EGGC4214 Systems Engineering & Economy Lecture 10 Inflation & Price Changes

EGGC4214 EGGC4214 Systems Engineering & EconomySystems Engineering & Economy

Lecture 10Lecture 10Inflation & Price ChangesInflation & Price Changes

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Inflation: IntroductionInflation: Introduction

Inflation reflectsInflation reflects: the change in the purchasing power of currency during a : the change in the purchasing power of currency during a period of time.period of time.

All of our previous analysis has ignored inflationAll of our previous analysis has ignored inflation . . It is important to take inflation into account, as it can have significant long-run effects.It is important to take inflation into account, as it can have significant long-run effects.

Some FactsSome Facts A good starting master’s salary in 1962 was about $10,000.A good starting master’s salary in 1962 was about $10,000. In 1962, a 1-year old Volkswagen Beetle cost about $2,100.In 1962, a 1-year old Volkswagen Beetle cost about $2,100.

Occasionally inflation gets out of controlOccasionally inflation gets out of control After World War I, in Germany money had so little value that a week’s wages had to be After World War I, in Germany money had so little value that a week’s wages had to be

transported in a wheelbarrow. During this time people were buying concert tickets transported in a wheelbarrow. During this time people were buying concert tickets using potatoes and beets for barter.using potatoes and beets for barter.

In recent years in Mexico, people have bought new cars and put them up on blocks In recent years in Mexico, people have bought new cars and put them up on blocks because they retained their value reasonably well in hyper-inflationary circumstances.because they retained their value reasonably well in hyper-inflationary circumstances.

Effect of inflation:Effect of inflation: More money is needed than before to achieve the same amount of purchasing powerMore money is needed than before to achieve the same amount of purchasing power . . It’s the It’s the purchasing powerpurchasing power that’s important. that’s important.

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Imagine that everybody in the U.S. agreed to multiply Imagine that everybody in the U.S. agreed to multiply allall monetary values by 10 on the first monetary values by 10 on the first day of the year 2001. A loaf of bread that cost $1.00 in 2000 would cost $10.00 in 2001. day of the year 2001. A loaf of bread that cost $1.00 in 2000 would cost $10.00 in 2001. Your income would also be multiplied by 10, your savings and investments would be Your income would also be multiplied by 10, your savings and investments would be multiplied by 10, etc. Effectively, multiplied by 10, etc. Effectively, the monetary measurement scale has been changedthe monetary measurement scale has been changed..

Call a 2000 dollar an Call a 2000 dollar an old dollarold dollar, and a 2001 dollar , and a 2001 dollar a new dollara new dollar. It now takes 10 new dollars . It now takes 10 new dollars to have the buying power of one old dollar. If your 2000 annual salary was $30,000 in old to have the buying power of one old dollar. If your 2000 annual salary was $30,000 in old dollars, then your 2001 annual salary would be $300,000 in new dollars.dollars, then your 2001 annual salary would be $300,000 in new dollars.

Questions: Questions: 1.1. Would it then make any sense to say that your total salary income for 2000 and 2001 was $330,000? Would it then make any sense to say that your total salary income for 2000 and 2001 was $330,000?

2.2. Does it make sense to add new dollars and old dollars?Does it make sense to add new dollars and old dollars?

3.3. What if we say, What if we say, measured in old dollarsmeasured in old dollars, your total salary income for 2000 and 2001 was $60,000? Is this , your total salary income for 2000 and 2001 was $60,000? Is this reasonable?reasonable?

4.4. What if, What if, measured in new dollarsmeasured in new dollars, your total salary income for 2000 and 2001 was $600,000? Is this , your total salary income for 2000 and 2001 was $600,000? Is this reasonable?reasonable?

5.5. Suppose you had invested $1000 old dollars at the first of 2000. By the end of 2000 it had grown to $1,100 Suppose you had invested $1000 old dollars at the first of 2000. By the end of 2000 it had grown to $1,100 old dollars. At the first of 2001 it would be worth $11,000 new dollars.old dollars. At the first of 2001 it would be worth $11,000 new dollars.

6.6. Does this mean you have earned 100 (11000-1000)/1000 = 1000%, or based on old dollars 100 (1100-Does this mean you have earned 100 (11000-1000)/1000 = 1000%, or based on old dollars 100 (1100-1000)/1000 = 10%?1000)/1000 = 10%?

7.7. Does this mean you earned: 100 (11000-10000)/10000 = 10%, based on new dollars?Does this mean you earned: 100 (11000-10000)/10000 = 10%, based on new dollars?

Inflation: IntroductionInflation: IntroductionHypothetical Inflation Example for Insight

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ConclusionConclusion

It is important to It is important to use either new dollars or old dollars for use either new dollars or old dollars for measurement purposesmeasurement purposes. Mixing them gives wrong results. We also . Mixing them gives wrong results. We also need to know need to know how to converthow to convert between old dollars and new dollars between old dollars and new dollars (multiply or divide by 10).(multiply or divide by 10).

