Price Changes and Exchange Rates 11/25/2018 12:01 AM CHAPTER 8 Price Changes and Exchange Rates Dr. Mohammad Abuhaiba, PE

8.1 Introduction General Price Inflation 11/25/2018 12:01 AM 8.1 Introduction General Price Inflation An increase in the average price paid for goods and services bringing about a reduction in the purchasing power of money. General Price Deflation A decrease in the average price paid for goods in services, resulting in an increase in the purchasing power of money. Dr. Mohammad Abuhaiba, PE

8.1 Introduction Consumer Price Index (CPI) 11/25/2018 12:01 AM 8.1 Introduction Consumer Price Index (CPI) One measure of price changes in our economy An estimate of general price inflation A composite price index that measures price changes in food, shelter, medical care, transportation, apparel, and other selected goods and services used by average individuals and families Dr. Mohammad Abuhaiba, PE

11/25/2018 12:01 AM 8.1 Introduction Dr. Mohammad Abuhaiba, PE

11/25/2018 12:01 AM 8.1 Introduction CPI shows how the prices that consumers pay change from year to year or month to month The Producer Price Index (PPI) shows how the prices paid to producers change from year to year or month to month The Implicit Price Deflator or GDP deflator shows how all prices in the economy change from one time period to another time period Dr. Mohammad Abuhaiba, PE

8.2 Terminology and Basic Concepts 11/25/2018 12:01 AM 8.2 Terminology and Basic Concepts Actual dollars (A$): (Current time frame) cash-flow dollars : also current dollars, then-current dollars, or inflated dollars Real dollars (R$): Dollars in terms of purchasing power at some stated time period (i.e., base year): also constant dollars General price inflation (f): Measure of change in purchasing power from one time to another Combined (nominal) interest rate (ic): Market interest rate: actual dollars paid for use of capital Real interest rate - (ir): Inflation-free interest rate: real dollars paid for use of capital Base period (b): Purchasing-power time reference Dr. Mohammad Abuhaiba, PE

11/25/2018 12:01 AM 8.2 Terminology and Basic Concepts Relationship between Actual Dollars to Real Dollars Use the following to convert actual dollars, as of time k, to real dollars of constant purchasing power (𝑅$) 𝑘 = (𝐴$) 𝑘 1 1+𝑓 𝑘−𝑏 = (𝐴$) 𝑘 𝑃 𝐹 ,𝑓%,𝑘−𝑏 The equation changes as follows for a specific type cash flow (i.e. specific good or service “j” ) In the base period, purchasing power of actual dollar and real dollar are the same Dr. Mohammad Abuhaiba, PE

Example 8.1 Real dollar purchasing power of your salary Suppose that your salary is $45,000 in year one, will increase at 4% per year through year four, and is expressed in actual dollars as shown in the table. If the general price inflation rate (f) is expected to average 6% per year, what is the real dollar equivalent of these actual dollar salary amounts? Assume that the base time period is one (b=1). End of year k Salary (A$) 1 45,000 2 46,800 3 48,672 4 50,619 Dr. Mohammad Abuhaiba, PE

Example 8.2 Real dollar equivalent of actual after tax cash flow An engineering project team is analyzing the potential expansion of an existing production facility. Different design alternatives are being considered. The estimated after tax cash flow (ATCF) in actual dollars for one alternative is shown in column 2 of Table 8.1. If the general price inflation rate (f) is estimated to be 5.2% per year during the eight year analysis period, what is the real dollar ATCF that is equivalent to the actual dollar ATCF? The base time period is year zero (b=0). Dr. Mohammad Abuhaiba, PE

Example 8.3 Inflation and household income According to government statistics, the median household income in the United State in 1953 was $3,700 per year. Based on the CPI, this is equivalent to $30,000 in 2008 dollars. What was the annual compound rate of growth in median household income from 1953 to 2008? By 1978, median household income was actually $15,000. Based on your answer in Part(a), what is the equivalent household income in 2008? Was the actual median household income in 1978 higher than what you would have predicted in Part (a)? if so, give some reasons for this phenomenon. Dr. Mohammad Abuhaiba, PE

If cash flows are in terms of A$, use market interest rate, im 11/25/2018 12:01 AM 8.2 Terminology and Basic Concepts The correct interest rate to use in engineering economy studies If cash flows are in terms of A$, use market interest rate, im If cash flows are in terms of R$, use real interest rate, ir Dr. Mohammad Abuhaiba, PE

