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論文進度報告

論文進度報告. 指導教授 戴天時 博士 學生 鄭傑仁. Agenda. Introduction Merton’s Model Black and Cox’s Model. Introduction. VL=D+E =VA+TB-BC VL: Leverage value of the firm VA: Asset value of the firm TB: Tax benefit BC: Bankruptcy cost E: Equity D: Debt. Merton’s Model. Merton:. 45 度線.

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論文進度報告

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  1. 論文進度報告 指導教授 戴天時 博士 學生鄭傑仁

  2. Agenda • Introduction • Merton’s Model • Black and Cox’s Model

  3. Introduction VL=D+E =VA+TB-BC VL: Leverage value of the firm VA: Asset value of the firm TB: Tax benefit BC: Bankruptcy cost E: Equity D: Debt

  4. Merton’s Model

  5. Merton: 45度線 Leverage Value Equity BC Debt Debt Asset Value D

  6. Merton: 45度線 Leverage Value TB Equity τCDT α BC Debt Debt Asset Value D+(1-τ)CDT

  7. VL=D+E Equity D+(1-τ)CDT α BC Debt 1-α Debt Debt Asset Value D+(1-τ)CDT Asset Value D+(1-τ)CDT D+(1-τ)CDT

  8. 45度線 45度線 • VL=VA+TB-BC TB D+(1-τ)CDT τCDT α α BC BC Asset Value Debt Asset Value D+(1-τ)CDT

  9. Initial asset value=1000, Coupon rate=0.05, Maturity=1, Tax rate=0.35, 破產成本比例(α)=0.4, Risk free rate=0.1, Volatility=0.3, Debt=0~2000 The Optimal Debt=463, Equity holder=567.5968, Debt holder=439.0555, VL=1006.6523

  10. Merton(SB+RE): 45度線 TB2 Leverage Value Equity TB1 RE mixEquity τCDT α BC SB SB SB Asset Value V” D1+(1-τ)C1D1T

  11. VL=D+E,Equity部分 Equity V” 45度線 mixEquity mixEquity D1+(1-τ)C1D1T D1+(1-τ)C1D1T V”

  12. VL=D+E,Debt部分 V” α BC SB RE 1-α SB SB Asset Value Asset Value D1+(1-τ)C1D1T Asset Value D+(1-τ)CDT D1+(1-τ)C1D1T

  13. Equity: + 乘上比例 Equity V” 乘上比例 + RE: V” mixEquity mixEquity RE SB + SB D1+(1-τ)C1D1T D1+(1-τ)C1D1T 1-α SB: Asset Value Asset Value D1+(1-τ)C1D1T D1+(1-τ)C1D1T

  14. 45度線 45度線 45度線 • VL=VA+TB-BC TB1 TB2 D1+(1-τ)C1D1T τ(C1D1+C2D2)T V” τC1D1T α α BC BC Asset Value SB Asset Value D+(1-τ)CDT

  15. Initial asset value=1000, SB Coupon rate=0.05, RE Coupon rate=0.05, Maturity=1, Tax rate=0.35,破產成本比例(α)=0.4, Risk free rate=0.1, Volatility=0.3, Number of initial Stock=100,SB/D=0.5, Debt=0~2000 The Optimal Debt=922, Equity holder=255.3810, SB holder=437.1939, RE holder=316.4728, VL=1009.0478

  16. D_ratio=SB佔全部Debt的比例, Initial asset value=1000, SB Coupon rate=0.05, RE Coupon rate=0.05, Maturity=1, Tax rate=0.35, 破產成本比例(α)=0.4, Risk free rate=0.1, Volatility=0.3, Number of initial Stock=100, Debt=0~2000

