Quantitative Risk in Cost and Budget

Quantitative Risk Analysis in
Budgeting and Cost Analysis

John C. Goodpasture
Square Peg Consulting

John.g@sqpegconsulting.com

Copyright 2001, all rights reserved

Budgets are estimates

There are no facts about the
future, only estimates
Simple budget estimates do not
account for risk
Risk is handled by estimating the
impact of uncertainties on future
cash flows (uses of funds and
sources of funds)


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


Capital budgeting*
Present value (PV) = Value at future date * Discount factor
Discount 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

Time $ Outflows

Economic Value Add = After-tax operating income - k (Capital invested)
where k is the cost of capital rate, %

Expected Monetary Value = Σ $OutcomeNth * ProbabilityNth
for all possible outcomes

*The flow of cash and not expenses

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.


NPV
$ Benefits, Expected Value

Time
$ Investment

Future benefits are “discounted” to the
present to account for RISK in the future.

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

Σ {present values}


Two-dimensional risks
Discount for
•Inflation
Present •Risk of getting paid
•Capital cost
Time •Denied opportunity EV
•Market uncertainty

Distribution of estimate

Future Time

Estimate Uncertainty


PV table
Year 0 1 2 3 4
Discount

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
PV = Value before discount * factor at intersection of
Discount and Year

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


NPV example

Mathematically:
$297 = -$500/(1 + 12%)0 +
$1000/(1 + 12%)2
$297 = -$500 + $797


NPV and EVA in project
selection
A valuable project has positive, or at
worst $0, NPV
A valuable project must earn back more
than, or at worst equal, the cost of the
capital invested: EVA > $0
Discount rate used in NPV and EVA for
project approval is the “hurdle rate”
IRR is the maximum discount rate for
EVA or NPV = $0


Paul’s project
$500K investment required
12.8% hurdle rate
$700K+ benefit stream estimated
over 5 years
Is this a good deal?


Paul’s project, NPV
Paul's Project
$000
Cash Benefits Face Benefits Present
Year PV Cash Flow
Investment Value Value @ 12.8%
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.

EVA
After-Tax
Earnings

EVA
Net Cash
Benefits from Opportunity Cost
Project of Capital
Alternative Employed
Alternative
$0 Competing
Competing
for Capital
for Capital

Capital Employed to Execute a Project CE x discount rate = CCE

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


Paul’s 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

Capital employed
$500.00 $400.00 $300.00 $200.00 $100.00
(CE)

Cost of capital rate
12.80% 12.80% 12.80% 12.80% 12.80%
(CCR)
Cost of capital
$64.00 $51.20 $38.40 $25.60 $12.80 $192.00 employed (CCE) =
CE x CCR

$56.74 $40.24 $26.75 $15.81 $7.01 $146.55 PV CCE


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

Project goal ($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

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

Present value of EVA of cash
earnings and NPV of cash flow are
equal!


Risk analysis in expense (cost)
estimating

1. Begin with WBS
2. 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 EVs
5. Sum EVs and deterministic costs for
project estimate


Project WBS

Project NEW PRODUCT

Integration and Deployment
Product Design
Test 6
2
4

PM Office Training and
1 Software Support
Development 5
3


“3-point estimate” and the error of
“Most Likely”
Project Cost Estimates and Ranges
$000
Most
WBS Element Optimistic Pessimistic
Likely
2. Product
$4 $6 $10
Design

3. SW Design $16 $20 $35

4. Integration &
$11 $15 $23
Test
Total WBS
$41
2,3,4
All WBS cost estimates are PV

EV is a better estimate
Project Cost Estimates and Ranges
$000
WBS Element Most Likely Expected Value*

2. Product Design $6 $6.67

3. SW Design $20 $23.67
4. Integration &
$15 $16.33
Test
Total WBS 2,3,4 $41 $46.67
(14% greater than Most Likely)

•Triangular distribution assumed
*The EMV from a decision tree outcome for a WBS element
would go in this column

What’s been learned?

Capital budgeting is about cash
flow
NPV and EVA are equivalent
Good projects have positive NPV
and EVA
EV math reduces risk of WBS cost
estimates


Quantitative Risk in Cost and Budget

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