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Discount Rate for LCCA

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The term real discount rate, also known as the real interest rate, is commonly used in engineering economics to refer to the rate of change over time in the true value of money, taking into account fluctuations in both investment interest rates and the rate of inflation. This value differs from a nominal discount rate, which reflects expected inflation and is used to discount inflated dollars or nominal benefits and costs (e.g., real discount rate ≈ nominal discount rate – inflation rate). That is to say, today’s costs can be used as proxies for future costs only if the real discount rate is used in the LCCA. All state highway agencies currently use today’s costs (e.g., non-inflated dollars) and real discount rates in their LCCAs.

The real discount rate is given by the following equation[1]:

1 + iint d = – 1 [Eqn 2-1] 1 + iinf where: d = the real discount rate, % iint = the interest rate, % iinf = the in.aton rate, %

For example, for an interest rate (iint) of 10% and an in.aton rate (iinf) of 6%, the real discount rate is: 1.10 d = – 1 = 0.038 or 3.8% 1.06 If the interest rate exceeds the in.aton rate, the fol­lowing approximaton may be used: d ˜ iint – iinf [Eqn 2-2] For the previous example, the approximated real dis­count rate is 10% – 6% = 4%, slightly greater than the more precisely calculated real discount rate of 3.8%. Through applicaton of an appropriate real discount rate (which may di.er for alternates with di.erent material in.aton rates), the worth or value of all ini­tal and future costs can be expressed in terms of constant dollars, (i.e., in terms of the costs of those items as if they were incurred in the year in which the life-cycle cost analysis is conducted). High real discount rates tend to reduce the impact that high future expenditures have on the net pres­ent value or the alternate. Thus, it can be said that high real discount rates favor alternates that have low inital costs and high future costs, while low real discount rates favor alternates with higher ini­tal costs and lower future costs. As an example, consider Figure 2-1, which shows the present worth (discussed in Step 7) of $1 spent in various years under various real discount rates. If the real discount rate is 2%, a dollar spent in year 30 is worth 55 cents today; if the real discount rate is 6%, that same dol­lar in year 30 would be worth just 17 cents today. Thus, the higher real discount rate would more greatly discount future costs and could result in the selecton of an alternate with much higher maintenance costs even if the inital cost is only slightly lower.

Interest rates and in.aon rates .uctuateover tme, but the relatve di.erence between them, while not constant, is less variable. The real discount rate se­lected should take into account past trends in appro­priate interest and in.aton rates over relatvely long tme periods, as well as future economic projectons. The appropriate interest and in.aon rates to use in calculatng the real discount rate for the evalua­ton of public-sector investments, such as road proj­ects, are the subject of much debate for the reasons discussed in the rest of this secton. Of entmes, a single “standard” real discount rate might be used to avoid the complexites in calculatng a local or mate­rial-specific real discount rate, but this practce can lead to the selecton of an alternate that is not the most cost-e.ectve (Snyder 2008).

The real discount rate also must be rounely up­datedto re.ect current and forecasted economic conditons. The practce of using a single “standard” real discount rate does not allow for such considera­ton. The use of the United State’s O.ce of Manage­ment and Budget (OMB) real discount rate, which is updated annually, does, however, account for such changes in economic conditons. If local interest and in.aton rates are not readily available to develop and regularly update a local real discount rate, ACPA supports the use of this OMB real discount rate.

Basic Steps in a Life-Cycle Cost Analysis (LCCA) for a Single Project

The following seconsdiscuss how to establish ap­propriate interest and in.aton rates. Guidance is then provided on how best to determine the real dis­count rate.

Selecting an Interest Rate

An abundance of con.ictng opinion and guidance exists on the subject of choosing an interest rate for use in LCCA of pavement alternatves. Funds for paving projects are obtained by 1) levying taxes, 2) borrowing money (i.e., selling bonds), and/or 3) charging users for services (e.g., toll revenue). The interest rate assumed for the LCCA of a project should re.ect the type of entty raising the money and the method(s) used to raise it. Public enes (e.g., local, State, and Federal agen­cies)fund projects by borrowing money through the sale of bonds and/or levying taxes. Opinions di.er on whether the interest rate that applies to a public agency’s analysis of project alternatves should be based on an assumpton of .nancing by borrowing, .nancing by taxes, or a combinaton of the two. An­other school of thought considers the interest rate to be a re.ecton of “opportunity or investment fore­gone” (i.e., money spent on one actvity is money that cannot be spent on another actvity or invest­ment that might also produce revenue or bene.t).

