### 論文進度報告 指導教授 戴天時博士 學生 林昆鋒 Straight bond

```論文進度報告

Straight bond

Coupon + Face value
Coupon
0
P
Coupon
T
Reverse exchangeable

cash

Reverse
exchangeable
Underlying stock

Cont.
Coupon + Terminal value(ST ,S0)
Coupon
0
P
Coupon
T
Cont.
• Terminal value of reverse exchangeable
 F ( cash ), if S T  S 0

T erm inal value   F
shares of stock , if S T  S 0
S
 0

F
S0
Terminal value
F
0
S0
ST
m in( S 0 , S T )
What if…

cash

Reverse
exchangeable
Underlying stock
Underlying stock

• 考慮到Reverse Exchangeable的發行公司同時也是
uderlying stock的股票發行公司，所以當公司不破

(1)發現金 (2)發新股 (3)庫藏股 等三種delivery方式
(1)發現金
Debt value at T=
F+C
(F/S0)ST
(1-α)AT
+(1-τ)C+S
0*Eos
, if SATT≧≧S0Fand
AT ≧ (1-τ)C
τ)C ≦ AT <≧(1F +(1-τ)C+S
0*Eos
,if S(1τ)C
T ≦S0 and A
T
, if AT < (1- τ)C
Equity value at T=
≧S0
F +(1-τ)C+S
*Eos
AT-F-(1-τ)C
(=ST*Eos) ,if A
STT ≧
and AT ≧ 0(1-τ)C
τ)C ≦ A < F +(1-τ)C+S0*Eos
AT-(F/S0)ST- (1-τ)C (=ST*Eos) ,if S(1T ≦S0 andTAT ≧(1- τ)C
0
,if AT < (1- τ)C
When ST=S0,
AT-F-(1-τ)C= S0*Eos
AT-(F/S0)S0-(1-τ)C= S0*Eos
=>AT =F +(1-τ)C+S0*Eos
(2)發新股
Debt value at T=
F+C
(F/S0)ST
(1-α)AT
≧S0F and
+(1-τ)C+S
, if SATT≧
AT ≧ (1-τ)C
0*Eos
τ)C
≦ AATT<≧(1F +(1-τ)C+S
,if S(1τ)C
0*Eos
T ≦S
0 and
, if AT < (1- τ)C
Equity value at T=
≧SF0 and
+(1-τ)C+S
AT - F-(1-τ)C
(=ST*Eos) ,if SATT≧
AT ≧ (1-τ)C
0*Eos
(AT - (1-τ)C)/(Eos+ F/S0)*Eos (=ST*Eos) ,if S(1τ)C 0*Eos
τ)C
≦ ATA<T ≧(1F +(1-τ)C+S
T ≦S
0 and
0
,if AT < (1- τ)C
When ST=S0,
AT - F - (1-τ)C= S0*Eos
A T  (1   ) C
E os 
F
S0
* E os  S 0 * E os
=>AT =F+(1-τ)C+S0*Eos
Firm A
B/S
Asset
Debt
(Straight
bond)
Equity
Firm B
B/S
Asset
Debt
(Reverse
Exchangeable)
Equity
Leverage Firm value
Show
Firm
B
value
>
Firm
A
value
= Unleveraged Firm value + Tax Benefit - Bankruptcy cost
Valuing firm A value(straight bond)
Assume the firm’s asset value follows this lognormal diffusion
process:
665
dAt
 rd t   d z
At
Default boundary
`
Valuing firm A value, example
• A公司發行一張面額800一年期的straight bond，

tax rate τ=0.5
bankruptcy cost α=0.5
volatility of asset value σ=0.3
risk-free rate=3%
time steps =2
outstanding shares Eos=100
Default boundary=F+(1-τ)C=800+(1-0.5)*800*0.05=820
1915.65
E F+C=840
0.4825
AE-F-(1-τ)C=1095.65
1549.5
827.49
Pu
1000
Pm
771.76
225.69
741.73
0.5175
F
1253.34
F+C=840
AF-F-(1-τ)C=433.34
1013.78
827.49
205.98
G
Pd
Firm A value=
997.45
663.34
536.03
820
F+C=840
0
0
H 536.57
(1-α)AH=268.29
0
Time steps =252
r=0.03
σ=0.3
Tax rate=0.35
Bankruptcy cost=0.4
Coupon rate=5%
Valuing firm B (Reverse exchangeable)
F+(1-τ)C+S0*Eos
Default boundary
Valuing firm B value, example
• B公司發行一張面額800一年期的Reverse exchangeable,

tax rate τ=0.5
bankruptcy cost α=0.5
volatility of asset value σ=0.3
risk-free rate=3%
time steps =2
Eos=100
initial stock price S0 = 3.1348
Default boundary= (1-τ)C = (1-0.5)*800*0.1= 40
F+(1-τ)C+S0*Eos = 800+(1-0.5)*80+3.1348*100=1153.48
1755.91
E
F+C=800+80=880
0.4827
AE-F-(1-τ)C=1755.91-800-0.5*80=915.91
0.5173 F
1153.48
1423.17
867.15
595.43
0.2109
1000
F+C=880
AF-F-(1-τ)C=1153.48-800-0.5*80=313.48
934.89
725.72 0.7201 722.21
313.48
252.1
G 757.73
0.0689
Firm B value=
1039.2
614.14
(F/S0)*SG+C=595.67
491.75
SG*Eos=202
128.87
H
602.71
(F/S0)*SH+C=409.2
SH*Eos=129
Time steps =252
r=0.03
σ=0.3
Tax rate=0.35
Bankruptcy cost=0.4
Coupon rate=10%
Tax Benefit – Bankruptcy cost
```