  17. Merton(SB+RE): 45度線 TB2 Leverage Value Equity TB1 RE mixEquity τCDT α BC SB SB SB Asset Value ？ V” D1+(1-τ)C1D1T

  18. To solve V”

  19. Black and Cox’s Model(First-Passage Model)

  20. Black and Cox: 45度線 Leverage Value Equity BC Debt α BC Debt Debt Asset Value D DB

  21. Black and Cox: 45度線 Leverage Value TB Equity τCDT α BC Debt α BC Debt Debt Asset Value D+(1-τ)CDT DB

  22. Black and Cox: Leverage Value D+(1-τ)CDT DB Time T

  23. VL=D+E Equity D+(1-τ)CDT Leverage Value Leverage Value α BC Debt 1-α α BC Asset Value Debt Debt Debt Debt Asset Value Asset Value D+(1-τ)CDT D+(1-τ)CDT D+(1-τ)CDT DB DB

  24. 45度線 45度線 • VL=VA+TB-BC TB DB D+(1-τ)CDT τCDT Leverage Value Leverage Value α α BC BC Asset Value α α BC BC Debt Debt Asset Value Asset Value D+(1-τ)CDT D+(1-τ)CDT DB DB

  25. Initial asset value=1000, Coupon rate=0.05, Maturity=1, Tax rate=0.35, 破產成本比例(α)=0.4, Risk free rate=0.1, Volatility=0.3, Debt=0~2000 Default Boundary=(D+(1-tau)*C*D*T)*0.2 The Optimal Debt=463, Equity holder=567.5968, Debt holder=439.0555, VL=1006.6523

  26. Initial asset value=1000, Coupon rate=0.05, Maturity=1, Tax rate=0.35, 破產成本比例(α)=0.4, Risk free rate=0.1, Volatility=0.3, Debt=0~2000 Default Boundary=(D+(1-tau)*C*D*T)*0.9 The Optimal Debt=455, Equity holder=575.0264, Debt holder=431.5437, VL=1006.5701

  27. Black and Cox:(SB+RE): 45度線 TB2 Leverage Value Equity TB1 RE mixEquity τCDT α BC SB SB α BC SB SB Asset Value V” DB D1+(1-τ)C1D1T

  28. VL=D+E,Equity部分 Equity V” 45度線 mixEquity mixEquity D1+(1-τ)C1D1T D1+(1-τ)C1D1T V”

  29. VL=D+E,Debt部分 V” Leverage Value Leverage Value α BC SB RE 1-α α BC Asset Value Asset Value SB SB SB SB Asset Value Asset Value D1+(1-τ)C1D1T D+(1-τ)CDT D+(1-τ)CDT DB DB

  30. Equity: + 乘上比例 Equity V” 乘上比例 + RE: V” mixEquity mixEquity SB RE 1-α + D1+(1-τ)C1D1T D1+(1-τ)C1D1T SB: Asset Value Asset Value SB SB D1+(1-τ)C1D1T D+(1-τ)CDT DB

  31. 45度線 45度線 45度線 • VL=VA+TB-BC TB1 TB2 DB D1+(1-τ)C1D1T τ(C1D1+C2D2)T V” τC1D1T Leverage Value Leverage Value α α BC BC Asset Value α α BC BC SB SB Asset Value Asset Value D+(1-τ)CDT D+(1-τ)CDT DB DB

  32. Initial asset value=1000, SB Coupon rate=0.05, RE Coupon rate=0.05, Maturity=1, Tax rate=0.35,破產成本比例(α)=0.4, Risk free rate=0.1, Volatility=0.3, Number of initial Stock=100,SB/D=0.5, Debt=0~2000 Default Boundary=(D+(1-tau)*C*D*T)*0.2 The Optimal Debt=922, Equity holder=255.3810, SB holder=437.1939, RE holder=316.4728, VL=1009.0478

  33. Initial asset value=1000, SB Coupon rate=0.05, RE Coupon rate=0.05, Maturity=1, Tax rate=0.35,破產成本比例(α)=0.4, Risk free rate=0.1, Volatility=0.3, Number of initial Stock=100,SB/D=0.5, Debt=0~2000 Default Boundary=(D+(1-tau)*C*D*T)*0.9 The Optimal Debt=909, Equity holder=263.7002, SB holder=431.0778, RE holder=314.1912, VL=1008.9692

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