chapter 7 corporate finance

8/9/2019 Chapter 7 Corporate Finance

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© 2003 The McGraw-Hill Companies, Inc. All rights

Interest Rates andBond Valuation

Lecture 6


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McGraw-Hill!Irwin © 2003 The McGraw-Hill Companies, Inc. All rights

7.2 Lecture Outline

• Bonds and Bond Valuation• Bond Markets

• Inflation and Interest Rates

– Fisher Effect• Determinants of Bond Yields


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7. Bond Definitions

• Bond• !ar "alue #face "alue$

• %ou&on rate

• %ou&on &a'ment• Maturit' date

• Yield or Yield to maturit'


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7.( Present Value of Cash Flows as Rates Change

• Bond Value ) !V of cou&ons * !V of &ar • Bond Value ) !V annuit' * !V of lum& sum

• Remem+er, as interest rates increase the !V-s

decrease• o, as interest rates increase, +ond &rices

decrease and "ice "ersa


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7./ Valuing a Discount Bond with Annual Coupons

• %onsider a +ond 0ith a cou&on rate of 13 andcou&ons &aid annuall'. 4he &ar "alue is 51

and the +ond has / 'ears to maturit'. 4he 'ield to

maturit' is 113. 6hat is the "alue of the +ond

– 8sin9 the formula:

• B ) !V of annuit' * !V of lum& sum

• B ) 1;1 – 1?./? * /?.(/ ) ?>.(


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7.> Graphical Relationship Between Price andYieldto!aturit"


7/25McGraw-Hill!Irwin © 2003 The McGraw-Hill Companies, Inc. All rights

7.7 Bond Prices# Relationship Between Couponand Yield

• If Y4M ) cou&on rate, then &ar "alue ) +ond &rice

• If Y4M @ cou&on rate, then &ar "alue @ +ond

&rice – 6h' – ellin9 at a discount, called a discount +ond

• If Y4M A cou&on rate, then &ar "alue A +ond &rice

– 6h'

– ellin9 at a &remium, called a &remium +ond



7. $he BondPricing %&uation

t

t

r$#1

F

r

r$#1

1C1

%ValueBond ++

+=



7.? %'a!ple ()*

%ou&on rate ) 1(3, semiannual cou&onsY4M ) 1>3

Maturit' ) 7 'ears

!ar "alue ) 51Find &resent "alues +ased on the &a'ment &eriod

– o0 man' cou&on &a'ments are there

– 6hat is the semiannual cou&on &a'ment – 6hat is the semiannual 'ield

– B ) 7;1 – 1



7.1 Interest Rate Ris+

• !rice Risk – %han9e in &rice due to chan9es in interest rates

– on9Cterm +onds ha"e more &rice risk than shortC

term +onds

• Rein"estment Rate Risk

– 8ncertaint' concernin9 rates at 0hich cash flo0s

can +e rein"ested

– hortCterm +onds ha"e more rein"estment rate risk

than lon9Cterm +onds



7.11 Figure (),



7.12 Co!puting Yieldto!aturit"

• YieldCtoCmaturit' is the rate im&lied +' thecurrent +ond &rice

• Findin9 the Y4M reuires trial and error if'ou do not ha"e a financial calculator and is

similar to the &rocess for findin9 r 0ith anannuit'

• %onsider a +ond 0ith a 13 annual cou&on

rate, 1/ 'ears to maturit' and a &ar "alue of51. 4he current &rice is 5?2.?. – 6ill the 'ield +e more or less than 13


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7.17 Factors Affecting Re&uired Return

• Default risk &remium and an'thin9 else thataffects the risk of the cash flo0s to the +ondholders

• 4aGa+ilit' &remium – remem+er munici&al

"ersus taGa+le• iuidit' &remium – +onds that ha"e more

freuent tradin9 0ill 9enerall' ha"e lo0er

reuired returns



7.1 Bond Pricing $heore!s

• Bonds of similar risk #and maturit'$ 0ill +e &riced to 'ield a+out the same return,

re9ardless of the cou&on rate

•If 'ou kno0 the &rice of one +ond, 'ou canestimate its Y4M and use that to find the &rice

of the second +ond

• 4his is a useful conce&t that can +e transferred

to "aluin9 assets other than +onds



7.1? %'a!ple ().

• H taGa+le +ond has a 'ield of 3 and amunici&al #not taGa+le$ +ond has a 'ield of >3

– If 'ou are in a (3 taG +racket, 0hich +ond do

'ou &refer

• 3#1 C .($ ) (.3

• 4he afterCtaG return on the cor&orate +ond is (.3,

com&ared to a >3 return on the munici&al

– Ht 0hat taG rate 0ould 'ou +e indifferent +et0eenthe t0o +onds

• 3#1 – 4$ ) >3

• 4 ) 2/3



7.2 Bond /uotations

– 6hat com&an' are 0e lookin9 at

– 6hat is the cou&on rate If the +ond has a

51 face "alue, 0hat is the cou&on &a'ment

each 'ear

– 6hen does the +ond mature

– 6hat is the current 'ield o0 is it com&uted

– o0 man' +onds trade that da'

– 6hat is the uoted &rice

– o0 much did the &rice chan9e from the

&re"ious da'



7.21 $reasur" /uotations

– 6hat is the cou&on rate on the +ond

– 6hen does the +ond mature

– 6hat is the +id &rice 6hat does this mean

– 6hat is the ask &rice 6hat does this mean

– o0 much did the &rice chan9e from the &re"ious

da'

– 6hat is the 'ield +ased on the ask &rice



7.22 Inflation and Interest Rates

• Definition of Inflation• Real rate of interest – chan9e in &urchasin9

&o0er

• ominal rate of interest – uoted rate ofinterest, chan9e in &urchasin9 &o0er and

inflation

• 4he eG ante nominal rate of interest includesour desired real rate of return &lus an

adJustment for eG&ected inflation



7.2 $he Fisher %ffect

• 4he Fisher Effect defines the relationshi& +et0een real rates, nominal rates and inflation

• #1 * R$ ) #1 * r$#1 * h$, 0here

– R ) nominal rate – r ) real rate

– h ) eG&ected inflation rate

• H&&roGimation – R ) r * h



7.2( %'a!ple ()0

• If 0e reuire a 13 real return and 0e eG&ectinflation to +e 3, 0hat is the nominal rate

• R ) #1.1$#1.$ – 1 ) .1 ) 1.3

• H&&roGimation: R ) 13 * 3 ) 13• Because the real return and eG&ected inflation

are relati"el' hi9h, there is si9nificant

difference +et0een the actual Fisher Effectand the a&&roGimation.


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7.2/ $er! 1tructure of Interest Rates

• 4erm structure is the relationshi& +et0een timeto maturit' and 'ields, all else eual

• It is im&ortant to reco9niKe that 0e &ull out the

effect of default risk, different cou&ons, etc.

• Yield cur"e – 9ra&hical re&resentation of the

term structure

– ormal – u&0ardCslo&in9, lon9Cterm 'ields are

hi9her than shortCterm 'ields

– In"erted – do0n0ardCslo&in9, lon9Cterm 'ields are

lo0er than shortCterm 'ields


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7.2> Figure ()0 2 3pward1loping Yield Cur4e


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7.27 Figure ()0 2 Downward1loping Yield Cur4e

chapter 7 corporate finance

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