FIN 365 Business Finance Topic 8 Interest Rates and Inflation Larry Schrenk Instructor 08 54 PM 1 of 34 Today s Outline 1 Inflation 2 Term Structure Yield Curve 3 Implied Future Rates 08 54 PM 2 of 34 Inflation 08 54 PM 3 of 34 Inflation Basics Rise in the general level of prices Unit of currency buys less Erosion in purchasing power Measure Annualized percentage change in a general price index CPI 08 54 PM 4 of 34 Pro s and Con s Benefits Borrowers Costs Lenders Instability and planning uncertainty Discourage investment and saving Shortages and hoarding Distinguish Expected versus Unexpected 08 54 PM 5 of 34 Inflation History 08 54 PM 6 of 34 Inflation Example You want to be a millionaire by age 50 You save 546 23 month at 9 so that you have 1 000 000 at the end of 30 years You are technically a millionaire since you do have 1 000 000 in your investment account But in today s dollars that million is only worth 301 795 87 if the inflation rate is 4 In Today s Dollars 1 000 000 in 30 years will allow you to buy the same goods that 08 54 PM 7 of 34 301 795 87 buys today Simple Example A can of soda costs 1 00 today and 1 05 next year What is the inflation rate 1 05 1 00 5 1 00 At this rate of inflation what will a can of soda cost in 5 years 1 00 1 05 1 28 5 08 54 PM 8 of 34 Simple Example with Calculator At 5 inflation what will a 1 00 can of soda cost in 5 years 1 2 3 4 Input 5 Press N This is annual so N 5 Input 5 Press I Y Input 1 press press PV Press CPT FV to get 1 28 Do you recognize this pattern The following three questions are identical At 5 inflation what will a 1 00 can of soda cost in 5 years 1 28 At 5 growth how tall will a 1 foot tree be in 5 years 1 28 feet At a 5 interest rate what will be the future value of 1 00 5 years 1 28 08 54 PM 9 of 34 Real versus Nominal Values 08 54 PM 10 of Real versus Nominal Nominal Values Money of the Day Not Adjusted for Inflation The Dollar Value You Actually Pay Real Values Adjusted for Inflation Current Dollars Today s Dollars Constant Consumption Value 08 54 PM 11 of Real versus Nominal Values Case 1 Twice as much money to spend Price double Nominal Change Case 2 Twice as much money to spend Prices are unchanged Real Change Case 3 Twice as much money to spend Prices increase but less than double Mix of Nominal and Real Changes 08 54 PM 12 of Real versus Nominal CFs Nominal Values On price tags or in contracts Amount that we actually pay Real Values Remove the effects of inflation CFreal CFnominal t 1 i CFreal Real Cash Flow CFnominal Real Cash Flow i Inflation t Time 08 54 PM 13 of Real versus Nominal CFs If inflation is 5 per year and the nominal cash flow in year two is 150 00 then the corresponding real cash flow is CFreal 150 1 05 2 136 05 P Y 1 N 2 I Y 5 PV 136 05 PMT 0 FV 150 08 54 PM 14 of Real versus Nominal Rates Real rr and nominal rn interest rates rn 1 rr 1 i 1 rn Nominal Rate rr Real Rate i Inflation Rate Note There is an approximation formula rn rr i that should never be used 08 54 PM 15 of Real versus Nominal Values Discount the annual nominal cash flows rr 6 i 4 150 00 220 00 120 00 1 Convert the rate and discount or rn 1 rr 1 i 1 1 06r 1 04 1 10 24 150 00 220 00 120 00 PV 227 52 2 3 1 1024 1 1024 1 1024 08 54 PM 16 of Real versus Nominal Values 2 Discount the converted the cash flow 150 00 1 04 220 00 120 00 1 04 1 04 PV 2 3 1 06 1 06 1 06 2 3 227 52 You are mathematically certain to get the same answer for both procedures Simple Rule Be Consistent Discount Real Amounts with Real Rate Nominal Amounts with Nominal Rate 17 PM 08 54 17 of Calculator Mixed Stream CFs Cash Flow Worksheet CF NPV IRR Later Construct cash flows then operations Frequencies 08 54 PM 18 of TI Calculator Example What is the present value of the following annual cash flows 200 300 1 200 r 18 1 2 3 4 5 6 7 8 9 08 54 PM Press CF Input 0 Press Enter Press Input 200 Press Enter Press Default Frequency is 1 Press Input 300 Press Press Enter Press Press Input 1200 Press Enter Press NPV I Input 18 Press Enter Press CPT to get 684 39 i e 684 39 19 of HP Calculator Example What is the present value of the following annual cash flows 200 300 1 200 r 18 1 2 3 4 5 6 08 54 PM Input 0 Press CFj Input 200 Press CFj Input 300 Press Press CFj Input 1200 Press CFj Input 18 Press I YR Press orange NPV to get 684 39 i e 684 39 20 of TI 83 84 Calculator Example Cash flow functions in menu items 7 and 8 To find NPV APPS FINANCE scroll down to 7 npv and then press ENTER Rate 18 CF0 0 CO1 200 CO2 300 CO3 1200 FO1 1 FO2 1 FO3 1 npv 18 0 200 300 1200 1 1 1 and then press ENTER The screen should display NPV 684 39 08 54 PM 21 of 2 The Term Structure of Interest Rates 08 54 PM 22 of Term Structure of Interest Rates Term Structure of Interest Rates Yield Curve Graph Annual returns on bonds Not HPR Maturities 08 54 PM 23 of Yield Curve Variables Interest Rates Annual Returns on Bonds Maturities Not Time 7 00 6 80 6 60 6 40 6 20 6 00 5 80 5 60 5 40 5 20 Yield Curve 11 September 1997 Maturity 08 54 PM 24 of Term Structure of Interest Rates Yield Curve Shape Theories Pure Expectations Hypothesis Premiums Liquidity Maturity Default Yield Curve Shape Upward normal yield curve Downward inverted yield curve 08 54 PM 25 of Pure Expectations Hypothesis Yield curve function of expected inflation Increase expected LT ST Maturity risk premium for Treasuries is zero LT rates average of ST rates 08 54 PM 26 of Premiums Liquidity Maturity Default 08 54 PM 27 of 3 Implied Future Interest Rates 08 54 PM 28 of Implied Future Interest Rates If I know the average return of A one year bond x and A two year bond y I should be able to calculate The interest rate in year 2 f2 One Year Average x …