24-1 CHAPTER 24 Warrants and Convertibles McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 24-2 Executive Summary This chapter describes the basic features of warrants and convertibles The important questions are: How can warrants and convertibles be valued? What impact warrants and convertibles have on firm value? What are the differences between warrants, convertibles and call options? Under what circumstances are warrants and convertibles converted into common stock? McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 24-3 Chapter Outline 24.1 Warrants 24.2 The Difference between Warrants and Call Options 24.3 Warrant Pricing and the Black-Scholes Model (Advanced) 24.4 Convertible Bonds 24.5 The Value of Convertible Bonds 24.6 Reasons for Issuing Warrants and Convertibles 24.7 Why are Warrants and Convertibles Issued? 24.8 Conversion Policy 24.9 Summary and Conclusions McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 24-4 24.1 Warrants Warrants are call options that give the holder the right, but not the obligation, to buy shares of common stock directly from a company at a fixed price for a given period of time Warrants tend to have longer maturity periods than exchange traded options Warrants are generally issued with privately placed bonds as an “equity kicker” Warrants are also combined with new issues of common stock and preferred stock, given to investment bankers as compensation for underwriting services In this case, they are often referred to as a Green Shoe Option McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 24-5 24.1 Warrants The same factors that affect call option value affect warrant value in the same ways Stock price + Exercise price – Interest rate + Volatility in the stock price Expiration date + Dividends– McGraw-Hill/Irwin Corporate Finance, 7/e + © 2005 The McGraw-Hill Companies, Inc All Rights 24-6 24.2 The Difference Between Warrants and Call Options When a warrant is exercised, a firm must issue new shares of stock This can have the effect of diluting the claims of existing shareholders McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 24-7 Dilution Example Imagine that Mr Armstrong and Mr LeMond are shareholders in a firm whose only asset is 10 ounces of gold When they incorporated, each man contributed ounces of gold, then valued at $300 per ounce They printed up two stock certificates, and named the firm LegStrong, Inc Suppose that Mr Armstrong decides to sell Mr Mercx a call option issued on Mr Armstrong’s share The call gives Mr Mercx the option to buy Mr Armstong’s share for $1,500 If this call finishes in-the-money, Mr Mercx will exercise, Mr Armstrong will tender his share Nothing will change for the firm except the names of the shareholders McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 24-8 Dilution Example Suppose that Mr Armstrong and Mr LeMond meet as the board of directors of LegStrong The board decides to sell Mr Mercx a warrant The warrant gives Mr Mercx the option to buy one share for $1,500 Suppose the warrant finishes in-the-money, (gold increased to $350 per ounce) Mr Mercx will exercise The firm will print up one new share McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 24-9 Dilution Example The balance sheet of LegStrong Inc would change in the following way: Balance Sheet Before (Book Value) Liabilities and Equity Assets Gold: $3,000 Debt Equity (2 shares) Total Assets $3,000 McGraw-Hill/Irwin Corporate Finance, 7/e Total $3,000 $3,000 © 2005 The McGraw-Hill Companies, Inc All Rights 2410 Dilution The balance sheet of LegStrong Inc would change in the following way: Balance Sheet Before (Market Value) Liabilities and Equity Assets Gold: $3,500 Debt Equity (2 shares) Total Assets $3,500 McGraw-Hill/Irwin Corporate Finance, 7/e Total $3,500 $3,500 © 2005 The McGraw-Hill Companies, Inc All Rights 2412 Warrant Pricing and the Black-Scholes Model (Advanced) Warrants are worth a bit less than calls due to the dilution To value a warrant, value an otherwise-identical call and multiply the call price by: n n + nw Where n = the original number of shares nw = the number of warrants McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 2413 Warrant Pricing and the Black-Scholes Model (Advanced) To see why, compare the gains from exercising a call with the gains from exercising a warrant The gain from exercising a call can be written as: share price −exercise price Note that when n = the number of shares, share price is: Firm's value net of debt n Thus, the gain from exercising a call can be written as: Firm's value net of debt −exercise price n McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 2414 Warrant Pricing and the Black-Scholes Model (Advanced) The gain from exercising a warrant can be written as: share price after warrant exercise −exercise price Note that when n = the original number of shares and nw = the number of warrants, share price = Firm's value net of debt + exercise price × nw after n + nw warrant exercise Thus, the gain from exercising a warrant can be written as: Firm' s value net of debt + exercise price × nw −exercise price n + nw McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 2415 Warrant Pricing and the Black-Scholes Model (Advanced) The gain from exercising a warrant can be written as: Firm's value net of debt − exercise price n Firm's value net of debt + exercise price × nw − exercise price n + nw A bit of algebra shows that these equations differ by a factor of n n + nw So to value a warrant, multiply the value of an otherwise-identical call by McGraw-Hill/Irwin Corporate Finance, 7/e n n + nw © 2005 The McGraw-Hill Companies, Inc All Rights 2416 24.4 Convertible Bonds A convertible bond is similar to a bond with warrants The most important