Dollars in one period of time are Dollars in one period of time are not equivalentnot equivalent to dollars in another. to dollars in another.

It is important to It is important to make comparisons on an equivalent basis.make comparisons on an equivalent basis.

We must We must incorporate the effects of inflationincorporate the effects of inflation in our analysis of in our analysis of alternatives.alternatives.

Inflation: IntroductionInflation: Introduction

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Inflation: Inflation: Basic ExampleBasic Example

You invest $1000 today at 5.5%.You invest $1000 today at 5.5%. f = 2% is the f = 2% is the inflation rate; inflation rate; i = 5.5% is the i = 5.5% is the market interest ratemarket interest rate . .

$1000 grows in a year to $1055, $1000 grows in a year to $1055, but - because of inflation - in today’s dollars it is only worth 1055/(1.02) but - because of inflation - in today’s dollars it is only worth 1055/(1.02)

= $1034.31. = $1034.31.

This means, in today’s dollars, the real rate of return is:This means, in today’s dollars, the real rate of return is:(1034.31-1000)/1000 = 0.03431, or 3.431%.(1034.31-1000)/1000 = 0.03431, or 3.431%.

Note that 1034.31 = 1000(1+i)/(1+f). Note that 1034.31 = 1000(1+i)/(1+f). This makes:This makes:

i’ = [1000(1+i)/(1+f) – 1000]/1000 = [(1+i)/(1+f)] - 1.i’ = [1000(1+i)/(1+f) – 1000]/1000 = [(1+i)/(1+f)] - 1.

Note i’ is independent of 1000. Thus: Note i’ is independent of 1000. Thus: i’ = [(1+i)/(1+f)] –1 = (i – f)/(1 + f) i’ = [(1+i)/(1+f)] –1 = (i – f)/(1 + f) i’ + i’ f = i – f i’ + i’ f = i – f i = i’ + f + i’ fi = i’ + f + i’ f

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Fundamental ConclusionFundamental Conclusion

i’ = (i-f)/(1+f)i’ = (i-f)/(1+f) i = i’ + f + i’ f.i = i’ + f + i’ f.

5.5% = 3.431% + 2% + 3.431%*2%5.5% = 3.431% + 2% + 3.431%*2%

market interest rate = real interest rate + inflation rate market interest rate = real interest rate + inflation rate

+ (real interest rate ) + (real interest rate ) (inflation rate) (inflation rate)

Market interest rate (i):Market interest rate (i):

Includes both real growth and the effect of inflationIncludes both real growth and the effect of inflation..

Exact: Exact: i = i’ + f + i’ fi = i’ + f + i’ f

Approximate: Approximate: i = i’ + f, since i’f i = i’ + f, since i’f 0. 0.

Real interest rate (i’):Real interest rate (i’):

Exact: i’ = (i-f)/(1+f)Exact: i’ = (i-f)/(1+f)

Approximate: i’ = i - fApproximate: i’ = i - f

Inflation: Basic ExampleInflation: Basic Example

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Inflation: Inflation: DefinitionsDefinitions

Actual Dollars (A$):Actual Dollars (A$): The number of dollars associated with a cash flow as it occurs. The number of dollars associated with a cash flow as it occurs. These dollars are “actual” and exist physically.These dollars are “actual” and exist physically. Actual dollars are called Actual dollars are called inflated dollarsinflated dollars, because they carry any , because they carry any

inflation that has reduced their worth.inflation that has reduced their worth.

Real or Constant Dollars (R$ or C$):Real or Constant Dollars (R$ or C$): Dollars expressed in terms of some constant purchasing power “base” Dollars expressed in terms of some constant purchasing power “base”

year. An example would be year. An example would be 1982-based dollar1982-based dollars. s. They are also called They are also called inflation-free dollarsinflation-free dollars. .

Inflation Rate:Inflation Rate: The change in the purchasing power of dollar during a period of time.The change in the purchasing power of dollar during a period of time. More money is required to buy something whose price is inflated.More money is required to buy something whose price is inflated.

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Inflation: Inflation: DefinitionsDefinitions

Combined Interest Rate:Combined Interest Rate: The interest rate found in the general marketplaceThe interest rate found in the general marketplace It incorporates the effect of both real money growth and inflationIt incorporates the effect of both real money growth and inflation Interest rates on passbook savings, checking, and certificates of Interest rates on passbook savings, checking, and certificates of

deposit quoted at the bank are all market rates.deposit quoted at the bank are all market rates.

Real Interest RateReal Interest Rate:: Measures the real growth of the money, excluding inflationMeasures the real growth of the money, excluding inflation Also called inflation-free rate, or the rate adjusted for inflation.Also called inflation-free rate, or the rate adjusted for inflation.

