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Interest Rates (Ch. 4)Compounding interestQuoting conventionsSlide 4Employing compounded interest in PV/FV calculations (rules to follow)Slide 6Nominal and Real Interest RatesSlide 8Risk-free Rate and PremiumsSlide 10Slide 11Slide 12Interest Rates (Ch. 4)Interest Rates (Ch. 4)04/17/0604/17/06Compounding interestCompounding interest•Thus far, we have assumed that interest is compounded (or Thus far, we have assumed that interest is compounded (or paid/earned) once during the period.paid/earned) once during the period.•However, often interest is compounded more frequently However, often interest is compounded more frequently than once a period.than once a period.•This means that interest is earned (but not necessarily paid) This means that interest is earned (but not necessarily paid) more than once during the period.more than once during the period.•We examine here what the effect of the frequency of We examine here what the effect of the frequency of compounding has on interest rates.compounding has on interest rates.Quoting conventionsQuoting conventions•Annual Percentage Rate (APR):Annual Percentage Rate (APR):–a.k.a. nominal, stated or quoted ratea.k.a. nominal, stated or quoted rate–Rate required to be disclosed in lending Rate required to be disclosed in lending agreements (Truth-in-lending laws)agreements (Truth-in-lending laws)–Does not reflect the actual interest Does not reflect the actual interest earned/paidearned/paidAPR = periodic interest rate * compounding periods per year APR = periodic interest rate * compounding periods per year (C/Y)(C/Y)Quoting conventionsQuoting conventions•Effective Annual Rate (EAR)Effective Annual Rate (EAR)–The annual rate of interest actually paid or earned.The annual rate of interest actually paid or earned.–Incorporates the effect of compoundingIncorporates the effect of compounding–The EAR is equal to the The EAR is equal to the annual percentage yield annual percentage yield (APY) (APY) which is the rate required to be disclosed in which is the rate required to be disclosed in savings products (Truth-in-savings laws)savings products (Truth-in-savings laws)where where mm is the compounding frequency (or C/Y) is the compounding frequency (or C/Y)–For continuously compounded interest, For continuously compounded interest, 11 mmAPREAR1APReEAREmploying compounded Employing compounded interest in PV/FV calculations interest in PV/FV calculations (rules to follow)(rules to follow)•For lending (savings) products, assume For lending (savings) products, assume that the interest rate stated is the APR that the interest rate stated is the APR (APY) unless otherwise specified.(APY) unless otherwise specified.•Ensure that the frequency of cash flows Ensure that the frequency of cash flows and interest rate used is consistent.and interest rate used is consistent.–If APR is compounded and the compounding If APR is compounded and the compounding frequency (C/Y) is the same as the cash flow frequency (C/Y) is the same as the cash flow frequency, use APR/ (C/Y) for the interest rate.frequency, use APR/ (C/Y) for the interest rate.Employing compounded Employing compounded interest in PV/FV calculations interest in PV/FV calculations (rules to follow)(rules to follow)•Ensure that the frequency of cash flows and Ensure that the frequency of cash flows and interest rate used is consistent. (contd.)interest rate used is consistent. (contd.)–If cash flows are annual, use EAR regardless of the If cash flows are annual, use EAR regardless of the compounding frequencycompounding frequency–For simple (single cash flow) PV/FV problems, use For simple (single cash flow) PV/FV problems, use EAREAR–If you are provided with an interest rate over the If you are provided with an interest rate over the same period as the cash flow period, no same period as the cash flow period, no adjustments need to be made adjustments need to be madeNominal and Real Interest Nominal and Real Interest RatesRates•APR and Periodic Rates are nominal ratesAPR and Periodic Rates are nominal rates•Nominal Rates have two componentsNominal Rates have two components–Real RateReal Rate–Expected Inflation RateExpected Inflation Rate•Real Rate is the reward for savingReal Rate is the reward for saving•Expected Inflation is the rising price of a Expected Inflation is the rising price of a goodgoodNominal and Real Interest Nominal and Real Interest RatesRates•Fisher EffectFisher Effect–Relationship between real rate, expected Relationship between real rate, expected inflation, and nominal rateinflation, and nominal rate(1+r) = (1+r(1+r) = (1+r**) x (1+h)) x (1+h)where r is the nominal rate, rwhere r is the nominal rate, r** is the real rate, is the real rate, and h is expected inflationand h is expected inflation-We can get an approximate value for r:We can get an approximate value for r:r r ≈ r≈ r** + h + hRisk-free Rate and Risk-free Rate and PremiumsPremiums•Nominal interest rates (of return) Nominal interest rates (of return) associated with a particular associated with a particular investment or asset are based on investment or asset are based on four components. four components. –Risk-free rateRisk-free rate–Default RiskDefault Risk–Maturity Maturity –LiquidityLiquidityRisk-free Rate and Risk-free Rate and PremiumsPremiums•Risk-free rate (rRisk-free rate (rff) ) – – a “guaranteed” rate available to investors a “guaranteed” rate available to investors – – 3-month U.S. Treasury Bill rate3-month U.S. Treasury Bill rate•Default RiskDefault Risk–Different Investments have different default risk Different Investments have different default risk based on the issuers ability to meet future promised based on the issuers ability to meet future promised paymentspayments–Credit ratings (by Standard and Poors, etc.) evaluate Credit ratings (by Standard and Poors, etc.) evaluate the default risk of public companies.the default risk of public companies.Risk-free Rate and Risk-free Rate and PremiumsPremiums•Maturity Premium Maturity Premium –Investors demand more compensation for Investors demand more compensation for investing in longer-maturity investmentsinvesting in longer-maturity investments–The The term structure of interest ratesterm structure of interest rates and and yield yield curve curve reflects the difference in rates as the reflects the difference in rates


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OSU BA 340 - Interest Rates

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