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Advanced Finance 2006-2007 Warrants-Convertible bonds

Advanced Finance 2006-2007 Warrants-Convertible bonds. Professor André Farber Solvay Business School Université Libre de Bruxelles. Warrants. Give to its owners the right to buy new shares issued by the company during a period of time at a price set in advance.

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Advanced Finance 2006-2007 Warrants-Convertible bonds

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  1. Advanced Finance2006-2007 Warrants-Convertible bonds Professor André Farber Solvay Business School Université Libre de Bruxelles

  2. Warrants • Give to its owners the right to buy new shares issued by the company during a period of time at a price set in advance. • Most of the time, warrants are issued with bonds • A price is the set for a “package” bond + warrant(s) • Later on, both components are traded separately • Warrants are similar to call option except for two differences: • Warrants are sold by companies • If exercised, new shares are created Note: “warrants” are also long term (maturity 2-5 years) call options sold by financial institutions Advanced Finance 2007 Warrant & convertible

  3. Warrant issue Initial Balance Sheet Fixed Assets 10,000 Book Equity 10,000n = 100 shares Price per share P0 = €100 • Company issues m = 50 warrants • Maturity = 2 years • Exercise price K = €120/share • Issue price = €8/warrant • Proceed of issue (400 = 50 * 8) paid out to shareholders as a dividend. Final Balance Sheet Fixed Assets 10,000 Book Equity 9,600n = 100 shares P0 = €96 Warrant 400 Advanced Finance 2007 Warrant & convertible

  4. What happens at maturity? • Suppose market value of company at maturity is VT = 15,000 • If warrant exercised: • Company issues 50 new shares • Receives 50 x 120 = 6,000 in cash • Market value of company becomes: • VT + m * K = 15,000 + 6,000 = 21,000 • Allocation of shares Type Number Percentage ValueOld 100 2/3 14,000New 50 1/3 7,000 • Gain for warrantholders = Value of shares – Price to pay = m * PT - m * K = 50 * 140 – 50 * 120 = 1,000 (20/warrant) Advanced Finance 2007 Warrant & convertible

  5. To exercise or not to exercise? • If they exercise, warrantholders own a fraction q of the shares • q = Number of new shares / Total number of shares • = m / (m+n) • They should exercise if the value of their shares is greater than the price they have to pay to get them: Exercise if: q (VT + m K)> m K q VT > (1-q) m K VT > n K • In previous example, exercise if: VT> 100 * 120 = 12,000 Advanced Finance 2007 Warrant & convertible

  6. Value of warrants at maturity m WT q = 1/3 1,000 VT nK12,000 15,000 Advanced Finance 2007 Warrant & convertible

  7. Warrants compared to call options • Consider now 100 calls on the shares with exercise price 120. • They will be exercised if stock price > 120 • Value of warrants at maturity = 1/3 value of calls • 50 WT = (1/3) * Max(0, VT – 12,000) • In general: • m WT = q Max(0,VT – n K) 100 Calls 3,000 1,000 50 Warrants 12,000 15,000 VT Proof:m WT = Max[0, q(VT+mK)-mK] = Max[0, qVT – m(1-q)K] = q Max(0,VT – nK) Advanced Finance 2007 Warrant & convertible

  8. Valuing one warrant at maturity • m WT = q Max(0,VT – n K) • As: VT = n PT • and: q = m/(m+n) • we get: • The value one warrant at maturity is equal to the value one call option multiplied by an adjustment factor to reflect dilution. • In previous example, for VT = 15,000: • PT = 150 • CT = 150 – 120 = 30 • WT = (1 – 1/3) 30 = 20 Advanced Finance 2007 Warrant & convertible

  9. Current value of warrant • 2 steps: • Value a call option • Multiply by adjustment factor 1-q • Back to initial example. Assume volatility of company = 22.3% • Use binomial option pricing with time step = 1 year Evolution of stock price Call = (0.622)² (36)/(1.08)² = 11.94 Warrant = (1-q) C = 7.96 Advanced Finance 2007 Warrant & convertible

  10. Issuing bonds with warrants • Consider now issuing a zero-coupon with warrants. • Face value 6,000 • Number of bonds 50 • Maturity 2 years • 1 warrant / bond • Maturity 2 years • Exercise price 120 • Issue price 107 • Proceed from issue 5,350 (=50 * 107) • Suppose that the issue is used to buy new assets. Advanced Finance 2007 Warrant & convertible

