Introduction. 18: Inflation and Deflation. Percentage Change in Prices Basics of Inflation. Base Year. Nominal and Real Dollars

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1 18: Inflation and Deflation Introduction Inflation: same items cost more over time Variety of possible causes, some of which are Increase in money supply w/o increasing goods and services Shifts in international currency rates Changes in availabilities of basic commodities Consumer expectations Deflation: same items cost less over time Not as common in modern economies Focus is on how to incorporate price changes into economic analyses, not why they occur 18.1 Basics of Inflation Percentage Change in Prices Rate of inflation or deflation measures percentage changes in the price of a collection of goods and services known as a market basket Inflation same as percent growth in a savings Item costs $10 today and inflation rate is 6% Price in 2 years will be 10(1.06) 2 Price 2 years ago was 10(1.06) 2 With deflation, the rate is negative Item costs $10 today and deflation rate is 6% Price in 2 years will be 10(0.94) 2 Price 2 years ago was 10(0.94) 2 Base Year Prices frequently computed at rate f relative to a base year b Price in yr j = (Price in base yr b) (1+f ) j b Price is $10 in base year 3 w/ inflation at 6% Price in year 5 will be 10(1.06) 5 3 Price in year 1 was 10(1.06) 1 3 Nominal and Real Dollars Nominal dollars are the number of dollar bills that change hands Real dollars measure purchasing power relative to a market basket in a base year $13.31 handed to a salesperson 3 years hence to purchase CDs costing $10 today Nominal dollars for purchase = $13.31 Real dollars (relative to today's CD market) for purchase = $10.00

2 Generalization Apply symbols to foregoing CD costing Rb in the base yr b requires N j = Rb (1+f ) j b nominal dollars in year j Solve for Rb to get purchasing power of N j N j nominal dollars in yr j buys same goods as Rb = N j (1+f ) ( j - b) real dollars in year b's market Increasing and decreasing number of nominal dollars for same goods and services referred to as inflating and deflating dollars, respectively Example Real and Nominal Dollars Retiring parents will have fixed yearly income of $40,000 (nominal) after taxes Future purchasing power relative to today if inflation is 5% For example, $24,557 = 40,000(1.05) (10-0) Known as fixed income problem Yr Real $ 5 31, , , , , ,255 Money is worth only what it can buy, so the real cash flows can be very important for planning Price Indexes Nominal dollars required to purchase same $100 market basket as in some base period Index on right uses avg prices during as a base Market basket cost $98 nominal dollars in 96 and $105 nominal dollars in 98 Computing indexes same as compounding or discounting with non-constant interest rates Let fj be the inflation rate during year j Year Index Multiply or divide by 1 plus intervening rates Ij = 100(1+ f b +1)(1+ f b + 2 ) (1+ fj ), j > b Ij = 100 / (1+ f j +1)(1+ f j + 2) (1+ fb), j < b Calculating Price Indexes Year Index Rate Computation Base % 100(1.040) % 100(1.040)(1.045) % 100(1.040)(1.045)(1.055) If constant rate of inflation, preceeding equations simplify to Ij = 100(1+ f ) j b At 5%, index for two years ago is 100(1.05) 2 At 5%, index for two years hence is 100(1.05) 2 Computing with Price Indexes Interpret indexes based on $100 as percentages Index for 2003 relative to 2000 is market basket costs (2000 price)114.7% Symbolically Nj = Rb Ij In base yr, Rb nom dollars = Rb real dollars $100 real dollars in 2004 relative to 2004 is $100 nominal dollars If nominal dollars are known, then real dollars are Rb = Nj / Ij Revenues of $1,147 nominal dollars in 2003 will allow purchase of goods and services costing 1,147 / or $1,000 in 2000 Average Rate of Inflation If f is the avg inflation rate for a purchase costing $100 today and $114.7 after 3 years, then = 100(1+f )3 Solve for f to obtain f = 4.67% = (114.7/100)1/3 1 Symbolically for times t > s f = (N t / N s ) 1 / (t s) 1 Indexes are in terms of nominal dollars, so f = (I t / I s ) 1 / (t s) 1

