Topics Covered. Debt Instruments. Coupon paying bond. Zeros. Chapter 3. Valuing Bonds

Transcription

1 hape Valuing Bonds inciples of opoae Finance enh Ediion Slides by Mahew Will and Bo Sjö 1 opics oveed Deb Insumens he basics Using he esen Value Fomula o Value Bonds How Bond ices vay Wih Inees Raes he em Sucue of Inees Raes (Biefly) Explaining he em Sucue Real and Nominal Raes of Inees opoae Bonds and he Risk of Defaul Examinaion does no cove Duaion! - McGaw-Hill/Iwin opyigh 11 by he McGaw-Hill ompanies, Inc. All ighs eseved. Deb Insumens - - Money make vs Fixed income make Bonds deb insumens Zeo coupon bonds vs. oupon paying bonds Beae bonds vs. Regiseed bonds Fixed oupons o Floaes, Index bonds, eal bonds Bonds ae legal conacs he Indenue ells abou deails ovenans egulaes behavio; Resicions on he issue, meges, collaeal, callable bonds, wha o do in case of defaul ec. (debenue=unsecued in he US, bu secued in he UK) Bond: When you buy a bond, you buy a nominal value o be paid ou on he day of mauiy (), and coupon paymens. Face value = Nominal value = a Value YM : yield o mauiy, he yield you ge if buy oday and hold he bond unil mauiy In he US gov. bonds ypically pays coupons wice a yea, in Euope once a yea. Zeos - oupon paying bond - A Zeo-coupon bond, pays no coupon. ypically you buy one fuue nominal value FV. ice oday, ime o Mauiy =, YM = = FV (1 ) c = coupon ae oupon paymen: = c * FV ime o mauiy = in yeas YM =, ice oday is, hee annual coupons = ( 1 ) ( ) = 1 1 FV

2 V = (1 ) 1 (1 )... 1, ( 1 ) (1 ) Example If oday is Ocobe 1, 1, wha is he value of he following bond? An IBM Bond pays $ evey Sepembe fo yeas. In Sepembe 1 i pays an addiional $1 and eies he bond. YM is 7.% ash Flows: Sep Example coninued If oday is Ocobe 1, 1, wha is he value of he following bond? An IBM Bond pays $ evey Sepembe fo yeas. In Sepembe 1 i pays an addiional $1 and eies he bond. YM is 7.%) V = , ( ) ( ) ( ) ( 1.7) Example - Fance In Decembe 8 you puchase 1 Euos of bonds in Fance which pay a 8.% coupon evey yea. If he bond maues in 1 and he YM is.%, wha is he value of he bond? V = = 1. Euos ( 1.) ( 1.) ( 1.) = $1,11.8 Don be Supid use Annuiy -11 Annuiy in pacice -1 Much simple o use annuiy fomulas insead esen value annuiy faco A Fom fomula o able V = * A 1 1 A = (1 ) FV = (1 ) (1 ) = 1 FV = * A (1 ) In Decembe 8 you puchase 1 Euos of bonds in Fance which pay a 8.% coupon evey yea. If he bond maues in 1 and he YM is.%, wha is he value of he bond? (lease use fomula, check esuls wih ables) = = = = 8. (1.) (1.)..(1.) (1.) = 8.* *.888= = 1.

3 -1 Semi-annual bond fomula -1 Example - USA In Febuay 9 you puchase a yea US Govenmen bond. he bond has an annual coupon ae of.87%, paid semi-annually. If invesos demand a.% semiannual eun, wha is he pice of he bond? V =.7 1. = $1, ( 1.) ( 1.) ( 1.) ( 1.) ( 1.) Yields (), and coupon aes should always be quoed in yeas, so also fo ime o mauiy (). hus, he semiannual coupon bond fomula is, whee m is numbe fequency of coupon paymens, /m is he acual yield, and *m acual numbe of peiods o discoun. = (c/)*fv (Use annuiies and ge he esul as above) * m * = = * m 1 = = 1 m FV * m m * FV * -1 Inees Rae on 1y easuies -1 Example coninued - USA ake he same yea US Govenmen bond. If invesos demand a.% semiannual eun, wha is he new pice of he bond? Recaluae use he annuiy fomula V = 1. ( 1.) ( 1.) ( 1.) ( 1.) ( 1.) Yield, % = $ Yea Yield cuve -17 icing of Bonds -18 Bonds ae issued by ove diffeen hoizons. A govenmen issues fom one-monh o yeas. If you gaph all YM:s, agains ime you ge he Yield cuve. he slope of he yield cuve is efeed o as he ems-sucue of inees aes he slope and changes in he slope eflecs expecaions abou fuue inflaion and buiness cycle. enal bankes use his egulaly, and speculaos A IO: coupon paying bonds ae pice o mach exising simila bonds. oupon ae = YM on simila bonds iced o a c = YM => ice = nominal value (face value) If pice > face value, sell above pa If pice < face value sell below pa, = discoun bond

