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A quantitative look at the risk in budgeting cost, taking into account discounted cash flows for cost and benefits.
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Square Peg ConsultingCopyright 2001, all rights reserved
Quantitative Risk Analysis in Budgeting and Cost Analysis
John C. GoodpastureSquare Peg Consulting
Square Peg ConsultingCopyright 2001, all rights reserved
Budgets are estimates
There are no facts about the future, only estimatesSimple budget estimates do not account for riskRisk is handled by estimating the impact of uncertainties on future cash flows (uses of funds and sources of funds)
Square Peg ConsultingCopyright 2001, all rights reserved
Terms in risk-managed budgeting
Discounting – takes into account the risks of receiving or paying funds in the future
Expected Value – takes into account the uncertainty of estimate
Net Present Value – cash value at time zero (now)
Internal Rate of Return – discount required for NPV = 0
Economic Value Add (EVA) – profit-based calculation of discounted value
Square Peg ConsultingCopyright 2001, all rights reserved
Capital budgeting*Present value (PV) = Value at future date * Discount factorDiscount factor = 1/(1-k)n where n is the number of accounting periods between the present and the future and k is the cost of capital factor
Net Present Value (NPV) = Σ PV of cash inflows - Σ PV of cash outflows
$ Inflows
$ OutflowsTime
Economic Value Add = After-tax operating income - k (Capital invested)where k is the cost of capital rate, %
Expected Monetary Value = Σ $OutcomeNth * ProbabilityNthfor all possible outcomes
*The flow of cash and not expenses
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PM influences NPV via the project timeline
First, the value of money decays over time. This decay is due to the effects of inflation, the uncertainty that future flows will continue or begin, and the uncertainty that a better investment is available elsewhere. In all cases, the “present value” is more than the “future value.”
Second, the value of the project is the net of the present value of all the cash outlays for investment and inflows from operations and salvage.
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NPV
Future benefits are “discounted” to the present to account for RISK in the future.
Time
$ Benefits, Expected Value
NPV is the Σ benefits + investment in the present value.IRR is the discount rate that makes NPV equal to $0.
$ Investment
Σ {present values}
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Two-dimensional risks
Present Time
Future Time
Estimate Uncertainty
Discount for•Inflation•Risk of getting paid•Capital cost•Denied opportunity•Market uncertainty
Distribution of estimate
EV
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PV tableYear 0 1 2 3 4
5% 1.0 0.952 0.907 0.864 0.823
8% 1.0 0.926 0.857 0.794 0.735
12% 1.0 0.893 0.797 0.712 0.636
13% 1.0 0.885 0.783 0.693 0.613
14% 1.0 0.877 0.769 0.675 0.592
Discount
PV = Value before discount * factor at intersection of Discount and Year
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NPV example$500 investment made now, that yields a $1000 benefit 2 years from now, at a discount factor of 12%, has an NPV of $?.
Answer: From the table of present values, find the factor for 12% 2 years from now; multiply the FV by the factor to get the PV; net with the investment-$500 + 1000 * 0.797 = $297
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NPV example
Mathematically: $297 = -$500/(1 + 12%)0 +$1000/(1 + 12%)2
$297 = -$500 + $797
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NPV and EVA in project selection
A valuable project has positive, or at worst $0, NPVA valuable project must earn back more than, or at worst equal, the cost of the capital invested: EVA > $0Discount rate used in NPV and EVA for project approval is the “hurdle rate”IRR is the maximum discount rate for EVA or NPV = $0
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Paul’s project
$500K investment required12.8% hurdle rate$700K+ benefit stream estimated over 5 yearsIs this a good deal?
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Paul’s project, NPVPaul's Project
$000
Year Cash Investment
Benefits Face Value
Benefits Present Value @ 12.8% PV Cash Flow
0 ($500.00) ($500.00)
1 $141.46 $125.41 ($374.59)
2 $141.46 $111.18 ($263.42)
3 $141.46 $98.56 ($164.85)
4 $141.46 $87.38 ($77.48)
5 $141.46 $77.46 ($0.01)
Totals ($500.00) $707.30 $499.99 ($0.01)
NPV = $0; IRR is 12.8%–A-risk-neutral investor would take $0 or the project opportunity indifferently–Spreadsheet “add-in” Resolver will iteratively solve for benefits given the investment and hurdle rate.
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EVA
Alternative Competing for Capital
Alternative Competing for Capital
EVANet Cash
Benefits from Project
Opportunity Cost of Capital Employed
After-Tax Earnings
$0
CE x discount rate = CCECapital Employed to Execute a Project
EVA = (Present value of after-tax earnings) – (Benefits from the next best competing opportunity)
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Paul’s project EVADepreciate $500K annually at $100K per year, discount rate 12.8%
Depreciation Schedule for Paul's Project $000
Year 1 Year 2 Year 3 Year 4 Year 5 Total
$100.00 $100.00 $100.00 $100.00 $100.00 $500.00 Depreciation
$500.00 $400.00 $300.00 $200.00 $100.00 Capital employed
(CE)
12.80% 12.80% 12.80% 12.80% 12.80% Cost of capital rate (CCR)
$64.00 $51.20 $38.40 $25.60 $12.80 $192.00Cost of capital employed (CCE) =
CE x CCR
$56.74 $40.24 $26.75 $15.81 $7.01 $146.55 PV CCE
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Paul's Project Plan with EVA = $0 $000
Outlays shown as ($000), Discount factor 12.8%
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 TOTAL
($500.00) Investment
$56.74 $40.24 $26.75 $15.81 $7.01 $146.55 PV CCE
$29.31 $29.31 $29.31 $29.31 $29.31 $146.55 PV after-tax earnings
($27.43) ($10.93) $2.56 $13.50 $22.50 $0.00 PV EVA
$33.06 $37.29 $42.07 $47.45 $53.53 $213.40 FV after-tax earnings
$100.00 $100.00 $100.00 $100.00 $100.00 $500.00 FV depreciation
$133.06 $137.29 $142.07 $147.45 $153.53 $713.40 FV cash benefits
($500.00) $117.96 $107.90 $98.99 $91.08 $84.07 $0.00 NPV cash benefits
Project goal
NPV of Net Cash Flow = EVA of after-tax earnings
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Present value of EVA of cash earnings and NPV of cash flow are equal!
Square Peg ConsultingCopyright 2001, all rights reserved
Risk analysis in expense (cost) estimating
1. Begin with WBS2. Use decision trees to evaluate EMV of
alternatives in each WBS, as appropriate
3. For uncertain cost elements, estimate a distribution
4. Obtain PV of all EVs5. Sum EVs and deterministic costs for
project estimate
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Project WBS
Project NEW PRODUCT
Product Design2
PM Office1 Software
Development3
Integration and Test
4
Deployment6
Training and Support
5
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“3-point estimate” and the error of “Most Likely”
$41Total WBS 2,3,4
$23$15$114. Integration & Test
$35$20$163. SW Design
$10$6$42. Product Design
PessimisticMost LikelyOptimisticWBS Element
Project Cost Estimates and Ranges$000
All WBS cost estimates are PV
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EV is a better estimate
$46.67(14% greater than Most Likely)
$41Total WBS 2,3,4
$16.33$154. Integration & Test
$23.67$203. SW Design
$6.67$62. Product Design
Expected Value*Most LikelyWBS Element
Project Cost Estimates and Ranges$000
•Triangular distribution assumed*The EMV from a decision tree outcome for a WBS element would go in this column
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What’s been learned?
Capital budgeting is about cash flowNPV and EVA are equivalentGood projects have positive NPV and EVAEV math reduces risk of WBS cost estimates