CHAPTER 8CHAPTER 8CHAPTER 8CHAPTER 8

PRICE CHANGES AND PRICE CHANGES AND EXCHANGE RATESEXCHANGE RATES

PRICE CHANGES AND PRICE CHANGES AND EXCHANGE RATESEXCHANGE RATES

GENERAL PRICE INFLATIONGENERAL PRICE INFLATIONGENERAL PRICE INFLATIONGENERAL PRICE INFLATION

An increase in the average price An increase in the average price paid for goods and services paid for goods and services bringing about a reduction in the bringing about a reduction in the purchasing power of money.purchasing power of money.

An increase in the average price An increase in the average price paid for goods and services paid for goods and services bringing about a reduction in the bringing about a reduction in the purchasing power of money.purchasing power of money.

GENERAL PRICE DEFLATIONGENERAL PRICE DEFLATIONGENERAL PRICE DEFLATIONGENERAL PRICE DEFLATION

A decrease in the average A decrease in the average price paid for goods in price paid for goods in services, resulting in an services, resulting in an increase in the purchasing increase in the purchasing power of money.power of money.

A decrease in the average A decrease in the average price paid for goods in price paid for goods in services, resulting in an services, resulting in an increase in the purchasing increase in the purchasing power of money.power of money.

CONSUMER PRICE INDEXCONSUMER PRICE INDEX(CPI)(CPI)

CONSUMER PRICE INDEXCONSUMER PRICE INDEX(CPI)(CPI)

• One measure of price changes in our One measure of price changes in our economyeconomy

• An estimate of general price inflationAn estimate of general price inflation• Tabulated by the U S GovernmentTabulated by the U S Government• A composite price index that measures price A composite price index that measures price

changes in food, shelter, medical care, changes in food, shelter, medical care, transportation, apparel, and transportation, apparel, and other selectedother selected goods and services used by average goods and services used by average individuals and families individuals and families

• One measure of price changes in our One measure of price changes in our economyeconomy

• An estimate of general price inflationAn estimate of general price inflation• Tabulated by the U S GovernmentTabulated by the U S Government• A composite price index that measures price A composite price index that measures price

changes in food, shelter, medical care, changes in food, shelter, medical care, transportation, apparel, and transportation, apparel, and other selectedother selected goods and services used by average goods and services used by average individuals and families individuals and families

CONSUMER PRICE INDEXCONSUMER PRICE INDEXCONSUMER PRICE INDEXCONSUMER PRICE INDEX

CPICPIkk = ( = (QQk-1k-1 x P x Pkk) / () / (QQk-1k-1 x P x Pk-1k-1))• QQk-1k-1 = Preceding year quantities = Preceding year quantities

• PPkk = Current-year prices = Current-year prices

• PPk-1k-1 = Preceding Year Prices = Preceding Year Prices

CPICPIkk = ( = (QQk-1k-1 x P x Pkk) / () / (QQk-1k-1 x P x Pk-1k-1))• QQk-1k-1 = Preceding year quantities = Preceding year quantities

• PPkk = Current-year prices = Current-year prices

• PPk-1k-1 = Preceding Year Prices = Preceding Year Prices

INFLATION-RELATED TERMINOLOGYINFLATION-RELATED TERMINOLOGYINFLATION-RELATED TERMINOLOGYINFLATION-RELATED TERMINOLOGY• Actual dollars (A$)Actual dollars (A$) - (Current time frame) cash- - (Current time frame) cash-

flow dollars flow dollars : : alsoalso current dollars, then-current dollars, current dollars, then-current dollars, or inflated dollarsor inflated dollars

• Real dollars (R$)Real dollars (R$) - Dollars in terms of purchasing - Dollars in terms of purchasing power at some stated time period (i.e., base year): power at some stated time period (i.e., base year): also constant dollars also constant dollars