If project(s) will be funded by the sale of bonds, money is available at atractve, relatvely low in­terest rates. While government bonds are in direct competton with other investment opportunites, they are presumed to be lower-risk than private in­vestments because governments are beter posi­toned to cope with risk. Bonds sold by government agencies are backed by the issuer’s credit and taxing power – i.e., the “full faith and credit” of the govern­ment agency, which consttutes an unconditonal commitment to pay interest and principal on the debt. For analyses of projects to be .nanced by the Federal government, the appropriate interest rate generally is taken to be the rate on long-term (30­year) U.S. Treasury bills (OMB 1992). State and mu­nicipal bonds typically carry somewhat higher risk and, thus, higher interest rates (Thuesen and Fab­rycky 1984).

If project(s) will be funded with tax revenues (espe­cially dedicated revenues, such as highway user fees, tolls or fuel taxes that cannot be used for other purposes), the owner-agency does not .nance the revenue and there is no "opportunity cost" associ­ated with it. Therefore, the interest rate for the use of the money must be zero (e.g., iint = 0%). The use of a zero interest rate results in undiscounted (or negatvely discounted) future expenditures, making future, relatvely uncertain costs just as important (if not more so) to the decision as today’s well-known costs (Thuesen and Fabrycky 1984). While this is contrary to current practce and the assumptons made in calculaton of the OMB real discount rate, this viewpoint is gaining popularity and legitmacy among transportaton economists. State and local agencies typically cannot .nance allof the roadway projects necessary to keep their net­work in ideal condion using only tax revenues. Thus, these agencies routnely sell bonds to supple­ment tax revenues. This can result in an ever-in­creasing backlog of projects that cannot be programmed with currently available funds because more and more money must be dedicated to paying out interest on the bonds. In this scenario, the most realistc interest rate may be a weighted average of the interest rate associated with tax revenues (e.g., 0%) and the interest rate associated with the bonds sold (Snyder 2008). Quasi-private enes (e.g., toll authories)fund projects by borrowing money through the sale of bonds; user fees (tolls) are charged to pay o. those bonds and cover annual operatng costs. New bonds might necessarily be issued periodically to raise capi­tal for major constructon projects. Because bonds issued by a quasi-private entty are backed solely by the toll revenue to be generated by the project(s) being .nanced, such bonds typically have higher in­terest rates than those issued by less-risky public en­ttes. If no tax revenues will be used to fund the project, the interest rate used should be that of the bonds issued by the quasi-private entty for construc­ton of the project(s).

Private enes (e.g., concessionaires)can neither levy taxes nor sell their own bonds, so they must raise capital from their own investments. For exam­ple, they might borrow money from private investors or use income from other investments to fund their constructon projects. The appropriate interest rate for analyzing projects built by private enttes can vary widely, but is ofen taken as that of a long-term corporate bond rate.

Selecting an Inflation Rate

The inflation rate chosen for use in a life-cycle cost analysis of pavement alternatves may be:

  1. a single value if it is assumed that all components of future costs inflate at a uniform rate or
  2. several di.erent values for various cost components when there are signi.cant di.erences in in.aton among the cost components.

Several general in.aon indicesare compiled regu­larly by the Bureau of Labor Statstcs (BLS) in the U.S. Department of Labor, including:

  • The Consumer Price Index (CPI), which repre­sents the change in retail prices for a selected set of purchases of clothing, food, housing, transportaton, medical care, entertainment, educaton, and other items throughout the

U.S. The CPI serves to quantfy the e.ect of retail price changes on a .xed standard of liv­ing for the “average” consumer, serving as a general barometer of in.aton

in the U.S. (Thuesen and Fabrycky 1984; Riggs and West 1986).

• The Highway and Street Constructon (BHWY) Producer Price Index (PPI), which tracked the cost of materials used in highway construc­ton. PPIs re.ect changes over tme in

the prices received by domestc producers for goods and services. The BHWY PPI was, how­ever, discontnued in 2010. The PPI for all commodites (WPU000000) also can be

used as a general in.aton index or combined with the BHWY PPI to extend the BHWY PPI from 2010 to present.