Base time period:Base time period: The reference or base time period used to define the purchasing power The reference or base time period used to define the purchasing power

of real (constant) dollarsof real (constant) dollars

Engineering Studies: A$ vs. R$Engineering Studies: A$ vs. R$ Both A$ and R$ methods result in the same equivalent worthBoth A$ and R$ methods result in the same equivalent worth Need to account for both types of cash flowNeed to account for both types of cash flow Final recommendations are usually best stated in R$.Final recommendations are usually best stated in R$.

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Inflation: Inflation: ExampleExampleExampleExample

Tiger Woods invests Tiger Woods invests $1000$1000 in a bank for a year. The bank pays in a bank for a year. The bank pays 5.5%5.5% compounded annually. Find Tiger’s real rate of return if the rate of compounded annually. Find Tiger’s real rate of return if the rate of inflation is either inflation is either 2%2% or or 8%8% a year. a year.

Part 1: f = 2% a year, i = 5.5% a year.

Amount in bank = 1000*(1.055) = $1055 (A$)

i’ = (i-f)/(1+f) = (.055-.02)/(1+.02) = .03431 = 3.431%

3.431% more purchasing power than one year ago.

How many golf balls can he buy:

EOY 0: Quantity = $1000/$5 = 200 ballsEOY 1: Quantity = $1055/($5*1.02) = 207 balls

Golf balls cost $5.10=$5*1.02 at EOY 1207 is equivalent to 3.431 more balls than one year ago (200 balls).

Part 2: f = 8% a year, i = 5.5% a year.

Amount in bank = 1000*(1.055) = $1055 (A$) i’ = (i-f)/(1+f) = (.055-.08)/(1+.08) = -.023 = -2.3%

2.3% is less purchasing power than one year ago.

EOY 0: Quantity = $1000/$5 = 200 ballsEOY 1: Quantity = $1055/($5*1.08) =195.3704

195 ballsGolf balls cost $5.40 = $5*1.08 at EOY 1195 is equivalent to 2.3% less balls than one year ago (200 balls).

Key point: Under either inflation scenarios, Tiger still has $1055 in the bank. But inflation will effect his purchasing power.

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Inflation – Principles in using A$ and R$Inflation – Principles in using A$ and R$

Key ideas:Key ideas: i relates A$ for various periodsi relates A$ for various periods i’ relates R$ for various periodsi’ relates R$ for various periods f relates A$ to R$ for the # periods of interestf relates A$ to R$ for the # periods of interest

f for 0 periods

t nTime

f for n-t periods

R(base t) $ at (t)

A$ at (t)

R(base t) $ at (n)

A$ at (n)

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Inflation – Principles in using A$ and R$Inflation – Principles in using A$ and R$

When dealing with actual dollars (A$), use a market interest rate (i). When When dealing with actual dollars (A$), use a market interest rate (i). When discounting A$ over time, also use i.discounting A$ over time, also use i.

(A$)t = (A$)n (P/F, i%, n-t) = (A$)n (1+i)-(n-t)

When dealing with real dollars (C/R$), use a real interest rate (i’). When When dealing with real dollars (C/R$), use a real interest rate (i’). When discounting R$ over time, also use i’.discounting R$ over time, also use i’.

(R$)t = (R$)n (P/F, i’%, n-t) = (R$)(1+i’)-(n-t)

To translate between R$ and $A (or vice versa), use the inflation rate f for To translate between R$ and $A (or vice versa), use the inflation rate f for the appropriate number of periods.the appropriate number of periods.

(R$) = (A$) (P/F, f%, n-t) = (A$) (1+f)-(n-t)

Don’t forget that (A$)t= (R$) t

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Inflation: ExampleInflation: ExampleA stadium was built in A stadium was built in 19451945, at a total cost of , at a total cost of 1.2 million dollars1.2 million dollars. An alumnus . An alumnus also gave also gave 1.2 million1.2 million dollars in dollars in 19451945 to fund a future replacement. The to fund a future replacement. The university invested the 1.2 million gift at a market interest rate of university invested the 1.2 million gift at a market interest rate of 8.0%8.0% per year per year in in 19451945. University administrators are considering building the new facility in the . University administrators are considering building the new facility in the year 2000. Inflation is year 2000. Inflation is 6.0%6.0% per year from per year from 1945 to 20001945 to 2000. .

ObservationsObservations::f = 6.0%, f = 6.0%, i = 8.0%, i = 8.0%, i’ = (i-f)/(1+f) = 0.02/(1.06) i’ = (i-f)/(1+f) = 0.02/(1.06) 1.887% per year. 1.887% per year.

Year 2000 A$Year 2000 A$

The 1.2 million A$ grows at the 8% market rate: The 1.2 million A$ grows at the 8% market rate:

A$ in 2000 = A$ in 1945 (F/P,i,55 years) = $82,701,600.A$ in 2000 = A$ in 1945 (F/P,i,55 years) = $82,701,600.