3 18.2 Cash Flows Multiple Indexes Inflation can occur at different rates in different sectors of the economy Energy and electronics If energy inflates at 6%, then price of $100 after 5 years is $ =100(1.06)5 If electronics deflates at 2%, then price of $100 after 5 years is $90.39 = 100(0.98)5 CPI uses a market basket of goods and services typically purchased by end consumers PPI uses a market basket of goods and services typically purchased by industrial firms Index sources: U.S. DOC and trade journals Before-Tax Cash Flows Inflating a project's cash flows to determine nominal dollars can require multiple indexes, such as energy and electronics Once all nominal flows known, add them together to determine net, nominal flows Then deflate the net, nominal flows to determine what they can buy (real dollars) Depends on what the nominal dollars will be used to purchase Individuals reinvested in consumer goods and services, so use CPI Industrial cash flows reinvested in general producer goods and services, so use PPI Example Before-Tax Cash Flows Estimates can be either real or nominal IC is $10,000 (t = 0, so either nom or real) Sales are $8,000 / yr real dollars w/ nominal dollars expected to increase at 5% / yr O&M costs $2,000 / yr real dollars w/ nominal dollars inflating at 3% per year Project lasts 2 years, w/ nominal salvage value of $4,000 Profits reinvested in producer goods and services with prices that increase at 4% / yr Determine the real, BTCF First compute the various indexes Compute net nominal Example Solution Deflate net nominal by PPI (industrial study) Yr Sales Costs PPI x 8,000 x 2,000 = Yr N j, Asset N j, Sales N j, Costs N j, Net R j, Net 0-10,000-10,000-10, ,400-2,060 6,340 6, ,000 8,820-2,122 10,698 9,891 After-Tax Cash Flows Taxes based on BT nominal dollars, so computing ATCFs begins w/ BT nominal dollars Revenues and costs tend to respond to inflation, but depreciation is fixed by law Depr tax savings generally do not respond to inflation Tax savings equal depreciation tax rate, and tax rates do not change much Tax brackets increase in response to inflation, a practice known as indexing Before indexing, inflation pushed taxpayers into higher brackets via bracket creep

4 Ex Real ATCFs with Single Inflation Rate Project financial data Machine costs $10,000 and has depreciation charges of $3,000 per year for next 2 years Real yearly profits of $5,000 Real $4,000 amount realized Profits and AR inflate at 5% Tax rates are 30% on OI and 25% on disposals Ex 18.3 Solution Nom Yr BV/D Nom Real BTCF j TI Taxes ATCF ATCF 0-10,000-10,000-10, ,250 3,000 2, ,575 4,357 5,513 3,000 2, ,758 4, ,410 4, ,307 3,907 Taxes based on nominal dollars, so convert all cash flows to nominal BTCF (real $5,000 and AR of $4,000) inflated at 5%, but not depr and BV Nominal TI, taxes, and ATCF computed Real ATCF calculated by deflating nominal ATCF at 5% Ex 18.4 Real ATCFs w/ Multiple Inflation Rates Earlier BTCF example with multiple inflation rates Determine real ATCF OI rate is 30% Disposal rate is 20% Remember deflate based on use of ATCFs Industrial reinvestment PPI (used here) Personal use CPI Yr N j, Asset N j, Sales N j, Costs N j, Net 0-10,000-10, ,400-2,060 6,340 8,820-2,132 6, ,000 4,000 Ex 18.4 Three Step Solution Nom Yr BTCF BV/D Nom Real j TI Tax ATCF ATCF 0-10,000-10,000-10, ,340 5,000 1, ,938 5,710 6,688 4,000 2, ,882 5, ,000 1,000 3, ,400 3, Use as many indexes as necessary to determine net, nominal BTCF for ordinary income and disposal items 2. Use depreciation, tax credits, and so forth to compute nominal ATCF 3. Deflate nominal ATCF to real ATCF using appropriate deflator Basics 18.3 Economic Analyses Decisions can be based on real or nom dollars FTWA = $1,000,000 and FTWB = $900,000 Project A preferred regardless of whether the dollars are real or nominal However, fixed income problem indicates sometimes need to express results in real terms to do informed planning