The FHWA compiled, for many years, an index itcalled the Bid Price Index (BPI)to track the prices of several installed components of highway construc­ton (thus

including labor, overhead, and material costs). Due to issues related to the quality of the data underlying the computaton of the FHWA BPI, it was discontnued in 2006

(FHWA 2006 and 2007a). In 2010, the FHWA replaced the BPI with a Natonal Highway Constructon Cost Index (NHCCI), with data startng in 2003 (FHWA 2010a). Rather than

tracking individual components as the BPI did, the new index is an aggregate of all highway constructon costs, sim­ilar to the BLS’s BHWY PPI. It is important to

note, however, that neither of these indices includes the cost of price escalaton clauses (e.g., material price escalators). Therefore, these indices can greatly un­

derestmate a material’s in.aton rate in states where material price escalators are used. See Step 3 for more informaton on material price escalators. To compare all of these general in.aon indices, Figure 2-2 shows the BLS’s BHWY PPI, the FHWA’s BPI, the BLS’s CPI and the FHWA’s NHCCI (NOTE: the BHWY PPI started in 1986, making 1986 the earliest startng point for

comparison, and the FHWA NHCCI index was started in 2006 at the end value of the FHWA BPI). Across the 24 years shown, the average compound annual growth rate (CAGR)

for each index was: • BLS’s BHWY PPI: 3.25%

• FHWA’s BPI + NHCCI: 2.34%

• BLS’s CPI: 2.90%



Figure 2-3 shows the annual (e.g., year-over-year) in­.aton rates for the indices shown in Figure 2-2. As shown, the highway constructon cost-speci.c in­dices are more

volatle than the much more general CPI. Despite their increased volatlity, the construc­ton cost indices have had CAGRs comparable to that of the more general CPI over

the last 24 years and, in fact, the constructon cost indices were in.atng at a rate that was signi.cantly less than that of the CPI untl 2004. The constructon cost

indices have in­creased sharply since that tme and have become much more volatle. According to the FHWA, these recent surgesare due primarily to the escalang costs of commodiessuch as steel, asphalt, cement, and crushed stone (FHWA 2007a). These

unprecedented constructon cost increases may have potentally signi.cant im­pacts on state agencies, the highway industry and the general public (FHWA 2011a). Thus,

while a very general in.aton index such as the BLS’s CPI could be used in LCCAs, it is clearly not representatve of his­toric or present price .uctuatons in the

highway and road sector. The importance of recent increases in material/commodity costs, as noted by the FHWA, underscores the importance of accountng for indi­vidual

cost components in a pavement LCCA when there is signi.cantly di.erent in.aton among cost components between alternates. Material-speci.c in.aon ratescan be developed to forecast prices for various materials by considering their respectve historic prices and trends. While current

material costs can be known with a relatvely high degree of reliability, forecastng future material costs for the purposes of an LCCA requires special consideraton

(MIT 2011a). Figure 2-4 shows index values of the BLS’s PPIs for concrete products and asphalt paving mixtures and blocks for the last 54 years (NOTE: the asphalt paving mixtures

and blocks PPI started in 1958, making 1958 the earliest startng point for comparison; this also is a reasonable investgaton tmeframe when using previous trends to

forecast future prices in an LCCA with an analysis period of 40+ years). Also shown are the BLS’s CPI and standard deviaton rates of monthly values within each year.



The PPI for concrete products has tracked relavely • While concrete prices and the CPI have in- closely to the CPI, but the asphalt paving mixtures creased by about 500% to 700% in the last 54 and blocks PPI shows signi.cantly di.erent in.aton. years, asphalt paving mixture prices have in- Table 2-2 presents a summary of some of the general creased 1,640%. trends for the last 54 years, of note: • The CAGR of the concrete products PPI and the CPI over this tmeframe are similar (3.6% • The concrete products PPI has had a lower av­ and 3.9%, respectvely), while the in.aton erage yearly standard deviaton than that for rate of the asphalt paving mixtures and blocks the CPI (e.g., 2.9 versus 4.2). Thus, concrete PPI is signi.cantly higher (5.5%). This di.er- prices are very stable and easy to forecast into ence in in.aton between materials is signi.­ the future. cant enough that it should be accounted for in a comprehensive LCCA.