Year 2000 R$ Year 2000 R$

R (base 1945) dollars in 2000 = (A$ in 2000) (P/F,f,55) = $82,701,600/(1.06)R (base 1945) dollars in 2000 = (A$ in 2000) (P/F,f,55) = $82,701,600/(1.06) 5555

= $3,357,000= $3,357,000

The $82,701,600 is really worth $3,357,000The $82,701,600 is really worth $3,357,000

In other words $In other words $3,357,0003,357,000 yearyear-19451945 dollars has the purchasing power of dollars has the purchasing power of $82,701,600$82,701,600 yearyear-20002000 dollars dollars

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Inflation: Example (cont’d)Inflation: Example (cont’d)Year 2000 R$:Year 2000 R$: This process is called “This process is called “stripping out 55 years of 6% inflationstripping out 55 years of 6% inflation.” .” We are not physically moving the dollars in time in this case. We are simply We are not physically moving the dollars in time in this case. We are simply

removingremoving inflation from these dollars one year at a time using the P/F inflation from these dollars one year at a time using the P/F factor.factor.

Using the real interest rate i’ to calculate Year 2000 R$:Using the real interest rate i’ to calculate Year 2000 R$: The real interest rate The real interest rate i’ i’ 1.887% 1.887% and does not include inflation. and does not include inflation. R$ (2000) = A$ (1945) (F/P, i’, 55) = 1,200,000*(1.01887)R$ (2000) = A$ (1945) (F/P, i’, 55) = 1,200,000*(1.01887)5555

= $= $3,355,0003,355,000

Quality of new stadiumQuality of new stadium:: The new stadium will NOT be 82.7/1.2 = 68.92 times betterThe new stadium will NOT be 82.7/1.2 = 68.92 times better More accurately, the new stadium can be 3.355/1.2 = More accurately, the new stadium can be 3.355/1.2 = 2.96 times better2.96 times better

than the 1945 stadium.than the 1945 stadium. C/R$ is more accurate measure of the purchasing power.C/R$ is more accurate measure of the purchasing power.

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Factors that Influence InflationFactors that Influence Inflation

Money Supply:Money Supply: The amount of money in the national economyThe amount of money in the national economy.. Too muchToo much supply (as compared to available goods and services to supply (as compared to available goods and services to

purchase) it tends to decrease the value of dollars – purchase) it tends to decrease the value of dollars – inflationinflation. . Not enoughNot enough, dollars become more valuable – , dollars become more valuable – deflationdeflation. . The Federal Reserve Board controls the flow of money in the economy. The Federal Reserve Board controls the flow of money in the economy.

Exchange Rates:Exchange Rates: The strength of the US $ relative to other currencies.The strength of the US $ relative to other currencies.

As corporate profits are weakened in some markets due to exchange rates, As corporate profits are weakened in some markets due to exchange rates,

prices may be raised in other markets to compensate.prices may be raised in other markets to compensate.

INFLATION:INFLATION: Cost-Push Inflation:Cost-Push Inflation: Producers of goods and services “push” their Producers of goods and services “push” their

increasing operating costs along to the customer through higher prices. increasing operating costs along to the customer through higher prices. Demand-Pull Inflation:Demand-Pull Inflation: Demand-pull inflation occurs when consumers Demand-pull inflation occurs when consumers

spend money freely on goods and services. spend money freely on goods and services. As more and more people As more and more people demand certain goods and services, their prices will risedemand certain goods and services, their prices will rise – demand exceeds – demand exceeds supply.supply.

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Inflation – Investment Strategies ExampleInflation – Investment Strategies Example

Mr O’Leary buries Mr O’Leary buries $1,000$1,000 in dollar bills in a jar in his yard in in dollar bills in a jar in his yard in 19241924. They . They are intended as a nest egg for his first great-grandchild. Gabrielle, his are intended as a nest egg for his first great-grandchild. Gabrielle, his first great-grandchild, is born in first great-grandchild, is born in 19941994..

Data for 1924-1994:Data for 1924-1994: Inflation averaged Inflation averaged 4.5%4.5% The stock market averaged The stock market averaged 15%15% Guaranteed government obligations averaged Guaranteed government obligations averaged 6.5%6.5%

1. What was the relative purchasing power of the jar of bills when 1. What was the relative purchasing power of the jar of bills when Gabrielle was born?Gabrielle was born?

2. Did Mr. O’Leary have better investments he could have chosen? 2. Did Mr. O’Leary have better investments he could have chosen? NOTE: The jar of bills is in actual dollars in both 1924 and in 1994!!NOTE: The jar of bills is in actual dollars in both 1924 and in 1994!!

Option 1:Option 1: Strip out 70 Years of Inflation:Strip out 70 Years of Inflation:

R$(base 1924) in 1994 = A$ in 1994 (P/F,f,70) = 1000(1+f)R$(base 1924) in 1994 = A$ in 1994 (P/F,f,70) = 1000(1+f)-70-70 = = $45.90$45.90

It’s purchasing power was about 4.6% of what it was in 1924.It’s purchasing power was about 4.6% of what it was in 1924.

