Inflation

1. Inflation Don’t put your money in your mattress

2. Topics for today • The reasons for inflation and its effect on prices • Expressing cash flows in real or actual dollars • Economic analysis with inflation • Economic analysis with inflation and taxes

3. Consumer’s Price Index • Shows prices relative to a base year

4. Inflation Rate • Shows the percentage increase per year

5. Different Inflation Rates • There may be different rates of inflation for different items • Computers • Food • Fuel Oil • Scarce resources • Medical Expenses • The General Inflation rate is denoted with f

6. Inflation Function • Inflation is an exponential function • If the cost of something is $C today and is increasing at a x% rate, the cost in n years is: $C(1 + x/100)n.

7. Estimating Future Costs with Inflation • The tuition is $2000 today. We expect college costs to increase at a 6% annual rate. What will tuition be in 10 years? • Tuition of tomorrow = $2000(1 + 0.06)10 = $3582

8. Estimating Past Cost with Inflation • The cost of a hamburger is $3 today, what did it cost 40 years ago? Assume the average rate of inflation during that time was 5%, • Hamburger of yesterday = $3/(1 + 0.05)40 = $0.43

9. Why do we Have Inflation? • Too many dollars chasing too few goods bid prices up • Government creates too much money • Money not backed by hard currency • Decreasing amounts of raw materials • Unreasonable demands by labor • Unreasonable price increases by business

10. Why do we Have Inflation? (cont’d) • Inflationary expectations (Inflationary spiral) • Uncertainty about government survival and policies • Governments benefit by inflation • Borrowed money is easier to pay back • Proportion of income taxed goes up in a progressive tax system

11. Effect of Inflation • Is inflation good or bad? • It depends on whether you are a borrower or an investor • It is confusing for decision makers • Can inflation be controlled? • It is a primary concern of Alan Greenspan and the Federal Reserve • How do we make economic decisions considering inflation?

12. Expressing Cash Flows • Cash flows may be in real or actual dollars • Consider an estimated cash flow n years from today. • If the cash flow is expressed in terms of today’s dollars, we say the amount is in real (or year-0, or constant) dollars. • If the cash flow is expressed in terms of the dollars that will be used in n years, we say the amount is in actual (or year-n, or current) dollars.

13. From Real to Actual Dollars • Assume a general inflation rate of f per year. • If some cash flow at year n is the amount $C expressed in real dollars, the amount in actual dollars is

14. From Actual to Real Dollars • If some cash flow at year n is the amount $D expressed in actual dollars, the amount expressed in real dollars is

15. Economic Analyses Considering Inflation • The MARR is different with and without inflation • We denote • the market MARR (with inflation) with ic • the real MARR (without inflation) with ir , ic > ir. • the inflation rate with f • The MARR considering inflation should be ic =ir + f + ir f • If f and ic are given, then ir. = ( ic -f )/( 1+f )

16. Estimating Cash Flows Estimate of Cash Flow

17. Changing Estimates to Actual Dollars Estimate of Cash Flow Actual Dollar Cash Flow ej is the total escalation rate and may differ by component

18. Changing Actual Dollars to Real Dollars Actual Dollar Cash Flow Real Dollar Cash Flow Do the economic analysis using either real dollars or actual dollars.

19. Present Worth Analysis

20. Cash Flow Analysis with NPW • If cash flows are in actual dollars, • Use ic to compute NPW • If cash flows are in real dollars, • Use ir to compute NPW • NPW is the same in both real and actual dollars

21. Example 1 • All components of the cash flow escalate at the same rate as general inflation • The investment is $10,000 and the life is ten years with no salvage. • Based on today’s prices, we estimate operating costs at $500 per year, and revenues at $2000 per year. • All costs and revenues are fully responsive to inflation.Escalation rates are the same as general inflation. • The MARR without inflation is 4%. • The general inflation rate is 5%. • Therefore, the MARR with inflation is 0.04 + 0.05 +( 0.04)(0.05) = 0.092 = 9.2%