difference is that a bond with warrants can be separated into different securities and a convertible bond cannot Recall that the minimum (floor) value of convertible: Straight or “intrinsic” bond value Conversion value The conversion option has value McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 2417 24.5 The Value of Convertible Bonds The value of a convertible bond has three components: Straight bond value Conversion value Option value McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 2418 Convertible Bond Problem Litespeed, Inc., just issued a zero coupon convertible bond due in 10 years The conversion ratio is 25 shares The appropriate interest rate is 10% The current stock price is $12 per share Each convertible is trading at $400 in the market What is the straight bond value? What is the conversion value? What is the option value of the bond? McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 2419 Convertible Bond Problem (continued) What is the straight bond value? SBV = $1,000 = $385.54 10 (1.10) –What is the conversion value? 25 shares × $12/share = $300 –What is the option value of the bond? $400 – 385.54 = $14.46 McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 2420 24.5 The Value of Convertible Bonds Convertible Bond Value Convertible bond values Conversion Value floor value Straight bond value floor value = conversion ratio McGraw-Hill/Irwin Corporate Finance, 7/e Option value Stock Price © 2005 The McGraw-Hill Companies, Inc All Rights 2421 24.6 Reasons for Issuing Warrants and Convertibles A reasonable place to start is to compare a hybrid like convertible debt to both straight debt and straight equity Convertible debt carries a lower coupon rate than does otherwise-identical straight debt Since convertible debt is originally issued with an out-of-themoney call option, one can argue that convertible debt allows the firm to sell equity at a higher price than is available at the time of issuance However, the same argument can be used to say that it forces the firm to sell equity at a lower price than is available at the time of exercise McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 2422 Convertible Debt vs Straight Debt Convertible debt carries a lower coupon rate than does otherwiseidentical straight debt If the company subsequently does poorly, it will turn out that the conversion option finishes out-of-the-money But if the stock price does well, the firm would have been better off issuing straight debt In an efficient financial market, convertible bonds will be neither cheaper or more expensive than other financial instruments At the time of issuance, investors pay the firm for the fair value of the conversion option McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 2423 Convertible Debt vs Straight Equity If the company subsequently does poorly, it will turn out that the conversion option finishes out-of-the-money, but the firm would have been even better off selling equity when the price was high But if the stock price does well, the firm is better off issuing convertible debt rather than equity In an efficient financial market, convertible bonds will be neither cheaper or more expensive than other financial instruments At the time of issuance, investors pay the firm for the fair value of the conversion option McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 2424 24.7 Why are Warrants and Convertibles Issued Convertible bonds reduce agency costs, by aligning the incentives of stockholders and bondholders Convertible bonds also allow young firms to delay expensive interest costs until they can afford them Support for these assertions is found in the fact that firms that issue convertible bonds are different from other firms: The bond ratings of firms using convertibles are lower Convertibles tend to be used by smaller firms with high growth rates and more financial leverage Convertibles are usually subordinated and unsecured McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 2425 24.8 Conversion Policy Most convertible bonds are also callable When the bond is called, bondholders have about 30 days to choose between: Converting the bond to common stock at the conversion ratios Surrendering the bond and receiving the call price in cash From the shareholder’s perspective, the optimal call policy is to call the bond when its value is equal to the call price In the real world, most firms wait to call until the bond value is substantially above the call price Perhaps the firm is afraid of the risk of a sharp drop in stock prices during the 30-day window McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 2426 24.9 Summary and Conclusions Convertible bonds and warrants are like call options However, there are important differences: Warrants are issued by the firm Warrants and convertible bonds have different effects on corporate cash flow and capital structure Warrants and convertibles cause dilution to existing shareholder’s claims Many arguments, both plausible and implausible, are given for issuing convertible securities Convertible bonds give lends the chance to benefit from risks and reduces the conflicts between bondholders and stockholders concerning risk McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights ... circumstances are warrants and convertibles converted into common stock? McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 24-3 Chapter Outline 24.1 Warrants... Convertibles Issued? 24.8 Conversion Policy 24.9 Summary and Conclusions McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 24-4 24.1 Warrants Warrants are... services In this case, they are often referred to as a Green Shoe Option McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 24-5 24.1 Warrants The same factors