公司理财教学资料chap007.ppt
Chapter 7Interest Rates and Bond Valuation9/7/2023Chapter Outline Bonds and Bond Valuation Bond Features Bond Ratings Some Different Types of Bonds Bond Markets Inflation and Interest Rates Determinants of Bond Yields7-29/7/2023Market Values($Trillion)Value of outstanding issues9/7/2023Bonds and Bond Valuation A bond is a legally binding agreement between a borrower and a lender that specifies the:Par(face)value Coupon rate Coupon payment Maturity Date The yield to maturity is the required market interest rate on the bond.Do not confuse the coupon rate with the required market interest rateBond Definitions Bond Par value(face value)Coupon rate Coupon payment Maturity date Yield or Yield to maturity(required return,market rate)7-59/7/2023 The Bond-Pricing EquationTTr)(1Frr)(11-1C Value BondNotice that:qThe first term is the present value of the coupon payments(an annuity);and,qThe second term is the present value of the bonds par valueBond=Present Value of Cash Flows Bond Value=PV of coupons+PV of par Bond Value=PV of annuity+PV of lump sum As interest rates increase,present values decrease So,as interest rates increase,bond prices decrease and vice versa7-79/7/2023Valuing a Discount Bond with Annual Coupons Consider a bond with a coupon rate of 10%and annual coupons.The par value is$1,000,and the bond has 5 years to maturity.The yield to maturity is 11%.What is the value of the bond?Using the formula:B=PV of annuity+PV of lump sum B=1001 1/(1.11)5/.11+1,000/(1.11)5 B=369.59+593.45=963.04 Using the calculator:N=5;I/Y=11;PMT=100;FV=1,000 CPT PV=-963.047-89/7/2023Valuing a Premium Bond with Annual Coupons Suppose you are reviewing a bond that has a 10%annual coupon and a face value of$1000.There are 20 years to maturity,and the yield to maturity is 8%.What is the price of this bond?Using the formula:B=PV of annuity+PV of lump sum B=1001 1/(1.08)20/.08+1000/(1.08)20 B=981.81+214.55=1196.36 Using the calculator:N=20;I/Y=8;PMT=100;FV=1000 CPT PV=-1,196.367-99/7/2023Graphical Relationship Between Price and Yield-to-maturity(YTM)Bond PriceYield-to-maturity(YTM)7-109/7/2023Bond Prices:Relationship Between Coupon and Yield If YTM=coupon rate,then par value=bond price If YTM coupon rate,then par value bond price Why?The discount provides yield above coupon rate Price below par value,called a discount bond If YTM coupon rate,then par value bond price Why?Higher coupon rate causes value above par Price above par value,called a premium bond7-119/7/2023The Bond Pricing Equationttr)(1FVrr)(11-1C Value Bond7-129/7/2023Example 7.1 p.196 Coupon rate=14%,semiannual coupons YTM=16%;Maturity=7 years Par value=$1,000 Find present values based on the payment period How many coupon payments are there?What is the semiannual coupon payment?What is the semiannual yield?B=701 1/(1.08)14/.08+1,000/(1.08)14=917.567-139/7/2023Interest Rate Risk Price Risk Change in price due to changes in interest rates Long-term bonds have more price risk than short-term bonds Low coupon rate bonds have more price risk than high coupon rate bonds Reinvestment Rate Risk Uncertainty concerning rates at which cash flows can be reinvested Short-term bonds have more reinvestment rate risk than long-term bonds High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds7-149/7/2023Figure 7.2 p.1977-159/7/2023Computing Yield to Maturity Yield to Maturity(YTM)is the rate implied by the current bond price It is not the coupon rate!Finding the YTM requires trial and error if you do not have a financial calculator If you have a financial calculator,enter N,PV,PMT,and FV,remembering the sign convention(PMT and FV need to have the same sign,PV the opposite sign)7-169/7/2023YTM with Annual Coupons Consider a bond with a 10%annual coupon rate,15 years to maturity and a par value of$1,000.The current price is$928.09.Will the yield be more or less than 10%?N=15;PV=-928.09;FV=1,000;PMT=100 CPT i=11%7-179/7/2023YTM with Semiannual Coupons Suppose a bond with a 10%coupon rate and semiannual coupons,has a face value of$1,000,20 years to maturity and is selling for$1,197.93.Is the YTM more or less than 10%?What is the semiannual coupon payment?How many periods are there?N=40;PV=-1,197.93;PMT=50;FV=1,000;CPT i=4%(Is this the YTM?)YTM=4%*2=8%7-189/7/2023Table 7.17-199/7/2023Current Yield vs.Yield to Maturity Current Yield=annual coupon/price Yield to maturity=current yield+capital gains yield Example:10%coupon bond,with semiannual coupons,face value of 1,000,20 years to maturity,$1,197.93 price Current yield=100/1,197.93=.0835=8.35%Price in one year,assuming no change in YTM=1,193.68 Capital gain yield=(1,193.68 1,197.93)/1,197.93=-.0035=-.35%YTM=8.35-.35=8%,which is the same YTM computed earlier7-209/7/2023Bond Pricing Theorems Bonds of similar risk(and maturity)will be priced to yield about the same return,regardless of the coupon rate If you know the price of one bond,you can estimate its YTM and use that to find the price of the second bond This is a u
