INDR 202

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ENGINEERING ECONOMICS

CHAPTER 4 INFLATION

SPRING 2015

INSTRUCTOR: BORA ÇEKYAY

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INFLATION

2

Measure of Inflation

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INFLATION

3

Investment opportunity

INFLATION

DEFLATION

VALUE OF MONEY

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EXAMPLE 1: PRICE OF BREAD

4

2006: 35 Kuruş

2010: 60 Kuruş

2006

100 TL

2006 2010

100 TL = 58.33 TL (2006)=(100/285.7)*166.7

100 TL could buy 285.7

loaves in 2006. 100 TL could buy 166.7 loaves in 2010.

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EXAMPLE 2: PRICE OF GASOLINE

5

2000: $1.52/gallon

2013: $3.58/gallon

2000 $100

2000 2013

$100 = $42.46 (2000)

$100 could buy 65.79

gallons in 2000. $100 could buy 27.93 gallons in 2013.

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EXAMPLE 3: PRICE OF MILK

6

Last year: $1.57/liter

Now: $1.25/liter

-1

$100

-1 0

$100 = $125.60 (-1)

$100 could buy 63.69

liters a year ago. $100 can now buy 80 liters.

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PRICE INDICES

7 PRODUCER PRICE INDEX (PPI)

industrial price change (e.g., raw materials, finished products, operating costs)

CONSUMER PRICE INDEX (CPI)

price change for goods & services in major expenditure groups (e.g., food, housing, medical care) typically

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CONSUMER PRICE INDEX (CPI)

8

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MARKET BASKET: CONTENT & WEIGHTS

9

Food & Beverages (breakfast cereal, milk, chicken, wine) Housing (rent, furniture)

Apparel (men's shirts, women's dresses, jewelry)

Transportation (new vehicles, airline fares, gasoline) Medical Care (prescription drugs, hospital services)

Recreation (televisions, pets, sports equipment)

Education & Communication (college tuition, telephone) Other (smoking products, haircuts, funeral expenses)

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CONSUMER PRICE INDEX (CPI)

11

MARKET BASKET

Base Period = 1967

2011

$100

$669.41

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CONSUMER PRICE INDEX (CPI)

12

MARKET BASKET

Base Period =

2003

2008

2013

100 TL

154.66 TL

222.33 TL

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INFLATION RATE

13 AVERAGE INFLATION RATE _𝒇

single rate that accounts for the effect of varying yearly inflation rates over a period of several years

GENERAL INFLATION RATE _𝒇"

average inflation rate based on CPI for all items in market basket

SPECIFIC INFLATION RATE

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AVERAGE INFLATION RATE

14

YEAR 0

BASE PRICE

YEAR 1 PRICE

YEAR 2 PRICE

YEAR 1

4% INFLATION 8% INFLATIONYEAR 2

Actual inflated price at the end of year 2

$1 1 + 0.04 1 + 0.08 = $1.1232

Average inflation rate

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AVERAGE INFLATION RATE

15

$1

$1.1232

0 1

2

4% 8%

$1

$1.1232

0 1

2

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Example 11.1 Average Inflation Rate

Sample Calculation for Average Inflation rate

for Gasoline:

Given: P = 127.3, F =

175.3, N = 2009-‐2000 = 9.

Find: f

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EXAMPLE 5: AVERAGE INFLATION RATE

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Item 2011 Price 2000 Price Average

Inflation Rate Consumer Price Index (CPI)

(Base period: 82-84) $223.47 $171.20 2.45%

Postage $0.44 $0.33 2.65%

Homeowners Insurance $674 $500 2.75%

Private College Tuition, Fees $27,293 $15,518 5.27%

Gasoline (per gallon) $3.64 $1.56 8.01%

Haircut $21.00 $10.50 6.50%

Car (Toyota Camry) $22,590 $21,000 0.67%

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GENERAL INFLATION RATE

18

𝑓̅

general inflation rate

CPI

₇

CPI at the end of period

𝑛

CPI

₉

CPI at the base period

CPI

₇

= CPI

₉

1 + 𝑓̅

7

𝑓̅ =

CPI

7

CPI

₉

:/7

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ANNUAL GENERAL INFLATION RATE

19

𝑓̅

₇

general inflation rate in period

𝑛

CPI

₇

CPI at the end of period

𝑛

CPI

_7=:

CPI at the end of period

𝑛 − 1

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EXAMPLE 6: UTILITY COMPANY

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A utility company’s cost of supplying a fixed amount of power to a housing development Year Cost 0 $504,000 1 $538,400 2 $577,000 3 $629,500

𝑓̅_: = $538,400 − $504,000

$504,000 = 6.83%

𝑓̅_. = $577,000 − $538,400

$538,400 = 7.17%

𝑓̅_A = $629,500 − $577,000

$577,000 = 9.1%

𝑓̅ = $629,500 $504,000

:/A

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ACTUAL VS. CONSTANT DOLLARS

21

Actual Dollars (

_𝐴

₇

)

