – Decision Rule
• If NPV is positive, accept the project• NPV > 0 means:
– Project is expected to add value to the firm– Will increase the wealth of the owners
• NPV is a direct measure of how well this project will meet the goal of increasing shareholder wealth.
8-7
Sample Project Data• You are looking at a new project and have
estimated the following cash flows, net income and book value data:– Year 0: CF = -165,000– Year 1: CF = 63,120 NI = 13,620– Year 2: CF = 70,800 NI = 3,300– Year 3: CF = 91,080 NI = 29,100– Average book value = $72,000
• Your required return for assets of this risk is 12%.• This project will be the example for all problem
exhibits in this chapter.
8-8
Computing NPV for the Project
• Using the formula:
NPV = -165,000/(1.12)0 + 63,120/(1.12)1 + 70,800/(1.12)2 + 91,080/(1.12)3 = 12,627.41
Capital Budgeting Project NPVRequired Return = 12%
Year CF Formula Disc CFs0 (165,000.00) =(-165000)/(1.12)^0 = (165,000.00)1 63,120.00 =(63120)/(1.12)^1 = 56,357.142 70,800.00 =(70800)/(1.12)^2 = 56,441.333 91,080.00 =(91080)/(1.12)^3 = 64,828.94
12,627.41
n
0tt
t
)R1(
CFNPV
8-9
Display You Enter C00 165000 C01 63120 F01 1 C02 70800 F02 1 C03 91080 F03 1 I 12 NPV 12,627.41
Cash Flows:
CF0 = -165000
CF1 = 63120
CF2 = 70800
CF3 = 91080
Computing NPV for the ProjectUsing the TI BAII+ CF Worksheet
8-10
Calculating NPVs with Excel• NPV function: =NPV(rate,CF01:CFnn)
– First parameter = required return entered as a decimal (5% = .05)– Second parameter = range of cash flows beginning with year 1
• After computing NPV, subtract the initial investment (CF0)
2
3
4
5
6
7
8
9
10
11
A B C D
Required Return = 12%Year CF Formula Disc CFs
0 (165,000.00) =(-165000)/(1.12)^0 = (165,000.00)1 63,120.00 =(63120)/(1.12)^1 = 56,357.142 70,800.00 =(70800)/(1.12)^2 = 56,441.333 91,080.00 =(91080)/(1.12)^3 = 64,828.94
12,627.41
EXCEL =NPV(D2,B5:B7) 177,627.41NPV + CF0 12,627.41
8-11
Net Present Value Sum of the PVs of all cash flows.
n
0tt
t
)R1(
CFNPV << CALCULATOR
<< EXCEL0
n
1tt
t CF)R1(
CFNPV
8-12
Rationale for the NPV Method
• NPV = PV inflows – Cost NPV=0 → Project’s inflows are “exactly
sufficient to repay the invested capital and provide the required rate of return”
• NPV = net gain in shareholder wealth
• Rule: Accept project if NPV > 0
8-13
NPV Method
–Meets all desirable criteria• Considers all CFs• Considers TVM• Adjusts for risk• Can rank mutually exclusive projects
–Directly related to increase in VF
–Dominant method; always prevails
8-14
Payback Period• How long does it take to recover the initial
cost of a project?• Computation
– Estimate the cash flows– Subtract the future cash flows from the initial
cost until initial investment is recovered– A “break-even” type measure
• Decision Rule – Accept if the payback period is less than some preset limit
8-15
Computing Payback for the Project
• Do we accept or reject the project?
Capital Budgeting Project
Year CF Cum. CFs0 (165,000)$ (165,000)$ 1 63,120$ (101,880)$ 2 70,800$ (31,080)$ 3 91,080$ 60,000$
Payback = year 2 ++ (31080/91080)
Payback = 2.34 years
8-16
Advantages and Disadvantages of Payback
• Advantages– Easy to understand– Adjusts for
uncertainty of later cash flows
– Biased towards liquidity
• Disadvantages– Ignores the time value of money– Requires an arbitrary cutoff point– Ignores cash flows beyond the cutoff date– Biased against long-term projects, such as
research and development, and new projects
ASKS THE WRONG QUESTION!