Table 2-2. Summary of Concrete Products PPI, AsphaltThe variability (or volality) of these indicesis as Paving Mixtures and Blocks PPI, and CPI Trends fromimportant as

the overall historic increase. Figure 2-5 1958 to 2011shows the annual (e.g., year-over-year) in.aton rate Index Average Yearly Standard Deviaon Index Increase (1958 to 2011) Compound Annual Growth Rate (CAGR) Concrete Products PPI 2.9 560% 3.6% Asphalt Paving Mixtures PPI 20.9 1,640% 5.5% CPI 4.2 674% 3.9%

for the concrete products PPI, the asphalt paving mixtures and blocks PPI, and the CPI. The annual in­.aton rate of the concrete products PPI follows very closely

that of the CPI; the asphalt paving mixtures and blocks PPI, however, is much more volatle, in­creasing by over 20% year-over-year 7 di.erent tmes (13% of the 54

years) and increasing by over 100% once (see Appendix 2 for comments on why the as­phalt paving mixtures and blocks PPI is so volatle). Variability such as this can be

accounted for in an LCCA through the use of a probabilistc analysis (see Step 7).


As noted, the CPI’s CAGR from 1986 to 2010 was 2.90%. The higher CPI CAGR of 3.9% from 1958 to 2011 is more in line with the commonly quoted 4% general long-term

in.aton in the U.S. This empha­sizes the importance of tmeframe in LCCA. The need to discern between materials with signi.­cantly di.erent in.aon ratesis becoming more im­portant as state agencies apply LCCAs to more and more paving

projects and technologies advance to ease such calculatons. One method of doing this, as noted previously, is to utlize di.erent real discount rates for materials

whose in.aton rates di.er signi.­cantly from the general in.aton rate used in the LCCA. For example, if a 4% general in.aton rate is used, based on the CPI of the

last 50+ years, the con­crete in.aton rate might be assumed to be the same (though it is slightly lower over the same tmeframe) and an asphalt in.aton rate of 5.5%

might be used. Another means of accountng for the di.erence is by applying an escalatng factor to future costs before discountng all costs for all alternates at the

general discount rate (MIT 2011a and Mack 2011); this method, which can also capture the impact of volatl­ity in pricing, ofen is preferred by economists and is

discussed more in Step 7. Calculatng the Real Discount Rate As discussed, more than one real discount rate may be necessary if di.erent elements of the LCCA have signi.cantly di.erent in.aton rates and future costs are not

escalated, when necessary, to account for the di.erent in.aton rates. Consider .rst the calcu­laton of a general or standard real discount rate. As an example of the calculaton of a general real dis­count rate, consider Figure 2-6, where historical val­ues for the 30-year Treasury bond yield are used as the

interest rate, year-over-year change in the CPI is used as the in.aton rate, and the real discount rate is calculated using Equaton 1. While the interest and in.aton

indices used for calculaton of the real dis­count rate can and should vary, the average real dis­count rate obtained from the use of the 30-year Treasury bond as the

interest rate and BLS’s CPI as the in.aton rate averaged 2.1% over the last 5 years of data shown in Figure 2-6. Chapter 2 – Basic Steps in a Life-Cycle Cost Analysis (LCCA) for a Single Project This average rate agrees fairly well with the real dis­count rates used by various state highway agencies across the U.S. (Table 2-3), recent OMB real discount rates,

and the 2% to 4% range that FHWA recom­mends (FHWA 2008). Table 2-3. Summary of the Real Discount Rates Used by U.S. State Highway Agencies in Their LCCAs (aer Mack2011; MDOT 2009 and Rangaraju, et al. 2008) Real Discount Rate (%) Percent of Responding Agencies State Agency < 3 18% MI*, MN*, MO*, NV*, OH*, SC*, WV* 3 15% GA, IA, IL, KS, MD, MT 3 to 4 10% AR, CO*, FL, NE 4 49% AK, AL, CA, CT, DE, ID, IN, LA, MS, NC, NJ, NM, NY, PA, TN, UT, VA, WA, WY 4 to 5 3% SD 5 5% KY, WI

  • Denotes a state whose real discount rate is based either on the OMB or a moving average of the OMB.