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Inflation – Investment Strategies ExampleInflation – Investment Strategies Example

Option 2:Option 2: Put the money in the Stock Market:Put the money in the Stock Market:

A$ in 1994 = (A$ in 1924) (1.15)A$ in 1994 = (A$ in 1924) (1.15)7070 $17,435,720. $17,435,720.

Gabrielle would have been very wealthy!!!Gabrielle would have been very wealthy!!!

R$ (base 1924) = (A$ in 1994) (P/F, f,70) = $17,435,720/(1+f)R$ (base 1924) = (A$ in 1994) (P/F, f,70) = $17,435,720/(1+f)7070 = = 17,435,720/(1.045)17,435,720/(1.045)7070 $ $814,158814,158

Equivalently,Equivalently,i’ = (i – f)/(1+f) = (0.105)/(1.045) i’ = (i – f)/(1+f) = (0.105)/(1.045) 0.100478468, 0.100478468,1000(1+i’)1000(1+i’)7070 = 1000 (814.158) = $814,158 in C/R$ = 1000 (814.158) = $814,158 in C/R$

Option 3:Option 3: Put the money in Government Securities Put the money in Government Securities

A$ in 1994 = (A$ in 1924) (1.065)A$ in 1994 = (A$ in 1924) (1.065)7070 = 1000 (82.1245) = $82,124.5 = 1000 (82.1245) = $82,124.5

i’ = (i – f)/(1+f) = (0.02)/(1.045) i’ = (i – f)/(1+f) = (0.02)/(1.045) 1.914%, 1.914%,

R$ (base 1924) in 1994 = R$ (base 1924) (P/F,i’,70) = (A$ in 1924) (P/F,i’,70)R$ (base 1924) in 1994 = R$ (base 1924) (P/F,i’,70) = (A$ in 1924) (P/F,i’,70) = 1000(1+i’)= 1000(1+i’)7070 = 1000(1.01914) = 1000(1.01914)7070 $ $3,7703,770

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Inflation – Investment StrategiesInflation – Investment Strategies

ActionsActions A$ Results, 1994A$ Results, 1994 Measured in 1924 C/RMeasured in 1924 C/R$$

Bury MoneyBury Money $1,000$1,000 $45.90$45.90

Gvt. SecuritiesGvt. Securities $ $82,12482,124 $3,770$3,770

Stock MarketStock Market $17,735,720$17,735,720 $814,158$814,158

Warning: There is no guarantee Mr. O’Leary could have averaged 15% in the stock market. (Analysis ignores risk)

Question: What if there had been deflation for 70 years? Would Mr. O’Leary’s actions have made more sense?

Summary. There are basically two ways to handle inflation in economic analysis:

1) Incorporate inflation in the analysis: use the market interest rate i, and the actual dollars A$.

2) Ignore inflation in the analysis: use constant/real dollars (C/R$) and the real interest rate i’.

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Inflation: ExampleInflation: Example

The Waygate (WG) Corporation plans to finance development of a new video The Waygate (WG) Corporation plans to finance development of a new video display technology (VDT). display technology (VDT).

Two companies propose to develop the VDT. Two companies propose to develop the VDT.

WG think they will deliver equivalent products in WG think they will deliver equivalent products in 5 years5 years. .

WG has a WG has a MARR of 25%,MARR of 25%, and assumes and assumes f = 3.5%f = 3.5% each year. each year.

Company Alpha ProposalCompany Alpha Proposal:: Development costs will be Development costs will be $150,000$150,000 in year 1, in year 1,

and will increase and will increase 5%5% each year (in terms of actual each year (in terms of actual dollars).dollars).

Company Beta ProposalCompany Beta Proposal:: Development costs will be a constant Development costs will be a constant $150,000$150,000 each each year year

(in terms of today’s dollars).(in terms of today’s dollars).

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Using a R$ Analysis:Using a R$ Analysis:

The PW of each CFS is based on the real interest rateThe PW of each CFS is based on the real interest ratei’ = (0.25 – 0.035)/(1.035) = 20.8%i’ = (0.25 – 0.035)/(1.035) = 20.8%

Year Year A$ Alpha CostsA$ Alpha Costs R$ Alpha CostsR$ Alpha Costs R$ Beta CostsR$ Beta Costs

11 $150,000 (1.05)$150,000 (1.05) 00 = $150,000 = $150,000 $150,000 / (1.035)$150,000 / (1.035)

11 = $144,698 = $144,698 $150,000$150,000

22 $150,000 (1.05)$150,000 (1.05) 11 = $157,500 = $157,500 $157,500 / (1.035)$157,500 / (1.035)

22 = $147,028 = $147,028 $150,000$150,000

33 $150,000 (1.05)$150,000 (1.05) 22 = $163,375 = $163,375 $163,375 / (1.035)$163,375 / (1.035)