8-17
Internal Rate of Return
• Most important alternative to NPV• Widely used in practice • Intuitively appealing• Based entirely on the estimated cash
flows • Independent of interest rates
8-18
IRR Definition and Decision Rule
• Definition: – IRR = discount rate that makes the
NPV = 0
• Decision Rule: – Accept the project if the IRR is greater
than the required return
8-19
NPV vs. IRR
NPV)R1(
CFn
0tt
t
IRR: Enter NPV = 0, solve for IRR.
NPV: Enter r, solve for NPV
0)IRR1(
CFn
0tt
t
8-20
Computing IRR For The Project
• Without a financial calculator or Excel, this becomes a trial-and-error process.
• Calculator– Enter the cash flows as for NPV– Press IRR and then CPT– IRR = 16.13% > 12% required return
• Do we accept or reject the project?
8-21
Display You Enter C00 165000 C01 63120 F01 1 C02 70800 F02 1 C03 91080 F03 1 IRR 16.1322
Cash Flows:
CF0 = -165000
CF1 = 63120
CF2 = 70800
CF3 = 91080
Computing IRR for the ProjectUsing the TI BAII+ CF Worksheet
8-22
Calculating IRR with Excel
• Start with the cash flows as you did to solve for NPV
• Use the IRR function– Enter the range of cash flows, beginning with
the initial cash flow (Cash flow 0)– You can enter a guess, but it is not necessary– The default format is a whole percent
8-23
Calculating IRR with Excel
1
2
3
4
5
6
7
8
A B C
Year CF0 (165,000.00)1 63,120.002 70,800.003 91,080.00
EXCEL =IRR(B3:B6) 16.13%
IRR
8-24
NPV Profile For The Project
-20,000
-10,000
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
Discount Rate
NP
V IRR = 16.13%
8-25
IRR - Advantages • Preferred by executives
– Intuitively appealing– Easy to communicate the value of a project
• If the IRR is high enough, may not need to estimate a required return
• Considers all cash flows• Considers time value of money
8-26
IRR - Disadvantages
• Can produce multiple answers• Cannot rank mutually exclusive projects• Reinvestment assumption flawed
8-27
Summary of Decisions for the Project
Net Present Value Accept*
Payback Period ???
Internal Rate of Return Accept*
*For a normal, single project these two criteria always agree
8-28
NPV vs. IRR• NPV and IRR will generally give the same
decision• Exceptions
– Non-conventional cash flows • Cash flow sign changes more than once
– Mutually exclusive projects• Initial investments are substantially different• Timing of cash flows is substantially different• Will not reliably rank projects
8-29
IRR & Non-Conventional Cash Flows
• “Non-conventional” – Cash flows change sign more than once– Most common:
• Initial cost (negative CF)• A stream of positive CFs• Negative cash flow to close project.• For example, nuclear power plant or strip mine.
– More than one IRR …. – Which one do you use to make your decision?
8-30
Multiple IRRs• Descartes Rule of Signs
• Polynomial of degree n→n roots– When you solve for IRR you are solving for the
root of an equation– 1 real root per sign change– Rest = imaginary (i2 = -1)
0)IRR1(
CFn
0tt
t
8-31
Non-Conventional Cash Flows
• Suppose an investment will cost $90,000 initially and will generate the following cash flows:– Year 1: 132,000– Year 2: 100,000– Year 3: -150,000
• The required return is 15%.• Should we accept or reject the project?
8-32
Non-Conventional Cash FlowsSummary of Decision Rules
• NPV > 0 at 15% required return, so you should Accept
• IRR =10.11% (using a financial calculator), which would tell you to Reject
• Recognize the non-conventional cash flows and look at the NPV profile
I = 15%YR CF0 -$90,0001 $132,0002 $100,0003 -$150,000
NPV $1,769.54 > 0IRR-1 10.11% < 15%IRR-2 42.66% > 15%
8-33
NPV Profile
($10,000.00)
($8,000.00)
($6,000.00)
($4,000.00)
($2,000.00)
$0.00
$2,000.00
$4,000.00
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
Discount Rate
NP
V
IRR = 10.11% and 42.66%
When you cross the x-axis more than once, there will be more than one return that solves the equation
8-34
Independent versus Mutually Exclusive Projects
• Independent–The cash flows of one project are
unaffected by the acceptance of the other.
