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(c) 2001 Contemporary EngineeringEconomics

1

Chapter 13

Inflation and Its Impact on Project

Cash Flows

Meaning and Measureof Inflation

EquivalenceCalculations underInflation

Effects of Inflation onProject Cash Flows

Rate of Return Analysisunder Inflation

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2

Inflation and Economic Analysis

What is inflation?

How do we measure inflation?

How do we incorporate the effect of inflationin economic analysis?

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3

What is Inflation?

Value of Money

Earning Power

Purchasing Power

Earning Power

Purchasing power

Investment Opportunity

Decrease in purchasing power (inflation)

Increase in purchasing Power (deflation)

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4

Purchasing Power

1990

$100

1990 2001

$100

You could buy 50 Big Macsin year 1990.

You can only buy 40 BigMacs in year 2001.

$2.00 / unit $2.50 / unit25%

Price change

due toinflation

The $100 in year 2001 has only $80

worth purchasing power of 1990

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5

-2 -1 0 1

$100

-2 -1 0 1

$100

You could purchase63.69 gallons of

unleaded gasoline

a year ago.

You can now purchase80 gallons of unleaded

gas.

$1.57 / gallon $1.25 / gallon

Price change due to

deflation

20.38%

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6

Price Increase Due to Inflation

Item 1967 Price 2000 Price % Increase

Consumer price index (CPI) 100 512.9 413

Monthly housing expense $114.31 $943.97 726

Monthly automobile expense 82.69 471.38 470

Loaf of bread .22 1.84 736

Pound of hamburger .39 2.98 564

Pound of coffee .59 4.10 595

Candy bar .10 0.90 800Mens dress shirt 5.00 39.00 680

Postage (first-class) 0.05 0.33 660

Annual public college tuition 294.00 3,960.00 1,247

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7

Inflation Terminology - I

Producer Price Index: a statistical measure of industrial pricechange, compiled monthly by the BLS, U.S. Department of Labor

Consumer Price Index: a statistical measure of change, overtime, of the prices of goods and services in major expendituregroupssuch as food, housing, apparel, transportation, and medicalcaretypically purchased by urban consumers

Average Inflation Rate (f): a single rate that accounts for theeffect of varying yearly inflation rates over a period of several years.

General Inflation Rate ( ): the average inflation ratecalculated based on the CPI for all items in the market basket.

f_

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8

Measuring Inflation

Consumer Price Index (CPI): the CPIcompares the cost of a sample market basket of

goods and services in a specific period relative to

the cost of the same market basket in an earlier

reference period. This reference period is designatedas the base period.

Market basket

Base Period (1967) 2001$100 $512.9

CPI for 2001 = 512.9

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9

Selected Price Indexes

Year

Base Period

New CPI

1982-84

Old CPI

1967

Gasoline

1982

Steel

1982

Passenger Car

1982

1991 135.2 405.1 66.9 110.6 124.2

1992 139.5 417.9 65.6 107.1 127.3

1993 144.0 461.2 67.9 106.7 129.8

1994 147.4 441.4 59.5 111.9 133.3

1995 152.2 455.0 67.7 121.7 134.0

1996 156.6 468.2 76.4 114.9 135.2

1997 160.2 479.7 72.7 116.4 135.21998 162.5 487.1 54.0 115.4 132.2

1999 166.2 497.8 64.4 105.3 121.4

2000 171.2 512.9 92.6 109.8 133.4

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10

Average Inflation Rate (f)Fact:

Base Price = $100 (year 0)Inflation rate (year 1) = 4%

Inflation rate (year 2) = 8%

Average inflation rate over 2 years?

Step 1: Find the actual inflated price at the end of year 2.$100 ( 1 + 0.04) ( 1 + 0.08) = $112.32

Step 2: Find the average inflation rate by solving thefollowing equivalence equation.