  11. To exercise or not to exercise? • Suppose VT = 21,000 • If warrants exercised, value of equity after repaying the debt is: • VT – F + m K = 21,000 – 6,000 + 6,000 = 21,000 • As previously, warrantholders own a fraction q (=1/3) of equity. • Their gain is: • q (VT – F + m K) – m K = (1/3)(21,000) – 6,000 = 1,000 • Conclusion: exercise if: q (VT – F + m K) > m K VT > [(1-q)/q] m K + F VT > n K + F Advanced Finance 2007 Warrant & convertible

  12. Example • In our example, warrant will be exercised if: • VT > 100 * 120 + 6,000 = 18,000 • The value of all warrants is equal to 1/3 of the value of 100 calls with strike price equal to 180 • m WT = q Max[0, VT – (nK+D)] Bonds + warrants Do not exercise Exercise 1/3 6,000 VT 18,000 6,000 Advanced Finance 2007 Warrant & convertible

  13. Valuation using binomial model Bonds+Warrants = 5,806 Price / bond = 116 Issuing price (107) undervalued Market value of equity drops accordingly Advanced Finance 2007 Warrant & convertible

  14. Convertible bond • A bond with a right to convert into a number of shares. • Similar to bond with warrants except: • Right to convert cannot be separated from the bond • If converted, the bond disappear. • Back to previous example: • Current stock price = 100 (number of shares n = 100) • Issue 50 zero-coupon convertible with face value 120 • Each bond is convertible into 1 share • Conversion ratio = # shares/ bond = 1 • Conversion value = Conversion ratio * Stock price = 100 • Conversion price = Face value/Conversion ratio = 120 • Conversion premium = (Conversion price – Stock price)/(Stock price) = 20% Advanced Finance 2007 Warrant & convertible

  15. Valuing the convertible bond • Valuation similar to valuation of bond with warrants. • Value 5,806 • Straight bond 5,144 • Conversion right 662 • Yield to maturity on convertible bond: • Solve • Is this cheap debt? Advanced Finance 2007 Warrant & convertible

  16. Binomial Valuation of Convertible Bond Advanced Finance 2007 Warrant & convertible

  17. No free lunch! Source: Ross, Westerfield, Jaffee Chap 22 Table 22.2 Advanced Finance 2007 Warrant & convertible

  18. Conversion Policy • Convertible bonds are very often callable by the firm. • If bond called, holder of convertible can choose between: • Converting the bond to common stock at the conversion ratio. • Surrendering the bond and receiving the call price in cash. • Convert if conversion value greater than call price (force conversion) • In theory: • companies should call the bond when conversion value = call price • Empirical evidence: • Bonds called when conversion value >>call price Advanced Finance 2007 Warrant & convertible

  19. Force conversion: example Assume convertible callable in year 1 Call price = 125 Total call value = 6,250 Firm’s decision: If not called: D = 6,705 > 6,250 Firm calls CBs Bonholder’s decision: Convert: (1/3)(19.188) = 6,396Receive call price: 6,250 Bondholders convert Current values incorporate force conversion in year 1 Advanced Finance 2007 Warrant & convertible

  20. Why Are Warrants and Convertible Issued? • Companies issuing convertible bonds • Have lower bond rating than other firms • Are smaller with high growth opportunities and more financial leverage • Possible explanations: • Matching cash flows • Low intial interest costs when cash flows of young risky and growing company are low • Lower sensitivity to volatility of firm • If volatility increases: straight bond but warrants • Protection against mistakes of risk evaluation • Mitigation of agency costs Advanced Finance 2007 Warrant & convertible

  21. Convertible bond and volatility Advanced Finance 2007 Warrant & convertible

  22. Matching financial and real options • Ref: Mayers, D., Why firms issue convertible bonds: the matching of financial and real options, Journal of Financial Economics 47 (1998) pp.83-102 • Sequential financing problem: investment option at future date • Providing fund up front for both initial investment and investment options difficult because of overinvestment (free-cash flow) problem • Issuing security is costly: avoid multiple issues • Convertible bonds are a solution: • Leaves funds in the firm if investment option valuable • Funds returned to bondholders if investment option not valuable • Call provision allows to force the financing plan when investment option valuable • Empirical evidence: call of convertible debt by 289 firmes 1971-1990 • Increase in investment and new financing at the time of the calls of convertibles. Advanced Finance 2007 Warrant & convertible

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