33 = $149,159 = $149,159 $150,000$150,000

44 $150,000 (1.05)$150,000 (1.05) 33 = $173,644 = $173,644 $173,644 / (1.035)$173,644 / (1.035)

44 = $151,321 = $151,321 $150,000$150,000

55 $150,000 (1.05)$150,000 (1.05) 44 = $182,326 = $182,326 $182,326 / (1.035)$182,326 / (1.035)

55 = $153,514 = $153,514 $150,000$150,000

PWPW $436,000$436,000 $441,000$441,000

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Using a A$ Analysis:Using a A$ Analysis:

The PW of each CFS is based on the market interest rate, The PW of each CFS is based on the market interest rate, i = 25%i = 25%

Year Year A$ Alpha CostsA$ Alpha Costs A$ Beta CostsA$ Beta Costs

11 $150,000 (1.05)$150,000 (1.05) 00 = $150,000 = $150,000 $150,000 (1.035)$150,000 (1.035)

11 = $155,250 = $155,250

22 $150,000 (1.05)$150,000 (1.05) 11 = $157,500 = $157,500 $150,000 (1.035)$150,000 (1.035)

22 = $160,684 = $160,684

33 $150,000 (1.05)$150,000 (1.05) 22 = $163,375 = $163,375 $150,000 (1.035)$150,000 (1.035)

33 = $166,308 = $166,308

44 $150,000 (1.05)$150,000 (1.05) 33 = $173,644 = $173,644 $150,000 (1.035)$150,000 (1.035)

44 = $172,128 = $172,128

55 $150,000 (1.05)$150,000 (1.05) 44 = $182,326 = $182,326 $150,000 (1.035)$150,000 (1.035)

55 = $178,153 = $178,153

PWPW $436,000$436,000 $441,000$441,000

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Price Change with IndexesPrice Change with Indexes

Price indexes provide help in choosing an inflation ratePrice indexes provide help in choosing an inflation rate– A price index can be for a specific commodity or for a A price index can be for a specific commodity or for a bundlebundle (composite) (composite)

of commodities. of commodities. – Price indexes can be used to measure historical price changes for Price indexes can be used to measure historical price changes for

individual cost items (labor or material costs) as well as general costs individual cost items (labor or material costs) as well as general costs (like consumer products). (like consumer products).

– We assume future price fluctuations will be similar to past ones. We assume future price fluctuations will be similar to past ones.

Consider a hypothetical Letter Cost Index (LCI) Consider a hypothetical Letter Cost Index (LCI) – The stamp price was The stamp price was $0.06$0.06 in in 19701970 and and $0.33$0.33 in in 19991999..– An approximate inflation rate for stamps from An approximate inflation rate for stamps from 19701970 to to 19991999 is: is:

6 * (1 + f) 6 * (1 + f) 2929 = 33 = 33 f = f = 0.06060.0606, or about , or about 6%6% a year. a year.

Consider an index value of 100 in 1970Consider an index value of 100 in 1970– Since Since 33/6 = 550/ 10033/6 = 550/ 100, we can solve:, we can solve: 100 * (1 + f) 100 * (1 + f) 2929 = 550 = 550– f can also be called a geometric average or average rate of increase.f can also be called a geometric average or average rate of increase.

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Composite vs. Commodity Composite vs. Commodity IndexesIndexes

Cost indexes are usually either Cost indexes are usually either commodity-specificcommodity-specific, or , or composite indexescomposite indexes..

– Commodity-specificCommodity-specific indexes might be for green beans, or indexes might be for green beans, or for iron ore, utility commodities, labor costs, and purchase for iron ore, utility commodities, labor costs, and purchase prices.prices.

– Composite indexesComposite indexes measure the historical prices of groups measure the historical prices of groups or bundles of assets. Examples include the Consumer Price or bundles of assets. Examples include the Consumer Price Index (CPI) and Producer Price Index (PPI).Index (CPI) and Producer Price Index (PPI).

Source of IndexesSource of IndexesUS Department of Commerce and Labor: Department of US Department of Commerce and Labor: Department of

Economic Analysis and Bureau of Labor Statistics. Economic Analysis and Bureau of Labor Statistics. http://www.bls.gov/http://www.bls.gov/

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Inflation: ExampleInflation: ExampleYou plan to give your new niece, Veronica, a pony for her fifth birthday. You plan to give your new niece, Veronica, a pony for her fifth birthday. You want to know how much to put into your passbook savings account today You want to know how much to put into your passbook savings account today (earning (earning 4% a year4% a year, market rate) to buy a pony and saddle for her in five years. , market rate) to buy a pony and saddle for her in five years. You are not sure how much to put into your account, because of inflation. You are not sure how much to put into your account, because of inflation. Suppose we have the following information. Suppose we have the following information. In In 10 years10 years,,

The Little Pony Price Index (LPPI) has gone from The Little Pony Price Index (LPPI) has gone from 213213 to to 541541.. The Leather Saddle Index (LSI) has gone from The Leather Saddle Index (LSI) has gone from 10461046 to to 12291229..