22. Example 1 (cont’d)

23. Neglecting Inflation • Sometimes inflation can be neglected • For an economic analysis, if all receipts and expenses expand at the same rate as the general inflation rate, forget about inflation. • Do the analysis with real dollars and ir(the MARR without inflation)

24. Different Inflation Rates • If some components of receipts and disbursements do not have the same escalation rate either: • Express all cash flows in actual (year-n) dollars and use ic • Express all cash flows in real (year-0) dollars and use ir

25. Example 2 • Some components of the cash flow escalate at different rates than general inflation • The investment is $10,000 and the life is ten years with no salvage. • Based on today’s prices, we estimate that operating costs as $500 per year and revenues at $2000 per year. • We expect the general inflation rate to be 5%. Operating costs escalate at the same rate as general inflation. Revenues do not increase with time. • The MARR w/o inflation is 4%.

26. Example 2 (cont’d): Actual Dollars

27. Example 2 (cont’d): Real Dollars

28. Alternative Computation: Short Cut • Computing NPW when components have different escalation rates • Investment - Not affected by inflation • A cash flow component that is fully responsive to inflation • Use the MARR w/o inflation (ir) • A cash flow component that does not change with time (escalation rate is 0) • Use the MARR with inflation (ic) • A cash flow component that is increasing at a rate ej • Use [(1 + ic)/(1 + ej)]- 1

29. Example 2: Using Short Cut • Investment is $10,000 • Estimate annual costs of $500. They escalate at a 5% rate • Estimate annual revenues of $2000. They are fixed and do not escalate. • MARR w/o inflation is 4%. • Assume general inflation rate is 5%. NPW = -10000 + 2000 (P/A, 0.092, 10) - 500(P/A, 0.04, 10)= -1332

30. Cash Flow Analysis with NAW • To find the annual worth in actual dollars, • Use ic to compute NAW, or • Use NAWc = NPW (A/P, ic , N) • To find the annual worth in real dollars, • Use ir to compute NAW, or • Use NAWr = NPW (A/P, ir , N) • NAWr (in real dollars) is the most reasonable for comparisons

31. Computing the NAW

32. Example 2: Revisited with NAW • When comparing alternatives with the NAW method, it is only rational to compare the NAW expressed in real dollars. • Compute the NAW as follows: • NAWr = NPW(A/P, ir, n), where ir is the MARR without inflation. NAWr = -1332(A/P, 0.04, 10) = -1332 (0.1233) = -$164 per year.

33. Cash Flow Analysis with ROR • If cash flow are in actual dollars, • Compute RORc • This RORc is with inflation • Compare with ic • If cash flow are in real dollars, • Compute RORr • This RORr is without inflation • Compare with ir • You can find one from the other:

34. Rate of Return Method

35. Analysis with Taxes • Depreciation does not adjust with inflation. It is always in actual dollars. • An after-tax analysis always requires that inflation be considered. • Either express after tax cash flows in actual dollars and use ic, • or express the after tax cash flows in real dollars and use ir

36. Example 3 • After-tax analysis includes taxes and depreciation. • The Investment is $10,000 and the life is ten years with no salvage. • Without adjusting for inflation, we estimate that operating costs as $500 per year and revenues at $2000 per year. • Both revenue and costs increase at the same rate as general inflation. • The general inflation rate is 5%. • The asset is depreciated with the straight-line method. The tax rate is 40%. • The after tax MARR without inflation is 4%.

37. Example 3: After-Tax Analysis • Inflation reduces the attractiveness of investments requiring depreciation • Assuming 5% inflation, After-tax MARR w/ inflation = 9.2%, Tax Rate = 40%.

38. Summary • When all cash flow components escalate at the general inflation rate, use real dollars and ir. • When some cash flow components escalate at different rates, either use real dollars and ir or actual dollars and ic. • When depreciation is involved, always consider the effects of inflation in an after tax analysis.