8.2 Terminology and Basic Concepts Relationship among im, ir, and f 𝒊 𝒓 = 𝒊 𝒎 −𝒇 𝟏+𝒇 Dr. Mohammad Abuhaiba, PE

Example 8.4 Real dollar equivalent of an investment Suppose that $1,000 is deposited each year for five years into an equity (common stock) account earning 8% per year. During this period, general inflation is expected to remain at 3% per year. At the end of five years, what is the dollar value if the account in terms of today’s purchasing power (i.e., real dollars)? Dr. Mohammad Abuhaiba, PE

Example 8.5 Equivalent of real dollar and actual dollar cash flows In example 8.1, your salary was projected to increase at the rate if 4% per year, and the general price inflation rate was expected to be 6% per year. Your resulting estimated salary for the four years in actual and real dollars was as follows: What is the present worth of the four year actual and real dollar salary cash flows at the end of year one (base year) if your personal MARRm is 10% per year (im)? End of year k Salary (A$) Salary (R$), b=1 1 45,000 2 46,800 44,151 3 48,672 43,318 44 50,619 42,500 Dr. Mohammad Abuhaiba, PE

8.3 Fixed and Responsive Annuities 11/25/2018 12:01 AM 8.3 Fixed and Responsive Annuities Cash flows predetermined by contract - bonds or fixed annuities do not respond to general price inflation Future amounts that are not predetermined may, by varying degrees, respond to general price inflation Dr. Mohammad Abuhaiba, PE

Example 8.6 Impact of deflation on the current piece of bond Suppose the deflation occurs in the U.S. economy and that the CPI (as measure of f) is expected to decrease an average of 2% per year for the next five years. A bond with a face (par) value of $10,000 and a life of five years (i.e., it will be redeemed in five years) pays an interest (bond) rate of 5% per year. The interest is paid to the owner of the bond once each year. If an investor expects a real rate of return of 4% per year, what is the maximum amount that should be paid now for this bond? Dr. Mohammad Abuhaiba, PE

11/25/2018 12:01 AM Example 8.7 After tax analysis: A mixture of fixed and responsive cash flows The cost of a new and more efficient electrical circuit switching equipment is $18,000. It is estimated (in base year dollars, b[0) that the equipment will reduce current net operating expenses by $36,000 per year (for 10 years) and will have a $30,000 market value at the end of the 10th year. For simplicity these cash flow are estimated to increase at a general price inflation rate (f= 8% per year). Due to new computer control features on the equipment, it will be necessary to contract for some maintenance support during the first three years. The maintenance contract will cost $2,800 per year. This equipment will be depreciated under the MACRS (GDS) method, and it is in the five year property class. The effective income tax rat (t) is 38%; selected analysis period is 10 years; and the MARRm (after taxes) is im = 15% per year: Based on actual dollar after tax analysis, is this capital investment justified? Develop the AFCF in real dollars. Dr. Mohammad Abuhaiba, PE

Example 8.8 Saving to meet a retirement goal Sarah B. Goode wishes to retire in the year 2022 with personal saving of $500,000 (1997 spending power). Assume that the expected inflation rate in the economy will average 3.75% per year during this period. Sara plans to invest in a 7.5% per year savings account, and her salary is expected to increase by 8% per year between 1997 and 2022. Assume that Sara’s 1997 salary was $60,000 and that the first deposit took place at the end of 1997. What percent of her yearly salary must Sara put aside for retirement purposes to make her retirement plan a reality? Dr. Mohammad Abuhaiba, PE

CALCULATING AN EFFECTIVE GENERAL PRICE INFLATION RATE 11/25/2018 12:01 AM f = An (estimated) effective general price inflation rate for a period of N years f = PNk=1( 1 + f k ) 1 / N- 1 Dr. Mohammad Abuhaiba, PE

DIFFERENTIAL PRICE INFLATION 11/25/2018 12:01 AM DIFFERENTIAL PRICE INFLATION Variation between general price inflation rate and the best estimate of future price changes for specific goods and services e Ij -- The increment ( % ) of price change above or below the general price inflation rate for a given time period for good or service “ j “ Caused by: changes in supply, changes in demand, technological improvements, productivity changes, regulatory requirements Dr. Mohammad Abuhaiba, PE

