1. Corporate Valuation and Financing Convertibles and warrants Prof H. Pirotte

2. IntroductionH. Pirotte 2 Remember the binomial model for bond prices… Data: Market Value of Unlevered Firm: 100,000 Risk-free rate per period: 5% Volatility: 40% Company issues 1-year zero-coupon Face value = 70,000 Proceeds used to pay dividend or to buy back shares V = 100,000 E = 34,854 D = 65,146 V = 67,032 E = 0 D = 67,032 V = 149,182 E = 79,182 D = 70,000 ∆t = 1 Binomial option pricing: review Up and down factors: Risk neutral probability : 1-period valuation formula

3. Introduction From there...  The binomial tree can be used to articulate any final payoff function based on the same underlying, i.e. the value of the firm »Subordinated debt »Convertibles »Warrants »Etc... Prof H. Pirotte 3

4. Introduction Two special mezzanine products  Convertible bonds »You can convert your bonds into equity, based on a predefined “strike” »The option to convert is “embedded” into the product  Bonds + warrants »You can trade separately the warrants from the bond. »The warrant is in this case a call option like any other...  Special difficulty »Exercising the convertibles or the warrants implies an issuance of new shares, so some “dilution” that has to be valued into the convertibles. Prof H. Pirotte 4

5. Introduction Payoff functions  Convertibles »3 payoffs potentially at the end: V (default) F (medium case) A fraction  of V T (high case) »Take the max of 0, F, qV T where q = m/(m+n)  Warrants »Same idea, but the value of the bond itself must be considered separately and prior to the warrant. »Take the max of 0, qV T - F Prof H. Pirotte 5

6. IntroductionH. Pirotte 6 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: 1.Warrants are sold by companies 2.If exercised, new shares are created Note: “warrants” are also long term (maturity 2-5 years) call options sold by financial institutions

7. IntroductionH. Pirotte 7 Warrant issue  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. Initial Balance Sheet Fixed Assets10,000Book Equity10,000 ( n = 100 shares P 0 = €100) Final Balance Sheet Fixed Assets10,000Book Equity9,600 ( n = 100 shares P 0 = €96) Warrant 400

8. IntroductionH. Pirotte 8 What happens at maturity?  Suppose market value of company at maturity is V T = 15,000  If warrant exercised: »Company issues 50 new shares »Receives 50 x 120 = 6,000 in cash »Market value of company becomes: V T + m * K = 15,000 + 6,000 = 21,000 »Allocation of shares TypeNumberPercentageValue Old1002/314,000 New 501/3 7,000 »Gain for warrantholders = Value of shares – Price to pay = m * P T - m * K =50 * 140 – 50 * 120 = 1,000 (20/warrant)

9. IntroductionH. Pirotte 9 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 (V T + m K) > m K q V T > (1-q) m K V T > n K  In previous example, exercise if: V T > 100 * 120 = 12,000

10. IntroductionH. Pirotte 10 Value of warrants at maturity nK 12,000 15,000 1,000 q = 1/3 VTVT m W T

11. IntroductionH. Pirotte 11 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 (all) warrants at maturity = 1/3 value of calls »50 W T = (1/3) * Max(0, V T – 12,000)  In general: »m W T = q Max(0,V T – n K) 1,000 3,000 12,00015,000VTVT 100 Calls 50 Warrants Proof: m W T = Max[0, q(V T +mK)-mK] = Max[0, qV T – m(1-q)K] = q Max(0,V T – nK)

12. IntroductionH. Pirotte 12 Valuing one warrant at maturity  m W T = q Max(0,V T – n K) »As: V T = n P T »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 V T = 15,000: »P T = 150 »C T = 150 – 120 = 30 »W T = (1 – 1/3) 30 = 20

13. IntroductionH. Pirotte 13 Current value of warrant  2 steps: 1.Value a call option 2.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 012Call 15636 125 100 0 80 640 Evolution of stock price Call = (0.622)² (36)/(1.08)² = 11.94 Warrant = (1-q) C = 7.96

14. IntroductionH. Pirotte 14 Issuing bonds with warrants  Consider now issuing a zero-coupon bond with warrants. »Face value6,000 »Number of bonds50 »Maturity2 years »1 warrant / bond Maturity2 years Exercise price120 »Issue price107 »Proceed from issue5,350 (=50 * 107)  Suppose that the issue is used to buy new assets.

15. IntroductionH. Pirotte 15 To exercise or not to exercise?  Suppose V T = 21,000  If warrants exercised, value of equity after repaying the debt is: »V T – 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 (V T – F + m K) – m K = (1/3)(21,000) – 6,000 = 1,000  Conclusion: exercise if: q (V T – F + m K) > m K V T > [(1-q)/q] m K + F V T > n K + F

16. IntroductionH. Pirotte 16 Example  In our example, warrant will be exercised if: »V T > 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 W T = q Max[0, V T – (nK+D)] 6,000 18,000 VTVT 1/3 Do not exerciseExercise Bonds + warrants

17. IntroductionH. Pirotte 17 Valuation using binomial model Bonds+Warrants = 5,806 Price / bond = 116 Issuing price (107) undervalued Market value of equity drops accordingly

18. IntroductionH. Pirotte 18 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 disappears.  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%

19. IntroductionH. Pirotte 19 Valuing the convertible bond  Valuation similar to valuation of bond with warrants. Value5,806 »Straight bond5,144 »Conversion right662  Yield to maturity on convertible bond: »Solve  Is this cheap debt?

20. IntroductionH. Pirotte 20 Binomial Valuation of Convertible Bond

21. IntroductionH. Pirotte 21 No free lunch! If Firm Subsequently Does Poorly If Firms Subsequently Prospers Convertible bonds (CBs) Compared to: No conversion because of low stock price Conversion because of high stock price Straight bondsCBs provide cheap financing because coupon rate is lower CBs provide expensive financing because bonds are converted which dilutes existing equity Common stockCBs provide expensive financing because firm could have issued common stock at high price CBs provide cheap financing because firm issues stock at high price when bonds are converted. Source: Ross, Westerfield, Jaffee Chap 22 Table 22.2

22. IntroductionH. Pirotte 22 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

23. IntroductionH. Pirotte 23 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) = 6,396 Receive call price: 6,250 Bondholders convert Current values incorporate force conversion in year 1

24. IntroductionH. Pirotte 24 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

25. IntroductionH. Pirotte 25 Convertible bond and volatility

26. IntroductionH. Pirotte 26 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 firms 1971-1990 »Increase in investment and new financing at the time of the calls of convertibles.

27. Introduction Convertible Bond Arbitrage  How does it work? Prof H. Pirotte 27

28. Introduction Other types  Automatic convertibles Prof H. Pirotte 28