1.1. We use these facts to compute (geometric) average price changes:We use these facts to compute (geometric) average price changes:– LPPI:LPPI: solve solve (1+f*)(1+f*)1010 213 = 541 213 = 541 to get to get f* f* 9.8%. 9.8%. (higher inflation) (higher inflation)– LSI:LSI: solve solve (1+f*)(1+f*)1010 1046 = 1229 1046 = 1229 to get to get f* f* 1.6%. 1.6%.

2.2. Next we find the current price of a registered pony is Next we find the current price of a registered pony is $600$600, while a leather saddle , while a leather saddle costs costs $350$350. F. Future Cost Estimates in Actual Dollars:uture Cost Estimates in Actual Dollars:

– Pony Cost in 5 years = Pony Cost in 5 years = (1.098)(1.098)55 600 = $958. 600 = $958.– Saddle Cost in 5 years = Saddle Cost in 5 years = (1.016)(1.016)55 350 = $378. 350 = $378.– Total Cost in 5 years = Total Cost in 5 years = $958 + $378 = $1,336.$958 + $378 = $1,336.

PW of PW of $1,336$1,336 needed in 5 years: needed in 5 years: 1336/(1.04)1336/(1.04)55 = $1,098 = $1,098 today!!! today!!!

Conclusion:Conclusion: You need to put You need to put $1,098$1,098 into your passbook savings today. Note the cost to buy into your passbook savings today. Note the cost to buy a pony with saddle today is a pony with saddle today is $950$950. Your passbook savings account is not keeping up . Your passbook savings account is not keeping up with “pony-inflation.”with “pony-inflation.”

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Composite Cost IndexesComposite Cost Indexes

GeneralizationGeneralization:: 1) Use commodity indexes to measure past price changes for both commodities.1) Use commodity indexes to measure past price changes for both commodities. 2) Inquire to find out current costs.2) Inquire to find out current costs. 3) Use the geometric average price increase values for each commodity to estimate their 3) Use the geometric average price increase values for each commodity to estimate their

future cost.future cost. 4) Calculate how much you need to invest today to cover these future costs.4) Calculate how much you need to invest today to cover these future costs.

The CPI measures the effects of prices as experienced by consumers in the US The CPI measures the effects of prices as experienced by consumers in the US marketplace.marketplace.– It tracks the cost of a standard bundle of consumer goods from year-to-year. This It tracks the cost of a standard bundle of consumer goods from year-to-year. This

bundle includes housing, clothing, food, transportation, entertainment, and others.bundle includes housing, clothing, food, transportation, entertainment, and others.– People often use the CPI as a substitute measure for general inflation in the People often use the CPI as a substitute measure for general inflation in the

economy.economy.

The PPI measures prices as felt by producers of goods.The PPI measures prices as felt by producers of goods.

Composite indexes can be used in much the same way as commodity-specific Composite indexes can be used in much the same way as commodity-specific indexes. indexes. – Use a commodity-specific indexes if terms are tracked this wayUse a commodity-specific indexes if terms are tracked this way– If no commodity-specific indexes are kept, use an appropriate composite index that If no commodity-specific indexes are kept, use an appropriate composite index that

tracks this quantity. If such an index does not exist, use a specific index for a very tracks this quantity. If such an index does not exist, use a specific index for a very closely related commodity.closely related commodity.

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Inflation Effect on After-Tax Inflation Effect on After-Tax CalculationCalculation

Example:Example:A A $12,000$12,000 investment will return annual benefits for investment will return annual benefits for six yearssix years, with no salvage value after six , with no salvage value after six

years. years.

Assume straight line depreciation and a 46% income tax rate. Assume straight line depreciation and a 46% income tax rate.

The problem is to be solved for both before and after-tax rates of return for the following two The problem is to be solved for both before and after-tax rates of return for the following two cases: cases:

Option A: Option A: No inflationNo inflation. The annual benefits are constant at $2918/year.. The annual benefits are constant at $2918/year. Option B: Option B: Inflation of 5%:Inflation of 5%: The benefits from the investment increase at the same rate. The benefits from the investment increase at the same rate.

They continue to be the equivalent of $2918 in Year-0 based dollars.They continue to be the equivalent of $2918 in Year-0 based dollars.

YearYearAnn. Benefit for both Ann. Benefit for both situations, in year-0 situations, in year-0

based dollarsbased dollars

No Inflation,No Inflation,

A$ received A$ received

= R$ received = R$ received

5% inflation, A$ received 5% inflation, A$ received

(multiply $2918 by (1.05)(multiply $2918 by (1.05) jj,,

i.e. inflate R$ 2918)i.e. inflate R$ 2918)

11 $2918$2918 $2918$2918 $3064$3064

22 29182918 29182918 32173217

33 29182918 29182918 33783378

44 29182918 29182918 35473547

55 29182918 29182918 37243724

66 29182918 29182918 39103910

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Before-tax ROR.Before-tax ROR.CFS (-12000,2918, 2918, …, 2918) for CFS (-12000,2918, 2918, …, 2918) for option A has ROR = 11.99%.option A has ROR = 11.99%.

