(c) 2001 contemporary engineering economics 1 chapter 13 inflation and its impact on project cash...

(c) 2001 Contemporary Engineering Economics

1

Chapter 13Inflation and Its Impact on Project

Cash Flows

• Meaning and Measure of Inflation

• Equivalence Calculations under Inflation

• Effects of Inflation on Project Cash Flows

• Rate of Return Analysis under Inflation


2

Inflation and Economic Analysis

• What is inflation?

• How do we measure inflation?

• How do we incorporate the effect of inflation in economic analysis?


3

What is Inflation?

• Value of Money

• Earning Power

• Purchasing Power

Earning PowerPurchasing power

Investment Opportunity

Decrease in purchasing power (inflation)Increase in purchasing Power (deflation)


4

Purchasing Power

1990

$100

1990 2001

$100

You could buy 50 Big Macs in year 1990.

You can only buy 40 Big Macs in year 2001.

$2.00 / unit $2.50 / unit25% Price change due to inflation

The $100 in year 2001 has only $80 worth purchasing power of 1990


5

-2 -1 0 1

$100

-2 -1 0 1

$100

You could purchase 63.69 gallons of unleaded gasoline a year ago.

You can now purchase 80 gallons of unleaded gas.

$1.57 / gallon $1.25 / gallonPrice change due to

deflation

20.38%


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 0.90 800

Men’s 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


7

Inflation Terminology - I

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

• Consumer Price Index: a statistical measure of change, over time, of the prices of goods and services in major expenditure groups—such as food, housing, apparel, transportation, and medical care—typically purchased by urban consumers

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

• General Inflation Rate ( ): the average inflation rate calculated based on the CPI for all items in the market basket.f

_


8

Measuring Inflation

Consumer Price Index (CPI): the CPI compares 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 designated as the base period.

Market basket

Base Period (1967) 2001

$100 $512.9

CPI for 2001 = 512.9


9

Selected Price IndexesYear

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 72.7 116.4 135.2

1998 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


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 the following equivalence equation.

$100 ( 1+ f) = $112.32f = 5.98%

2

$100

$112.32

0 1

2


11

Average Inflation Rate

Item 1967 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 6.88

Men’s 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


12

General Inflation Rate (f)

Average inflation rate based on the CPI

CPI CPI f

fCPI

CPI

f

CPI n

CPI

nn

nn

n

0

0

1

0

1

1

( ) ,_

_ /

_

where The genreal inflation rate,

The consumer price index at the end period ,

The consumer price index for the base period.


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 ratesand the average inflation rate over 3 years?

SolutionInflation 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


14

Inflation Terminology – II

• Actual Dollars (An ): Estimates of future cash flows for year n that take into account any anticipated changes in amount caused by inflationary or deflationary effects.

• Constant Dollars (An’ ): Estimates of future cash flows for year n in constant purchasing power, independent of the passage of time (or base period).


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

3ConstantDollars

n

f

3

8%_

$1,000

3ActualDollars

$1,260

3


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


17

01 2 3 4 5

01 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

,000

(1+

0.05

)0

$100

,000

(1+

0.05

)

$110

,000

(1+

0.05

)2

$120

,000

(1+

0.05

)3

$130

,000

(1+

0.05

)4

$120

,000

(1+

0.05

)5


18

Conversion from Actual to Constant Dollars

A A f A P F f nn nn

n' ( ) ( / , , )_ _

1

ConstantDollars $1,260 (1 + 0.08)

= $1,000

-3

n

f

3

8%_

$1,000

3ActualDollars

$1,260

3


19

Conversion from Actual to Constant Dollars

End of period

Cash Flow in Actual $

Conversion at f = 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


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 MethodAdjusted-discount method


21

Inflation Terminology - III

• Inflation-free Interest Rate (i’): an estimate of the true earning power of money when the inflation effects have been removed (also known as real interest rate).

• Market interest rate (i): interest rate which takes into account the combined effects of the earning value of capital and any anticipated changes in purchasing power (also known as inflation-adjusted interest rate).


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.


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 the evaluation of many long-term public 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.


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.


