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6 Mishkin/Eakins •Mishkin/Eakins • Financial Mark Financial Markets and Institutioets and Institutions,ns, Seventh EditionSeventh Edition
Chapter 12
Chapter 12
The Bond Market
The Bond Market
Answers to End-of-Chapter
Answers to End-of-Chapter
Questions
Questions
1.
1. Investors use Investors use capital markets capital markets for long-term for long-term investment purpinvestment purposes. Thoses. They use money use money markets !ey markets !hichhich
have lo!er yields primarily for
have lo!er yields primarily for temporary or transaction purposes.temporary or transaction purposes.
".
". The primary capThe primary capital market secuital market securities are stockrities are stocks and #onds and #onds. Most os. Most of these are f these are purchased and purchased and o!nedo!ned
#y households. #y households. $.
$. The primary The primary market is for market is for securities #esecurities #eing issued for the ing issued for the very first tvery first time and the ime and the issuer receives issuer receives thethe
funds paid for the security. The secondary market is for securities that have #een issued previously funds paid for the security. The secondary market is for securities that have #een issued previously #ut are #eing traded among inves
#ut are #eing traded among investors.tors.
%.
%. The par value is The par value is the amount the ithe amount the issuer !ill pay tssuer !ill pay the holder !hen he holder !hen the #ond matuthe #ond matures. The coupon inres. The coupon interestterest
rate is multiplied times the par value to determine the interest payment the issuer must make each year. rate is multiplied times the par value to determine the interest payment the issuer must make each year. The maturity date is !hen the issuer must pay the holder the
The maturity date is !hen the issuer must pay the holder the par value.par value.
&.
&. Treasury #iTreasury #ills mature in less lls mature in less than 1 year than 1 year Treasury notTreasury notes mature in 1 es mature in 1 to 1' years and to 1' years and Treasury Treasury #onds#onds
mature in 1' to $' years. mature in 1' to $' years. (.
(. The risk that The risk that a #ond)s pra #ond)s price !ill change due to ice !ill change due to changes in mchanges in market interest arket interest rates is called rates is called interest rate interest rate risk.risk.
*.
*. +gencies that +gencies that issue securitiissue securities include ,ines include ,innie Mae formerly tnie Mae formerly the ,overnment he ,overnment ational Mortgagational Mortgagee
+ssociation the 0ederal ousing
+ssociation the 0ederal ousing +dministration+dministration the the 2e2eterans +dministration the 0ederal terans +dministration the 0ederal ationalational
Mortgage +ssoc
Mortgage +ssociation and the iation and the Student 3oan Marketing +ssociation. The first four Student 3oan Marketing +ssociation. The first four fund mortgagefund mortgage
loans and the last
loans and the last funds college student loans.funds college student loans.
4.
4. 0irms like havin0irms like having the fle5i#ig the fle5i#ility to ad6uslity to ad6ust their capital structure #y pt their capital structure #y paying off de#aying off de#t they no lot they no longer nger
need. They also need to pay off de#t to remove restrictive covenants. 7all provisions permit #oth need. They also need to pay off de#t to remove restrictive covenants. 7all provisions permit #oth these actions at the issuer)s discretion.
these actions at the issuer)s discretion. 8.
8. + s+ sinking fund inking fund contains funds set ascontains funds set aside #y the issuide #y the issuer of a #ond to per of a #ond to pay for the redempay for the redemption of the #tion of the #ondond
!hen it matures. 9ecause a sinking fund increases the likelihood that a firm !ill have the
!hen it matures. 9ecause a sinking fund increases the likelihood that a firm !ill have the funds tofunds to
pay off the #onds as re:uired
pay off the #onds as re:uired investors like the feature. +s a result interest rates are lo!er on investors like the feature. +s a result interest rates are lo!er on
securities !ith sinking funds. securities !ith sinking funds. 1'.
1'. The list The list of terms of a of terms of a #ond is #ond is kno!n as kno!n as the indentthe indenture.ure.
11.