TOTAL PRICE ESCALATION 11/25/2018 12:01 AM TOTAL PRICE ESCALATION Price changes caused by some combination of general price and differential price inflation e j -- The total rate (%) of price change during a time period for good or service “ j “ Includes the effects of both the general price inflation rate ( f ) and the differential price inflation rate (e Ij ) on price changes e Ij = ( e j - f ) / ( 1 + f ) (A$) k j = (A$) b j (F / P, e j %, k - b ) (A$) b j = (A$) b j (F / P, e Ij %, k - b ) Dr. Mohammad Abuhaiba, PE

DETERMINING A CONVENIENCE RATE FOR GEOMETRIC CASH FLOW SEQUENCES 11/25/2018 12:01 AM Actual dollar analysis ( A$ ) iCR = ( ic - e j ) / ( 1 + e j ) Real dollar analysis ( R$ ) iCR = ( ir - e Ij ) / ( 1 + e Ij ) Dr. Mohammad Abuhaiba, PE

8.5 Foreign Exchange Rates and Purchasing Power Concepts 11/25/2018 12:01 AM 8.5 Foreign Exchange Rates and Purchasing Power Concepts Changes in the exchange rate between two currencies over time are analogous to changes in the general inflation rate because the relative purchasing power between the two currencies is changing similar to the relative purchasing power between A$ and R$ amounts. Dr. Mohammad Abuhaiba, PE

11/25/2018 12:01 AM 8.5 Foreign Exchange Rates and Purchasing Power Concepts - market interest rate rate of return Exchange rate relative to u.s. dollars iUS = market (combined ) interest rate of return relative to USD ifc = market (combined ) interest rate of return relative to foreign country currency fe = Annual rate of change in exchange rate - annual devaluation rate between foreign country currency and USD fe+: foreign currency devalued relative to dollar fe-: dollar devalued relative to foreign currency 𝒊 𝑼𝑺 = 𝒊 𝒇𝒎 − 𝒇 𝒆 𝟏+ 𝒇 𝒆 Dr. Mohammad Abuhaiba, PE

Example 8.9 Investing in a foreign assembly plant The CMOS electronics company is considering a capital investment of 50,000,000 pesos in an assembly plant located in a foreign country. Currency is expressed in pesos, and the exchange rate is now 100 pesos per USD. The country has followed a policy of devaluing its currency against the dollar by 10% per year to build up its export business to the United States. This means that each year the number of pesos exchanged for a dollar increase by 10% (fe = 10%), so in two years (1.10)2 (100) = 121 pesos would be traded for one dollar. Labor is quite inexpensive in this country, so management of CMOS Electronics feels that the proposed plant will produce the following rather attractive ATCF, stated in pesos: Dr. Mohammad Abuhaiba, PE

Example 8.9 Investing in a foreign assembly plant EOY 1 2 3 4 5 ATCF (millions of pesos) -50 +20 +30 If CMOS Electronics requires a 15% IRR per year, after taxes, in U.S. dollars (ius) on its foreign investments, should this assembly plant be approved? Assume that there are no unusual risks of nationalization of foreign investments in this country. Dr. Mohammad Abuhaiba, PE

Example 8.10 Estimating future exchange rates The monetary (currency) unit of another country, A, has a present exchange rate of 10.7 units per USD. If the average devaluation of currency A in the international market is estimated to be 4.2% per year (for the next five years) relative to USD, what would be the exchange rate three years from now? If the average devaluation of U.S. dollar )for the next five years) is estimated to be 3% per year relative to currency A, what would be the exchange rate three years from now? Dr. Mohammad Abuhaiba, PE

Example 8.11 Profitability analysis of a foreign investment EOY Net Cash flow   -850,000,000 1 270,000,000 2 3 4 5 6 6(MV) 120,000,000 A U.S. firm is analyzing a potential investment project in another country. The present exchange rate is 425 of their currency units (A) per U.S. dollar. The best estimate is that currency A will be devalued in the international market at an average of 2% per year relative to the U.S. dollar over the next several years. The estimated before tax net cash flow (in currency A) of the project is as follows: If the MARR value of the U.S. firm (before and based on the U.S. dollar) is 20% per year, is the project economically justified? Instead, if the U.S. dollar is estimated to be devalued in the international market an average 2% per year over the next several years, what would be the rate of return based on the U.S. dollar? Is the project economically justified? Dr. Mohammad Abuhaiba, PE

Home Work Assignment Due: 11/25/2018 12:01 AM Dr. Mohammad Abuhaiba, PE

Case Study Resolve case study on pp376-379 8-52, 8-53, 8-54 Due: 11/25/2018 12:01 AM Case Study Resolve case study on pp376-379 8-52, 8-53, 8-54 Due: Dr. Mohammad Abuhaiba, PE