$100 ( 1+f) = $112.32

f= 5.98%

2

$100

$112.32

0 1

2

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11

Average Inflation Rate

Item1967 Price 2000 Price Average Inflation

Rate

Consumer price index (CPI) 100 512.9 5.07%

Monthly housing expense $114.31 $943.97 6.61

Monthly automobile expense 82.69 471.38 5.42

Loaf of bread 0.22 1.84 6.64

Pound of hamburger 0.39 2.98 6.36

Pound of coffee 0.59 4.10 6.05

Candy bar 0.10 0.90 6.88Mens dress shirt 5.00 39.00 6.42

Postage (first-class) 0.05 0.33 5.89

Annual public college tuition 294.00 3,960.00 8.19

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13

Example 13.2: Yearly and Average Inflation Rates

Year Cost

0 $504,000

1 538,000

2 577,000

3 629,500

What are the annual inflation rates

and the average inflation rate over 3 years?

Solution

Inflation rate during year 1 (f1):

($538,400 - $504,000) / $504,000 = 6.83%.

Inflation rate during year 2 (f2):

($577,000 - $538,400) / $538,400 = 7.17 %.

Inflation rate during year 3 (f3):($629,500 - $577,000) / $577,000 = 9.10%.

The average inflation rate over 3 years is

f ($629,

$504,) . ./

500

0001 0 0769 7 69%1 3

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15

Conversion

from Constant to Actual Dollars

A A f A F P f nn nn

n' ( ) ' ( / , , )_ _

1

$1,000 (1 + 0.08)

= $1,260

3

Constant

Dollars

n

f

3

8%_

$1,000

3Actual

Dollars

$1,260

3

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16

Conversion from Constant to Actual

Dollars

Period Net Cash Flow in

Constant $

Conversion

Factor

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

5 120,000 (1+0.05)5 153,154

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17

0

1 2 3 4 5

0

1 2 3 4 5

$250,000

$105,000$121,275

$138,915 $158,016

$153,154

Years

(b) Actual dollars

$250,000

$100,000$110,000

$120,000 $130,000

$120,000

Years

(a) Constant dollars

$250,0

00(1+0.0

5)0

$100,000(1+0.0

5)

$110,0

00(1+0.0

5)2

$120,0

00

(1+0.0

5)3

$130,0

00(1+0.0

5)4

$120

,000(1+0.0

5)5

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18

Conversion

from Actual to Constant Dollars

A A f A P F f nn nn

n' ( ) ( / , , )_ _

1

Constant

Dollars $1,260 (1 + 0.08)= $1,000

-3

n

f

3

8%_

$1,000

3Actual

Dollars

$1,260

3

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19

Conversion from Actual to Constant

Dollars

End of

period

Cash Flow

in Actual $

Conversion

atf = 5%

Cash Flow in

Constant $

Loss in

Purchasing

Power

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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20

Equivalence Calculation Under Inflation

1. Types of Interest Rate

2. Types of Cash Flow

3. Types of Analysis Method

Market Interest rate (i)

Inflation-free interest rate (i)

In Constant DollarsIn Actual Dollars

Constant Dollar AnalysisActual Dollar Analysis

Deflation Method

Adjusted-discount method

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21

Inflation Terminology - III

Inflation-free Interest Rate (i): an estimate of thetrue earning power of money when the inflation

effects have been removed (also known as realinterest rate).

Market interest rate (i): interest rate which takes

into account the combined effects of the earningvalue of capital and any anticipated changes inpurchasing power (also known as inflation-adjusted interest rate).

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22

Inflation and Cash Flow Analysis

Constant Dollar analysis

- Estimate all future cash flows in constant dollars.

- Use i as an interest rate to find equivalent worth.

Actual Dollar Analysis

- Estimate all future cash flows in actual dollars.

- Use i as an interest rate to find equivalent worth.

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23

Constant Dollar Analysis

In the absence of inflation, all economic analyses

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

Constant dollar analysis is common in theevaluation of many long-termpublic projects,

because government do no pay income taxes.

For private sector, income taxes are levied based

on taxable income in actual dollars, actual dollar

analysis is more common.

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24

Actual Dollars Analysis

Method 1: Deflation Method

- Step 1: Bring all cash flows to have

common purchasing power.

- Step 2: Consider the earning power.

Method 2: Adjusted-discount Method

- Combine Steps 1 and 2 into one step.

