Lectures in Engineering Economy Prof. Corrado lo Storto DIEG, Dept. of Economics and Engineering Management School of Engineering, University of Naples Federico II phone:

Major issues Engineering Economy/inflation/ 2005 /prof. corrado lo storto What is inflation? How do we measure inflation? How we can deal with inflation in engineering economic studies, i.e. how do we incorporate the effect of inflation in equivalence calculation?

Inflation and price change Technically, inflation is the phenomenon of (continuously) rising prices bringing about as a result a decline over time of the purchasing power of a given unit of money. Inflation is worrisome for economy, but tend to be inevitable. It is a fact of life and can significantly affect the economic comparison of alternatives. Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Purchasing Power: inflation 1990 $ $100 You could buy 50 Big Macs in year You can only buy 40 Big Macs in year $2.00 / unit $2.50 / unit 25% Price change due to inflation The $100 in year 2003 has only $80 worth purchasing power of 1990 Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Purchasing Power: deflation $ $100 You could purchase gallons of unleaded gas a year ago. You can now purchase 80 gallons of unleaded gas. $1.57 / gallon$1.25 / gallon Price change due to deflation 20.38% Engineering Economy/inflation/ 2005 /prof. corrado lo storto

All-Time Top 10 Movies Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Practice Problem - How to Compare the Winning Prizes in Two Different Points in Time Dollars Jack Nicklaus won his first Master Tournament in The prize was $20,000. Phil Mickelson won his first Master Tournament in The prize amount was $1.17M Engineering Economy/inflation/ 2005 /prof. corrado lo storto

What is the worth of $1.17M in terms of purchasing power in 1963? The average inflation rate between 1963 and 2004 is about 4.53% per year. $1.17M in 2004 would have a purchasing power of $190,616 in 1963 Engineering Economy/inflation/ 2005 /prof. corrado lo storto

What is the worth of $1.17M in terms of purchasing power in 1963? If Jack invested his prize money in 1963 at 5.65% (inflation-free interest rate), the prize money would grow to match Phil’s 2004 prize $20,000 $190, Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Inflation measurement A price index is usually calculated to measure historical price level changes for a particular good or the general cost of living. A price index is the ratio of the historical price of some commodity or service at some point in time to the price at some earlier point. The earlier point in time is usually selected as a base year. The price index in question and other indexes are therefore related to the same base. Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Measuring Inflation Consumer Price Index (CPI): the CPI compares the cost of a sample “market basket” of goods and services in a specific period relative to the cost of the same “market basket” in an earlier reference period. This reference period is designated as the base period. Market basket Base Period ( ) 2002 $100$179.9 CPI for 2002 = Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Inflation measurement: an example base year: 1967  price index 1967 =100 commodity price 1967 = $1.46/lb commodity price 2001 = $6.37/lb then Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Computing the inflation rate f The historical annual rate of price increase can be computed from any of the several available indexes. Using the CPI values, the annual inflation rate can be calculated as where CPI t is the index of consumer prices Most economic studies require the use of estimates that depend on expectations of future inflation rates. The determination of these rates should be based on trends of historical rates, predicted economic conditions, judgment, etc. The accurate prediction of future inflation rates is a difficult endeavour. Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Estimating rate f from CPI Data Example 1: Average inflation rate for 1990 Example 2: Average inflation rate using CPI data for 1987 to 1990: YearCPI Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Inflation rate Annual rates of inflation vary widely for different types of goods and services and over different periods of time. Rates of inflation also vary for different countries in the same period of time. Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Factors affecting inflation rate Several factors in the economy push prices for goods and services upward or downward: - government policies (i.e., price supports, deficit financing, etc.) tend to reduce prices -an increase in productivity of production processes -an increase in the availability of goods The combined cumulative effect of all these factors determine the amount of price change. tend to increase prices Engineering Economy/inflation/ 2005 /prof. corrado lo storto

