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