Ø estimates of future cash flows for year 𝑛 that take into

account any anticipated changes in amount caused by inflationary & deflationary effects

Ø amount of money paid or received regardless of how

much it is worth

Constant Dollars (

_𝐴

C₇

)

Ø estimates of future cash flows for year _𝑛 in constant

purchasing power independent of the passage of time

Ø measure of worth with respect to base period

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EXAMPLE 7: ACTUAL & CONSTANT DOLLARS

22

CONSTANT DOLLARS

$1,000

3

ACTUAL

DOLLARS $1,260

3

𝑛 = 3, 𝑓̅ = 8%

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EXAMPLE 7: ACTUAL & CONSTANT DOLLARS

23

𝑛 = 3, 𝑓̅ = 8%

$1,260 1 + 0.08

=A

= $1,000

CONSTANT DOLLARS

$1,000

3

ACTUAL

DOLLARS $1,260

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EXAMPLE 8: MANUFACTURING

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Year _SalesUnit Net Cash Flows (constant $)

0 -250,000

1 1,000 100,000

2 1,100 110,000

3 1,200 120,000

4 1,300 130,000

5 1,200 120,000

Traffic-signal switching boxes Current price: $550

Manufacturing cost: $450

Start-up investment: $250,000

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EXAMPLE 8: MANUFACTURING

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Year Net Cash Flow _{in Constant $} Conversion _Factor Net Cash Flow _{in Actual $}

0 -$250,000 (1+0.05)0 -$250,000

1 $100,000 (1+0.05)1 $105,000

2 $110,000 (1+0.05)2 $121,275

3 $120,000 (1+0.05)3 $138,915

4 $130,000 (1+0.05)4 $158,016

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EXAMPLE 8: MANUFACTURING

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EXAMPLE 9: LAND LEASE

$20,000 (in actual dollars) to be paid at the beginning of each year for 5 years

General inflation rate 5% End of

Year in Actual $Cash Flow Conversion Factor Cash Flow in Constant $ Purchasing PowerPercent Loss in

0 $20,000 (1+0.05)0 $20,000 0

1 $20,000 (1+0.05)-1 $19,048 4.76

2 $20,000 (1+0.05)-2 $18,141 9.30

3 $20,000 (1+0.05)-3 $17,277 13.62

4 $20,000 (1+0.05)-4 $16,454 17.73

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EQUIVALENCE CALCULATIONS

28 TYPES OF INTEREST RATES

§ Market Interest Rate

§ Inflation-Free Interest Rate

TYPES OF CASH FLOWS § Constant Dollars

§ Actual Dollars § Mixed

TYPES OF ANALYSIS METHODS § Constant-Dollar Analysis

§ Actual-Dollar Analysis (Deflation &

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INTEREST RATES

29

Market interest rate

_𝑖

(

inflation-adjusted

or

nominal

interest rate) combines the effects of the

earning power & any anticipated changes in

purchasing power.

Inflation-free interest rate

_𝑖

C

(

real

interest rate)

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ANALYSIS METHODS

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Constant-dollar analysis

estimates all future cash

flows in constant dollars.

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When do we Prefer Constant Dollar Analysis?



In the absence of inflation, all economic analyses up

to this point is, in fact, the constant dollar analysis.



In constant dollar analysis, we should use the

inflation-‐free interest rate

𝒊′

.



Constant dollar analysis is common in the evaluation

of many long-‐term public projects, because

governments do not pay income taxes.



For private sector, income taxes are levied based on

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EXAMPLE 10: MASTERS TOURNAMENT

32

Year Champion Winner’s Share

1934 Horton Smith $1,500

1962 Arnold Palmer $20,000 1975 Jack Nicklaus $40,000

1997 Tiger Woods $486,000

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EXAMPLE 10: MASTERS TOURNAMENT

33

1962 90.42

2013

697.48

1967 100

CONSUMER PRICE INDEX

Average Inflation Rate

𝑓̅ = 697.48 90.42

:/J:

− 1 = 4.09%

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EXAMPLE 10: MASTERS TOURNAMENT

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If Arnold Palmer invested his prize in 1962 at inflation- free interest rate 4.477%,

$20,000 𝐹|𝑃, 4.477%, 51 = $186,675

Adam Scott’s prize in constant dollars w.r.t. 1962:

$1.44𝑀 𝑃|𝐹, 4.09%, 51 = $186,679

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ACTUAL-DOLLAR ANALYSIS

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Deflation Method

STEP 1: Convert all cash flows to constant dollars

(i.e., eliminate purchasing power discrepancy).

