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Engineering Economics in Canada Chapter 9 Inflation 9.1 Introduction • Inflation: An increase in the average price paid for goods and services over time. – Results in a reduction in purchasing power. – Value dose not equal to purchasing power. • Deflation: A decrease in the average price paid for goods in services over time. – Results in an increase in purchasing power. • Prices are likely to change over the life of an engineering project due to inflation or deflation • This chapter deals with how to take inflation into account when evaluating projects Copyright © 2006 Pearson Education Canada Inc. 9-2 9.2 Measuring the Inflation Rate • The inflation (deflation) rate is the rate of increase (decrease) in average prices of goods and services over a specified period. • A number of price indices are available to measure inflation, depending upon the type of goods or services we are dealing with. Copyright © 2006 Pearson Education Canada Inc. 9-3 9.2 Measuring the Inflation Rate • The most common price index is the Consumer Price Index (CPI) • The CPI is a composite price index that measures price changes in food, shelter, medical care, transportation, apparel, and other selected goods and services used by average individuals and families. • To compute the CPI, Statistics Canada periodically measures the cost to purchase a standard bundle of goods and services based on prevailing prices. Copyright © 2006 Pearson Education Canada Inc. 9-4 The CPI • The current cost of the bundle of goods and services is compared to the cost of the same bundle in a base year. – The current base year is 1992. • The CPI at a particular point in time is 100 x (current $)/($ in base year) • The CPI of the base year (1992) is 100. • The current year is measured with respect to the base year, 1992. Copyright © 2006 Pearson Education Canada Inc. 9-5 Other Uses of Price Indices • Contract Escalation – A mining company entering a long-term equipment purchase contract with a major distributor wants to establish guidelines which will govern the future prices of the equipment it buys. – Using the Mining, Quarrying and Ore dressing Machinery Index, the company ties the future price increases of equipment to those of the index. Copyright © 2006 Pearson Education Canada Inc. 9-6 Other Uses of Price Indices. .(con’t) • Tracking Selling Prices – A pharmaceutical firm wants to compare price changes for its products with those of the industry as a whole. – Using a series of Pharmaceutical Indexes, analysts can compare their price trends over time with those of the industry. In this way, they can get a sense of their own competitiveness. Copyright © 2006 Pearson Education Canada Inc. 9-7 9.3 Economic Evaluation with Inflation Actual Dollars: dollars at the time that cash flows occur • Their purchasing power changes due to inflation/deflation • Also as known as current or nominal dollars Real Dollars: dollars of constant purchasing power • We need a reference date called the base year (not necessarily the present) • Also known as constant dollars. Copyright © 2006 Pearson Education Canada Inc. 9-8 Actual or Real? • Past or current data from accounting records • Payment from an investment, annuity, bond, or trust • Contractual payments • Estimated costs or revenues Copyright © 2006 Pearson Education Canada Inc. 9-9 Actual and Real Dollars • Suppose that the food plan at UVic residence costs $1500 now and is expected to cost $1530 one year from now, based on an expectation that prices will increase at the general inflation rate of 2% per year. • The real (today's) dollar cost of the plan next year is $1500. • The actual dollar cost of the next year is $1530. (Actual: the price you pay) Copyright © 2006 Pearson Education Canada Inc. 9-10 Inflation Rates • We use forecasts of inflation to estimate how prices in a project will change over time (usually an increase). • We normally assume that estimates of inflation rates over the life of a project are available, and that all prices in a project change at that rate, but sometimes we have reason to believe that some prices will change at different rates. Copyright © 2006 Pearson Education Canada Inc. 9-11 9.3.1 Converting Between Real and Actual Dollars • If we have an estimate of the inflation rate per period over N periods, we can convert actual dollars in period N to real dollars. AN = actual dollars in year N AN is not an annuity amount R0,N = real dollars equivalent to AN relative to yr. 0 Year 0 = the base year f = the inflation rate per year Assumed to be constant from year 0 to year N Copyright © 2006 Pearson Education Canada Inc. 9-12 9.3.1 Converting Between Real and Actual Dollars • The conversion from actual dollars in year N to real dollars in year N is: R0,N AN (1 f )N • The base year (0) is usually omitted from the notation: RN AN (1 f )N • This can conveniently be written and computed with the Present Worth Factor: RN = AN(P/F, f, N) Copyright © 2006 Pearson Education Canada Inc. 9-13 Example 9-1 (Important) • The residence food plan in two years from now is expected to be $2050. Inflation is expected to be 1.5% per year for the next 2 years. • What is the real dollar cost of a food plan at that time (two years from now)? Copyright © 2006 Pearson Education Canada Inc. 9-14 Example 9-1: Answer • N = 2, f = 1.5%, AN= 2050 AN = (P/F, f, N) = 2050(P/F, 1.5%, 2) = 2050(0.97066) = 1888.66 • The real dollar cost of the