• Base period (b)Base period (b) - Purchasing-power time reference - Purchasing-power time reference• General price inflation ( f )General price inflation ( f ) - Measure of change in - Measure of change in

purchasing power from one time to anotherpurchasing power from one time to another• Combined (nominal) interest rate ( iCombined (nominal) interest rate ( icc)) - Market - Market

interest rate: actual dollars paid for use of capitalinterest rate: actual dollars paid for use of capital• Real interest rate - (iReal interest rate - (irr)) - Inflation-free interest rate: - Inflation-free interest rate:

real dollars paid for use of capitalreal dollars paid for use of capital

• Actual dollars (A$)Actual dollars (A$) - (Current time frame) cash- - (Current time frame) cash-flow dollars flow dollars : : alsoalso current dollars, then-current dollars, current dollars, then-current dollars, or inflated dollarsor inflated dollars

• Real dollars (R$)Real dollars (R$) - Dollars in terms of purchasing - Dollars in terms of purchasing power at some stated time period (i.e., base year): power at some stated time period (i.e., base year): also constant dollars also constant dollars

• Base period (b)Base period (b) - Purchasing-power time reference - Purchasing-power time reference• General price inflation ( f )General price inflation ( f ) - Measure of change in - Measure of change in

purchasing power from one time to anotherpurchasing power from one time to another• Combined (nominal) interest rate ( iCombined (nominal) interest rate ( icc)) - Market - Market

interest rate: actual dollars paid for use of capitalinterest rate: actual dollars paid for use of capital• Real interest rate - (iReal interest rate - (irr)) - Inflation-free interest rate: - Inflation-free interest rate:

real dollars paid for use of capitalreal dollars paid for use of capital

RELATING ACTUAL DOLLARS TO REAL RELATING ACTUAL DOLLARS TO REAL DOLLARSDOLLARS

RELATING ACTUAL DOLLARS TO REAL RELATING ACTUAL DOLLARS TO REAL DOLLARSDOLLARS

• Use the following to convert actual dollars, as of time k, to Use the following to convert actual dollars, as of time k, to real dollars of constant purchasing powerreal dollars of constant purchasing power

(R$)(R$)KK = (A$) = (A$)K K [1/ (1+f)][1/ (1+f)]K-bK-b

= (A$)= (A$)KK(P / F, f %, k-b)(P / F, f %, k-b)• The equation changes as follows for a specific type cash The equation changes as follows for a specific type cash

flow (i.e. specific good or service “flow (i.e. specific good or service “j j ” )” )

(R$)(R$)K K jj = (A$) = (A$)K K jj [1/ (1+f)][1/ (1+f)]K-bK-b

= (A$)= (A$)K K j j (P / F, f %, k-b)(P / F, f %, k-b)• In the base period, purchasing power of actual dollar and In the base period, purchasing power of actual dollar and

real dollar are the samereal dollar are the same

• Use the following to convert actual dollars, as of time k, to Use the following to convert actual dollars, as of time k, to real dollars of constant purchasing powerreal dollars of constant purchasing power

(R$)(R$)KK = (A$) = (A$)K K [1/ (1+f)][1/ (1+f)]K-bK-b

= (A$)= (A$)KK(P / F, f %, k-b)(P / F, f %, k-b)• The equation changes as follows for a specific type cash The equation changes as follows for a specific type cash

flow (i.e. specific good or service “flow (i.e. specific good or service “j j ” )” )

(R$)(R$)K K jj = (A$) = (A$)K K jj [1/ (1+f)][1/ (1+f)]K-bK-b

= (A$)= (A$)K K j j (P / F, f %, k-b)(P / F, f %, k-b)• In the base period, purchasing power of actual dollar and In the base period, purchasing power of actual dollar and

real dollar are the samereal dollar are the same

RELATING COMBINED AND REAL INTEREST RELATING COMBINED AND REAL INTEREST RATES AND GENERAL INFLATION RATERATES AND GENERAL INFLATION RATE

RELATING COMBINED AND REAL INTEREST RELATING COMBINED AND REAL INTEREST RATES AND GENERAL INFLATION RATERATES AND GENERAL INFLATION RATE

i i rr = ( i = ( i cc - f ) / ( 1 + f ) - f ) / ( 1 + f )

• Similarly, current-dollar internal rate Similarly, current-dollar internal rate of return is related to the real rate of of return is related to the real rate of return in the following way:return in the following way:

IRR IRR rr = (IRR = (IRR cc - f ) / ( 1 + f ) - f ) / ( 1 + f )

i i rr = ( i = ( i cc - f ) / ( 1 + f ) - f ) / ( 1 + f )