4 -19 Yield o Mauiy Yield o Mauiy - wo calculaions: 1) alculae pice given YM, o ) alculae YM given pice. Example A $1 easuy bond expies in yeas. I pays a coupon ae of 1.%. If he make pice of his bond is 17.88, wha is he YM? Example A $1 easuy bond expies in yeas. I pays a coupon ae of 1.%. If he make pice of his bond is 17.88, wha is he YM? alculae IRR = 8.% HOW? YM -1 YM - Ieaive mehod is needed In financial calculaos - makes hem quie expensive Excel We can do ial and eo! We know he following A bond is issued a pa A pa means ha he coupon ae (c) equals he YM, and = FV. Selling a pa: c=ym Selling above pa > FV Selling below pa < FV Since a bond is always issued a pa, you can look a oday s pice and ask whehe YM is highe o lowe han c? If he bond is selling below pa YM > c, y a YM value above c, and hen ohe one, and ohe one unil you find he YM ha =. Bonds - Global Inflaion Raes - Ae usually no inflaion poof, unless eal bonds, o index bonds, whee he coupon is adjused accoding o inflaion Socks ae bee in his espec he fac ha gov bond usually have been issued a nominal values, and coupons below inflaion => addiional income fo he govenmen (al. ax) Aveage Inflaion, % Aveages fom 19- Swizeland Nehelands USA anada Sweden Noway Ausalia Denmak UK Ieland Souh Afica Aveage Gemany (ex 19/) Belgium Spain Fance Japan Ialy

5 - Deb & Inees Raes Deb & Inees Raes - Nominal = Real expeced inflaion (appoximaion) Real is heoeically somewha sable Inflaion is a lage vaiable Appoximaion: = eal inflaion Q: Why do we cae? A: his heoy allows us o undesand he picing, and YM:s of bonds wih diffeen mauiies Acual fomula: Q: So Wha? A: he em Sucue ells us he acual cos of deb. ( nominal eal 1 ) = (1 )*(1 i) Gov. Bills vs. Inflaion ( - 8) -7 Gov. Bills vs. Inflaion ( - 8) -8 Unied Kingdom Unied Saes Inflaion 1. Inflaion % 1. -Bill Reuns %. -Bill Reuns hus -9 Defaul and Bankupcy - Inflaion and expecaions of fuue inflaion is one impoan pa of he bond yield and he pice. Gov. bonds ae called isk-fee becuase he pobabiliy of defaul is assumed o almos zeo. No oally coec, many many goveens defauls Fo isky bonds add a defaul isk pemium o he yield (equied eun) R_copoae = isk-fee defaul isk pemium Defaul isk pemium follows he defaul isk anking of he issue. See Damodoan s webb valuaion page. Defaul: Boowe canno fulfill paymens o 1%. Negociaions... Bankupcy: Deb holdes ake ove he emaing asses. Ofen a cosly legal pocedue.

6 -1 Defaul isk pemium How o se a defaul isk pemium? Look a hisoical defaul, use accouning daa, seco, ec. o calculae he pobabiliy of defaul. Divide fims ino diffeen classes depending on hei pobabiliy of defaul. Say fom AAA, AA exemy low isk, o BBB and D = aleady in defaul. Add pobabiliy of moving up and down in defaul pobabiliy (cash flow is going down) A lile human expeience Raing Invesmen banks ae all bond issues when he bond is issued and duing is life. No a pefec sysem, aing agencies has been manipulaed and is consanly unde aack fom mainly public insiuions o give hem a bee aing. ype You ae insuling and huing ou hones and had woking axpayes by lowe ou aing - Raing - Bond Raings - I is poblemaic o pedic defaul!!! Mos defaul siuaions ae no well pediced befoe hey happen Accouning manipulaions (hink Enon and Geece) opoae bonds, and sho-em commeical papes, only fo big esablished fims, wih a good cedi ecod. Key o bond aings. he highes-qualiy bonds ae aed iple A. Bonds aed iple B o above ae invesmen gade. Lowe-aed bonds ae called high-yield, o junk, bonds. Yield Spead - ices and Yields - Yield speads beween copoae and 1-yea easuy bonds. ices and yields of a sample of copoae bonds, Decembe 8. Yield spead beween copoae and govenmen bonds, % Spead on Baa bonds Spead on Aaa bonds Yeas Souce: Bond ansacions epoed on FINRA s RAE sevice: hp://cxa.makewach.com/fina/bondene

7 -7 Bond ading? Web Resouces -8 Analyse Slope of he yield cuve, edci inflaion and busines cycle Yield speads: long-em and sho em gov bonds opoae and govenmen bonds Domesic and foeignbonds lick o access web sies Inene connecion equied hp://cxa.makewach.com/fina/bondene hp://money.cnn.com/makes/bondcene