CPI measurement: an example year CPI Rate % year CPI Rate % year CPI Rate % ,5 1,7% ,5 6,5% ,3 4,8% ,2 2,9% ,4 7,7% ,4 5,4% ,0 2,9% ,4 11,3% ,0 4,2% ,2 4,2% ,8 13,5% ,3 3,0% ,8 5,4% ,4 10,4% ,7 3,0% ,3 5,9% ,1 6,1% ,0 2,6% ,3 4,3% ,4 3,2% ,5 2,8% ,3 3,3% ,1 4,3% ,9 2,9% ,1 6,2% ,2 3,6% ,8 2,3% ,7 11,0% ,4 1,9% ,3 1,6% ,2 9,1% ,4 3,7% ,6 1,9% ,5 5,8% ,3 4,1% ,0 2,3% Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Consumer Price Index Average inflation rate = 4.525% Engineering Economy/inflation/ 2005 /prof. corrado lo storto

CPI trend in USA from 1965 to 2000 Engineering Economy/inflation/ 2005 /prof. corrado lo storto

The CPI, the PPI, and the IPI indexes It is possible to prepare price indexes not only for the individual goods/commodities or classes of products, but also composite indexes. These composite indexes include the Consumer Price Index (CPI), the Producer Price Index (PPI), and the Implicit Price Index for the Gross National Product (IPI-GNP). Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Selected Price Indexes Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Inflation rate in USA from 1965 to 2000 Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Actual money versus real money According to definition, inflation describes the situation in which prices of fixed amounts of goods and services are increasing. And as prices rise, the value of money – its purchasing power – decreases correspondingly. Two kinds of money units can be defined:  actual money units  real or constant money units Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Actual and real money units  actual money units (i.e., actual Euros, Dollars): the actual number of money units as of the point in time they occur and the usual kind of money units in which people use to think. They are also called the current money units (or, the inflated money units). It can be denoted as “A€” if we adopt, for instance, Euros as money units;  real money units (i.e., real Euros, Dollars): money units of purchasing power as of some base point in time, regardless of the point in time the actual money units occur. They are also called constant money units, or constant worth money units, or even uninflated money units. It can be denoted as “R€” if for instance Euros are adopted as money units. If the base point in time, k, needs to be specified – that is the time of the study or the initial investment – it can be shown with a superscript, i.e. R€ (k) Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Actual and real money units At any time n actual money units can be converted into real money units at time n of purchasing power as of any base time k: where f is the average inflation rate per period over the n-k periods Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Conversion from Constant to Actual Dollars $1,000 ( ) = $1,260 3 Constant Dollars $1,000 3 Actual Dollars $1,260 3 Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Example: conversion from Constant to Actual Dollars Period Net Cash Flow in Constant $ Conversion Factor Cash Flow in Actual $ 0-$250,000(1+0.05) 0 -$250, ,000(1+0.05) 1 105, ,000(1+0.05) 2 121, ,000(1+0.05) 3 138, ,000(1+0.05) 4 158, ,000(1+0.05) 5 153,154 Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Example: conversion from Constant to Actual Dollars $250,000 $105,000 $121,275 $138,915 $158,016 $153,154 Years (b) Actual dollars $250,000 $100,000 $110,000 $120,000 $130,000 $120,000 Years (a) Constant dollars $250,000(1+0.05) 0 $100,000(1+0.05) $110,000(1+0.05) 2 $120,000(1+0.05) 3 $130,000(1+0.05) 4 $120,000(1+0.05) 5 Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Conversion from Actual to Constant Dollars Constant Dollars $1,260 ( ) = $1, $1,000 3 Actual Dollars $1,260 3 Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Example: conversion from Actual to Constant Dollars End of period Cash Flow in Actual $ Conversion at f = 5% Cash Flow in Constant $ Loss in Purchasing Power 0-$20,000(1+0.05) 0 -$20,0000% 120,000(1+0.05) , ,000(1+0.05) , ,000(1+0.05) , ,000(1+0.05) , Engineering Economy/inflation/ 2005 /prof. corrado lo storto

The average annual inflation rate Many studies use an average annual inflation rate when the projected life of the investment is long. This approach requires the estimate of a single average rate that represents a composite of the individual yearly rates. Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Average Inflation Rate (f) Fact: Base Price = $100 (year 0) Inflation rate (year 1) = 4% Inflation rate (year 2) = 8% Average inflation rate over 2 years? Step 1: Find the actual inflated price at the end of year 2. $100 ( ) ( ) = $ Step 2: Find the average inflation rate by solving the following equivalence equation. $100 ( 1+ f) = $ f = 5.98% $100 $ Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Example: The average annual inflation rate and inflation effects The average inflation rate in USA, f, from the end of 1966 to the end of 1980 (14 years) can be calculated as f=6.9% per year From the end of 1989 through 1998 (9 years) the average inflation rate was f=3.1% per year As a general expression, The concept of the average annual inflation rate facilitates inflation calculations. In most instances, the estimation of individual yearly inflation rates is time consuming and using these rates usually is no more accurate than using a single composite rate. Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Example: Average Inflation Rate Item2003 Price2000 Price Average Inflation Rate (%) Consumer price index (CPI)$184.20$ Postage Homeowners Insurance Private college tuition and fees18,27315, Gasoline Haircut Car (Toyota Camry)22,00021, Natural gas (MBTU) Baseball tickets Cable TV Engineering Economy/inflation/ 2005 /prof. corrado lo storto

General Inflation Rate (f) Average inflation rate based on the CPI Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Example: Yearly and Average Inflation Rates YearCost 0$504, , , ,500 What are the annual inflation rates and the average inflation rate over 3 years? Solution Inflation rate during year 1 (f 1 ): ($538,400 - $504,000) / $504,000 = 6.83%. Inflation rate during year 2 (f 2 ): ($577,000 - $538,400) / $538,400 = 7.17 %. Inflation rate during year 3 (f 3 ): ($629,500 - $577,000) / $577,000 = 9.10%. The average inflation rate over 3 years is Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Exercise 1: The average annual inflation rate Suppose Mr Smith can invest $ 100 at the present time with the expectations to earn 15% annually for the next 5 years. At the present Mr Smith can purchase one automobile tire for $ 100, but suppose that these tires are increasing in price at an annual rate of 10%. What Mr Smith will decide? Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Solution to exercise 1 At the end of 5 years the accumulated amount will be At the end of 5 years the same tire will cost Under these conditions, Mr Smith would be misled if he ignored the change in prices. He would then have the erroneous impression that if he invested now, the money to purchase two tires would be available at the end of five years. Actually, the money he would receive from the investment would purchase only 1.25 tires. Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Inflation and engineering economic studies  If all cash flows in an economic comparison of alternatives are inflating at the same rate, inflation can be disregarded in before-tax studies.  Vice versa, when all incomes and all expenses are not inflating at the same rate, inflation gives rise to differences in economic attractiveness among alternatives. In this case it should be taken into account.  Not including the effects of inflation in an engineering economy study, leads to an erroneous choice among competing alternatives. Henceforth, by assuming that inflation affects all investment opportunities to the same extent may lead to reversal in preference, and compromise the objective to maximize shareholders’wealth. Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Real interest rate, combined interest rate, and inflation rate We define several types of rates:  Real interest rate: it is the increase in real purchasing power expressed as a percent per period, or the interest rate at which RMU outflow is equivalent to RMU inflow. It is also called real monetary rate or uninflated rate and is denoted as i r  Combined interest rate: it is the increase in dollar amount necessary to cover real interest and inflation expressed as a percent per period. It is the interest rate at which AMU outflow is equivalent to AMU inflow. It is also called as actual rate or inflated rate and is denoted as i c  Inflation rate: it is defined the increase in price of given goods or services as a percent per time period. It is denoted as f. The overall rate for an individual or organizations is sometimes called the general inflation rate. Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Inflation-Free Interest Rate i  Represents only earning power of capital  Ideal market rates when there is no inflation  All rates you have used till now are inflation-free  Also called real-, or constant-money interest rate Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Market Interest Rate i c  Includes combined effects of: earning power of capital expected inflation  Examples: rates stated by financial institutions (loans, bank accounts, bond and stock returns) MARR set by firms  Also called composite, or inflation-adjusted Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Real interest rate, combined interest rate, and inflation rate The real interest rate and the inflation rate have a multiplicative or compounding effect. Also, In the case f is not large relative to the desired accuracy, then and Engineering Economy/inflation/ 2005 /prof. corrado lo storto

