Advanced Finance Warrants-Convertible bonds Professor André Farber Solvay Business School Université Libre de Bruxelles

June 27, 2015 Advanced Finance 2007 Warrant & convertible |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: 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

June 27, 2015 Advanced Finance 2007 Warrant & convertible |3 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 Price per share P 0 = €100 Final Balance Sheet Fixed Assets10,000Book Equity9,600 n = 100 shares P 0 = €96 Warrant 400

June 27, 2015 Advanced Finance 2007 Warrant & convertible |4 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 = 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)

June 27, 2015 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 (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

June 27, 2015 Advanced Finance 2007 Warrant & convertible |6 Value of warrants at maturity nK 12,000 15,000 1,000 q = 1/3 VTVT m W T

June 27, 2015 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 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)

June 27, 2015 Advanced Finance 2007 Warrant & convertible |8 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

June 27, 2015 Advanced Finance 2007 Warrant & convertible |9 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 Evolution of stock price Call = (0.622)² (36)/(1.08)² = Warrant = (1-q) C = 7.96

June 27, 2015 Advanced Finance 2007 Warrant & convertible |10 Issuing bonds with warrants Consider now issuing a zero-coupon 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.

June 27, 2015 Advanced Finance 2007 Warrant & convertible |11 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 = 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

June 27, 2015 Advanced Finance 2007 Warrant & convertible |12 Example In our example, warrant will be exercised if: V T > 100 * ,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

June 27, 2015 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

June 27, 2015 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: 1.Right to convert cannot be separated from the bond 2.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%

June 27, 2015 Advanced Finance 2007 Warrant & convertible |15 Valuing the convertible bond Valuation similar to valuation of bond with warrants. Value5,806 »Straight bond5,144 »Conversion right 662 Yield to maturity on convertible bond: Solve Is this cheap debt?

June 27, 2015 Advanced Finance 2007 Warrant & convertible |16 Binomial Valuation of Convertible Bond

June 27, 2015 Advanced Finance 2007 Warrant & convertible |17 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

June 27, 2015 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

June 27, 2015 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) = 6,396 Receive call price: 6,250 Bondholders convert Current values incorporate force conversion in year 1

June 27, 2015 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

June 27, 2015 Advanced Finance 2007 Warrant & convertible |21 Convertible bond and volatility

June 27, 2015 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 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 –Increase in investment and new financing at the time of the calls of convertibles.