Pricing of Bonds Chapter 2

Time of Value Future Value Future Valuewhere: n = number of periods n = number of periods P n = future value n periods from now (in dollars) P o = original principal (in dollars) r = interest rate per period (in decimal form) r = interest rate per period (in decimal form) Future Value of on Ordinary Annuity Future Value of on Ordinary Annuity

Time Value of Money Present Value Present Value Present Value of a Series of Future Values Present Value of a Series of Future Values

Time Value of Money Present Value of an Ordinary Annuity Present Value of an Ordinary Annuity

Bond Pricing price = PV of all future cash flows price = PV of all future cash flows to find price, you need to find price, you need expected CFs expected CFs coupon payments coupon payments par value par value yield yield

Bond Pricing price – yield relationship price – yield relationship inverse because as yield falls, PV of CFs increases and price of bond increases inverse because as yield falls, PV of CFs increases and price of bond increases price-yield curve is convex for noncallable bonds price-yield curve is convex for noncallable bonds discount / premium to par when coupon rate required yield discount / premium to par when coupon rate required yield market price changes when market price changes when yield changes due to credit quality of issuer yield changes due to credit quality of issuer change in price of bond selling at discount/premium because getting closer to maturity change in price of bond selling at discount/premium because getting closer to maturity change in yield required by market for bonds of similar risk change in yield required by market for bonds of similar risk

Bond Pricing floater – security that has coupon rate that changes when market rates change floater – security that has coupon rate that changes when market rates change coupon = reference rate plus spread coupon = reference rate plus spread reset periodically reset periodically cap / floor cap / floor inverse floater inverse floater created using a fixed rate bond (collateral) created using a fixed rate bond (collateral) create floater and inverse floater so that create floater and inverse floater so that total coupon interest paid to two bonds in each period is less than or equal to collateral’s coupon interest in each period total coupon interest paid to two bonds in each period is less than or equal to collateral’s coupon interest in each period total par value of two bonds is less than or equal to collateral’s total par value total par value of two bonds is less than or equal to collateral’s total par value ie., two securities created so that CFs from collateral can satisfy obligation of floater and inverse floater ie., two securities created so that CFs from collateral can satisfy obligation of floater and inverse floater

(1) Price Quote (2) Converted to a Decimal [ = (1)/100] (3) Par Value (4) Dollar Price [ = (2) x (3)] $ 10,000 $ 9, / ,000 85, / ,000 4, / ,000 8, / ,000, , / ,000 86, ,000 50, ,000 1, / , , / ,000 26, / ,000,000 1,035, Prices Converted into a Dollar Price