What interest rate to use in engineering economy studies? The interest rate which is appropriate for time-value calculation in engineering economy studies depends on the type of cash flow estimates: method If cash flows are estimated in terms of Then the interest rate to use is AActual MU, AMU Combined interest rate, i c B Real MU, RMU Real interest rate, i r The above is made intuitively consistent if one thinks in terms of method A as working with inflated (actual) monetary units (i.e., Euros) and interest. Method A is the most natural to use because we usually think in terms of AMU. Since interest paid or earned is based on AMU, it is a combined interest rate i c. However, method B is sometimes easier to use. Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Examples: Market vs. Inflation-Free Interest Rates f: average inflation rate i: inflation-free rate i c : market interest rate Example: inflation rate 6%, interest rate 12% Example: inflation rate 6%, interest rate 12% compounded monthly Formula holds for effective interest rates Nominal rates must first be converted to effective Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Consistency in Economic Evaluations  Consistent use of cash flows and interest rates  Cash flows in actual dollars must be discounted at market interest rates (inflation-adjusted)  Cash flows in constant dollars must be discounted at inflation-free interest rates Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Consistency in Economic Evaluations Example: Project P has initial cost of $2000 and produces net benefit of $850/yr in real dollars for 3 yrs. MARR=15%, which incorporates estimated inflation rate of 5%. Should the project be accepted?  Wrong Solution: Use constant $ with inflation- adjusted MARR Reject the project Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Consistency in Economic Evaluations  Correct Solution 1: Use actual $ with inflation- adjusted MARR Accept the project  Correct Solution 2: Use constant $ with inflation-free MARR Accept the project Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Inflation in Economic Analysis 1.Uniform inflation: All cash flows inflate at the same rate 2.Differential inflation: Different rates apply to different cash flows  Tax considerations in economic study leads to differential inflation Depreciation charges are not responsive to inflation Interest on debt is fixed, based on estimates of future inflation rates; is not adjusted to actual inflation in subsequent years Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Inflation and Cash Flow Analysis  Constant Dollar analysis Estimate all future cash flows in constant dollars. Use i’ as an interest rate to find equivalent worth.  Actual Dollar Analysis Estimate all future cash flows in actual dollars. Use i as an interest rate to find equivalent worth. Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Analysis under Uniform Inflation  Uniform-inflation analysis: All cash flows inflate at a uniform rate Before-tax analysis  Two methods when inflation is uniform: Constant cash flows discounted at inflation-free interest rates Actual cash flows discounted at market interest rates  Both methods give the same results  Constant-dollar analysis is more intuitive – familiarity with today’s values  Textbook refers to this case as before-tax analysis Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Analysis under Uniform Inflation Same PW with both methods: 1.Constant dollars discounted at inflation-free rate 2.Actual dollars discounted at inflation-adjusted rate Proof: C t : CF for year t in constant $ A t =C t (1+f) t : CF for year t in actual $ (adjusted for inflation) i: inflation-free discount rate i f =(1+i)(1+f)-1: inflation- adjusted discount rate 1.PW(at i): 2.PW(at i f ): For interest rates: Thus: PW 1 =PW 2 Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Analysis under Uniform Inflation Exercise: Asset price $100, yr life with no salvage value. Net annual benefit $28,000 without considering inflation. MARR=15% w/o inflation. Inflation rate 8%. Evaluate using both the constant- and the actual-dollar method. No tax considerations. 1. Constant $: i=15% 2. Actual $: i f =(1.15)(1.08)-1=24.2% Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Differential Inflation 1.Prices of different classes of goods and services inflate at different rates –Effects of inflation might result in selecting a different alternative than the one favored in the absence of inflation –Analysis: actual dollar CF and market interest rates –Example: two proposals have the same initial cost and annual net benefits (in constant $). Proposal A generates energy savings, while proposal B savings in labor. Energy prices escalate at 20% annually, while the cost of labor at 10% annually.  Proposal A should be selected Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Differential Inflation 2.Interest on debt is not responsive to inflation Interest rate on a loan: –Determined at the time of the agreement –Specifies future payments in actual dollars –Incorporates estimates of future inflation –Is not adjusted when actual inflation is different than the estimated ones When inflation rises faster than it was anticipated at the time of the agreement: –borrower’s benefit –a project funded mainly through borrowed capital might be preferable to one funded by equity capital Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Differential Inflation 3.After-tax analysis involves cash flows non-responsive to inflation Depreciation charges: based only on the initial expenditure and do not escalate with inflation Interest on borrowed capital is predetermined and is not adjusted for inflation  Textbook refers to differential-inflation analysis as after-tax actual cash flow analysis Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Summary of main concepts

What is Inflation?  Value of Money  Earning Power  Purchasing Power Earning Power Purchasing power Investment Opportunity Decrease in purchasing power (inflation) Increase in Purchasing Power (deflation) Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Inflation Terminology Producer Price Index: a statistical measure of industrial price change, compiled monthly by the BLS, U.S. Department of Labor Consumer Price Index: a statistical measure of change, over time, of the prices of goods and services in major expenditure groups—such as food, housing, apparel, transportation, and medical care— typically purchased by urban consumers Average Inflation Rate (f): a single rate that accounts for the effect of varying yearly inflation rates over a period of several years. General Inflation Rate (f ): the average inflation rate calculated based on the CPI for all items in the market basket. Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Inflation Terminology Actual Money Units (i.e. Dollars) (A n ): Estimates of future cash flows for year n that take into account any anticipated changes in amount caused by inflationary or deflationary effects. Constant Money Units (i.e. Dollars) (A n ’ ): Estimates of future cash flows for year n in constant purchasing power, independent of the passage of time (or base period). Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Inflation Terminology Inflation-free Interest Rate (i’): an estimate of the true earning power of money when the inflation effects have been removed (also known as real interest rate). Market interest rate (i): interest rate which takes into account the combined effects of the earning value of capital and any anticipated changes in purchasing power (also known as inflation-adjusted interest rate). Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Constant vs. actual dollars Constant, or real dollars:  Money units with constant purchasing power  Approach suitable for before-tax analysis, when all cash flows inflate uniformly Actual, or future, or then-current dollars:  Estimate of the amount of money units exchanged at the time of the transaction  More intuitive and versatile approach Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Constant vs. actual dollars f: expected rate of inflation per year N: year at which the cash flow occurs Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Where Does f Come From?  Measuring Inflation: price indices compiled periodically measure changes in prices of goods and services Department of Commerce and Department of Labor  Consumer Price Index: most commonly used measure of inflation prices of: foods and beverages, housing, apparel and upkeep, transportation, medical care, entertainment, and other (education, personal care, etc.) Use past CPI data to estimate future average inflation rate Engineering Economy/inflation/ 2005 /prof. corrado lo storto

Equivalence Calculation Under Inflation 1. Types of Interest Rate 2. Types of Cash Flow 3. Types of Analysis Method Market Interest rate (i) Inflation-free interest rate (i’) In Constant Dollars In Actual Dollars Constant Dollar Analysis Actual Dollar Analysis Deflation Method Adjusted-discount method Engineering Economy/inflation/ 2005 /prof. corrado lo storto

XXXXXXX prossima lezione XXXXXX Copyright 2005 – prof. corrado lo storto