food plan two years from now is $1888.66. Copyright © 2006 Pearson Education Canada Inc. 9-15 9.4 Actual and Real Interest Rates • Engineers must be aware of potential changes in price levels over the life of a project. • If inflation is anticipated, the MARR needs to be increased in order to avoid rejecting good projects. Copyright © 2006 Pearson Education Canada Inc. 9-16 9.4.1 Effect of Inflation on the MARR • If we expect inflation, the actual dollars returned by a project does not reflect the actual purchasing power of the future cash flow. • The purchasing power depends on the real dollar value of the earnings Copyright © 2006 Pearson Education Canada Inc. 9-17 Effect of Inflation on the MARR… • Consider the (actual) value of $M invested for one year at an actual interest rate i: M (1 + i) • If the inflation rate over the next year is f, the real value of our cash flow is: M(1+i)/(1+f) • The real interest rate, i’, is the interest rate that would yield the same number of real dollars in the absence of inflation as the actual interest rate yields in the presence of inflation: M (1 i ' ) M (1 i ) /(1 f ) i ' (1 i ) /(1 f ) 1 Copyright © 2006 Pearson Education Canada Inc. 9-18 Effect of Inflation on the MARR… • An investor who wishes to get a real rate of i’ and who expects inflation at a rate f will require an actual interest rate of: i = i’ + f + i’f. Summary: • Converting from actual to real dollars: i’ =(1+i)/(1+f)-1 Converting from real to actual dollars: i = i’ + f + i’f. Copyright © 2006 Pearson Education Canada Inc. 9-19 Example 9-2 (Very Important) • As of today, Canada Trust offers a 4% interest rate for a 1-year Guaranteed Investment Certificate (GIC). • If you require a real rate of return of 3% on your investments and you expect inflation to be 1.5% in the coming year, is a GIC a good investment for you? Copyright © 2006 Pearson Education Canada Inc. 9-20 Example 9-2: Answer • First, note the GIC provides 4% actual interest and your real MARR is 3%. • Your actual MARR is: i i' f i' f 0.03 0.015 (0.03)(0.015) 0.04545, or 4.545% • No, the GIC is not a good investment because it provides an actual interest rate less than your actual MARR. Copyright © 2006 Pearson Education Canada Inc. 9-21 Example 9-2: Answer • Alternatively, we can calculate a real interest rate for the GIC: i' = (1 + i)/(1 + f) –1 = (1 + 0.04)/(1 + 0.015) –1 = 2.46% • The real interest rate is less than your real MARR don’t invest. • Comparing the real interest rate to the real MARR also leads to the same decision to not invest. Copyright © 2006 Pearson Education Canada Inc. 9-22 9.4.2 The Effect of Inflation on the IRR (Internal Rate of Return) • The effect of expected inflation on the actual IRR of a project is similar to the effect of inflation on the actual MARR. • Say we have a project with a first cost A0 and actual cash flows A1, A2, …, AT • The actual IRR can be found by solving for i in: A1 A2 AT PW - A0 0 2 T (1 i ) (1 i ) (1 i ) Copyright © 2006 Pearson Education Canada Inc. 9-23 The Effect of Inflation on the IRR… • An annual inflation rate f is expected over the T year life of the project. • In terms of real dollars (base year = now), the stream of actual cash flows can be written as (note: R0 =A0) R0, R11 f , R2 1 f 2 , ..., RT 1 f T • The expression which gives the actual IRR can be rewritten as: R11 f R2 1 f 2 RT 1 f T PW R0 + + + 0 2 T (1 i ) (1+ i ) (1+ i ) Copyright © 2006 Pearson Education Canada Inc. 9-24 The Effect of Inflation on the IRR… • The real IRR is the rate of return obtained on the real dollar cash flows associated with the project. It is the solution for i’ in: R0 R1 R2 RT ... 0 2 T (1 i ' ) (1 i ' ) 1 i ' • What is the relationship between the real IRR and the actual IRR? IRR real (1 IRR actual ) /(1 f ) 1 or IRR actual IRR real f IRR real f Copyright © 2006 Pearson Education Canada Inc. 9-25 Example 9-3 (Very Important) • Ken insulated one of his company's buildings. The energy savings are estimated at $15 000 annually, based on today’s energy prices, starting one year from now. • Inflation is expected to average 4% per year and Ken’s actual MARR is 8%. What is the present worth of the energy savings over the next 10 years? Copyright © 2006 Pearson Education Canada Inc. 9-26 Example 9-3: Answer • Method 1: Work with real cash flows and find the real MARR using an estimate of f. • Method 2: Adjust the real cash flows for inflation (i.e. get estimates of the actual cash flows using f) and apply the actual MARR. Copyright © 2006 Pearson Education Canada Inc. 9-27 Example 9-3: Answer • Method 1: Note that the $15 000 savings will increase if the cost of energy rises with inflation $15 000 is a real cash flow MARRREAL ( 1 MARRACTUAL )/(1 f) 1 ( 1 0.08 )/(1 0.04 ) 1 3.85% PW(total) = 15 000 (P/A, MARRREAL, N) = 15 000(P/A, 3.85%, 10) = 122 600.59 Copyright © 2006 Pearson Education Canada Inc. 9-28 Example 9-3: Answer • Method 2: Adjust real to actual cash flows: PW(Nth payment) = 15 000(P/F, MARRACTUAL, N)(1 + f)N = 15 000 (P/F, 8%, N)(1 + 0.04)N e.g. For N = 4, PW = 12 898.21 PW(total) = 122 600.59 Copyright © 2006 Pearson Education Canada Inc. 9-29 Summary • Inflation and deflation defined • Measuring the inflation rate • Economic Evaluation with Inflation – Converting between real and actual dollars • The Effect of Correctly Anticipated Inflation – The effect of inflation on the MARR – The effect of inflation on the IRR Copyright © 2006 Pearson Education Canada Inc. 9-30