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25

Step 1:

Convert actual dollars to Constant

dollars

n Cash Flows in Actual

Dollars

Multiplied by

Deflation

Factor

Cash Flows in

Constant Dollars

0 -$75,000 1 -$75.000

1 32,000 (1+0.05)-1 30,476

2 35,700 (1+0.05)-2 32,381

3 32,800 (1+0.05)-3 28,334

4 29,000 (1+0.05)-4 23,858

5 58,000 (1+0.05)-5 45,445

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(c) 2001 Contemporary EngineeringEconomics 26

Step 2:

Convert Constant dollars to Equivalent

Present Worthn Cash Flows in

Constant Dollars

Multiplied by

Discounting Factor

Equivalent

Present Worth

0 -$75,000 1 -$75,000

1 30,476 (1+0.05)-1 27,706

2 32,381 (1+0.05)-2 26,761

3 28,334 (1+0.05)-3 21,288

4 23,858 (1+0.05)-4

16,2955 45,445 (1+0.05)-5 28,218

$45,268

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Deflation Method (Example 13.6):Converting actual dollars to constant dollars and then to

equivalent present worth

-$75,000 $30,476 $32,381 $28,334 $23,858 $45,455

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

-$75,000

$27,706$26,761 $21,288

$16,295

$28,218

$45,268

Actual

Dollars

Constant

Dollars

Present

Worth

n = 0 n = 1 n = 2 n = 3 n = 4 n = 5

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Adjusted-Discount Method

PA

i

A

i

A

f i

i i i

i f i f

nn

n

n

n

n

n n

( )

( ) ( ) ( ' )

( ) ( )( ' )

' '

1

1 1 1

1 1 1

1

P

A

f

in

n

n

n

( )

( ' )

1

1

A

f i

n

n n( ) ( ' )1 1

A

f i

n

n n( ) ( ' )1 1 i i f i f ' '

Step 1

Step 2

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Adjusted-Discounted Method

n Cash Flows in Actual

Dollars

Multiplied

by

Equivalent

Present Worth

0 -$75,000 1 -$75,000

1 32,000 (1+0.155)-1 27,706

2 35,700 (1+0.155)-2 26,761

3 32,800 (1+0.155)-3 21,288

4 29,000 (1+0.155)-4 16,296

5 58,000 (1+0.155)-5 28,217

$45,268

i i f i f ' '

. . ( . )( . )

.

0 10 0 05 0 10 0 05

15 5%

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Adjusted-discount method

0

1 2 3 4 5

- $75,000

$27,706

$26,761

$21,288$16,295

$28,218

$45,268

$32,000$35,700

$32,800$29,000

$58,000

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Adjusted Discount Method: Example 13.7Converting actual dollars to present worth dollars by

applying the market interest rate

n = 0 n = 1 n = 2 n = 3 n = 4 n = 5

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

Actual

Dollars

-$75,000

$27,706$26,761 $21,288

$16,295

$28,218

$45,268

Present

Worth

%5.15fifii

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Equivalence Calculation with Composite

Cash Flow Elements

Age College expenses

(in todays dollars)

College expenses

(in actual dollars)

18 (Freshman) $30,000 $30,000(F/P,6%,13) = $63,988

19 (Sophomore) 30,000 30,000(F/P,6%,14) = 67,827

20 (Junior) 30,000 30,000(F/P,6%,15) = 71,897

21 (senior) 30,000 30,000(F/P,6%,16) = 76,211

Approach: Convert any cash flow elements in constant dollars into

actual dollars. Then use the market interest rate to find the

equivalent present value.

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V1 = C(F/A, 2%, 48)

V2 = $229,211

Let V1 = V2 and solveforC:

C= $2,888.48

Required Quarterly Contributions to College Funds

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Effects of Inflation on Project Cash

Flows

Item Effects of Inflation

Depreciation

expense

Depreciation expense is

charged to taxable income indollars ofdeclining values;

taxable income is overstated,

resulting in higher taxes

Note: Depreciation expenses are based on historical costs and

always expressed in actual dollars

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Salvage value Inflated salvage value

combined with book valuesbased on historical costs

results in higher taxable gains.

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Loan repayments Borrowers repay historical

loan amounts with dollars ofdecreased purchasing power,

reducing the debt-financing

cost.