• Mutually Exclusive –The acceptance of one project precludes
accepting the other.
8-35
Reinvestment Rate Assumption
• IRR assumes reinvestment at IRR• NPV assumes reinvestment at the firm’s
weighted average cost of capital(opportunity cost of capital)– More realistic – NPV method is best
• NPV should be used to choose between mutually exclusive projects
8-36
Example of Mutually Exclusive Projects
Period Project A Project B
0 -500 -400
1 325 325
2 325 200
IRR 19.43% 22.17%
NPV 64.05 60.74
The required return for both projects is 10%.
Which project should you accept and why?
8-37
NPV Profiles
($40.00)
($20.00)
$0.00
$20.00
$40.00
$60.00
$80.00
$100.00
$120.00
$140.00
$160.00
0 0.05 0.1 0.15 0.2 0.25 0.3
Discount Rate
NP
V AB
IRR for A = 19.43%
IRR for B = 22.17%
Crossover Point = 11.8%
8-38
Two Reasons NPV Profiles Cross
• Size (scale) differences. – Smaller project frees up funds sooner for
investment. – The higher the opportunity cost, the more
valuable these funds, so high discount rate favors small projects.
• Timing differences. – Project with faster payback provides more
CF in early years for reinvestment. – If discount rate is high, early CF especially
good
8-39
Conflicts Between NPV and IRR
• NPV directly measures the increase in value to the firm
• Whenever there is a conflict between NPV and another decision rule, always use NPV
• IRR is unreliable in the following situations:– Non-conventional cash flows– Mutually exclusive projects
8-40
Profitability Index
• Measures the benefit per unit cost, based on the time value of money– A profitability index of 1.1 implies that for
every $1 of investment, we create an additional $0.10 in value
• Can be very useful in situations of capital rationing
• Decision Rule: If PI > 1.0 Accept
8-41
Profitability Index
• For conventional CF Projects:
PV(Cash Inflows)
Absolute Value of Initial Investment0
n
1tt
t
CF)r1(
CF
PI
8-42
Advantages and Disadvantages of Profitability Index
• Advantages– Closely related to
NPV, generally leading to identical decisions• Considers all CFs• Considers TVM
– Easy to understand and communicate
– Useful in capital rationing
• Disadvantages– May lead to
incorrect decisions in comparisons of mutually exclusive investments (can conflict with NPV)
8-43
Profitability IndexExample of Conflict with NPV
A BCF(0) (10,000.00) (100,000.00)PV(CIF) 15,000.00 125,000.00PI 1.50 1.25NPV 5,000.00 25,000.00
8-44
Capital Budgeting In Practice
• Consider all investment criteria when making decisions
• NPV and IRR are the most commonly used primary investment criteria
• Payback is a commonly used secondary investment criteria
• All provide valuable information
8-45
Summary
Calculate ALL -- each has value
Method What it measures Metric
NPV $ increase in VF $$
Payback Liquidity Years
IRR E(R), risk %
PI If rationed Ratio
9-46
Evaluating Projects
• Steps in Evaluation:–Determine the relevant cash flows
for a proposed investment–Analyze the project’s projected
cash flows–Calculate and interpret estimated
NPV
9-47
Relevant Cash Flows
• Include only cash flows that will only occur if the project is accepted
• Incremental cash flows• The stand-alone principle allows us
to analyze each project in isolation from the firm simply by focusing on incremental cash flows
9-48
Relevant Cash Flows:Incremental Cash Flow for a Project
Corporate cash flow with the project
Minus
Corporate cash flow without the project
9-49
Relevant Cash Flows
• “Sunk” Costs ………………………… N• Opportunity Costs …………………... Y• Side Effects/Erosion……..…………… Y• Net Working Capital………………….. Y• Financing Costs….………..…………. N• Tax Effects ………………………..….. Y
9-50
Pro Forma Statements and Cash Flow
• Pro Forma Financial Statements – Projects future operations
• Operating Cash Flow:OCF = EBIT + Depr – Taxes
OCF = NI + Depr if no interest expense
• Cash Flow From Assets:CFFA = OCF – NCS –ΔNWC
