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Options and Corporate Financial Management

Options and Corporate Financial Management. University of Macau December 2009 Andrew Chen Southern Methodist University. Outline. Pricing Corporate Debt Securities Financial Innovations in Issuing Securities Protecting Downside Risk of Equity Holdings Post Merger

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Options and Corporate Financial Management

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  1. Options and Corporate Financial Management University of Macau December 2009 Andrew Chen Southern Methodist University

  2. Outline • Pricing Corporate Debt Securities • Financial Innovations in Issuing Securities • Protecting Downside Risk of Equity Holdings Post Merger • Hedging Costs of Employee Stock Options AC:2

  3. Payoff to Bondholders • The payoffs to the bondholders at the maturity depend on whether or not the firm is solvent. • If the terminal firm value is greater than the total promised payment of the debt, the bondholders get paid in full • If the terminal firm value is less than the total promised payment, the firm is declared bankrupt and the firm is taken over by the bondholders. AC: 3

  4. Payoff to Bondholders { H if VT > H (1) YD = VT otherwise (2) = Min [H,VT] Therefore, the payoffs to the bondholders can be expressed as follows: AC: 4

  5. Payoff to Stockholders { VT – H if VT > H (3) YE = 0 otherwise = Max [VT – H, 0] (4) The payoffs to the stockholders can be expressed as follows AC: 5

  6. Pricing of Equity and Nonconvertible Debt • The structure of the payoffs to the stockholders as in (4) is the same as that of a call option at expiration: • CT = Max [ST – K, 0], where ST is the stock price at the call option’s expiration date and K is the strike price of the call option. • Owning the common equity of a levered firm, stockholders can be viewed as owning a call option to buy back the firm from the bondholders at a strike price equal to the total promised payments of the debt. • The option pricing model can be applied to value the common equity and the risky straight debt of a firm. AC: 6

  7. Value of Common Equity (5) Let VE be the current market value of common equity and VD be the current market value of the straight debt of the firm, then we can obtain the following results from the Black-Scholes OPM: Where σ = The Standard Deviation of changes in firm value AC: 7

  8. Value of Nonconvertible Debt (6) VD = V – VE AC: 8

  9. Example I: Pricing Nonconvertible Debt • Assumptions: • Total current asset value of the firm = $20 Million. • Capital Structure: One Million shares of common stock and nonconvertible debt issue. • Debt issue has one-year maturity, and composed of discount bonds with aggregate face value of $18 Million. • With an equal probability, the firm’s assets value will either increase or decrease 20% every six-month. • For the bionomial tree model of option pricing, we have u=1.2 and d=0.8, and Δt=0.5. Given that the annual risk-free interest rate is 5%. What is the fair market value of the firm’s straight debt? AC: 9

  10. Pricing Nonconvertible Debt Step 1: View the equity of the levered firm as a call option and apply the binomial tree approach to find the value of the firm’s equity. Step 2: The value of the firm’s straight debt can be obtained by subtracting the equity value from the current total asset value. Given the percentage up and down movements in each time step, we know the derived probability for the up-movement in each time step, p = 0.5633. Further, we know that Cuu=10.8, Cud=1.2, and Cdd=0. AC: 10

  11. Pricing Nonconvertible Debt $28.8 D 10.8 $24 B $19.2 E $20 A 1.2 3.8534 $16 C $12.8 F 0 Apply the two-period call option pricing formula, we can find the fair value of the firm’s equity as a call option as follows: = 3.8534 Therefore, the fair market value of the firm’s common equity is $3.8534 million. And the fair market value of the firm’s straight debt is $16.1466 million (= 20 – 3.8534). AC: 11

  12. Example II: Pricing of Convertible Debt • Continued Assumptions: • Current firm value is $20 million • The firm has 1 million shares of common stock. • Further assume that with an equal probability the firm’s value will either increase 20% or decrease 20% every six-month. • The firm’s one-year maturity debt which has a par value of $18 million is a convertible bond with a conversion price of $6.0 instead of the nonconvertible bond analyzed in the previous section. • Therefore, the bondholders can receive 3 million shares of the firm’s common stock if they decide to convert their bond into common stock. • If the fully-diluted market price of the firm’s common stock at maturity of the bond is greater than the bond’s conversion price: • Bondholders will exercise their conversion option or conversion privilege to purchase a proportion of the firm’s common stock, at a strike price equal to the face value of the bond. AC: 12