STEP 2: Incorporate the earning power. (inflation-

free interest rate)

Adjusted-Discount Method

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36

EXAMPLE 11: DEFLATION METHOD

𝑛 Cash Flows in _{Actual Dollars}

0 -$75,000 1 $32,000 2 $35,700 3 $32,800 4 $29,000 5 $58,000

General inflation rate 5%

Deflation Factor _{Constant Dollars}Cash Flows in

1 -$75,000

(1+0.05)-1 $30,476

(1+0.05)-2 $32,381

(1+0.05)-3 $28,334

(1+0.05)-4 $23,858

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EXAMPLE 11: DEFLATION METHOD

𝑛 _{Constant Dollars}Cash Flows in

0 -$75.000 1 $30,476 2 $32,381 3 $28,334 4 $23,858 5 $45,445

Inflation-free interest rate 10%

$45,268

Discount Factor _{Present Worth}Equivalent

1 -$75,000

(1+0.10)-1 $27,706

(1+0.10)-2 $26,761

(1+0.10)-3 $21,288

(1+0.10)-4 $16,295

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EXAMPLE 11: DEFLATION METHOD

$32,000

-$75,000 $35,700 $32,800 $29,000 $58,000

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

Actual Dollars

$30,476

-$75,000 $32,381 $28,334 $23,858 $45,455

Constant Dollars

$27,706

-$75,000 $26,761 $21,288 $16,295 $28,218

Present Worth

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ADJUSTED-DISCOUNT METHOD

𝑃

₇

=

𝐴

7

1 + 𝑓̅

7

1 + 𝑖

C 7

=

𝐴

₇

1 + 𝑖

7

Market Interest Rate

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EXAMPLE 11: ADJUSTED-DISCOUNT METHOD

𝑛 Cash Flows in _{Actual Dollars}

0 -$75,000 1 $32,000 2 $35,700 3 $32,800 4 $29,000 5 $58,000

Market interest rate

𝑖 = 1 + 0. 05 1 + 0.10 − 1 = 15.5%

$45,268

Conversion

Factor Present WorthEquivalent

1 -$75,000

(1+0.155)-1 $27,706

(1+0.155)-2 $26,761

(1+0.155)-3 $21,288

(1+0.155)-4 $16,295

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EXAMPLE 11: ADJUSTED-DISCOUNT METHOD

0

1 2 3 4 5

= $32,000 ( P |F , 15.5% , 1)

= $35,700 ( P|F , 15.5% , 2) = $32,800 ( P |F , 15.5% , 3)

= $29,000 ( P|F , 15.5% , 4)

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EXAMPLE 11: ADJUSTED-DISCOUNT METHOD

$32,000

-$75,000 $35,700 $32,800 $29,000 $58,000

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

Actual Dollars

$27,706

-$75,000 $26,761 $21,288 $16,295 $28,218

Present Worth

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MARKET INTEREST RATE

DISCRETE COMPOUNDING

𝑖 = 𝑖

C

+ 𝑓̅ + 𝑖

C

𝑓̅

CONTINUOUS COMPOUNDING

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EXAMPLE 12: COLLEGE FUND

The parents of a 5-year old child make equal quarterly deposits into a college fund, starting at the end of 1st quarter until the child is 17.

The fund earns 8% interest compounded quarterly. The child will start college at the age of 18.

College expenses are estimated to be $30,000 per year (in today’s dollars).

College expenses will be paid at the beginning of every year for 4 years.

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EXAMPLE 12: COLLEGE FUND

STEP 1: Convert all cash flows in constant $s to actual $s.

General inflation rate 6%

Age College Expenses (in constant $s)

18 $30,000

19 $30,000

20 $30,000

21 $30,000

Inflation Factor College Expenses (in actual $s)

(1+0.06)13 $63,988

(1+0.06)14 $67,827

(1+0.06)15 $71,897

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EXAMPLE 12: COLLEGE FUND

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EXAMPLE 12: COLLEGE FUND

STEP 2: Use market interest rate to find present value.

𝑉_. = $63,988 𝑃|𝐹, 2%, 4 + $67, 827 𝑃|𝐹, 2%, 8

+$71,897 𝑃|𝐹, 2%, 12 + $76,211 𝑃|𝐹, 2%, 16 = $229,211

𝑉_: = 𝐶 𝐹|𝐴, 2%, 48 = 79.3535𝐶 𝑉_: = 𝑉_.

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SUMMARY

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Consumer Price Index (CPI) measures the change, over time, in prices of goods & services in major expenditure groups.

Inflation describes a decline in purchasing power evidenced by increasing prices.

Deflation describes an increase in purchasing power evidenced by decreasing prices.

General Inflation Rate _𝑓̅ is an average inflation rate based on CPI. Annual general inflation rate _𝑓̅₇ in year _𝑛 is:

𝑓̅₇ = CPI7 − CPI7=:

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SUMMARY

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Price changes for specific, individual commodities are not always at general inflation rate. An average inflation rate

can be computed for a specific commodity based on an index (i.e., record of historical costs) for that commodity.

Cash flows may be given in actual dollars (reflecting inflation/deflation rates) or in constant dollars (reflecting purchasing power in base period).

Interest rates may be given as market interest rates

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SUMMARY

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Present worth of actual dollars can be calculated with:

Ø Deflation Method

STEP 1: Convert actual dollars to constant dollars by deflating with general inflation rate.

STEP 2: Calculate the present worth of constant dollars by discounting at inflation-free interest rate.

Ø Adjusted-Discount Method

STEP 1: Calculate the market interest rate.