NCS = Net capital spending
9-51
Shark Attractant Project• Estimated sales 50,000 cans• Sales Price per can $4.00• Cost per can $2.50• Estimated life 3 years• Fixed costs $12,000/year• Initial equipment cost $90,000
– 100% depreciated over 3 year life• Investment in NWC $20,000• Tax rate 34%• Cost of capital 20%
9-52
Pro Forma Income StatementTable 9.1
Sales (50,000 units at $4.00/unit) $200,000
Variable Costs ($2.50/unit) 125,000
Gross profit $ 75,000
Fixed costs 12,000
Depreciation ($90,000 / 3) 30,000
EBIT $ 33,000
Taxes (34%) 11,220
Net Income $ 21,780
9-53
Projected Capital RequirementsTable 9.2
Year
0 1 2 3
NWC $20,000 $20,000 $20,000 $20,000
Net Fixed Assets
90,000 60,000 30,000 0
Total Investment
$110,000 $80,000 $50,000 $20,000
NFA declines by the amount of depreciation each year
Investment = book or accounting value, not market value
9-54
Projected Total Cash FlowsTable 9.5
Year
0 1 2 3
OCF $51,780 $51,780 $51,780
NWC -$20,000 20,000
Capital Spending
-$90,000
CFFA -$110,00 $51,780 $51,780 $71,780
Note: Investment in NWC is recovered in final year
Equipment cost is a cash outflow in year 0
9-55
Shark Attractant Project
OCF = EBIT + Depreciation – Taxes
OCF = Net Income + Depreciation (if no interest)
Year 0 1 2 3Sales 200,000 200,000 200,000Variable Costs 125,000 125,000 125,000Gross Profit 75,000 75,000 75,000Fixed Costs 12,000 12,000 12,000Depreciation 30,000 30,000 30,000EBIT 33,000 33,000 33,000Taxes 11,220 11,220 11,220Net Income 21,780 21,780 21,780
Operating Cash Flow 51,780 51,780 51,780Changes in NWC -20,000 20,000Net Capital Spending -90,000Cash Flow From Assets -110,000 51,780 51,780 71,780
Net Present Value $10,647.69IRR 25.76%
Pro Forma Income Statement
Cash Flows
9-56
Display You Enter ‘' C00 110000 S!#C01 51780 !# F01 2 !# C02 71780 !# F02 1 !#( I 20 !#NPV %10647.69 ) %25.76
Cash Flows:
CF0 = -110000
CF1 = 51780
CF2 = 51780
CF3 = 71780
Computing NPV for the ProjectUsing the TI BAII+ CF Worksheet
9-57
Making The Decision
• Should we accept or reject the project?
Operating Cash Flow 51,780 51,780 51,780Changes in NWC -20,000 20,000Net Capital Spending -90,000Cash Flow From Assets -110,000 51,780 51,780 71,780
Net Present Value $10,647.69IRR 25.76%
Cash Flows
9-58
The Tax Shield Approach to OCF
• OCF = (Sales – costs)(1 – T) + Deprec*T OCF=(200,000-137,000) x 66% + (30,000 x .34)
OCF = 51,780
• Particularly useful when the major incremental cash flows are the purchase of equipment and the associated depreciation tax shield – i.e., choosing between two different machines
9-59
Changes in NWC• GAAP requirements:
– Sales recorded when made, not when cash is received• Cash in = Sales - ΔAR
– Cost of goods sold recorded when the corresponding sales are made, whether suppliers paid yet or not• Cash out = COGS - ΔAP
• Buy inventory/materials to support sales before any cash collected
9-60
Depreciation & Capital Budgeting
• Use the schedule required by the IRS for tax purposes
• Depreciation = non-cash expense–Only relevant due to tax affects
• Depreciation tax shield = DT–D = depreciation expense–T = marginal tax rate
9-61
Computing Depreciation• Straight-line depreciation
D = (Initial cost – salvage) / number of years
Straight Line Salvage Value
• MACRS Depreciate 0 Recovery Period = Class Life
1/2 Year Convention
Multiply percentage in table by the initial cost
9-62
After-Tax Salvage
• If the salvage value is different from the book value of the asset,
then there is a tax effect• Book value = initial cost –
accumulated depreciation• After-tax salvage = salvage –
T(salvage – book value)
9-63
Tax Effect on Salvage
Net Salvage Cash Flow = SP - (SP-BV)(T)
Where:SP = Selling PriceBV = Book ValueT = Corporate tax rate
9-64
Example: Depreciation and After-tax Salvage
• Car purchased for $12,000 • 5-year property• Marginal tax rate = 34%.
