Chapter 6 Interest Rates and Bond Valuation

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1 Chaper 6 Ineres Raes and Bond Valuaion Definiion and Descripion of Bonds Long-erm deb-loosely, bonds wih a mauriy of one year or more Shor-erm deb-less han a year o mauriy, also called unfunded deb Bond-sricly speaking, secured deb; bu used o describe all long-erm deb Bond Valuaion Terminology (Symbols) Formula A. Par Value (Face Value): conracually se (muliples of $1000 denominaions) 1. paid back as he erminal cash flow (principle) 2. symbols F,, and M ofen used B. Coupon Rae: conracually se; used o deermine he periodic ineres (coupon) paymens 1. symbols CR (coupon rae) C. Coupon Paymen: he periodic ineres paymen (funcion of face value and coupon rae) 1. symbols PMT, CP (coupon paymen), or IT (ineres) used 2. CP = (Par)(CR) D. Marke Rae: he curren going rae for bonds of similar risk and erm 1. rae used for all TVM calculaions 2. Yield o Mauriy (YTM) when calculaed 3. symbols r d or k d (rae or cos of deb) ofen used E. Term: number of periods unil he bond maures and principle reurned 1. mus be adjused for compounding periods per year 2. symbol n ofen used A. Recognize ha he cash flow sream is an annuiy wih a se paymen of he coupon paymens (CP) and a lump sum in he amoun of he principle (Par) B. Recognize ha he presen value (price) of any cash flow sream is he sum of he presen values of he pars of he cash flow sream (in his case he annuiy componen and he lump sum componen PRICE PV CF n n CP 1 ( 1 kd ) 1 (1 1 k d ) (1 Par k 1. CP and Par will be given (conracually se) 2. Given marke rae (k d ) you can solve for PRICE 3. Given PRICE you can solve for k d (marke rae or yield o mauriy) d ) n Fin 311 Chaper 06 Handou R1.Doc Page 1

paid back as he erminal cash flow (principle) 2. symbols F,, and M ofen used B. Coupon Rae: conracually se; used o deermine he periodic ineres (coupon) paymens 1. symbols CR (coupon rae) C.

2 Sample Problem #1 Solving for Price A. Given a 4-year bond wih a $1000 face value and a 5% coupon rae, annual compounding (annual periodic ineres paymens), find he price of he bond if he marke rae for similar bonds is 6%. B. umerical Soluion 1. Sep 1: Calculae he coupon paymen CP = Par(CR) = $1000 x 0.05 = $50 2. Sep 2: Assign values o he variables 3. Sep 3: Apply he formula PRICE PV 4 1 1, (1.06) (1.06) 1 C. Tabular Soluion $ Sep 1 & Sep 2: Same as above 2. Sep 3: Deermine able values for boh he annuiy and lump sum (ener he ables wih n and k d ) 3. Sep 4: Apply he formula Price = PV = V B = 50(PVIFA 4, 6% ) + 1,000(PVIF 4, 6% ) Price = PV = V B = 50(3.4651) + 1,000(0.7921) = $ D. Calculaor soluion I 1. Sep 1 & Sep 2: Same as above 2. Sep 3: Inpu variables ino calculaor 3. Sep 4: Compue price Cp PV Page 2 Fin 311 Chaper 06 Handou R1.Doc

umerical Soluion 1. Sep 1: Calculae he coupon paymen CP = Par(CR) = $1000 x 0.05 = $50 2. Sep 2: Assign values o he variables 3. Sep 3: Apply he formula PRICE PV 4 1 1,000 50 4 (1.06) (1.06) 1 C.

3 BOD PRICE Sample Problem #2 Solving for Yield o Mauriy Given Price A. Assume now ha you are given a quoe on he price for he bond in Problem #1 and i is selling for $ Wha is he yield o mauriy (marke rae for deb) for he bond? B. umerical and Tabular Soluions require rial and error o solve. C. Calculaor Soluion 1. Sep 1: Assign values o he variables 2. Sep 2: Inpu variables ino calculaor 3. Compue r d Cp I PV V: Bond Pricing Principles A. These five simple rules will allow you o beer undersand he relaionship beween PRICE and yield (k d ) for a given bond (inverse relaionship) 1. When coupon rae = k d he bond sells a par value (PRICE = Par) 2. When coupon rae > k d he bond sells a a premium (PRICE > Par) 3. When coupon rae < k d he bond sells a a discoun (PRICE < Par) 4. A mauriy PRICE = Par for all values of k d 5. The longer he ime o mauriy he greaer he premium (discoun) B. Discuss he graph below BOD VALUES $2, $1, $1, PREMIUM BOD VALUE PAR BOD VALUE $ DISCOUT BOD VALUE $ YEARS TO MATURITY Fin 311 Chaper 06 Handou R1.Doc Page 3

Sep 2: Inpu variables ino calculaor 3. Compue r d Cp I PV V: Bond Pricing Principles A.

4 Bond fac #1: There is an inverse relaionship beween ineres raes and bond prices. If ineres raes increase, bond prices decrease. If ineres raes decrease, bond prices increase. Bond fac #2: Ineres rae risk is he risk ha if ineres raes increase, bond prices will decrease. All else he same, a longer erm bond will have more ineres rae risk han a shorer erm bond. Bond fac #3: All else he same, here is an inverse relaionship beween he coupon rae and ineres rae risk. A bond wih a lower coupon has more ineres rae risk han a bond wih a higher coupon. Page 4 Fin 311 Chaper 06 Handou R1.Doc

All else he same, a longer erm bond will have more ineres rae risk han a shorer erm bond.

5 Zero coupon bonds Suppose we have he following bond: Par = $1,000 Coupon rae = 0% Mauriy = 15 years YTM = 9% Wha is he price of he bond? I Cp PV Wha is he price of he bond if we use semi-annual compounding? I Cp PV Fin 311 Chaper 06 Handou R1.Doc Page 5

6 Read Secion 6.2 Read Secion 6.3 Read Secion 6.4 Read Secion 6.5 Read Secion 6.6 Term Srucure of Ineres Raes Page 6 Fin 311 Chaper 06 Handou R1.Doc

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613. Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised