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# Quantitative Risk in Cost and Budget

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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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### Quantitative Risk in Cost and Budget

1. 1. Quantitative Risk Analysis in Budgeting and Cost Analysis John C. Goodpasture Square Peg Consulting John.g@sqpegconsulting.com Square Peg Consulting Copyright 2001, all rights reserved
2. 2. 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) Square Peg Consulting Copyright 2001, all rights reserved
3. 3. 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 Consulting Copyright 2001, all rights reserved
4. 4. 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 Square Peg Consulting Copyright 2001, all rights reserved
5. 5. 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. Square Peg Consulting Copyright 2001, all rights reserved
6. 6. 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} Square Peg Consulting Copyright 2001, all rights reserved
7. 7. 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 Square Peg Consulting Copyright 2001, all rights reserved
8. 8. 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 Square Peg Consulting Copyright 2001, all rights reserved
9. 9. 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 Square Peg Consulting Copyright 2001, all rights reserved
10. 10. NPV example Mathematically: \$297 = -\$500/(1 + 12%)0 + \$1000/(1 + 12%)2 \$297 = -\$500 + \$797 Square Peg Consulting Copyright 2001, all rights reserved
11. 11. 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 Square Peg Consulting Copyright 2001, all rights reserved
12. 12. Paul’s project \$500K investment required 12.8% hurdle rate \$700K+ benefit stream estimated over 5 years Is this a good deal? Square Peg Consulting Copyright 2001, all rights reserved
13. 13. 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. Square Peg Consulting Copyright 2001, all rights reserved
14. 14. 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) Square Peg Consulting Copyright 2001, all rights reserved
15. 15. 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 Square Peg Consulting Copyright 2001, all rights reserved
16. 16. 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 Square Peg Consulting Copyright 2001, all rights reserved
17. 17. Present value of EVA of cash earnings and NPV of cash flow are equal! Square Peg Consulting Copyright 2001, all rights reserved
18. 18. 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 Square Peg Consulting Copyright 2001, all rights reserved
19. 19. Project WBS Project NEW PRODUCT Integration and Deployment Product Design Test 6 2 4 PM Office Training and 1 Software Support Development 5 3 Square Peg Consulting Copyright 2001, all rights reserved
20. 20. “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 Square Peg Consulting Copyright 2001, all rights reserved
21. 21. 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 Square Peg Consulting Copyright 2001, all rights reserved
22. 22. 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 Square Peg Consulting Copyright 2001, all rights reserved