• Similarly, current-dollar internal rate Similarly, current-dollar internal rate of return is related to the real rate of of return is related to the real rate of return in the following way:return in the following way:

IRR IRR rr = (IRR = (IRR cc - f ) / ( 1 + f ) - f ) / ( 1 + f )

FIXED AND RESPONSIVE FIXED AND RESPONSIVE ANNUITIESANNUITIES

FIXED AND RESPONSIVE FIXED AND RESPONSIVE ANNUITIESANNUITIES

• Cash flows predetermined by Cash flows predetermined by contract -- bonds or fixed annuities -- contract -- bonds or fixed annuities -- do not respond to general price do not respond to general price inflationinflation

• Future amounts that are not Future amounts that are not predetermined may, by varying predetermined may, by varying degrees, respond to general price degrees, respond to general price inflationinflation

• Cash flows predetermined by Cash flows predetermined by contract -- bonds or fixed annuities -- contract -- bonds or fixed annuities -- do not respond to general price do not respond to general price inflationinflation

• Future amounts that are not Future amounts that are not predetermined may, by varying predetermined may, by varying degrees, respond to general price degrees, respond to general price inflationinflation

CALCULATING AN EFFECTIVE GENERAL CALCULATING AN EFFECTIVE GENERAL PRICE INFLATION RATEPRICE INFLATION RATE

CALCULATING AN EFFECTIVE GENERAL CALCULATING AN EFFECTIVE GENERAL PRICE INFLATION RATEPRICE INFLATION RATE

• f = An (estimated) effective general price f = An (estimated) effective general price inflation rate for a period of N years inflation rate for a period of N years

f = f =

k=1k=1( 1 + f ( 1 + f k k ) ) 1 / N1 / N

- 1 - 1

• f = An (estimated) effective general price f = An (estimated) effective general price inflation rate for a period of N years inflation rate for a period of N years

f = f =

k=1k=1( 1 + f ( 1 + f k k ) ) 1 / N1 / N

- 1 - 1

MARKET INTEREST RATE RATE OF RETURN MARKET INTEREST RATE RATE OF RETURN

RELATIVE TO U.S. DOLLARS RELATIVE TO U.S. DOLLARS

MARKET INTEREST RATE RATE OF RETURN MARKET INTEREST RATE RATE OF RETURN

RELATIVE TO U.S. DOLLARS RELATIVE TO U.S. DOLLARS i i f c f c = i = i USUS + f + f ee + f + f ee ( i ( i USUS ) )

i i USUS = ( i = ( i f c f c - f - f ee ) / ( 1 + f ) / ( 1 + f ee ) )

• i i USUS = market (combined ) interest rate of = market (combined ) interest rate of

return relative to US dollarsreturn relative to US dollars

• i i f c f c = market (combined ) interest rate of return = market (combined ) interest rate of return

relative to foreign country currencyrelative to foreign country currency

• ffee = Annual rate of change in exchange rate -- = Annual rate of change in exchange rate --

annual devaluation rate -- between foreign annual devaluation rate -- between foreign country currency and US dollar country currency and US dollar

– ffee +: foreign currency devalued relative to dollar +: foreign currency devalued relative to dollar

– ffee - : dollar devalued relative to foreign currency - : dollar devalued relative to foreign currency

i i f c f c = i = i USUS + f + f ee + f + f ee ( i ( i USUS ) )

i i USUS = ( i = ( i f c f c - f - f ee ) / ( 1 + f ) / ( 1 + f ee ) )

• i i USUS = market (combined ) interest rate of = market (combined ) interest rate of

return relative to US dollarsreturn relative to US dollars

• i i f c f c = market (combined ) interest rate of return = market (combined ) interest rate of return

relative to foreign country currencyrelative to foreign country currency

• ffee = Annual rate of change in exchange rate -- = Annual rate of change in exchange rate --

annual devaluation rate -- between foreign annual devaluation rate -- between foreign country currency and US dollar country currency and US dollar

– ffee +: foreign currency devalued relative to dollar +: foreign currency devalued relative to dollar

– ffee - : dollar devalued relative to foreign currency - : dollar devalued relative to foreign currency