EQUIVALENCE CALCULATIONS UNDER INFLATION CHAPTER 4

Inflation and Economic Analysis What is inflation? How do we measure inflation? How do we include the effect of inflation in equivalence calculation?

What is inflation? Inflation is the rate of increase in the level of prices for goods and services, which affects the purchasing value of money. A loss in the purchasing power of money over time. The same dollar amount buys less of an item over time.

Decrease in purchasing power (inflation) Earning Power How much you currently make at your place of employment plays a major part in your earning power. Purchasing power The value of a currency expressed in terms of the amount of goods or services that one unit of money can buy. Decrease in purchasing power (inflation) Increase in Purchasing Power (deflation)

25% $2.00 / unit $2.50 / unit Purchasing Power 2000 $100 2000 2010 You could buy 50 Big Macs in year 2000. You can only buy 40 Big Macs in year 2010. 25% $2.00 / unit $2.50 / unit Price change due to inflation

$1.57 / gallon 20.38% $1.25 / gallon Deflation $100 $100 -2 -1 0 1 -2 -1 0 1 You could purchase 63.69 gallons of unleaded gas a year ago. You can now purchase 80 gallons of unleaded gas. $1.57 / gallon 20.38% $1.25 / gallon Price change due to deflation

Inflation Terminology - I Consumer Price Index (CPI) or cost-of-living index The Consumer Price Index (CPI) is a measure of the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services. Whose buying habits does the CPI reflect? The CPI reflects spending patterns for each of two population groups: all urban consumers and urban wage earners. The all urban consumer group represents about 87 percent of the total U.S. population. It is based on the expenditures of almost all residents of urban or metropolitan areas, including professionals, the self-employed, the poor, the unemployed, and retired people. This market basket normally consists of items from eight major groups – such as food and beverages, housing, apparel, transportation, entertainment, medical care, personal care and other goods and services.

What goods and services does the CPI cover? The CPI represents all goods and services purchased for consumption by the reference population. BLS has classified all expenditure items into more than 200 categories, arranged into eight major groups. Major groups and examples of categories are; FOOD AND BEVERAGES (breakfast cereal, milk, coffee, chicken, full service meals, snacks) HOUSING (rent of residence, owners' equivalent rent, fuel oil, bedroom furniture) APPAREL (men's shirts and sweaters, women's dresses, jewelry) TRANSPORTATION (new vehicles, airline fares, gasoline, motor vehicle insurance) MEDICAL CARE (prescription drugs and medical supplies, physicians' services, eyeglasses and eye care, hospital services) RECREATION (televisions, toys, pets and pet products, sports equipment, admissions); EDUCATION AND COMMUNICATION (college tuition, postage, telephone services, computer software and accessories); OTHER GOODS AND SERVICES (tobacco and smoking products, haircuts and other personal services, funeral expenses).

The CPI frequently is called a cost-of-living index, but it differs in important ways from a complete cost-of-living measure. BLS has for some time used a cost-of-living framework in making practical decisions about questions that arise in constructing the CPI. A cost-of-living index is a conceptual measurement goal, however, and not a straightforward alternative to the CPI. A cost-of-living index would measure changes over time in the amount that consumers need to spend to reach a certain utility level or standard of living. Both the CPI and a cost-of-living index would reflect changes in the prices of goods and services, such as food and clothing, that are directly purchased in the marketplace.

How is the CPI market basket determined? The CPI market basket is developed from detailed expenditure information provided by families and individuals on what they actually bought. For the current CPI, this information was collected from the Consumer Expenditure Surveys for 2007 and 2008. In each of those years, about 7,000 families from around the country provided information each quarter on their spending habits in the interview survey.

How are CPI prices collected and reviewed? Each month, BLS data collectors called economic assistants visit or call thousands of retail stores, service establishments, rental units, and doctors' offices, all over the United States, to obtain information on the prices of the thousands of items used to track and measure price changes in the CPI. Is the CPI the best measure of inflation? Inflation has been defined as a process of continuously rising prices or equivalently, of a continuously falling value of money. Various indexes have been developed to measure different aspects of inflation. The CPI measures inflation as experienced by consumers in their day-to-day living expenses;

Figure 4-1 Measuring inflation based on CPI CONSUMER PRICE INDEX For example, let us say that, in 1967, the prescribed market basket could have been purchased for $100. Suppose the same combination of goods and services costs $600.90 in 2006. We can then compute the CPI for 2006 by multiplying the ratio of the current price to the base-period price by 100. In our example, the price index is ($600.90/$100)100 = 600.90, which means that the 2006 price of the contents of the market basket is 600.90% of its base-period price. Figure 4-1 Measuring inflation based on CPI

Inflation Terminology - I What is the Producer Price Index (PPI)? The Producer Price Index is a family of indexes that measures the average change over time in the selling prices received by domestic producers of goods and services. PPIs measure price change from the perspective of the seller. This contrasts with other measures, such as the Consumer Price Index (CPI), that measure price change from the purchaser's perspective. The consumer price index is a good measure of the general price increase of consumer products. However, it is not a good measure of industrial price increases. When performing engineering economic analysis, the appropriate price indices must be selected accurately to estimate the price increases of raw materials, finished products, and operating costs. The BLS, provides the industrial-product price index for various industrial goods compiled monthly to evaluate wholesale price levels in the economy.

