1. (c) 2001 Contemporary Engineering Economics 1 Chapter 13 Inflation 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. (c) 2001 Contemporary Engineering Economics 2 Inflation and Economic Analysis What is inflation? A loss in the purchasing power of money over time. The cost of an item tends to increase over time, or the same dollar amount buys less of an item over time. How do we measure inflation? Economists have developed a measure called Consumer price index (CPI), based on a typical market basket of goods and services required by the average consumer. This market basket consists of items from eight major groups: 1. food and beverages, 2. housing, 3.apperal, 4. transportation, 5. medical care, 6. entertainment, 7. personal care, and 8. other goods and services.

3. (c) 2001 Contemporary Engineering Economics 3 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 / unit 25% Price change due to inflation The $100 in year 2001 has only $80 worth purchasing power of 1990

4. (c) 2001 Contemporary Engineering Economics 4 -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 / gallon Price change due to deflation 20.38%

5. (c) 2001 Contemporary Engineering Economics 5 Price Increase Due to Inflation example for monthly housing expense 943.97 – 114.31 / 114.31 = 7.257 x 100 = 725.7 or 726% Item1967 Price2000 Price% Increase Consumer price index (CPI)100512.9413 Monthly housing expense$114.31$943.97726 Monthly automobile expense82.69471.38470 Loaf of bread.221.84736 Pound of hamburger.392.98564 Pound of coffee.594.10595 Candy bar.100.90800 Men’s dress shirt5.0039.00680 Postage (first-class)0.050.33660 Annual public college tuition294.003,960.001,247

6. (c) 2001 Contemporary Engineering Economics 6 Inflation Terminology - I Producer Price Index: a statistical measure of wholesale industrial price change, compiled monthly by the BLS, to evaluate wholesale price levels in the economy. Its components are broken down by industry sector, product. 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, entertainment—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. The market interest rate is expected to respond to this general inflation rate.

7. (c) 2001 Contemporary Engineering Economics 7 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

8. (c) 2001 Contemporary Engineering Economics 8 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) = $112.32 f = 5.98% 2 $100 $112.32 0101 2 2

9. (c) 2001 Contemporary Engineering Economics 9 Average Inflation Rate Example 13.1 Item 1967 Price2000 PriceAverage Inflation Rate Consumer price index (CPI) 100512.95.07% Monthly housing expense $114.31$943.976.61 Monthly automobile expense 82.69471.385.42 Loaf of bread 0.221.846.64 Pound of hamburger 0.392.986.36 Pound of coffee 0.594.106.05 Candy bar 0.100.906.88 Men’s dress shirt 5.0039.006.42 Postage (first-class) 0.050.335.89 Annual public college tuition 294.003,960.008.19

10. (c) 2001 Contemporary Engineering Economics 10 General Inflation Rate ( f ) Average inflation rate based on the CPI

11. (c) 2001 Contemporary Engineering Economics 11 Example 13.2: Yearly and Average Inflation Rates YearCost 0$504,000 1538,000 2577,000 3629,500 What are the annual inflation rates and the average inflation rate over 3 years? Solution Inflation rate during year 1 (f 1 ): ($538,400 - $504,000) / $504,000 = 6.83%. Inflation rate during year 2 (f 2 ): ($577,000 - $538,400) / $538,400 = 7.17 %. Inflation rate during year 3 (f 3 ): ($629,500 - $577,000) / $577,000 = 9.10%. The average inflation rate over 3 years is

12. (c) 2001 Contemporary Engineering Economics 12 Inflation Terminology – II The effect of inflation into economic analysis Actual Dollars (A n ): Estimates of future cash flows for year n that take into account any anticipated changes in amount caused by inflationary or deflationary effects. Usually, these amounts are determined by applying an inflation rate to base-year dollar estimates. Constant (real) Dollars (A' n ): Represents constant purchasing power independent of the passage of time. We will assume that the base year is always time zero unless we specify otherwise.

13. (c) 2001 Contemporary Engineering Economics 13 Conversion from Constant to Actual Dollars $1,000 (1 + 0.08) = $1,260 3 Constant Dollars $1,000 3 Actual Dollars $1,260 3

14. (c) 2001 Contemporary Engineering Economics 14 Conversion from Constant to Actual Dollars (Example 13.3) PeriodNet Cash Flow in Constant $ Conversion Factor Cash Flow in Actual $ 0-$250,000(1+0.05) 0 -$250,000 1100,000(1+0.05) 1 105,000 2110,000(1+0.05) 2 121,275 3120,000(1+0.05) 3 138,915 4130,000(1+0.05) 4 158,016 5120,000(1+0.05) 5 153,154

15. (c) 2001 Contemporary Engineering Economics 15 0 12345 0 12345 $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

