Chapter 11 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 (c) 2001 Contemporary Engineering Economics

Inflation and Economic Analysis What is inflation? How do we measure inflation? How do we incorporate the effect of inflation in economic analysis? (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics 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) (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Purchasing Power 1990 $100 1990 2001 You could buy 50 Big Macs in year 1990. You can only buy 40 Big Macs in year 2001. 25% $2.00 / unit $2.50 / unit Price change due to inflation The $100 in year 2001 has only $80 worth purchasing power of 1990 (c) 2001 Contemporary Engineering Economics

You could purchase 63.69 gallons of unleaded gasoline $100 $100 -2 -1 0 1 -2 -1 0 1 You could purchase 63.69 gallons of unleaded gasoline a year ago. You can now purchase 80 gallons of unleaded gas. 20.38% $1.57 / gallon $1.25 / gallon Price change due to deflation (c) 2001 Contemporary Engineering Economics

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 (c) 2001 Contemporary Engineering Economics

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. (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics 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 (c) 2001 Contemporary Engineering Economics

Selected Price Indexes Year Base Period New CPI 1982-84 Old CPI 1967 Gasoline 1982 Steel Passenger Car 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 1997 160.2 479.7 72.7 116.4 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 (c) 2001 Contemporary Engineering Economics

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% $100 $112.32 0 1 2 2 (c) 2001 Contemporary Engineering Economics

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 (c) 2001 Contemporary Engineering Economics

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

Example 13.2: Yearly and Average Inflation Rates Cost $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 (c) 2001 Contemporary Engineering Economics

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). (c) 2001 Contemporary Engineering Economics

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

Conversion from Constant to Actual Dollars Period Net Cash Flow in Constant $ Conversion Factor Cash Flow in Actual $ -$250,000 (1+0.05)0 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 (1+0.05)5 153,154 (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics $130,000 $120,000 $110,000 $120,000 $100,000 1 2 3 4 5 Years (a) Constant dollars $250,000 $130,000(1+0.05)4 $120,000(1+0.05)5 $100,000(1+0.05) $120,000(1+0.05)3 $110,000(1+0.05)2 $250,000(1+0.05)0 $158,016 $138,915 $121,275 $153,154 $105,000 1 2 3 4 5 Years (b) Actual dollars $250,000 (c) 2001 Contemporary Engineering Economics

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

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 -$20,000 (1+0.05)0 0% 1 20,000 (1+0.05)-1 -19,048 4.76 2 (1+0.05)-2 -18,141 9.30 3 (1+0.05)-3 -17,277 13.62 4 (1+0.05)-4 -16,454 17.73 (c) 2001 Contemporary Engineering Economics

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 (c) 2001 Contemporary Engineering Economics

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). (c) 2001 Contemporary Engineering Economics

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. (c) 2001 Contemporary Engineering Economics

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. (c) 2001 Contemporary Engineering Economics

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. (c) 2001 Contemporary Engineering Economics

 Step 1: Convert actual dollars to Constant dollars Cash Flows in Actual Dollars Multiplied by Deflation Factor Cash Flows in Constant Dollars -$75,000 1 -$75.000 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 (c) 2001 Contemporary Engineering Economics

Step 2: Convert Constant dollars to Equivalent Present Worth Cash Flows in Constant Dollars Multiplied by Discounting Factor Equivalent Present Worth -$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 (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Deflation Method (Example 13.6): Converting actual dollars to constant dollars and then to equivalent present worth n = 0 n = 1 n = 2 n = 3 n = 4 n = 5 Actual Dollars -$75,000 $32,000 $35,700 $32,800 $29,000 $58,000 Constant Dollars -$75,000 $30,476 $32,381 $28,334 $23,858 $45,455 Present Worth $28,218 -$75,000 $21,288 $16,295 $26,761 $27,706 $45,268 (c) 2001 Contemporary Engineering Economics

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

Adjusted-Discounted Method Cash Flows in Actual Dollars Multiplied by Equivalent Present Worth -$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 (c) 2001 Contemporary Engineering Economics

Adjusted-discount method $58,000 $35,700 $32,000 $32,800 $29,000 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) - $75,000 $27,706 $26,761 $21,288 $16,295 $28,218 $45,268 = $29,000 (P/F, 15.5%, 4) = $58,000 (P/F, 15.5%, 5) (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Adjusted Discount Method: Example 13.7 Converting actual dollars to present worth dollars by applying the market interest rate n = 0 n = 1 n = 2 n = 3 n = 4 n = 5 Actual Dollars -$75,000 $32,000 $35,700 $32,800 $29,000 $58,000 Present Worth $28,218 -$75,000 $21,288 $16,295 $26,761 $27,706 $45,268 (c) 2001 Contemporary Engineering Economics

Equivalence Calculation with Composite Cash Flow Elements Approach: Convert any cash flow elements in constant dollars into actual dollars. Then use the market interest rate to find the equivalent present value. Age College expenses (in today’s dollars) (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(F/P,6%,15) = 71,897 21 (senior) 30,000(F/P,6%,16) = 76,211 (c) 2001 Contemporary Engineering Economics

Required Quarterly Contributions to College Funds V1 = C(F/A, 2%, 48) V2 = $229,211 Let V1 = V2 and solve for C: C = $2,888.48 (c) 2001 Contemporary Engineering Economics

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 and always expressed in actual dollars (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Item Effects of Inflation Salvage value Inflated salvage value combined with book values based on historical costs results in higher taxable gains. (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Item Effects of Inflation Loan repayments Borrowers repay historical loan amounts with dollars of decreased purchasing power, reducing the debt-financing cost. (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Item Effects of Inflation Working capital requirement Known as working capital drain, the cost of working capital increases in an inflationary environment. (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Item Effects of Inflation 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. (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Excel Example of an after-tax cash flow analysis including differential inflation (Example 13.14) (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics $3,876 $3,000 (c) 2001 Contemporary Engineering Economics

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 1 2 3 4 -$30,000 13,570 15,860 13,358 13,626 12,336 13,108 10,036 9,307 IRR 31.34% 19.40% Not correct IRR (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics 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. (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics 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. (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics 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 analysis Inflation-free interest rate (i’): A rate from which the effects of inflation have been removed; this rate is used with constant dollar analysis (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics 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. (c) 2001 Contemporary Engineering Economics