11. 7apital market securit7apital market securities may #e sold in a ies may #e sold in a pu#lic offering pu#lic offering or in a private plor in a private placement. In a pu#licacement. In a pu#lic
offering investment #ankers register the security !ith the SE7
offering investment #ankers register the security !ith the SE7 and market it through a net!ork ofand market it through a net!ork of
#rokerage houses. In a private placement
#rokerage houses. In a private placement the firm or an investment #anker sells the securities to a the firm or an investment #anker sells the securities to a
very limited num#er of
Quantitative Problems
1. + #ond pays ;4' per year in interest 4< coupon. The #ond has & years #efore it matures at !hich time it !ill pay ;1'''. +ssuming a discount rate of 1'< !hat should #e the price of the #ond =evie! 7hapter $>
Solution: ;8"%.14
". + ?ero coupon #ond has a par value of ;1''' and matures in "' years. Investors re:uire a 1'< annual return on these #onds. 0or !hat price should the #ond sell> ote@ Aero coupon #onds do not pay any interest. =evie! 7hapter $>
Solution: ;1%4.(%
$. 7onsider the t!o #onds descri#ed #elo!@
Bond A Bond B
Maturity 1& yrs "' yrs
7oupon =ate
Baid semiannually
1'< (<
Bar 2alue ;1''' ;1'''
a. If #oth #onds had a re:uired return of 4< !hat !ould the #onds) prices #e>
#. Cescri#e !hat it means if a #ond sells at a discount a premium and at its face amount par value. +re these t!o #onds selling at a discount premium or par>
c. If the re:uired return on the t!o #onds rose to 1'< !hat !ould the #onds) prices #e>
Solution:
a. 9ond += ;11*".8"
9ond 9= ;4'".'*
#. 9ond + is selling at a premium 9ond 9 is selling at a discount
c. 9ond += ;1'''
9ond 9= ;(&(.4"
%. + "-year ;1''' par ?ero-coupon #ond is currently priced at ;418.''. + "-year ;1''' annuity is currently priced at ;1*1".&". If you !ant to invest ;1'''' in one of the t!o securities !hich is a #etter #uy> Dou can assume
a. the pure e5pectations theory of interest rates holds
#. neither #ond has any default risk maturity premium or li:uidity premium and
c. you can purchase partial #onds.
Solution: ith PV= ;418F FV= ;1'''F PMT= 'F and N= " the yield to maturity on the t!o-year
?ero-coupon #onds is 1'.&< for the t!o-year annuities. PV= ;1*1".&"F PMT= 'F
FV=;"'''F and N= " gives a yield to maturity of 4.'*<. The ?ero-coupon #onds are
&. 7onsider the follo!ing cash flo!s. +ll market interest rates are 1"<.
Year 0 1 2 3 4
7ash 0lo! 1(' 1*' 14' "$'
a. hat price !ould you pay for these cash flo!s> hat total !ealth do you e5pect after "G years if you sell the rights to the remaining cash flo!s> +ssume interest rates remain constant.
#. hat is the duration of these cash flo!s>
c. Immediately after #uying these cash flo!s all market interest rates drop to 11<. hat is the impact on your total !ealth after "G years>
Solution:
a. Brice= 1(' + 1*' + 14' + "$' =;&&".(*
1.1" 1.1""
1.1"$
1.1"%
E5pected ealth =1(' ×1.1"1.& + 1*'× 1.1"&
+ 14' 1.1"& + "$' 1.1"1.& =;*$$.(8 1(' 1+ 1*' "+ 14' $+ "$' #. Curation= 1.1" 1.1" 1.1" 1.1" = ".&' &&".(*
c. E5pected ealth= 1('× 1.111.& +1*'× 1.11.&
+ 14' 1.11.&+ "$' 1.111.& =;*$$.*%
Since you are holding the cash flo!s for their duration you are essentially immuni?ed from interest rate changes in this simplistic e5ample.
(. The yield on a corporate #ond is 1'< and it is currently selling at par. The marginal ta5 rate is "'<. + par value municipal #ond !ith a coupon rate of 4.&'< is availa#le. hich security is a #etter #uy>
Solution: The e:uivalent ta5-free rate =ta5a#le interest rate ×1− marginal ta5 rate. In this case
'.1'×1− '."'=4<. The corporate #ond offers a lo!er after-ta5 yield given the
marginal ta5 rate so the municipal #ond is a #etter #uy.
*. If the municipal #ond rate is %."&< and the corporate #ond rate is (."&< !hat is the marginal ta5 rate assuming investors are indifferent #et!een the t!o #onds>
Solution: The e:uivalent ta5-free rate = ta5a#le interest rate × 1−marginal ta5 rate. In this case
'.'%"&= '.'("&× 1− X or X=$"<.
