CORPORATE BONDS
October 1999
1
Corporate Bonds
Spread depends on
1. Default Premium
2. State Taxes
3. Risk Premium
4. Liquidity
2
Major Problems
1. Valuation
2. Size of Risk Premium
3. Classification
3
Valuation
∑= +
= Tt tc
tr
tcf1
00 )1(
)( Value
where1. cf(t) is cash flow in t (Promised)2. c tr00 is corporate spot rate
4
Determining Risk Premium
Basic Idea If no risk premium would discount expected cashflow at riskless rate and on average get invoice price. Riskpremium is thus extra return so that on average invoice priceis correct.
IllustrationLet )]([ tcfE be expected cash flow in t then if no riskpremium
∑= +
=T
t tr
tcfEG
t1 )1(
)]([ Price Model
00
whereG
tr00 is riskless rate
and Model Price = invoice price on average
5
Let P be Premium then find P such that
Model Price = Invoice Price
∑= ++
=T
1t t)tPr1(
)]t(cf[EG
t00
Price Model
Note actually estimate
∑= +
=T
1t t)r1(
)]t(cf[Ec
t00
Price Model
and
Gt00
ct00t rrP −=
6
Determining Expected Cash Flow
A. Ignoring state taxes
Consider one Period Bond
State Cash FlowDoesn't Default Principal + Interest
default a • Principal
where a = recovery rate
100a 1P)100c)(1P1()]1(cf[E •++−=
7
Consider two Period Bond
in one )100a(Pc)P1( 11 •+−
in two )]100a(2P)100c)(2P1)[(1P1( •++−−
Consider three Period Bond
in one )100a(1Pc)1P1( •+−
in two )100a2Pc)2P1)((1P1( •+−−
in three )))()(()(( 100a3P3P1100c2P11P1 •+−+−−
8
B. Including state taxes
State taxes are deductable at federal level. Therefore,effective rate is )1( gtst −•
Also note cash flows are changed because of capital loss ifbankrupt
Consider One Period Bond
( )[ ] )())(()(])()[( gt1st100a1P100aP100gt1sctP11cfE 111 −−•+•++−−=
tax saving on capital loss
9
Consider Two Period Bond
in one
)()()()()( gt1st100a11P100a1Pgt1st c 1P1 −−+•+−−
in two
)]()(
)())()()[((
gt1st100a12P
100a2P100gt1sct2P11P1
−−+
•++−−−
If options use
value optionVV opt noopt +=
October 1999Determining Expected Cash FlowA. Ignoring state taxesConsider three Period BondConsider Two Period Bond
in one