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


26

Step 2:Convert Constant dollars to Equivalent

Present Worthn Cash Flows in

Constant DollarsMultiplied by

Discounting FactorEquivalent

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 16,295

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

$45,268


27

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

PresentWorth

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


28

Adjusted-Discount Method

PA

i

A

i

A

f i

i i i

i f i f

nn

n

nn

n

n n

( )

( ) ( ) ( ' )

( ) ( )( ' )

' '

1

1 1 1

1 1 1

1

P

Afin

nn

n

( )( ' )11

A

f in

n n( ) ( ' )1 1

A

f i

n

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

Step 1

Step 2


29

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%


30

Adjusted-discount method

0

1 2 3 4 5

- $75,000$27,706$26,761$21,288$16,295$28,218

$45,268

= $

32,0

00 (

P/F

, 15

.5%

, 1)

= $

35,7

00 (

P/F

, 15

.5%

, 2)

= $

32,8

00 (

P/F

, 15

.5%

, 3)

= $

29,0

0 0 (

P/F

, 15.

5%, 4

)

= $

58,0

00 (

P/F

, 15.

5%, 5

)

$32,000$35,700

$32,800$29,000

$58,000


31

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

PresentWorth

%5.15 fifii


32

Equivalence Calculation with Composite Cash Flow Elements

Age College expenses

(in today’s 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.


33

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

V2 = $229,211

Let V1 = V2 and solvefor C:

C = $2,888.48

Required Quarterly Contributions to College Funds


34

Effects of Inflation on Project Cash Flows

Item Effects of Inflation

Depreciation expense

Depreciation expense is charged to taxable income in dollars of declining values; taxable income is overstated, resulting in higher taxes

Note: Depreciation expenses are based on historical costs andalways expressed in actual dollars


35


Salvage value Inflated salvage value combined with book values based on historical costs results in higher taxable gains.


36


Loan repayments Borrowers repay historical loan amounts with dollars of decreased purchasing power, reducing the debt-financing cost.


37


Working capital requirement

Known as working capital drain, the cost of working capital increases in an inflationary environment.


38


Rate of Return and NPW

Unless revenues are sufficiently increased to keep pace with inflation, tax effects and/or a working capital drain result in lower rate of return or lower NPW.


39

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 0.2Contract $ 23500 Market interest rate 0.26Investment 15000 Income tax rate 0.4

Income Statement 0 1 2 3 4 5Inflation rate

Revenues $23,500 $23,500 $23,500 $23,500 $23,500Expenses:

O&M 8% $14,040 $15,163 $16,376 $17,686 $19,101Depreciation $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 $1,414Net Income $3,876 $2,122 $2,546 $2,451 $2,121


40

Cash Flow Statement 0 1 2 3 4 5Inflation rate

Operating Activities:Net Income $2,122 $2,546 $2,451 $2,121

Depreciation $3,876 $4,800 $2,880 $1,728 $864Investment Activities: $3,000

Investment $15,000Salvage 5% $1,276

Gains Tax $181Net cash flow (actual$) $15,000 $6,876 $6,922 $5,426 $4,179 $4,442Net 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 $1,399Net present worth $587

$3,876$3,000


41

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

0

1

2

3

4

-$30,000

13,570

15,860

13,358

13,626

-$30,000

12,336

13,108

10,036

9,307

IRR 31.34% 19.40%

ii

f'

.

..40%

_

1

11

1 0 3134

1 0 101

19Not correct IRR

f_

10%


42

Summary

• The Consumer Price Index (CPI) is a statistical measure of change, over time, of the prices of goods and services in major expenditure groups—such as food, housing, apparel, transportation, and medical care—typically purchased by urban consumers.

• Inflation is the term used to describe a decline in purchasing power evidenced in an economic environment of rising prices.

• Deflation is the opposite: An increase in purchasing power evidenced by falling prices.


43

• The general inflation rate (f) is an average inflation rate based on the CPI. An annual general inflation rate ( ) can be calculated using the following equation:

• Specific, individual commodities do not always reflect the general inflation rate in their price changes. We can calculate an average inflation rate for a specific commodity (j) if we have an index (that is, a record of historical costs) for that commodity.

f

fCPI CPI

CPInn n

n

1

1


44

• Project cash flows may be stated in one of two forms

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

Constant dollars (A’n): Year 0 dollars• Interest rates for project evaluation may be stated

in one of two forms:Market interest rate (i): A rate which combines the effects of interest and inflation; used with actual dollar analysisInflation-free interest rate (i’): A rate from which the effects of inflation have been removed; this rate is used with constant dollar analysis


45

• To calculate the present worth of actual dollars, we can use a two-step or a one-step process:Deflation method—two steps:1. Convert actual dollars by deflating with the general inflation rate of

2. Calculate the PW of constant dollars by discounting at i’Adjusted-discount method—one step

1. Compute the market interest rate. 2. Use the market interest rate directly to find the

present value.

f

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