4. MHE Inc. has an outstanding converti#le #ond. The #ond can #e converted into "' shares of common e:uity currently trading at ;&"/share. The #ond has & years of remaining maturity a ;1''' par value and a (< annual coupon. MHE)s straight de#t is currently trading to yield &<. hat is the minimum price of the #ond>
Solution: The price must e5ceed the straight #ond value or the value of conversion you !ill see !hy in the ne5t :uestion.
If converted the de#t is !orth ;&" ×"' =;1'%'.
+ssuming a &< DTM is correct the price of straight de#t is computed as@
PMT= ('F N= &F FV=1'''F I=&
7ompute PV F PV=1'%$."8
The #ond must #e trading for at least ;1'%$."8.
8. +ssume the de#t in the previous :uestion is trading at 1'$&. o! can you earn a riskless profit from this situation ar#itrage>
Solution:
a. Short "' shares of MHE at ;&"/share. 7ash
;1 '%*' I
#. Burchase a converti#le #ond. ;1'.$&
;&
c. 7onvert the #ond to shares and use to close short position.
+ssuming these transactions are completed simultaneously you make a riskless profit of ;&.
Typically small investors cannot short stock and have use of the proceedsJthe #roker retains it as collateral. So this doesn)t :uite !ork. 9ut the idea is correct.
1'. + 1'-year 1''' par value #ond !ith a &< annual coupon is trading to yield (<. hat is the current yield>
Solution: The current price of the #ond is computed as follo!s@
PMT=&'F N=1'F FV=1'''F I= (
7ompute PV F PV= 8"(.%'
The current yield =&'/8"(.%'=&.%<
11. + ;1''' par #ond !ith an annual coupon has only 1 year until maturity. Its current yield is (.*1$< and its yield to maturity is 1'<. hat is the price of the #ond>
Solution:
a. CY='.'(*1$=7oupon/Brice or 7oupon = '.'(*1$× Brice
#. Brice=7oupon+1'''/1.1'.
Su#stituting from 1 Brice ='.'(*1$×Brice+ 1'''/1.1'
Solve for priceF Brice = ;8(4.1*
1". + 1-year discount #ond !ith a face value of ;1''' !as purchased for ;8''. hat is the yield to maturity> hat is the yield on a discount #asis>
Solution: 8''=1'''/1+ DTM or DTM=11.11<
DC9= 1''' K 8''/1''' ×$('/$(&= 8.4(<
1$. + *-year ;1''' par #ond has an 4< annual coupon and is currently yielding *.&<. The #ond can #e called in " years at a call price of ;1'1'. hat is the #ond yielding assuming it !ill #e called
kno!n as the yield to call>
Solution: The current price of the #ond is computed as follo!s@
PMT=4'F N=*F FV=1'''F I= *.&
7ompute PV F PV=1'"(.%4
Lsing this the yield to call is calculated as follo!s@
PMT=4'F N="F FV=1'1'F PV=1'"(.%4
1%. + "'-year ;1''' par value #ond has a *< annual coupon. The #ond is calla#le after the 1'th year for a call premium of ;1'"&. If the #ond is trading !ith a yield to call of (."&< the #ond)s yield to maturity is !hat>
Solution: The current price of the #ond is computed using the yield to call as f ollo!s@
PMT=*'F N= 1'F FV=1'"&F I= (."&
7ompute PV F PV= 1'(4.18
Lsing this the yield to maturity is calculated as follo!s@
PMT=*'F N= "'F FV=1'''F PV=1'(4.18
7ompute I F I=(.$8<
1&. + 1'-year ;1''' par value #ond has a 8< semiannual coupon and a nominal yield to maturity of 4.4<. hat is the price of the #ond>
Solution: The price of the #ond is computed as follo!s@
PMT=%&F N= "'F FV=1'''F I= 4.4
7ompute PV F PV=1'1$.1"
1(. Dour company o!ns the follo!ing #onds@
Bond Market Value Duration
+ ;1$million "
9 ;14million %
7 ;"'million $
If general interest rates rise from 4< to 4.&< !hat is the appro5imate change in the value of the portfolio>
Solution: Bortfolio duration = "× 1$/&1+ %×14/&1+$ ×"'/&1=$.'8
Δ 2alue= −Curation× Δi/1+ i× riginal 2alue