For option B, first convert the CFS (-12000,3064, 3217, …., 3910) into For option B, first convert the CFS (-12000,3064, 3217, …., 3910) into today’s constant dollars, which just gives (-12000,2918, 2918, …., today’s constant dollars, which just gives (-12000,2918, 2918, …., 2918). 2918).

Thus, its Thus, its ROR for option B is also 11.99%.ROR for option B is also 11.99%.

After-Tax ROR (Option A – No Inflation):After-Tax ROR (Option A – No Inflation):

YearYear BTCFBTCF SL Depr.SL Depr. Taxab. Inc. Taxab. Inc. 46% Inc. Tax46% Inc. Tax ATCF ATCF

00 -$12000-$12000 -$12000-$12000

11 $2918$2918 $2000$2000 $918$918 -$422-$422 24962496

22 29182918 20002000 918918 -422-422 24962496

33 29182918 20002000 918918 -422-422 24962496

44 29182918 20002000 918918 -422-422 24962496

55 29182918 20002000 918918 -422-422 24962496

66 29182918 20002000 918918 -422-422 24962496

The ROR of after-tax CFS in the last column is 6.72%

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After-tax ROR (Option B – 5% inflation)After-tax ROR (Option B – 5% inflation)We first find the after-tax CFS in A$. We first find the after-tax CFS in A$. Then we convert this CFS to one with Year-0 based dollarsThen we convert this CFS to one with Year-0 based dollars..

The R$ CFS has a The R$ CFS has a ROR of about 4.93%.ROR of about 4.93%.

Key pointKey point: ROR or IRR is calculated in R$ or Year-0 A$.: ROR or IRR is calculated in R$ or Year-0 A$.

YearYearBTCFBTCF

A$A$SL Depr.SL Depr.

A$A$Taxab. Inc Taxab. Inc

A$A$

46% Inc. 46% Inc. TaxTax

A$A$

ATCFATCF

A$A$Convr. Convr. Fact.Fact.

ATCFATCF

R$R$

00 -$12000-$12000 -$12000-$12000 -$12000-$12000

11 $3064$3064 $2000$2000 $1064$1064 -$489-$489 25752575 /(1.05)/(1.05)11 24522452

22 32173217 20002000 12171217 -560-560 26572657 /(1.05) /(1.05) 22 24102410

33 33783378 20002000 13781378 -634-634 27442744 /(1.05) /(1.05) 33 23702370

44 35473547 20002000 15461546 -712-712 28352835 /(1.05) /(1.05) 44 23322332

55 37243724 20002000 17241724 -793-793 29312931 /(1.05) /(1.05) 55 22972297

66 39103910 20002000 19101910 -879-879 30313031 /(1.05) /(1.05) 66 22622262

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Inflation Effect on After-Tax CalculationInflation Effect on After-Tax Calculation

Important ObservationsImportant Observations:: The The before-tax ROR for both situations is the samebefore-tax ROR for both situations is the same. .

We expect this, because the benefits in the inflation situation increased in proportion to inflation.We expect this, because the benefits in the inflation situation increased in proportion to inflation.

Regardless of how future benefits fluctuate with changes in inflation (or deflation), the effects do Regardless of how future benefits fluctuate with changes in inflation (or deflation), the effects do not alter the Year-0 based dollars estimate.not alter the Year-0 based dollars estimate.

The after-tax ROR does depend on the situation. While benefits increase with inflation, The after-tax ROR does depend on the situation. While benefits increase with inflation, the the depreciation schedule does notdepreciation schedule does not. . – The inflation results in increased taxable income and, larger income tax payments;The inflation results in increased taxable income and, larger income tax payments;– but there are not sufficient increases in benefits to offset these extra disbursements. but there are not sufficient increases in benefits to offset these extra disbursements.

While the after-tax CFS in actual dollars increases, it is not enough to offset both inflation and While the after-tax CFS in actual dollars increases, it is not enough to offset both inflation and increased income taxes.increased income taxes.

NoteNote: inflation could cause equipment to have a salvage value that was not forecast, or a larger one : inflation could cause equipment to have a salvage value that was not forecast, or a larger one than had been projected. This effect would reduce the unfavorable consequences of inflation on the than had been projected. This effect would reduce the unfavorable consequences of inflation on the after-tax ROR.after-tax ROR.

SituationSituation ROR`s before taxesROR`s before taxes ROR`s after taxesROR`s after taxes

A) No A) No inflationinflation 11.99%11.99% 6.72%6.72%

B) 5% B) 5% inflationinflation 11.99%11.99% 4.93%4.93%

Documents

EGGC4214 Systems Engineering & Economy Lecture 10 Inflation & Price Changes