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Inflation and Discounting: Real Cost Increases, Differential
Inflation, and Discounting to
Present Value
November 6, 2007
Introduction
Life-Cycle ComparisonsInflationTime Value of Resources
Ideal basis for EA is the project’s whole life—its “life cycle”We prefer projects where the dollar value of life-cycle benefits most exceeds total costsProblem: We must adjust for the fact that the value of a dollar is not constant over time
Life-Cycle ComparisonsBasis for Economic Analysis (EA)
Life-Cycle ComparisonsTypical Life-Cycle Profile
16 17 18 19 20
Initial Capital
Cost
Year
Dollars
Benefits
Costs
1514131211109876543210
Life-Cycle ComparisonsDollar vs. Dollar
Two separate and distinct factors account for why the value of a dollar, as seen from the present, diminishes over time
InflationTime value of resources
Inflation is a general rise in prices due to more demand than supplyYear-to-year inflation is measured by various “price indices”Highway project budgets have experienced strong inflationary pressures since 2003 due to commodity prices
InflationWhat It Is
Indices for highway projects at www.fhwa.dot.gov/programadmin/contracts/price.cfm
FHWA Bid Price Index (BPI)States produce their own highway indicesProducer Price Index for Highway and Street Construction
General construction cost indices:ENR Construction IndexTurner Construction Co. Composite IndexRS Means Heavy Construction Cost Index
InflationHighway Construction Cost Indices
InflationSample of FHWA BPI
PortlandCement Bituminous Composite
Year Excavation Surfacing Surfacing Structures Index1997 117.6 161.2 119.2 132.7 130.61998 124.3 160.5 101.4 133.4 126.91999 120.9 159.5 130.9 138.3 136.52000 124.1 171.7 142.6 146.9 145.62001 125.9 191.5 141.7 138.8 144.82002 121.2 175.5 138.5 154.5 147.92003 142.3 162.6 132.0 159.5 149.82004 135.7 183.1 149.9 154.7 154.42005 164.6 226.8 184.9 176.0 183.62006 186.1 257.5 224.2 220.5 221.3
Until recently, the BPI behaved in a manner similar to broader measures of inflation, such as the Consumer Price Index for All Urban Consumers (CPI-U)This relationship has broken down since 2004, leading to a situation of differential inflation
InflationDifferential Inflation
Differential inflation is the difference in cost growth for a product or group of products compared to the general inflation rateIn the case of highway goods, the differential is due to the surge in oil prices and demand for building materials here and abroad
InflationCause of Differential Inflation
InflationEvidence of Recent Divergence for CPI
Comparison of BPI and CPI Since 1960
0
50
100
150
200
250
1960 1970 1980 1990 2000 2010
Year
Inde
x Va
lue
(198
7=10
0)
CPIBPI
In estimating costs, use the index that reflects actual price trends
Use construction indexes to adjust highway construction costsUse CPI to adjust the value of project benefits such as delay reductions
We will now see how to adjust for inflation in project construction costs
InflationTreatment of Differential Inflation
The purchasing power of dollars in different years can be standardized to that of the base year (year of analysis) by using price indices
Base year dollars, from which inflation has been removed, are also called “constant” or “real” dollarsDollars that include a component for inflation are known as “data year,”“nominal” dollars
InflationAdjusting for Inflation
To convert to base year dollars:
To convert to data year dollars:yeardata
yearbaseyeardatayearbase Index
IndexDollarsDollars
X =
yearbase
yeardatayearbaseyeardata Index
IndexDollarsDollars
x =
InflationFormulas for Adjusting
What if we want to update a 1999 asphaltic concrete resurfacing cost of $1 million to an equivalent cost in base year 2006 dollars?
