Chapter 13
Corporate Applications
±
Question 13.1
One could first value equity (
E
) as a call option and value the debt by subtracting equity from the asset
value (i.e.,
B
=
A
−
E
). We chose the “insurance” approach. We start with valuing default-free debt which
is equal to
008
120
.
T
e
−. ×
Insurance is the put option value:
Insurance
BSPut(100 120 0 30 0 08
0)
T
=,
,
.
,
.
,
,
The debt value, denote it as
0
,
T
B
,
is the difference:
120
Insurance.
T
e
−
The yield for a
T
maturity
bond is
0
ln(120/
)/ .
TT
B
T
ρ
,
=
Equity is the difference
00
100
.
AB
B
,,
−=
−
Doing this for each maturity,
we arrive at:
Maturity (
T
)
1
2
5
10
Default-Free Bond
110.7740
102.2573
80.4384
53.9195
Insurance
18.6705
18.1410
15.1037
10.1571
Debt
0
()
T
B
,
92.1034
84.1163
65.3347
43.7623
Yield
T
0.2646
0.1776
0.1216
0.1009
Equity
7.8966
15.8837
34.6653
56.2377
Debt-to-Equity
11.6637
5.2957
1.8847
0.7782
±
Question 13.2
Let
B
be the maturity value of the debt. We start with valuing default-free debt which is equal to
120
.
T
e
Insurance is the put option value:
Insurance
BSPut(100
0 30 0 08
0)
BT
,
.
,
.
,
,
The debt value, denote it as
0
,
T
B
,
is the difference:
Insurance.
T
Be
−
The yield for a
T
maturity bond
is
0
ln( /
)/ .
B
,
=
Equity is the difference
100
.
B
−
Doing this for each maturity, we
arrive at:
Maturity (
T
)
1
2
5
10
Face Value
B
127.42
135.3
161.98
218.65
Default-Free Bond
117.6235
115.2951
108.5784
98.2458
Insurance
23.6211
26.7229
31.8825
35.2832
Debt
0
T
B
,
94.0023
88.5722
76.6959
62.9626
Yield
T
0.3042
0.2118
0.1495
0.1245
Equity
5.9977
11.4278
23.3041
37.0374
Debt-to-Equity
15.6732
7.7506
3.2911
1.7000