How Does the Producer Price Index Differ from the Consumer Price Index? The Producer Price Index for Finished Goods tracks the average change in prices over time of domestically produced and consumed commodities. The index is comprised of prices for both consumer goods and capital equipment, but excludes prices for services. The All Items CPI measures the average change in prices over time of goods and services purchased for personal consumption by urban U.S. families. The conceptual and definitional distinctions of the PPI and CPI are consistent with the uses of these two major economic indicators. The PPI is used to deflate revenue to measure real growth in output and the CPI is used to adjust income and expenditures for changes in the cost of living.

Inflation Terminology - I Average Inflation Rate ( f ) a single rate that accounts for the effect of unstable yearly inflation rates over a period of several years. (inflation is different every year) General Inflation Rate ( f ) the average inflation rate calculated based on the CPI for all items in the market basket.

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

Consumer Price Indexes for 1963 and 2004 91.7 100 561.23 2004 1963 1967 Average inflation rate = 4.52%

Average Inflation Rate (%) Example 4.1 Calculating Average Inflation Rate F = P (1+ f )N $22,218 = $15,518 (1+ f )6 = – 1 f = 1.0616 – 1 = 0.0616 f = 6.16% Item (CPI) Base Period: 1982 - 84 = 100 2006 Price F 2000 Price P Average Inflation Rate (%) Consumer price index (CPI) $200.43 $171.20 2.66 Postage 0.39 0.33 2.82 Homeowners Insurance 617.00 500.00 3.57 Private college tuition and fees 22,218 15,518 6.16 Gasoline 2.56 1.56 8.61 Haircut 15.00 10.50 6.12 Car (Toyota Camry) 22,900 21,000 1.45 Natural gas (MBTU) 7.08 3.17 14.33 Baseball tickets 171.19 132.44 4.37 Health care (per year) 2,351.00 1,656.00 6.01

Yearly and Average Inflation Rates The accompanying table shows a utility company's cost to supply a fixed amount of power to a new housing development; the indices are specific to the utilities industry. Assume that year 0 is the base period. Determine the inflation rate for each period, and calculate the average inflation rate over the three years. Year Cost $504,000 1 538,000 2 577,000 3 629,500 Inflation rate during year 1 (f1): ($538,000 - $504,000) / $504,000 = 6.83% Inflation rate during year 2 (f2): ($577,000 - $538,000) / $538,000 = 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 = P (1+ f )N

General Inflation Rate ( f ) This average inflation rate is calculated on the basis of CPI for all items in the market basket. The market interest rate is expected to respond to this general inflation rate. In terms of CPI, we define the general inflation rate as

ACTUAL VERSUS CONSTANT DOLLARS Due to inflation, the purchasing power of the dollar changes over time. To compare dollar values of different purchasing power from one period to another, they need to be converted to dollar values of common purchasing power – conversion from actual to constant dollars or from constant to actual dollars. To introduce the effect of inflation into our economic analysis, we need to define two inflation – related terms.

Actual (current) Dollars (An ): Inflation Terminology – II The effect of inflation into economic analysis Actual (current) Dollars (An ): Estimates of future cash flows for year n that take into account any anticipated (expected) changes in amount caused by inflationary or deflationary effects. Actual dollars are the number of dollars that will be paid or received, regardless of how much these dollars are worth. 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 it is specified otherwise.

Conversion from Constant to Actual 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

Example The table shown lists the winners, and their prize monies in actual dollars, from the U. S. Open Golf Championship from 2002 to 2006. Convert the prize monies into equivalent 2006 dollars. In doing so, a) Determine the growth (average) rate of the prize money in actual dollars over the four-year period. b) Find the equivalent prize money for each winner, stated in terms of year 2006 dollars. c) Determine the growth rate of the prize money in constant (real) dollars. d) If the current trend continues, what would be the expected prize money be in actual dollars for the winner in 2007?