5 Real Economic Measures Flows on right are real dollars IRR of real flows is real IRR, r* r* = 13.07% is the solution to 0 = -10, ,000(P A, r*, 2) Real AMRR is the avg IRR of marginal projects when all cash flows expressed in real dollars Referred to as real discount rate 6,000 10,000 Real PW is PW of real flows computed using real discount rate Similarly, real EAW and real FW computed using real flows and real discount rate Ex 18.5 Real Economic Measures and Real Flows r* = 13.07% is the solution to 6,000 0 = -10, ,000(P A, r*, 2) Real discount rate is 10% Real PW is 10,000 $ = -10, ,000(P A,10%, 2) Real EAW $ = -10,000(A P,10%, 2) + 6,000 Real FW $ = -10,000(F P,10%, 2) + 6,000(F A,10%,2) Nominal and Real IRRs Real IRR is IRR of real flows, and nominal IRR is IRR of nominal flows Two IRRs are related Let real flow j be Rj, and nominal flow j be Nj r* solves 0 = R0 + R1(1+r*) Rm(1+r*)-m Nominal and Real IRRs (cont.) Rearranging 1+n* = (1+f )(1+r*) n* = r* + f + f r* r* = (n* f )/(1 + f ) N0 = R0 and Rj = Nj(1+f )-j for deflator f, so 0 = N0 + N1[(1+f )(1+r*)] Nm[(1+f )(1+r*)]-m n* solves 0 = N0 + N1(1+n*) Nm(1+n*)-m 1+n* = (1+f )(1+r*) Ex Computing Nominal and Real IRRs 6,000 10,000 f = 4% Already computed r* = 13.07% 6, , , Use relationship of n* and r* to obtain n* = 17.59% = (0.04)(0.1307) Easier than solving 0 = -10, ,240(P F, n*,1) + 6,489.60(P F, n*,2) Similarly, if already know that n* = 17.59%, then r* = 13.07% = ( ) / (1.04 ) Ex 18.7 Nom and Real Rates in Equiv Calc Deposit $1,000 (real) in account paying 10% at times 1, 2,, 10 Tax-free Roth IRA Inflation is 4% Two methods to determine real CA 1. Use real flows and the real rate to directly compute the real CA r = 5.77% = ( ) / (1.04) $13, = 1,000(F A, 5.77%, 10)

6 Ex 18.7 Nominal, then Deflate 2. Use nominal flows and nominal rate to compute the nominal CA and then deflate it Compute actual deposits and amounts in account First nominal deposit at time 1 is $1,040 = 1,000 (1.04) Remaining nominal deposits are 1,040( 1.04)1, 1,040( 1.04)2, Nominal compound amount is $19,300.64: 1,040(P A, g=4%, n = 10%, 10)(F P, 10%, 10) Real CA is, as before $13, = 19, / And the Moral of this Example Is... Use nominal rates on nominal dollars and real rates on real dollars Nominal and Real Surrogate Measures FTW R = Real FTW Uses real flows, real AHRR, and real AMRR Max real PW, EAW, or FW max real FTW FTW N = Nominal FTW Use nom flows, nom AHRR, and nom AMRR Max nom PW, EAW, or FW max nom FTW If inflation rate is f over m year planning horizon FTW R = FTW N (1+f )-m Proportional, so max one max the other Max either PW, EAW, FW max either FTW Just be consistent w/ flows and rates Nominal and Real PW Equal Nominal PW = Real PW Both measure worth at base time 0, at which time nominal dollars equal real dollars Mathematically shown as follows Let r be the real AMRR w/ inflation rate f Nominal AMRR n = r + f + fr Any real cash flow R j = Nj (1+f )-j Real PW of Rj = PW(R j ) = Rj (1+r ) -j = Nj (1+f ) -j (1+r )-j = Nj [(1+f )(1+r )] -j = Nj (1 + r+ f + fr ) -j = Nj (1 + n ) -j = PW(N j ) PW(R j ) = Rj (1 + r ) - j = Nj (1 + n ) -j = PW(N j ) Computing Surrogate Measures Nominal AMRR is nominal discount rate, aka Inflated discount rate Inflation adjusted discount rate EAW & FW Real: Compute using R j and r or EAW R = PW (A P, r, m) FW R = PW (F P, r, m) Nominal: compute using N j and n or EAW N = PW (A P, n, m) FW N = PW (F P, n, m) Ex Real and Nominal Measures PW A 6,000 10,000 B 7,000 16,000 Real ATCF Nominal ATCF Real discount rate r = 10% w/ f = 4% inflation n = 14.4% = (0.04)(0.10) Real / nom PW s using correct discount rates PW A = $ = -10, ,000(P A, 10%, 2) PW B = $ = -16, ,000(P A, 14.4%, 3)

