Determination of Interest Rates

Chapter TwoDetermination ofInterest Rates1McGraw-Hill/IrwinInterest Rate FundamentalsNominal interest rates: the interest rates actually observed in financial marketsaffect the values (prices) of securities traded in money and capital marketsaffect the relationships between spot and forward FX rates2McGraw-Hill/IrwinTime Value of Money and Interest RatesThe time value of money is based on the notion that a dollar received today is worth more than a dollar received at some future dateSimple interest: interest earned on an investment is not reinvestedCompound interest: interest earned on an investment is reinvested3McGraw-Hill/IrwinPresent Value of a Lump SumDiscount future payments using current interest rates to find the present value (PV) PV = FVt[1/(1 + r)]t = FVt(PVIFr,t)PV = present value of cash flowFVt = future value of cash flow (lump sum) received in t periodsr = interest rate per periodt = number of years in investment horizonPVIFr,t = present value interest factor of a lump sum4McGraw-Hill/IrwinFuture Value of a Lump SumThe future value (FV) of a lump sum received at the beginning of an investment horizon FVt = PV (1 + r)t = PV(FVIFr,t)FVIFr,t = future value interest factor of a lump sum5McGraw-Hill/IrwinRelation between Interest Rates and Present and Future ValuesPresent Value(PV)Interest RateFutureValue(FV)Interest Rate6McGraw-Hill/IrwinPresent Value of an AnnuityThe present value of a finite series of equal cash flows received on the last day of equal intervals throughout the investment horizon PMT = periodic annuity paymentPVIFAr,t = present value interest factor of an annuity7McGraw-Hill/IrwinFuture Value of an AnnuityThe future value of a finite series of equal cash flows received on the last day of equal intervals throughout the investment horizon FVIFAr,t = future value interest factor of an annuity8McGraw-Hill/IrwinEffective Annual ReturnEffective or equivalent annual return (EAR) is the return earned or paid over a 12-month period taking compounding into account EAR = (1 + r)c – 1c = the number of compounding periods per year9McGraw-Hill/IrwinFinancial CalculatorsSetting up a financial calculatorNumber of digits shown after decimal pointNumber of compounding periods per yearKey inputs/outputs (solve for one of five)N = number of compounding periodsI/Y = annual interest ratePV = present value (i.e., current price)PMT = a constant payment every periodFV = future value (i.e., future price)10McGraw-Hill/IrwinLoanable Funds TheoryLoanable funds theory explains interest rates and interest rate movementsViews level of interest rates in financial markets as a result of the supply and demand for loanable fundsDomestic and foreign households, businesses, and governments all supply and demand loanable funds11McGraw-Hill/IrwinSupply and Demand of Loanable FundsInterestRateQuantity of Loanable FundsSupplied and DemandedDemandSupply12McGraw-Hill/IrwinShifts in Supply and Demand Curves change Equilibrium Interest RatesIncreased supply of loanable fundsQuantity ofFunds SuppliedInterestRateDDSSSS*EE*Q*i*Q**i**Increased demand for loanable fundsQuantity of Funds DemandedDDDD*SSEE*i*i**Q*Q**InterestRate13McGraw-Hill/IrwinDeterminants of Interest Rates for Individual Securitiesij* = f(IP, RIR, DRPj, LRPj, SCPj, MPj)Inflation (IP)IP = [(CPIt+1) – (CPIt)]/(CPIt) x (100/1)Real Interest Rate (RIR) and the Fisher effectRIR = i – Expected (IP)14McGraw-Hill/IrwinDeterminants of Interest Rates for Individual Securities (cont’d)Default Risk Premium (DRP)DRPj = ijt – iTtijt = interest rate on security j at time tiTt = interest rate on similar maturity U.S. Treasury security at time tLiquidity Risk (LRP)Special Provisions (SCP)Term to Maturity (MP)15McGraw-Hill/IrwinTerm Structure of Interest Rates:the Yield CurveYield toMaturityTime to Maturity(a)(b)(c)(a) Upward sloping(b) Inverted or downward sloping(c) Flat16McGraw-Hill/IrwinUnbiased Expectations TheoryLong-term interest rates are geometric averages of current and expected future short-term interest rates1RN = actual N-period rate todayN = term to maturity, N = 1, 2, , 4, 1R1 = actual current one-year rate todayE(ir1) = expected one-year rates for years, i = 1 to N17McGraw-Hill/IrwinLiquidity Premium TheoryLong-term interest rates are geometric averages of current and expected future short-term interest rates plus liquidity risk premiums that increase with maturityLt = liquidity premium for period tL2 < L3 < <LN18McGraw-Hill/IrwinMarket Segmentation TheoryIndividual investors and FIs have specific maturity preferencesInterest rates are determined by distinct supply and demand conditions within many maturity segmentsInvestors and borrowers deviate from their preferred maturity segment only when adequately compensated to do so19McGraw-Hill/IrwinImplied Forward RatesA forward rate (f) is an expected rate on a short-term security that is to be originated at some point in the futureThe one-year forward rate for any year N in the future is:20McGraw-Hill/Irwin