Example Year Winner The prize money (in actual dollars) Consumer price index Inflation rate Equivalent Prize money in 2006 dollars 2002 Tiger Woods $1,000,000 179.8 2003 Jim Furyk $1,080,000 183.8 2004 Retief Goosen $1,125,000 188.0 2005 Micheal Campbell $1,170,000 194.6 2006 Geoff Ogilvy $1,225,000 200.43

Example Given Given Year Winner The prize money (in actual dollars) Consumer price index Inflation rate Equivalent Prize money in 2006 dollars 2002 Tiger Woods $1,000,000 179.8 $1,114,779 2003 Jim Furyk $1,080,000 183.8 2.22% $1,177,813 2004 Retief Goosen $1,125,000 188.0 2.29% $1,199,422 2005 Micheal Campbell $1,170,000 194.6 3.51% $1,205,100 2006 Geoff Ogilvy $1,225,000 200.43 3.00%

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

Inflation Terminology - III Inflation-free Interest Rate ( i' ): an estimate of the true earning power of money when the inflation effects have been removed. This rate is known as real interest rate, and it can be computed if the market interest rate and the inflation rate are known. Market interest rate ( i ) 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.

Inflation and Cash Flow Analysis Constant Dollar analysis (A' n) ……… (inflation free interest rate i' ) All cash flow elements are given in constant dollars Compute the equivalent present worth of constant dollars (A' n) in year n. In the absence of inflationary effect, we use i' to account the earning power of the money.

Inflation and Cash Flow Analysis Actual Dollar Analysis (An ) ………….. ( market interest rate i ) All the cash flow elements are estimated in actual dollars. To find the equivalent present worth of this actual dollar amount in year n. Given i’, We use two steps to convert actual dollars into equivalent present worth dollars.

Actual Dollars (An ) Analysis Method 1: Deflation Method a) Convert actual dollars into equivalent constant dollars by discounting with the general inflation rate, a step that removes the inflationary effect. Then: b) Now we can use i' (inflation free interest) to find the equivalent present worth. Method 2: Adjusted-discount Method Combine two steps into one step, which performs deflation and discounting in one step.

Net Cash Flows in Actual Dollars Example: Equivalence Calculation when cash flows are in actual dollars: Deflation Method Applied instrumentation, a small manufacturer of custom electronics to make investment to produce sensors and control systems that have been requested by a fruit drying company. The work would be done under a contract that would terminate in five years. The project is expected to generate the above cash flows in actual dollars: a) What are the equivalent constant dollars if the general inflation rate is 5% per year. b) Compute the present worth of these cash flows in constant dollars at i' = 10% n Net Cash Flows in Actual Dollars -$75,000 1 32,000 2 35,700 3 32,800 4 29,000 5 58,000

Step 1: Convert Actual dollars to Constant dollars Cash Flows in Actual Dollars Multiplied by Deflation Factor ( f ) = 5% Cash Flows in Constant Dollars -$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

Step 2: Convert Constant dollars to Equivalent Present Worth Cash Flows in Constant Dollars Multiplied by Discounting Factor i' = 10% Equivalent Present Worth -$75,000 1 30,476 (1+0.10)-1 27,706 2 32,381 (1+0.10)-2 26,761 3 28,334 (1+0.10)-3 21,288 4 23,858 (1+0.10)-4 16,295 5 45,445 (1+0.10)-5 28,218 $45,268

Deflation Method 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 -$75,000 $26,761 $21,288 $16,295 $28,218 $27,706 $45,268

Adjusted-Discount Method Perform Deflation and Discounting in One Step

Previous Example Adjusted - Discounted Method Cash Flows in Actual Dollars Multiplied By (15.5%) 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

Graphical Overview on Adjusted Discount Method: 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 $28,217 -$75,000 $21,288 $16,296 $26,761 $27,706 $45,268

MIXED DOLLAR ANALYSIS Consider situation that some cash flow elements are expressed in constant (or today’s) dollars. In this situation, we convert all cash flow elements into same dollar units (either constant or actual). If the cash flow elements are all converted into actual dollars, we can use the market interest rate i in calculating the equivalence value. If the cash flow elements are all converted into constant dollars, we can use the inflation-free interest rate i' Example 4.7 illustrates this situation.

Example 4.7 A couple wishes to establish a college fund at a bank for their five-year-old child. The college fund will earn 8% interest compounded quarterly. Assuming that the child enters college at age 18, the couple estimates that an amount of $30,000 per year in terms of today's dollars, will be required to support the child's college expenses for four years. College expenses are estimated to increase at an annual rate of 6%. Determine the equal quarterly deposits the couple must make until they send their child to college. Assume that the first deposit will be made at the end of the first quarter and that deposits will continue until the child reaches age 17. The child will enter college at age 18 and the annual college expense will be paid at the beginning of each college year. In other words. the first withdrawal will be made when the child is 18.