7 Ex 18.8 Real and Nominal Measures EAW & FW If EAWs or FWs desired For real, can convert all cash flows to real and use r = 10%, or EAW R = PW (A P, 10%, 3) FW R = PW (F P, 10%, 3) For nominal, can convert all cash flows to nominal and use n = 14.4%, or EAW N = PW (A P, 14.4%, 3) FW N = PW (F P, 14.4%, 3) 18.4 Combined Effect of Taxes and Inflation Objective Use relationships between before-tax and after-tax IRRs to estimate discount rates and understand effect of inflation on taxes Nominal Before-Tax and After-Tax IRRs n BT nominal before-tax IRR earn n BT dollars per $1 invested Pay roughly t n in taxes, so keep approximately (1- t ) n after taxes per $1 invested BT BT n AT (1- t ) n BT Relationship approximate unless n BT dollars equals TI Depr and disposal rules affect amounts and timing of TI, so relationship approximate for projects For savings accounts, the n BT dollars equal TI, so relationship exact Real Before-Tax and After-Tax IRRs Approximate real after-tax IRR For any IRR, before-tax or after-tax For after-tax r = (n f ) / (1 + f ) r AT = (n AT f ) / (1 + f ) and since n AT (1- t ) n BT r AT [(1- t ) n BT f ] / (1 + f ) Ex Historical Discount Rates Nominal Marginal projects have BT IRRs that avg 20% Historical BT discount rate for nominal flows n h,bt = 20% Marginal projects have AT IRRs that avg 12.5% Historical AT discount rate for nominal flows n h,at = 12.5% If no data on AT flows and combined marginal tax rate was 36%, then estimate of n h,at is n AT 12.8% = (1 0.36)20%

8 Ex Historical Discount Rates Real Inflation during projects 6%, historical real BT rate r h,bt = 13.21% = ( ) / 1.06 Historical real AT rate is n h,bt r h,at = 6.13% = ( ) / 1.06 n h,at If no data on AT flows and combined marginal tax rate was 36%, then estimate of r h,at is r h,at 6.42% = [(1 0.36) ] / 1.06 n h,bt Example Forecasting Discount Rates Suppose predicted real BT productivity of projects r p,bt about same as in previous example Changes t : 36% to 30% f : 6% to 4% Dis Rate BT AT Nominal 20.00% 12.50% Real 13.21% 6.13% Since n = r + f + fr whether BT or AT, then n p,bt = 17.74% = (0.04) Lose 30% of nominal earnings to taxes n p,at 12.42% = (1 0.30) Since r = (n f ) / (1 + f ) whether BT or AT, so rp,at 8.09% = ( ) / (1.04) Inflation Tax Refers to additional taxes that are caused by inflation instead of real earnings Concept serves only to show need to consider both inflation and taxes in economic analyses Ex Effect of Inflation Taxes on Savings Earlier example had $1,000 (real) t = 1, 2,, 10 in tax-free (TF), i N = 10%, f = 4% i R,4%,BT = 5.77% = ( ) / (1.04) CA R,4%,TF = $13, = 1,000(F A, 5.77%,10) Now suppose pay combined marginal t = 30% Real AT interest w/ same f = 4% exactly i R,4%, AT = 2.88% = [(1-0.30) ] / 1.04 Formula exact for saving account w/o depr Real AT CA account is CA R,4%, AT = $11, = 1,000(F A, 2.88%, 10) Ex (Continued) If no inflation, but still earn real 5.77% BT and deposit $1,000 (real), then with 30% taxes i R,0%,AT = 4.04% = [(1-0.30) ) / (1.00) CA R,0%, AT = $12, = 1,000(F A, 4.04%%, 10) f Taxes i R,BT Real CA Change 4% None 5.77% $13, % 30% 5.77% $12, $1, % 30% 5.77% $11, $ $1, change due to taxes only $ due to combined effect of taxes and inflation, the inflation tax