Chapter 4 Understanding Interest Rates I Measuring Interst Rates a Present Value a dollar today funds principal that must be repaid to the lender at the maturity date along with additional interest lender provides the borrower with an amount of a dollar paid from you one year from now is worth less than i Simple Loan 1 i interest rate i c P a b c interst amount paid c P principal 2 PV CF 1 i n a PV Present Value b CF future cash flow c I interst rate d N time in years e 3 CF PV 1 i n a PV Present value b P Principal c d n amount of time in years I interest rate b 4 types of Credit Market Instruments i Simple Loan lender provides the borrower with an amount of funds principal that must be repaid to the lender at the maturity date along with additional interest 1 commercial loans to businesses ii Fixed Payment Loan lender provides borrower with an maount of funds Which must be repaid by paying the lender the same payment every period monthy quarterly consisteing of part of the principal and interest 1 common for mortgages and auto loans iii Coupon Bonds pays the owner of the bond a fixed interest payment coupon payment every year until maturity date when a specified final amount is repaid par value 1 US Treasury Bonds 2 Corporate Bonds iv Discount Bond is bought at a price below its face value at a discount and the face value is repaid at the maturity date Does not make interst payments Bond holders make by the difference between discount rate and par value c Yield to Maturity flow payments received from a debt instrument with its value today the interest rate that equates the present value of cash i Todays value of a debt instrument with the present value of all of its future cash flow payments ii Calculations for 4 tupes of credit market instruments 1 Simple Loan a PV CF 1 i n b Only one where the i p YTM i PV Present Value ii CF Cash Flow iii N period in years 2 Fixed Payment Loan a LV FP 1 i 1 FP 1 i 2 FP 1 i n i LV Loan Value ii FP Fixed Yearly Payment iii N number of years until maturity 3 Coupon Bond a P C 1 i 1 C 1 i 2 C 1 i n F 1 i n i P Current Price ii C yearly coupon Payment iii F Face value of Bond iv N years till maturity b things to consider i When the coupon rate is priced at its face value the yield to maturity equals the coupon rate ii The price of a coupon bond and the yield to maturity are negatively related 1 YTM goes up bond prices fall 2 YTM goes down bond prices rise iii The YTM is greater then the face amount when the bond price is below face value c Perpetuity or Consol maturity but pays coupon every period indefinitely bond that has no date of i P C i 1 P Price of Perpetuity 2 C yearly payment I YTM of perpuity 3 4 Discount Bond a i F P P II Distinction b n interest rates and returns a Rate of Return ROR value expressed as a fraction of its price as the payments to the owner plus the change in i ROR on a bond will not necessarily equal the yield to maturity on that bond ii R C Pt 1 Pt Pt 1 R Return from holding the bond from time t to time t 1 2 Pt Price of bond at time t 3 Pt 1 Price of bond at time t 1 4 C Coupon Payment iii R Current Yield Rate of Capital Gains g ic 1 Current yield ic C Pt a Current yield coupon payment over purchse price the change in the bonds price relative 2 Rate of Capital Gains to its initial purchase price a ROCG Pt 1 Pt Pt g iv Things to remember 1 Return equals the initial yield to maturity when time to 2 maturity is same as the holding period rise in interest rate is associated with a fall in bond prices resulting in capital losses on bonds whose terms to maturity are longer than the holding period 3 Longer the maturity date away the greater the size of the percentage price change associated with an interest rate change 4 Longer maturity date is away the lower the ROR occues as an increase in interest rates 5 Prices and returns for longer term bonds are more volatile than those for shorter term bonds Interest Rate Risk a b Bonds with a maturity that is as short as the holding period have no interest rate risk III Difference between Real and Nominal Interest Rates a Nominal Interest Rates b Real Interest Rate interest rate not adjusted for inflation adjusted for by subtracting expected inflation i Ex ante prediction ii Ex Post Real interest Rate interst Rate actually adjusted for inflation after the fact c Fishcer Equation used to find nominal interst rate i i ir e i nominal interest Rate 1 2 ir real interest rate 3 e expected inflation d When real interest rates are low there is a great incentive to borrow but very little to lend Implied expected inflation ROR on US Treasury Bonds ROR on TIPS e f