Discounted Cash Flow Analysis (aka Engineering Economy)

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1 Discounted Cash Fow Anaysis (aka Engineering Economy) Objective: To provide economic comparison of benefits and costs that occur over time Assumptions: Future benefits and costs can be predicted A Benefits, Costs measured in money Singe point of view (generay, the project owner) + - P Cash Fow R Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 1 of 16 F time Issue - Vaue over time Money now has a different vaue than the same amount at a different date Comparabe to but not equa to interest rate Proper name: Discount Rate, r because future benefits/costs are reduced (that is, discounted ) to compare with present Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 2 of 16

2 Formuas for N Periods Singe amounts a) Future Amount = P (1 + r) N = P (caf) caf = Compound Amount Factor b) Present Amount = F/caf 1/caf = Present Worth Factor Finite Series c) F = Σ i R (1 + r) i = R [(1 + r) N -1] / r d) R = P (crf) = [P*r (1+r) N ] / [(1 + r) N -1] crf = Capita Recovery Factor Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 3 of 16 Formuas for N Periods (cont ) Infinite Series 1 << (1 + r) N => (1+ r) N / [(1 + r) N - 1] => 1 => crf = r Sma Periods (1 + r) N ==> e rn Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 4 of 16

3 Present Vaue Anaysis Present Vaue Anaysis puts a future amounts on a common basis, typicay the present It may be some other reference year that is convenient, such as year of proposed investment Net Present Vaue is the tota of the present vaues of a future amounts, typicay: Revenues Costs = Net Amount Referred to as NPV Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 5 of 16 Exampe Appication of Present Vaue Anaysis A by spreadsheets! Exampe: Year Investment Net Income Cash Fow NPV at 12% $0.79 Formua: NPV(12%, B9:K9) Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 6 of 16

4 Effect of Different Discount Rates Higher Discount rates => smaer vaue of future benefits discourages projects with ong pay back periods project advocates try to minimize discount rate Exampes: Massive Dams ; Airports; Aircraft projects Argument over Discount rates Often very difficut poiticay Not hard from technica perspective Generay higher than poiticians want, for exampe, US Government base case before 2000 was 7%, but under current administration it is ~5% (see ater sides) MORE DISCUSSION NEXT WEEK Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 7 of 16 US Govt base position on Discount rate (OMB Circuar A-94,1992,revised yeary) 1. Base-Case Anaysis. Constant-doar benefit-cost anayses of proposed investments and reguations shoud report net present vaue and other outcomes determined using a rea discount rate of 7 percent. This rate approximates the margina pretax rate of return on an average investment in the private sector in recent years. Significant changes in this rate wi be refected in future updates of this Circuar. 2. Other Discount Rates. Anayses shoud show the sensitivity of the discounted net present vaue and other outcomes to variations in the discount rate. The importance of these aternative cacuations wi depend on the specific economic characteristics of the program under anaysis. For exampe, in anayzing a reguatory proposa whose main cost is to reduce business investment, net present vaue shoud aso be cacuated using a higher discount rate than 7 percent. (accessed pre 2000) Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 8 of 16

5 Graphica view of Effect of Different Discount Rates and Lengths of Time Reative Present Vaue Reative Vaue r = 0 r = 5% r = 10% r = 15% r = 20% Year Increments Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 9 of 16 Discount Rate Approximation To appreciate effect of discounting: Rue of 72 or Rue of 70 e rn = 2.0 when rn = 0.72 (actuay = 0.693) Therefore, present amount doubes when future amount haves rn = 72 with r expressed in percent Exampes When woud $1000 invested at 10% doube? What is, at 9%, the vaue of $1000 in 8 years? Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 10 of 16

6 Effect of Different Time Horizons Longer Periods of Benefits Increase Present Vaues Increment depends on discount rate What ength of time matters? For US Government Rate, not much over 30 years For Rates commony used in business (15 to 20%), anything over 20 years has itte vaue Exception: If future benefits grow exponentiay, they may compensate for discounting of future revenues Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 11 of 16 Current US Government position on Discount rate (OMB Circuar A-94) Provides 2 rates: Nomina represents future purchasing power; refects infation Rea represents constant-doar; assumes no infation => Difference impies assumed rate of infation These rates change yeary (as of ast severa years) These rates differ according to period ower rates for shorter periods Note: assumed rate of infation differs by period (See next sides) Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 12 of 16

7 Discount rates by OMB Circ. A-94, Appendix C [Ref: Nomina Discount Rates. A forecast of nomina or market interest rates for 2007 based on the economic assumptions from the 2008 Budget are presented beow. These nomina rates are to be used for discounting nomina fows, which are often encountered in ease-purchase anaysis. Nomina Interest Rates on Treasury Notes and Bonds of Specified Maturities (in percent) 3-Year Year Year Year Year Year 5.1 Rea Discount Rates. A forecast of rea interest rates from which the infation premium has been removed and based on the economic assumptions from the 2008 Budget is presented beow. These rea rates are to be used for discounting rea (constant-doar) fows, as is often required in cost-effectiveness anaysis. Rea Interest Rates on Treasury Notes and Bonds of Specified Maturities (in percent) 3-Year Year Year Year Year Year 3.0 Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 13 of 16 However Guideines appear precise (2 significant figures) But they are highy variabe from year to year (see next side), so anaysis done in year N can be significanty off in year N+1 Woud seem to be poitica, as evidenced by comparing rates from ast 6 years with those given before 2000 (see side 8) Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 14 of 16

8 Previous Discount rates by OMB. A-94 Nomina Discount Rates for years into future For Year Rea Discount Rates for years into future For Year Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 15 of 16 Summary Formuas Simpe Especiay by Spreadsheets Discount rate is key issue High rates recommended (but see ater presentations) Longer term benefits not arge Engineering Systems Anaysis for Design Richard de Neufvie Massachusetts Institute of Technoogy Discounted Cash Fow Side 16 of 16

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