16. (c) 2001 Contemporary Engineering Economics 16 Conversion from Actual to Constant Dollars Constant Dollars $1,260 (1 + 0.08) = $1,000 -3 $1,000 3 Actual Dollars $1,260 3

17. (c) 2001 Contemporary Engineering Economics 17 Conversion from Actual to Constant Dollars (Example 13.4) 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 -$20,0000% 1-20,000(1+0.05) -1 -19,0484.76 2-20,000(1+0.05) -2 -18,1419.30 3-20,000(1+0.05) -3 -17,27713.62 4-20,000(1+0.05) -4 -16,45417.73

18. (c) 2001 Contemporary Engineering Economics 18 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 Dollars In Actual Dollars Constant Dollar Analysis Actual Dollar Analysis Deflation Method Adjusted-discount method

19. (c) 2001 Contemporary Engineering Economics 19 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 ): commonly known as the nominal interest rate, which takes into account the combined effects of the earning value of capital (earning power) and any anticipated inflation or deflation (purchasing power). Most firms use a market interest rate (also known as inflation- adjusted required rate of return) in evaluating their investment projects.

20. (c) 2001 Contemporary Engineering Economics 20 Inflation and Cash Flow Analysis Constant Dollar analysis ( inflation free interest rate i' ) - Estimate all future cash flows in constant dollars. - Use i' as an interest rate to find equivalent worth. Actual Dollar Analysis ( market interest rate i ) - Estimate all future cash flows in actual dollars. - Use i as an interest rate to find equivalent worth.

21. (c) 2001 Contemporary Engineering Economics 21 Constant Dollar ( A' n ) Analysis Constant dollar analysis is common in the evaluation of many long-term public projects. For private sector, income taxes are charged based on taxable income in actual dollars.

22. (c) 2001 Contemporary Engineering Economics 22 Actual Dollars (A n ) 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.

23. (c) 2001 Contemporary Engineering Economics 23 Step 1: Convert actual dollars to Constant dollars (Example 13.6) nCash Flows in Actual Dollars Multiplied by Deflation Factor Cash Flows in Constant Dollars 0-$75,0001-$75.000 132,000(1+0.05) -1 30,476 235,700(1+0.05) -2 32,381 332,800(1+0.05) -3 28,334 429,000(1+0.05) -4 23,858 558,000(1+0.05) -5 45,445

24. (c) 2001 Contemporary Engineering Economics 24 Step 2: Convert Constant dollars to Equivalent Present Worth nCash Flows in Constant Dollars Multiplied by Discounting Factor Equivalent Present Worth 0-$75,0001 130,476(1+0.10) -1 27,706 232,381(1+0.10) -2 26,761 328,334(1+0.10) -3 21,288 423,858(1+0.10) -4 16,295 545,445(1+0.10) -5 28,218 $45,268

25. (c) 2001 Contemporary Engineering Economics 25 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 = 1n = 2n = 3n = 4n = 5

26. (c) 2001 Contemporary Engineering Economics 26 Adjusted-Discount Method Step 1 Step 2

27. (c) 2001 Contemporary Engineering Economics 27 Adjusted-Discounted Method (Example 13.7) nCash Flows in Actual Dollars Multiplied by Equivalent Present Worth 0-$75,0001 132,000(1+0.155) -1 27,706 235,700(1+0.155) -2 26,761 332,800(1+0.155) -3 21,288 429,000(1+0.155) -4 16,296 558,000(1+0.155) -5 28,217 $45,268

28. (c) 2001 Contemporary Engineering Economics 28 Adjusted-discount method 0 1 2 3 45 - $75,000 $27,706 $26,761 $21,288 $16,295 $28,218 $45,268 = $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) = $58,000 (P/F, 15.5%, 5) $32,000 $35,700 $32,800 $29,000 $58,000

29. (c) 2001 Contemporary Engineering Economics 29 Adjusted Discount Method: Example 13.7 Converting actual dollars to present worth dollars by applying the market interest rate n = 0 n = 1n = 2n = 3n = 4n = 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

30. (c) 2001 Contemporary Engineering Economics 30 Equivalence Calculation with Composite Cash Flow Elements (Example 13.8) AgeCollege expenses (in constant or today’s dollars) College expenses (in actual dollars) 18 (Freshman)$30,000$30,000(F/P,6%,13) = $63,988 19 (Sophomore)30,00030,000(F/P,6%,14) = 67,827 20 (Junior)30,00030,000(F/P,6%,15) = 71,897 21 (senior)30,00030,000(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.

31. (c) 2001 Contemporary Engineering Economics 31 V 1 = C(F/A, 2%, 48) V 2 = $229,211 Let V 1 = V 2 and solve for C: C = $2,888.48 Required Quarterly Contributions to College Funds