PV= 1000/(1+0.05)^2=1000/1.1.25=907Calculating interest rate(reward) of holding different debt instrumentsSuppose your friend(trustworthy) is selling you two promises.Promise A: Pay her $100 now and receive $110 next yearPromise B: Pay her $100 now and receive $60 next year and another $60 in two yearsYield to Maturity or Reward- Interest rate from buying a debt instrument-Interest rate that equates present value of all future payments(fixed) to its current price(variable)
Debt InstrumentsCoupon Bond- Promise face value, coupon, or coupon rate, maturity issuer. Ex(Treasury bonds and notes, corporate bonds, Apple, Sprint)Discount Bond- Zero coupon bond which is sold at a discount. EX: Pay 98 dollars for 100 fave value bond receive $2) Ex: Treasury bills. Commercial PaperConsol Bond or perpetuity- Once you buy it there is no expiration date, makes coupon paymentswith no maturity dates.One-year discount bond: Yield to MaturityI=FV-P/P FV- Face value(fixed) P=prices (varies)Notice, yield varies inversely with a priceYield to Maturity of n-year coupon bondNeed to Know Coupon Payments, C, or Coupon Rate, CR= C/FCCurrent Price, p(varies)P=C/(1+i)+C/(1+i)^2+C/(1+i)^2+……..+C/(1+i)^n+FV/(1+i)^nYield and bond price are negatively related Explanation: Coupon Payments and face value are always fixed payments that bond holders receives. As bond price, which measures a buyer’s cost increases, it reduced benefits or reward or yield from owning a bond.Effectively buyer has to give up higher amount now to receive the same fixed paymentsWhen coupon bond is priced at its face value, yield to maturity equals the coupon ratePrice of coupon bond and yield to maturity are negatively related Yield to maturity is greater than coupon rate, when the bond price is below its face value. The following relationships are true for any type of coupon bond (any maturity) If P<FV, then YTM>CY>CRIf P>FV then YTM<CY<CR
If P=FV, then YTM= CY=CRBond prices and interest rates are negatively related Consol bondMakes fixed coupon payments forever. Has no face valueP=c/I or i=c/pPrice of a consol bond that makes $5 coupon payments forever at 8% is?= 5/0.08=65.5Yield to maturity- measures your return from buying a particular bond given that you hold till it maturesHowever, if you sell the bond before it matures, your return most likely will be different from your YTMWe need to take into account capitol gain or loss, the fact that the bond may appreciate or depreciate in value.One year holding period of return”R=Coupon/initial Price+ Change in Price/initial priceOr R= Current yield+ rate of capitol gain/lossR= Coupon Payment +Capitol gain/purchasing priceIf rate of capitol loss exceeds current yield, your overall return will be negativeInterest Rate Risk- Price of Financial asset will fluctuate in response to changing market interest rates.