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Unformatted text preview: CHAPTER 8 CHAPTER PRICE CHANGES AND PRICE EXCHANGE RATES EXCHANGE GENERAL PRICE INFLATION GENERAL An increase in the average price paid for goods and services bringing about a reduction in the purchasing power of money. purchasing GENERAL PRICE DEFLATION GENERAL A decrease in the average price paid for goods in services, resulting in an increase in the purchasing power of money. power CONSUMER PRICE INDEX CONSUMER (CPI) • One measure of price changes in our One economy economy • An estimate of general price inflation • Tabulated by the U S Government • A composite price index that measures composite price changes in food, shelter, medical care, transportation, apparel, and other selected goods and services used by selected average individuals and families CONSUMER PRICE INDEX CONSUMER CPI is a La Speyres type index CPIk = (Σ Qk-1 x Pk) / (Σ Qk-1 x Pk-1) • Qk-1 = Preceding year quantities • Pk = Current-year prices • Pk-1 = Preceding Year Prices CPI Annual Inflation Rate CPI = [ (CPIk - CPIk-1) / CPIk-1 ] x 100 (CPI 100 k-1 • CPIk = Consumer price index for the current year • CPIk-1 = Consumer price index for the preceding year Consumer k-1 OTHER INFLATION INDICATORS OTHER • While the CPI is shows how the prices that While consumers pay change from year to year or month to month month • The PPI (Producer Price Index) shows how The the prices paid to producers change from year to year or month to month year • The Implicit Price Deflator or GDP deflator The shows how all prices in the economy change from one time period to another time period • Actual dollars (A$) - (Current time frame) cashflow dollars : also current dollars, then-current dollars, also flow or inflated dollars or INFLATION-RELATED TERMINOLOGY INFLATION-RELATED • Real dollars (R$) - Dollars in terms of purchasing power at some stated time period (i.e., base year): also constant dollars • Base period (b) - Purchasing-power time reference • General price inflation ( f ) - Measure of change in purchasing power from one time to another purchasing • Combined (nominal) interest rate ( ic) - Market interest rate: actual dollars paid for use of capital interest • Real interest rate - (ir) - Inflation-free interest rate: real dollars paid for use of capital real • Use the following to convert actual dollars, as of Use time k, to real dollars of constant purchasing power power RELATING ACTUAL DOLLARS TO REAL DOLLARS DOLLARS (R$)K = (A$)K [1/ (1+f)]K-b [1/ = (A$)K(P / F, f %, k-b) (A$) • The equation changes as follows for a specific The type cash flow (i.e. specific good or service “j ” ) type (R$)K j = (A$)K j [1/ (1+f)]K-b [1/ = (A$)K j (P / F, f %, k-b) (A$) (P • In the base period, purchasing power of actual In dollar and real dollar are the same dollar RELATING COMBINED AND REAL INTEREST RATES AND GENERAL INFLATION RATE RATES ir=(ic-f)/(1+f) • Similarly, current-dollar internal rate Similarly, of return is related to the real rate of return in the following way: return IRR r = (IRR c - f ) / ( 1 + f ) IRR FIXED AND RESPONSIVE ANNUITIES ANNUITIES • Cash flows predetermined by Cash contract -- bonds or fixed annuities -do not respond to general price inflation inflation • Future amounts that are not Future predetermined may, by varying degrees, respond to general price inflation inflation CALCULATING AN EFFECTIVE GENERAL PRICE INFLATION RATE PRICE • f = An (estimated) effective general price An inflation rate for a period of N years f= Π Ν k=1 ( 1 + f k) 1/N -1 DIFFERENTIAL PRICE INFLATION DIFFERENTIAL • Variation between general price inflation rate and Variation the best estimate of future price changes for specific goods and services specific • 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 Caused demand, technological improvements, productivity changes, regulatory requirements productivity TOTAL PRICE ESCALATION TOTAL • Price changes caused by some combination of Price general price and differential price inflation general • 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 Includes inflation rate ( f ) and the differential price inflation I rate (e j ) on price changes on e j=(ej-f)/(1+f) (A$) k j = (A$) b j (F / P, e j %, k - b ) (A$) (F (A$) b j = (A$) b j (F / P, e j %, k - b ) (A$) (F I I DETERMINING A CONVENIENCE RATE FOR GEOMETRIC CASH FLOW SEQUENCES SEQUENCES • Actual dollar analysis ( A$ ) iCR = ( ic - e j ) / ( 1 + e j ) • Real dollar analysis ( R$ ) iCR = ( ir - e ) / ( 1 + e ) I j I j MARKET INTEREST RATE RATE OF RETURN RELATIVE TO U.S. DOLLARS i f c = i US + f e + f e ( i US ) US US i US = ( i f c - f e ) / ( 1 + f e ) US • i US = market (combined ) interest rate of US return relative to US dollars return • i f c = market (combined ) interest rate of return relative to foreign country currency relative • fe = Annual rate of change in exchange rate -annual devaluation rate -- between foreign country currency and US dollar – fe +: foreign currency devalued relative to dollar ...
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