  13. Pricing of Convertible Debt (7) The proportion of the firm’s value that the bondholders receive (called dilution factor) is equal to   where, N = the number of shares of common stock before conversion; n = the total number of shares for which the convertible bond can be exchanged. AC: 13

  14. Pricing of Convertible Debt (8) Thus, the value of a convertible bond is equal to the value of a regular nonconvertible bond plus the conversion privilege (CP), that is VCD = VD + CP. AC: 14

  15. Value of Convertible Debt • Dilution Factor: w = 0.75 [=3/(3+1)] • There are 1 million shares of firm’s stock before the conversion, and there will be 3 million shares ($18 million/$6.0) of new stock if the bond is converted. • The value of the conversion option or conversion privilege (CP) can be derived using the binomial tree approach as follows. • Since the bondholders will receive 75% of the value of the firm upon the conversion, we have to find 75% of the firm value in constructing the binomial tree to determine the value of CP with a strike price of $18 million. AC: 16

  16. Pricing of Convertible Debt $21.6 D 3.6 $18 B $14.4 E $15 A 0 1.0866 $12 C $9.6 F 0 • Using the two-period call option pricing formula: = 1.0866 AC: 16

  17. Pricng of Convertible Debt Therefore, we know that: VCD = 16.1466 + 1.0866 = 17.2332 VE = V – VCD = 20 – 17.2332 = 2.7668 In other word, the market value of the firm’s convertible bond is $17.2332 million and the value of the firm’s common equity after issuing the convertible bond with face value of $18 million is $2.7668 million. AC: 17

  18. Valuation of Convertible Bond Using Black/Scholes OPM (5) (6) From (5), we know the value of firm’s equity is: And from (6), we know the value of nonconvertible debt is: AC: 18

  19. Valuation of Convertible Bond Using Black/Scholes OPM • The value of Conversion Privilege (CP) is: where, w is the dilution factor which is defined as follows: Therefore, as we have seen in (8) before, the value of convertible bond is: VCD = VD + CP AC: 19

  20. Payoffs of Nonconvertible and Convertible Bonds AC: 20

  21. Payoffs of Nonconvertible and Convertible Bonds AC: 21

  22. Example III: Compound Option & Coupon Bond • III (A): One-year Single Coupon Bond: • Current Value of the firm: V = $100 • Promised Payments: H = $120, consisting of a Face Value = $100 and a single coupon = $20 payable at the end of one-year • Δt = 0.5 • u = 1.2 • d = 0.833 • r = 5% • p = 0.523 • 1 – p = 0.477 A-22

  23. Example III (A): Single Coupon Bond III (A): The firm values at t = 0, 1, and 2: $144 $120 $100 $100 $100 $83.33 $69.44 AC: 23

  24. Example III (A): Single Coupon Bond III (A): The Values of Call at t = 0, 1, and 2: Cuu = 24 Cu = 12.24 Cud = 0 6.24 Cd = 0 Cdd = 0 VE = $6.24 and VD = $93.76 AC: 24

  25. Example III (B): One-Year Multiple Coupon Bond Face value = $100 Semi-annual coupon = $10, payable at the end of six-month and the end of one-year Shareholder owns a compound option (Call on Call) with compound strike of $10 at t = 1 AC:25

  26. Example III (B): One-year Multiple Coupon Bond: Cuu = 34 Cu = 17.34 3.75 Cud = 0 (COC) Cd = 0 Cdd = 0 AC: 26

  27. Example III (B): One-year Multiple Coupon Bond Value of Compound Option: Call on Call (COC): COC = [p x Max(Cu-Ko,0) + (1-p) x Max(Cd-Ko,0)]e-r(Δt) VE = $3.75 and VD = $96.25 AC: 27

  28. Financial Innovations in Corporate Financing • Financial Innovation: “TRICK ME” T = Taxes and Transaction Costs R = Regulations I = Informational Asymmetry C = Completing Markets K = Knowledge Advancements M = Marketing E = Engineering AC: 28

  29. “Bond Declines May Spread World-Wide” “The U.S bond market is becoming increasingly linked to global credit markets, and world bond yields now tend to track changes in the U.S. economy closely. One of the reasons for this is the ability of large companies, such as General Electric, to issue bonds around the world at will. Mark VanderGriend, who operates the financing desk at Banque Paribas, said it took only 15 minutes to organize a 4 billion French franc ($791.6 million) deal for GE. Raising the money in francs and switching immediately to dollars allowed GE to save 0.05 percent, which comes to about $400,000 annually on the nine-year deal. “They have such a huge requirement for capital that they are constantly looking for arbitrages,” noted VanderGriend, adding that GE does not particularly care where the savings come from.” (WSJ, 04/09/96, p.C1) AC: 29