Depreciation 5-year Asset
Year Beg BV Depr % Deprec End BV1 12,000.00$ 20.00% 2,400.00$ 9,600.00$ 2 9,600.00$ 32.00% 3,840.00$ 5,760.00$ 3 5,760.00$ 19.20% 2,304.00$ 3,456.00$ 4 3,456.00$ 11.52% 1,382.40$ 2,073.60$ 5 2,073.60$ 11.52% 1,382.40$ 691.20$ 6 691.20$ 5.76% 691.20$ -$
100.00% 12,000.00$
9-65
Salvage Value & Tax EffectsDepreciation 5-year Asset
Year Beg BV Depr % Deprec End BV1 12,000.00$ 20.00% 2,400.00$ 9,600.00$ 2 9,600.00$ 32.00% 3,840.00$ 5,760.00$ 3 5,760.00$ 19.20% 2,304.00$ 3,456.00$ 4 3,456.00$ 11.52% 1,382.40$ 2,073.60$ 5 2,073.60$ 11.52% 1,382.40$ 691.20$ 6 691.20$ 5.76% 691.20$ -$
100.00% 12,000.00$
Net Salvage Cash Flow = SP - (SP-BV)(T)
If sold at EOY 5 for $3,000:NSCF = 3,000 - (3000 - 691.20)(.34) = $2,215.01
= $3,000 – 784.99 = $2,215.01If sold at EOY 2 for $4,000:
NSCF = 4,000 - (4000 - 5,760)(.34) = $4,598.40 = $4,000 – (-598.40) = $4,598.40
9-66
Evaluating NPV Estimates
• NPV estimates are only estimates• Forecasting risk:
–Sensitivity of NPV to changes in cash flow estimates • The more sensitive, the greater the
forecasting risk
• Sources of value • Be able to articulate why this project creates
value
9-67
Scenario Analysis
• Examines several possible situations:–Worst case
–Base case or most likely case
–Best case
• Provides a range of possible outcomes
9-68
Scenario Analysis Example
Note: “Lower” ≠ Worst
“Upper” ≠ Best
Base Lower UpperUnits 6,000 5,500 6,500 Price/unit 80.00$ 75.00$ 85.00$ Variable cost/unit 60.00$ 58.00$ 62.00$ Fixed cost/year 50,000$ 45,000$ 55,000$
BASE BEST WORST
Initial investment 200,000$ Depreciated to salvage value of 0 over 5 yearsDeprec/yr 40,000$
Project Life 5 yearsTax rate 34%Required return 12%
9-69
BASE WORST BESTUnits 6,000 5,500 6,500 Price/unit 80.00$ 75.00$ 85.00$ Variable cost/unit 60.00$ 62.00$ 58.00$ Fixed Cost 50,000$ 55,000$ 45,000$
Sales 480,000$ 412,500$ 552,500$ Variable Cost 360,000 341,000 377,000Fixed Cost 50,000 55,000 45,000Depreciation 40,000 40,000 40,000EBIT 30,000 (23,500) 90,500Taxes 10,200 (7,990) 30,770Net Income 19,800 (15,510) 59,730 + Deprec 40,000 40,000 40,000
TOTAL CF 59,800 24,490 99,730
NPV 15,566 (111,719) 159,504
IRR 15.1% -14.4% 40.9%
Scenario Analysis Example
9-70
Problems with Scenario Analysis
• Considers only a few possible out-comes
• Assumes perfectly correlated inputs–All “bad” values occur together and all
“good” values occur together• Focuses on stand-alone risk,
although subjective adjustments can be made
9-71
Sensitivity Analysis
• Shows how changes in an input variable affect NPV or IRR
• Each variable is fixed except one– Change one variable to see the effect on
NPV or IRR• Answers “what if” questions
9-72
Sensitivity Analysis: Unit Sales
Base Units UnitsUnits 6,000 5,500 6,500 Price/unit 80$ 80 80Variable cost/unit 60$ 60 60Fixed cost/year 50,000$ 50,000 50,000
