statistics in cost analysis

8/8/2019 Statistics in Cost Analysis

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Square Peg ConsultingCopyright 2001, all rights reserved

Quantitative Risk Analysis inBudgeting and Cost Analysis

John C. GoodpastureSquare Peg Consulting

[email protected]


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Budgets are estimates

There are no facts about thefuture, only estimates

Simple budget estimates do not

account for riskRisk is handled by estimating the

impact of uncertainties on futurecash flows (uses of funds andsources of funds)


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Terms in risk-managed budgeting

Discounting takes into account the risks of

receiving or paying funds in the futureExpected 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 = 0Economic Value Add (EVA) profit-based

calculation of discounted value


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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) = PV of cash inflows - 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 = $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 uncertaintythat future flows will continue or begin, and the

uncertainty that a better investment is available

elsewhere. In all cases, the present value is morethan the future value.

Second, the value of the project is the netof the present value of all the cash outlays forinvestment and inflows from operations and

salvage.


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NPV

Future benefits are discounted to thepresent to account forRISK in the future.

Time

$ Benefits, Expected Value

NPV is the benefits + investment in the present value.IRR is the discount rate that makes NPV equal to $0.

$ Investment

{present values}


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Two-dimensional risks

PresentTime

Future Time

Estimate Uncertainty

Discount forInflation

Risk of getting paid

Capital cost

Denied opportunity

Market uncertainty

Distribution of estimate

EV


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PV table

Year 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 fromnow, 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 factorto 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 atworst $0, NPV

A valuable project must earn back more

than, or at worst equal, the cost of thecapital invested: EVA > $0

Discount rate used in NPV and EVA for

project approval is the hurdle rateIRR is the maximum discount rate for

EVA or NPV = $0


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Pauls project

$500K investment required

12.8% hurdle rate

$700K+ benefit stream estimated

over 5 yearsIs this a good deal?


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Pauls project, NPVPaul's Project

$000

YearCash

InvestmentBenefits Face

ValueBenefits PresentValue @ 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 opportunityindifferently

Spreadsheet add-in Resolver will iteratively solve for benefits giventhe investment and hurdle rate.


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EVA

AlternativeCompetingfor Capital

AlternativeCompetingfor Capital

EVANet Cash

Benefits fromProject

Opportunity CostofCapital

Employed

After-TaxEarnings

$0

CE x discount rate = CCECapital Employed to Execute a Project

EVA = (Present value of after-tax earnings) (Benefits from the next bestcompeting opportunity)


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Pauls project EVA Depreciate $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 $100.00Capital 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 capitalemployed (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-taxearnings

($27.43) ($10.93) $2.56 $13.50 $22.50 $0.00PV EVA

$33.06 $37.29 $42.07 $47.45 $53.53 $213.40 FV after-taxearnings

$100.00 $100.00 $100.00 $100.00 $100.00 $500.00 FVdepreciation

$133.06 $137.29 $142.07 $147.45 $153.53 $713.40 FV cashbenefits

($500.00) $117.96 $107.90 $98.99 $91.08 $84.07 $0.00 NPV cashbenefits

Project goal

NPV of Net Cash Flow = EVA of after-tax earnings


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Present value of EVA of cashearnings and NPV of cash flow areequal!


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Risk analysis in expense (cost)

estimating

1. Begin with WBS

2. Use decision trees to evaluate EMV ofalternatives in each WBS, asappropriate

3. For uncertain cost elements, estimatea 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 Office

1 SoftwareDevelopment3

Integration andTest

4

Deployment6

Training and

Support5


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3-point estimate and the error of

Most Likely

$41Total WBS2,3,4

$23$15$114. Integration &Test

$35$20$163. SW Design

$10$6$4

2. Product

Design

PessimisticMostLikely

OptimisticWBS 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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Whats been learned?

Capital budgeting is about cashflow

NPV and EVA are equivalent

Good projects have positive NPVand EVA

EV math reduces risk of WBS costestimates

statistics in cost analysis

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