  30. Contingent Value Rights (CVRs) • A. Chen, K. Chen and B. Laiss, “Pricing Contingent Value Rights: Theory and Practice,” Journal of Financial Engineering, June 1993. • CVRs are really the “Bear Put Spreads” • In other words,CVR = P(TP) – P(BP) • CVRs are used for • Reducing informational asymmetry in M&A • Voluntary spin-offs • Privatizing firms from public enterprises • Infrastructural financing AC: 30

  31. CVRs Examples AC: 31

  32. CVRs AC: 32

  33. Payoff of CVR 15.77 15.77 (TP – BP) 45.77 (TP) 30 (BP) AC: 33

  34. Payoff of Stock + CVR 45.77 45.77 15.77 30 (BP) 45.77 (TP) AC: 34

  35. Binomial Tree Approach to value CVR • Example: • Given that the current market value of the GRE Company’s stock is $20 per share. • The company has just issued 100,000 units of a one-year CVR with a Base Price of $27.5 and a Target Price of $40. • We know that with an equal probability the GRE stock price will go up 35% or go down 25% at the end of each 6-month period and the current annual risk-free interest rate is 5%. • Use the two time-steps binomial tree approach to find the market value of each CVR. AC: 35

  36. Binomial Tree Approach to Value CVR • We know that • u = 1.35 • d = 0.75 • r = 0.05 • Δt = 0.5 • Thus, and 1 – p = 0.5411 e-2(.05)(0.5) = 0.9512 AC: 36

  37. Binomial Tree Approach to Value CVR P40 = [(.4589)2(3.55) + 2(.4589)(.5411)(19.75) + (.5411)2(28.75)] x (.9512) = 18.045 P27.5 = [2(.4589)(.5411)(7.25) +(.5411)2(16.25)]x(.9512) = 7.951 Therefore, CVR = P40 – P27.5 = $10.097 AC: 37

  38. Protecting Downside Risk of Shares Value Post Merger • Case Example: • The following are hedging strategies for CAH shares post merger • Protective Put Options • Zero Cost “Collar” • Zero Cost “Call Spread Collar” AC: 38

  39. Protective Put Options The investor owned CAH stock and was unable to sell the shares due to tax limitations could reduce downside risk by buying protective puts. Given the market price of CAH stock was $61 per share at the time. Investors could purchase a two-year European-style, cash-settled protective put option with strike price of $55 from Morgan Stanley for $4.50 per share. AC: 39

  40. Protective Put Options • Hedging outcomes with buying protective puts at option expirations are as follows: AC: 40

  41. Protective Put Options AC: 41

  42. Zero Cost “Collar” Shareholders could use “zero-cost collar” to reduce the downside risk without paying any option premium. Essentially the investors purchase a two-year, European style, cash-settle put options with strike price of $55.00 from Morgan Stanley. They finance the put premium by selling a two-year, European style, cash-settled call options with strike price of $77.00 from Morgan Stanley. AC: 42

  43. Zero Cost “Collar” • Hedging outcomes with zero cost “collar” at option expirations are as follows: AC: 43

  44. Zero Cost “Collar” AC: 44

  45. Zero Cost “Call Spread Collar” Shareholders have downside protection without giving away all future upside potential. The shareholders of CAH could enter into a “call spread collar” with Morgan Stanley by buying a two-year cash-settled call option with K = $75 and selling a two-year cash-settled call option with K = $61, that is, [C(K=75) – C(K=61)], then use the proceeds to buy a two-year cash-settled put option with K = $52. Thus, creating a zero-cost call-spread collar. AC: 45

  46. Zero Cost “Call Spread Collar” • Hedging outcomes with zero cost “call spread collar” at option expirations are as follows: AC: 46

  47. Zero Cost “Call Spread Collar” AC: 47

  48. Hedging Employee Stock Option Exposure • Cash Costs of Equity Exposure with employee Stock Option • Passive strategy and acting reactively vs. acting proactively • Hedging Alternatives • Buy Equity Forward • Buy Knock-In Barrier Call Options • Create the Zero-Cost “Reverse Collar” AC: 48

  49. Hedging Employee Stock Option Exposure Net Cash Costs without Hedging AC: 49

  50. Hedging Employee Stock Option Exposure Costs and Risk of Using Equity Forward AC: 50

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