Initial investment 200,000$ Depreciated to salvage value of 0 over 5 yearsDeprec/yr 40,000$
Tax rate 34%Required Return 12%
BASE UNITS UNITSUnits 6,000 5,500 6,500 Price/unit 80$ 80$ 80$ Variable cost/unit 60$ 60$ 60$ Fixed cost 50,000$ 50,000$ 50,000$
Sales 480,000$ 440,000$ 520,000$ Variable Cost 360,000 330,000 390,000 Fixed Cost 50,000 50,000 50,000 Depreciation 40,000 40,000 40,000 EBIT 30,000 20,000 40,000 Taxes 10,200 6,800 13,600 Net Income 19,800 13,200 26,400 + Deprec 40,000 40,000 40,000
TOTAL CF 59,800 53,200 66,400
NPV 15,566$ (8,226)$ 39,357$
Unit Sales Sensitivity
$(8,226)
$15,566
$39,357
-20,000.00
-10,000.00
0.00
10,000.00
20,000.00
30,000.00
40,000.00
50,000.00
5,500 6,000 6,500
Unit Sales
NP
V
9-73
Sensitivity Analysis: Fixed Costs
Fixed Cost Sensitivity
$27,461
$15,566
$3,670
0.00
5,000.00
10,000.00
15,000.00
20,000.00
25,000.00
30,000.00
$45,000 $50,000 $55,000
Fixed Cost
NP
VBase Fixed Cost Fixed Cost
Units 6,000 6,000 6,000 Price/unit 80$ 80 80Variable cost/unit 60$ 60 60Fixed cost/year 50,000$ 55,000 45,000
Initial investment 200,000$ Depreciated to salvage value of 0 over 5 yearsDeprec/yr 40,000$
Tax rate 34%Required Return 12%
BASE FC FCUnits 6,000 6,000 6,000 Price/unit 80$ 80$ 80$ Variable cost/unit 60$ 60$ 60$ Fixed cost 50,000$ 55,000$ 45,000$
Sales 480,000$ 480,000$ 480,000$ Variable Cost 360,000 360,000 360,000 Fixed Cost 50,000 55,000 45,000 Depreciation 40,000 40,000 40,000 EBIT 30,000 25,000 35,000 Taxes 10,200 8,500 11,900 Net Income 19,800 16,500 23,100 + Deprec 40,000 40,000 40,000
TOTAL CF 59,800 56,500 63,100
NPV 15,566$ 3,670$ 27,461$
9-74
Sensitivity Analysis:• Strengths
– Provides indication of stand-alone risk.– Identifies dangerous variables.– Gives some breakeven information.
• Weaknesses– Does not reflect diversification.– Says nothing about the likelihood of change
in a variable, – Ignores relationships among variables.
9-75
Disadvantages of Sensitivity and Scenario Analysis
• Neither provides a decision rule. –No indication whether a project’s
expected return is sufficient to compensate for its risk.
• Ignores diversification. –Measures only stand-alone risk, which
may not be the most relevant risk in capital budgeting.
9-76
Managerial Options• Contingency planning• Option to expand
– Expansion of existing product line– New products– New geographic markets
• Option to abandon– Contraction– Temporary suspension
• Option to wait• Strategic options
9-77
Capital Rationing
• Capital rationing occurs when a firm or division has limited resources– Soft rationing – the limited resources are
temporary, often self-imposed– Hard rationing – capital will never be available
for this project• The profitability index is a useful tool when
faced with soft rationing