There have been tmes in the history of the U.S. that, even when both the in.aton and interest rates were positve, the real discount rate was negatve because the rate

of in.aton was higher than interest rates (see Figure 2-6). Thus, a negave real discount ratemay exist even when both the in.aon and interestrates are posive. To avoid all of the complexiesin calculatng a real discount rate for general use in LCCAs, many state agencies elect to use real discount rates published annually by

the United State’s O.ce of Management and Budget (OMB). Current OMB real discount rates are available online (OMB 2011). 15%

10%

Annual Yield or Rate

5%

0%

-5%

Figure 2-6. 30-year Treasury bond yield, year-over-year change in consumer price index (CPI) and real dis­count rate calculated from the two (BLS 2011; Federal

Reserve 2010). If local interest and in.aton rates are not readily available to develop a local real discount rate, ACPA supports the use of the OMB real discount rate.If there is

concern with the variability in OMB real dis­count rates, a moving average of the value can be considered. Figure 2-7 shows OMB real discount rate and a real discount

rate calculated from the average annual CPI and 30-year Treasury rates from 1979 (the .rst year OMB data was available) to 2011. As shown, these values track relatvely

well in recent tmes. As mentoned previously, uncertainty in material prices translates into increased risk for a roadway agency. This presents a challenge not only to devel­oping accurate

LCCAs, but also in accurately predict­ing future material costs and budgetng for roadway improvement projects. Coupled with a degradaton of purchasing power, the

impact can st.e needed maintenance and capacity improvements unless ac­counted for properly during pavement LCCAs. The best way of preventng such problems is by

account­ing for di.erences in material price in.aton in cur­rent LCCAs.


If material-speci.c real discount rates are calcu­lated, the interest rate should be that which is used in the calculaton of the general real discount rate. The

in.aton rates, however, are those for each ma­terial whose price trends di.er greatly from that of general in.aton. For example, if the interest rate is 7% and the

concrete and asphalt material in.aton rates are 3.6% and 5.5%, respectvely, as they were (on average) from 1958 to 2011 (see Table 2-2), the concrete and asphalt real

discount rates would be 3.3% and 1.4%, respectvely. Note that the asphalt PPI is for asphalt paving mixtures, so this rate would only apply to asphalt-based items in

the bids (e.g., paving mixtures, sealers, etc.) and the general real discount rate would be used on other items (e.g., subbase/base, pipe culverts, striping, etc.). If it is determined that the use of di.erent discountrates for di.erent materials is too cumbersome, other methods exist to account for signi.cant di.er­ences in material in.aton by escalatng future mate­rial prices before discountng all future costs using a single

real discount rate (see Step 7). The Total Cost of Ownership State agencies typically have a set amount ofmoneythat can be allocated towards new construc­ton and preservaton/restoraton of pavements each year. Because of the

magnitude of lane-miles of pavements already in existence in the U.S., the alter­nave to not construcng or rehabilitang a newsecon of highway is not to invest the

money in aninterest-bearing account or the stock market; the al­ ternatve is to allocate the money towards the con­structon, reconstructon, or preservaton/ rehabilita­ton of another secton. Thus, excess money is not invested and the

case can be made that, to consider the true total cost of ownership of pavement alter­natves to the owner/agency and ultmately to tax­payers, an interest rate of 0%

should be used. Thetotal cost of ownership is, essenally, the in.atedcosts that the agency will spend over the life of thepavement.Thus, an alternate means of

calculatng the total cost of ownership is to directly in.ate all fu­ture costs by the appropriate in.aton rate and sum­ming the values for each alternate. If the interest rate (iint) is 0%, an in.aton rate (iinf) of 4% would yield a real discount rate of: 1 + 0.00 idisc = – 1 = –3.85% 1 + 0.04 While it may seem erroneous to apply a negavediscount rateto LCCAs of pavements, it is mathemat­ically the same as in.atng all future costs, the other means by which

the true cost of alternate pavement designs can be calculated. The total cost of ownership calculaton is not pre­sented here as an alternate method of calculatng the LCCA of pavement alternatves. Rather, it is pre­sented as

another method of analyzing the future .­nancial impact of the alternatves. Viewing the data is this manner can help provide perspectve on fu­ture outlays and present

the data in a format that might help with minimizing future budget de.cit contributons.

References

  1. Thuesen, G. J. and Fabrycky, W. J. 1984, Engineering Economy, sixth edition, Prentice-Hall, Inc.