Straight bond Coupon Face value Coupon 0 P
Straight bond 利率固定,到期一次償還固定本金的債券 Coupon + Face value Coupon 0 P Coupon T
Reverse exchangeable 花旗銀行 cash 投資人 Reverse exchangeable Underlying stock 台積電
Cont. Coupon + Terminal value(ST , S 0) Coupon 0 P Coupon T
Cont. • Terminal value of reverse exchangeable Terminal value F 0 ST
What if… 花旗銀行 台積電 cash 投資人 債權人 Reverse exchangeable Underlying stock 台積電
(1)發現金 Debt value at T= F+C (F/S 0)ST (1 -α)AT ≧SF and +(1 -τ)C+S *Eos , if SATT≧ AT ≧ 0(1 -τ)C 0 τ)C ≦ AT <≧(1 F +(1 -τ)C+S , if S(1τ)C 0*Eos T ≦S 0 and A T , if AT < (1 - τ)C Equity value at T= AT-F-(1 -τ)C (=ST*Eos) , if ASTT ≧ FS 0+(1 -τ)C+S and AT ≧ (1 -τ)C 0*Eos τ)C ≦ ATA<T F≧(1+(1 -τ)C+S AT-(F/S 0)ST- (1 -τ)C (=ST*Eos) , if (1 ST ≦S 0 and τ)C 0*Eos 0 , if AT < (1 - τ)C When ST=S 0, AT-F-(1 -τ)C= S 0*Eos τ)C+S 0*Eos AT-(F/S 0)S 0 -(1 -τ)C= S 0*Eos =>AT =F +(1 -
(2)發新股 Debt value at T= F+C (F/S 0)ST (1 -α)AT ≧ SF 0 +(1 -τ)C+S , if SATT≧ and AT ≧ 0*Eos (1 -τ)C 0 ≦ F +(1 -τ)C+S , if S(1 and. AATT<≧(1τ)C 0*Eos T ≦S , if AT < (1 - τ)C Equity value at T= AT - F-(1 -τ)C (=ST*Eos) , if A STT ≧ SF 0+(1 -τ)C+S and AT ≧ 0*Eos (1 -τ)C (AT - (1 -τ)C)/(Eos+ F/S 0)*Eos (=ST*Eos) , if (1 ST ≦S and. ATA<T ≧(1τ)C 0*Eos τ)C 0 ≦ F +(1 -τ)C+S 0 , if AT < (1 - τ)C When ST=S 0, AT - F - (1 -τ)C= S 0*Eos =>AT =F+(1 -τ)C+S 0*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 ` Default boundary
Valuing firm A value, example • A公司發行一張面額800一年期的straight bond, 票面利率5%,到期時償還本金及利息,中間不支 息 其他參數:initial asset value= 1000 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+(10. 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+S 0*Eos Default boundary
Valuing firm B value, example • B公司發行一張面額800一年期的Reverse exchangeable, 票面利率10% , 到期時償還本金及利息, 中間不支息 其他參數:initial asset value= 1000 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 S 0 = 3. 1348 Default boundary= (1 -τ)C = (1 -0. 5)*800*0. 1= 40 F+(1 -τ)C+S 0*Eos = 800+(10. 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 0. 2109 1000 595. 43 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 F+C=880 (F/S 0)*SG+C=595. 67 614. 14 SG*Eos=202 491. 75 128. 87 H 602. 71 (F/S 0)*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
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