Example 4.7 Equivalence Calculation with Composite Cash Flow Elements 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

Required Quarterly Contributions to College funds

CHAPTER 4 PRACTICE PROBLEMS 12; 13; 14; 15; 22

4.12) A company is considering buying workstation computers to support its engineering staff. In today’s dollars, it is estimated that the maintenance costs for the computers (paid at the end of each year) will be $20,000, $26,000, $34,000, $38,000, and $42,000 for years one through five, respectively. The general inflation rate is estimated to be 10% per year, and the company will receive 16% per year on its invested funds during the inflationary period. The company wants to pay for maintenance expenses in equivalent payment (in actual dollars) at the end of each of the five years. Find the amount of the company’s annual payment.

SOLUTION i = 16%, = 10% P = 20,000 (1.0545)-1 + 26,000 (1.0545)-2 + 34,000 (1.0545)-3 + 38,000 (1.0545)-4 + 42,000 (1.0545)-5 P =$134,289 Therefore A = $134,289 (A/P, 16%, 5) A = $41,012

4.13) Given the cash flows in actual dollars provided in the following table, convert the cash flows to equivalent cash flows in constant dollars if the base year is time 0. Assume that the market interest rate is 16% and that the general inflation rate is estimated at 4% per year. n Actual dollars $20,500 4 $41,500 5 $36,500 7 $55,500

SOLUTION n Actual dollars Constant Dollars $20,500 $20,500(P/F,4%,0) = $20,500.00 4 $41,500 $41,500(P/F,4%,4) = $35,474.37 5 $36,500 $36,500(P/F,4%,5) =$30,000.34 7 $55,500 $55,500(P/F,4%,7) = $42,175.44

4.14) The purchase of a car requires a $15,000 loan to be repaid in monthly installments for four years at 10% interest compounded monthly. If the general inflation rate is 6% compounded monthly, find the actual and constant dollar value of the 15th payment of this loan.

SOLUTION i = 0.1/12 = 0.00833 per month (1+f’m)^12=0.06 => f’m=0.004868 Using above formula with im=0.00833 and N=48, we obtain A = $386.68 actual Then using inflation rate we find A' = 386.68 (P/F, 0.004868, 15) A' = 386.68 x 0.92975 A' = $359.517 constant

4.15) A series of four annual constant dollar payments beginning with $50,000 at the end of first year is growing at the rate of 8% per year. Assume that the base year is the current year (n = 0). If the market interest rate is i = 16% per year and the general inflation rate is =10% per year, find the present worth of this series of payments, based on Constant dollar analysis Actual dollar analysis

PW on constant analysis by using SOLUTION EOY Constant Value Actual Value 1 50,000 50,000 x 1.1 = 55,000 2 50,000 × 1.08 = 54,000 54,000 × 1.12 = 65,340 3 50,000 × 1.082 = 58,320 58,320 × 1.13 = 77,624 4 50,000 × 1.083 = 62,985.6 62,985.6 × 1.14 = 92,217 PW on constant analysis by using P = 50K (1.0545)-1 + 54K (1.0545)-2 + 58,320 (1.0545)-3 + 62,985 (1.0545)-4 P = 47,415 + 48,562 + 49,736 + 50,939 = $196,654

PW on actual analysis by using EOY Constant Value Actual Value 1 50,000 50,000 x 1.1 = 55,000 2 50,000 × 1.08 = 54,000 54,000 × 1.12 = 65,340 3 50,000 × 1.082 = 58,320 58,320 × 1.13 = 77,624 4 50,000 × 1.083 = 62,985.6 62,985.6 × 1.14 = 92,217 PW on actual analysis by using A1=55,000, i=0.16, g=0.188, N=4 => P = 196633.2 g = g’ + f’ + f’ g’ P = 55K (1.16)-1 + 65,340 (1.16)-2 + 77,624 (1.16)-3 + 92,217 (1.16)-4 P = 47,414 + 48,558 + 49,730 + 50,931 = $196,633

4.22) The annual fuel costs to operate a small solid-waste treatment plant are projected to be $1.8 million, without considering for any future inflation. The best estimates indicate that the annual inflation free interest rate ( i' ) will be 7% and the general inflation rate = 4%. If the plant has a remaining useful life of five years, what is the present equivalent value of its fuel cost, using actual-dollar analysis?

SOLUTION A B = A x (1.04)N C = B x (1.1128) -N Period   A B = A x (1.04)N C = B x (1.1128) -N Period Net cash flow in constant $ Net cash flow in actual $ Equivalent present worth 1 $1.8M $1,872,000 $1,682,243 2 $1,946,880 $1,572,190 3 $2,024,755.20 $1,469,336 4 $2,105,745.40 $1,373,211 5 $2,189,975.22 $1,283,375 Total $7,380,355