First formula converts 1999 nominal dollars to 2006 base year dollarsNeed to select bituminous concrete index values from 1999 and 2006
InflationExample of Inflation Adjustment
Plug values into inflation formula:
Bituminous 1999
Bituminous 2006 X 1999 2006 9.130
2.224000,000,1$ =Dollars
$1,713,000 1.713x 000,000,1$ 2006 ==Dollars
Do calculations:
InflationExample (continued)
Economic analysis should be done in “real” dollars of the base year
Inflation is very difficult to forecastDifferential inflation trends are unlikely to continue over long term
Limit inflation adjustments to:Adjusting historical costs to presentProject budget submissions
InflationGuidance on Inflation
In some cases, the analyst may expect that a resource’s real cost will change over time due to scarcity or technology
That is, its cost in base year dollars will be higher (or lower) in the futureIf so, analyst would use a higher (or lower) real cost (i.e., base year dollar cost) for that resource in the futureWork with experts to adjust cost
InflationGuidance on Inflation
“Time value of resources” is the economic return that could be earned on invested resources in their next best alternative useDistinct concept from inflationAlways present, even without inflation
Time Value of ResourcesWhat It Is
Assume there will be no inflation for 10 yearsWould you then lend $1,000 to someone for 10 years without charging them interest?Answer: Probably not, because you could do something useful with that money during that time
Time Value of ResourcesIntuitive Explanation
The time value of resources is measured by an annual percentage return known as the “discount rate”Used to calculate the “present value”of a future sum of resources
What the future sum is worth to us now
Benefits and costs can be easily compared in present value dollars
Time Value of ResourcesRole of the Discount Rate
Time Value of ResourcesFormula for Discounting
tt Ar
PV ⎟⎟⎠
⎞⎜⎜⎝
⎛+
=)1(
1
where
PV = present value at time zero (base year)
r = discount rate
t = time (year number, as in 1, 2, 3 …)
A = amount of benefit or cost in year t
What if we want to determine how much a $1,000 benefit to be received in 30 years is worth to us today?
$1000 is in “real” dollars (i.e., in dollars with today’s purchasing power)Discount rate is 3%
Time Value of ResourcesExample of Discounting
Plug values into discounting formula:
$412 0.41199x 000,1$ ==PV
Time Value of ResourcesExample (continued)
30 30 000,1$)03.1(
1yearPV ⎟⎟
⎠
⎞⎜⎜⎝
⎛+
=
Do calculations:
Time Value of ResourcesDiscounting Over Life CycleFor multi-year project life cycles, discounting is applied to each year using the following summation formula:
Life-Cycle PV is often referred to as Net Present Value (NPV)
t
N
tt A
rPV ∑
=⎟⎟⎠
⎞⎜⎜⎝
⎛+
=0 )1(
1
Use “real” discount ratesTake government interest rate and remove inflation componentReal discount rates of 3 to 5 percent are typical
States may select higher or lower rates, but rate should be justifiedDo not adjust discount rate for risk
Time Value of ResourcesGuidance on Discount Rates
FHWA recommends discounting using a real discount rate on real dollars, but State may opt to use nominal discount rate (i.e., interest rate) on nominal dollars (dollars with inflation)Results should be the same as with real rate, but with more work
Time Value of ResourcesNominal Rates (With Inflation)
Time Value of ResourcesExample of Nominal Discounting
Nominal Discount Rate (NDR) = 7.12%Inflation Rate (IR) = 3%Real Disc. Rate = ((1+NDR)/(1+IR)) - 1 = 4%
Real Inflation NominalYear Cost Factor Cost
1 $100,000 1.030 $103,0002 $10,000 1.061 $10,6093 $10,000 1.093 $10,9274 $10,000 1.126 $11,2555 $50,000 1.159 $57,964
Real Cost Series Discounted at 4% = $163,934Nominal Cost Series Disc. at 7.12% = $163,934
Time Value of ResourcesDiscount Rate Matters
Higher the discount rate, the lower the present value of a future dollar
At 3%, $1,000 30 years from now is worth only $412 today (as in example)At 5%, is worth $231At 10%, is worth only $57
Discount rate can influence project selection or design
For Further InformationEconomic Analysis PrimerFHWA IF-03-032, August 2003
Contents:
• Economic Fundamentals
• Life-Cycle Cost Analysis
• Benefit-Cost Analysis
• Forecasting Traffic
• Risk Analysis
• Economic Impact Analysis
For Further InformationOther Economic Materials
FHWA’s Office of Asset Management, Evaluation and Economic Investment Team:www.fhwa.dot.gov/infrastructure/asstmgmt/invest.htm
Eric Gabler:(202) 366-4036eric.gabler@dot.gov
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