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Working capital

requirement

Known as working capital

drain, the cost of workingcapital increases in an

inflationary environment.

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Rate of Return

and NPW

Unless revenues are

sufficiently increased to keeppace with inflation, tax effects

and/or a working capital drain

result in lower rate of return or

lower NPW.

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Excel Example of an after-tax cash flow analysis

including differential inflation (Example 13.14)

INPUT: O&M Cost 13000 General Inflation rate 0.05Salvage 1000 Inflation-free interest 0.2

Contract $ 23500 Market interest rate 0.26

Investment 15000 Income tax rate 0.4

Income Statement 0 1 2 3 4 5

Inflation rate

Revenues $23,500 $23,500 $23,500 $23,500 $23,500

Expenses:

O&M 8% $14,040 $15,163 $16,376 $17,686 $19,101

Depreciation $3,000 $4,800 $2,880 $1,728 $864

Taxable Income $6,460 $3,537 $4,244 $4,086 $3,535Income taxes (40%) $2,584 $1,415 $1,697 $1,634 $1,414

Net Income $3,876 $2,122 $2,546 $2,451 $2,121

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Cash Flow Statement 0 1 2 3 4 5

Inflation rate

Operating Activities:

Net Income $2,122 $2,546 $2,451 $2,121

Depreciation $3,876 $4,800 $2,880 $1,728 $864

Investment Activities: $3,000

Investment $15,000

Salvage 5% $1,276

Gains Tax $181

Net cash flow (actual$) $15,000 $6,876 $6,922 $5,426 $4,179 $4,442

Net cash flow (constant $) $15,000 $6,549 $6,279 $4,687 $3,438 $3,480Equ. Present worth $15,000 $5,457 $4,360 $2,713 $1,658 $1,399

Net present worth $587

$3,876

$3,000

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Rate of Return Analysis under Inflation

Principle:True (real) rate of

return should be based on

constant dollars.

If the rate of return is

computed based on actual

dollars, the real rate of

return can be calculated as:

n

Net cash

flows in

actual

dollars

Net cash

flows in

constant

dollars

01

2

3

4

-$30,00013,570

15,860

13,358

13,626

-$30,00012,336

13,108

10,036

9,307

IRR 31.34% 19.40%i

i

f'

.

.

.40%

_

1

1 1

1 0 3134

1 0 101

19Not correct IRR

f_

10%

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Summary

The Consumer Price Index (CPI) is a statisticalmeasure of change, over time, of the prices ofgoods and services in major expenditure groupssuch as food, housing, apparel, transportation, and

medical caretypically purchased by urbanconsumers.

Inflation is the term used to describe a decline inpurchasing power evidenced in an economic

environment of rising prices. Deflation is the opposite: An increase in

purchasing power evidenced by falling prices.

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The general inflation rate (f) is an averageinflation rate based on the CPI. An annual general

inflation rate ( ) can be calculated using thefollowing equation:

Specific, individual commodities do not alwaysreflect the general inflation rate in their pricechanges. We can calculate an average inflationrate for a specific commodity (j) if we have anindex (that is, a record of historical costs) for thatcommodity.

f

fCPI CPI

CPIn

n n

n

1

1

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(c) 2001 Contemporary Engineering

Economics

44

Project cash flows may be stated in one of twoforms

Actual dollars (An): Dollars that reflect theinflation or deflation rate.

Constant dollars (An): Year 0 dollars

Interest rates for project evaluation may be statedin one of two forms:

Market interest rate (i): A rate which combinesthe effects of interest and inflation; used with

actual dollar analysisInflation-free interest rate (i): A rate fromwhich the effects of inflation have been removed;this rate is used with constant dollar analysis

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(c) 2001 Contemporary Engineering 45

To calculate the present worth of actual dollars,we can use a two-step or a one-step process:

Deflation methodtwo steps:

1. Convert actual dollars by deflating with thegeneral inflation rate of

2. Calculate the PW of constant dollars bydiscounting at i

Adjusted-discount methodone step

1. Compute the market interest rate.

2. Use the market interest rate directly to find thepresent value.

f

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