Dilution Example. Chapter 24 Warrants and Convertibles. Warrants. The Difference Between Warrants and Call Options. Warrants

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1 Chapter 24 Warrats ad Covertibles Warrats The Differece betee Warrats ad Call Optios Warrat Pricig ad the Black-Scholes Model Covertible Bods The Value of Covertible Bods Reasos for Issuig Warrats ad Covertibles Why are Warrats ad Covertibles Issued Coversio Policy Warrats Warrats are call optios that give the holder the right, but ot the obligatio, to buy shares of commo stock directly from a compay at a fixed price for a give period of time. Ted to have loger maturity periods Geerally issued ith privately placed bods as a equity kicker. Also combied ith e issues of commo ad preferred stock, give to ivestmet bakers as compesatio for uderritig services. I this case, they are ofte referred to as a Gree Shoe Optio. Warrats The same factors that affect call optio affect arrat i the same ays. Stock price + Exercise price Iterest rate + Volatility i the stock price + Expiratio date + Divideds The Differece Betee Warrats ad Call Optios Whe a arrat is exercised, a firm must issue e shares of stock. This ca have the effect of dilutig the claims of existig shareholders. Warrat Pricig Dilutio Example Stetso Ic. stock is curretly sellig for $15 per share. You o arrats that give you the right to purchase.25 shares of e commo stock for $5. per arrat. The price of the arrats are curretly $1.. Imagie that Mr. X ad Mr. Y are shareholders i a firm hose oly asset is 1 ouces of gold. Whe they icorporated, each ma cotributed 5 ouces of gold, the d at $3 per ouce. They prited up to stock certificates, ad amed the firm XY, Ic. Suppose that Mr. X decides to sell Ms. Z a call optio issued o Mr. X s share. The call gives Ms. Z the optio to buy Mr. X s share for $1,5. If this call fiishes i-the-moey, Ms. Z ill exercise, Mr. X ill teder his share. Nothig ill chage for the firm except the ames of the shareholders.

2 Dilutio Example Suppose that Mr. X ad Mr. Y meet as the board of directors of XY. The board decides to sell Ms. Z a arrat. The arrat gives Ms. Z the optio to buy oe share for $1,5. Suppose the arrat fiishes i-the-moey, (gold icreased to $35 per ouce). Ms. Z ill exercise. The firm ill prit up oe e share. Dilutio Example The balace sheet of XY Ic. ould chage i the folloig ay: Balace Sheet Before (Book Value) $3, Total $3, Liabilities ad (2 shares) Total $3, $3, Dilutio The balace sheet of XY Ic. ould chage i the folloig ay: Balace Sheet Before Warrat (after price chage) (Market Value) Total Liabilities ad (2 shares) Total Dilutio The balace sheet of XY Ic. ould chage i the folloig ay: Cash: Balace Sheet After Warrat (Market Value) $1,5 Total $5, Liabilities ad (3 shares) $5, Total $5, Warrat Pricig ad the Black-Scholes Model Warrat Pricig ad the Black-Scholes Model Warrats are orth a bit less tha calls due to the dilutio. To a arrat, a otherise-idetical call ad multiply the call price by: + Where = the origial umber of shares = the umber of shares created by the arrats To see hy, compare the gais from exercisig a call ith the gais from exercisig a arrat. The gai from exercisig a call ca be ritte as: share price ( S -E) Note that he = the umber of shares, share price is: Thus, the gai from exercisig a call ca be ritte as:

3 Warrat Pricig ad the Black-Scholes Model The gai from exercisig a arrat ca be ritte as: share price after arrat exercise Note that he = the origial umber of shares ad = the umber of arrats, share price Firm' s - debt + exercise price after = + arrat exercise Thus, the gai from exercisig a arrat ca be ritte as: Firm' s - debt + exercise price + Warrat Pricig ad the Black-Scholes Model The gai from exercisig a call ca be ritte as (from previous slide): Gai from exercisig a sigle arrat ca be ritte as (from previous slide): + exercise price + + Firm - Gai from exercisig a sigle arrat ca be ritte as: debt Exercise price [Gai from a call optio ith o arrats (above)] This shos that these equatios differ by a factor of + So to a arrat, multiply the of a otherise-idetical call by + Pricig Warrats usig the Ratio Stetso Ic. has assets of $1 millio ad debt of $25 millio. They have 1.9 millio shares outstadig ad they ill be issuig 15, arrats. Each arrat has the optio to buy 4 shares of commo for oe year. The exercise price is $35. Call optios o the firm s stock are sellig for $6.5. What is the of their arrats? What is the gai from the call ad arrat? Covertible Bods A covertible bod is similar to a bod ith arrats. The most importat differece is that a bod ith arrats ca be separated ito differet securities ad a covertible bod caot. Recall that the miimum (floor) of covertible: Straight or itrisic bod Coversio The coversio optio has. The Value of Covertible Bods Covertible Bods Terms The of a covertible bod has three compoets: 1. Straight bod 2. Coversio 3. Optio 1. Coversio = # shares x commo price 2. Coversio ratio = # shares received for each bod 3. Coversio price = bod face / coversio ratio = $1, / # shares received 4. Coversio premium = coversio price / commo price

4 Covertible Bod Problem Litespeed, Ic., just issued a zero coupo covertible bod due i 1 years. The coversio ratio is 35 shares. The appropriate iterest rate is 11%. The curret stock price is $1 per share. Each covertible is tradig at $39 i the market. What is the straight bod? What is the coversio? What is the optio of the bod? Covertible Bod Problem (cotiued) Maturity = 1 years, coversio ratio = 35 shares, stock price = $1 per share, covertible is tradig at $39, rate = 11% What is the straight bod? What is the coversio? What is the optio of the bod? The Value of Covertible Bods Reasos for Issuig Warrats ad Covertibles Covertible Bod Value Covertible bod s floor = coversio ratio Coversio Value floor Straight bod Optio Stock Price Start by comparig covertible debt to both straight debt ad straight equity. Covertible debt carries a loer coupo rate tha does otherise-idetical straight debt. Sice covertible debt is origially issued ith a out-of-themoey call optio, oe ca argue that covertible debt allos the firm to sell equity at a higher price tha is available at the time of issuace. But, the same argumet ca be used to say that it forces the firm to sell equity at a loer price tha is available at the time of exercise. Case for ad Agaist Covertible Bods (CB) Covertible Bods (CB) Compared to: Straight Bods Compared to: Commo Stock If Stock Does Poorly (after issued) No coversio because of lo stock price CB s provide cheap fiacig because coupo is loer CB s provide expesive fiacig because firm could have issued commo at higher (tha curret) prices If Stock Does Well (after issued) Coversio because of high stock price CB s provide expesive fiacig because bods are coverted, hich dilutes existig equity CB s provide cheap fiacig because firm issues stock at high prices he bods are coverted Covertible vs. Straight Covertible debt carries a loer coupo rate tha does otherise-idetical straight debt. If the compay subsequetly does poorly, it ill tur out that the coversio optio fiishes out-of-the-moey. But if the stock price does ell, the firm ould have bee better off issuig straight debt. I a efficiet fiacial market, covertible bods ill be either cheaper or more expesive tha other fiacial istrumets. At the time of issuace, ivestors pay the firm for the fair of the coversio optio.

5 Covertible vs. Straight Why are Warrats ad Covertibles Issued If the compay subsequetly does poorly, it ill tur out that the coversio optio fiishes out-of-the-moey, but the firm ould have bee eve better off sellig equity he the price as high. But if the stock price does ell, the firm is better off issuig covertible debt rather tha equity I a efficiet fiacial market, covertible bods ill be either cheaper or more expesive tha other fiacial istrumets. At the time of issuace, ivestors pay the firm for the fair of the coversio optio CB s reduce agecy costs, by aligig the icetives of stockholders ad bodholders. CB s also allo youg firms to delay expesive iterest costs util they ca afford them. Support for these assertios is foud i the fact that firms that issue covertible bods are differet from other firms: The bod ratigs of firms usig covertibles are loer. Covertibles ted to be used by smaller firms ith high groth rates ad more fiacial leverage. Covertibles are usually subordiated ad usecured. Coversio Policy Most covertible bods are also callable. Whe the bod is called, bodholders have about 3 days to choose betee: 1. Covertig the bod to commo stock at the coversio ratios. 2. Surrederig the bod ad receivig the call price i cash. Bodholders ill covert if coversio is above call price. Bodholders prefer the bods be called if bod s market is belo the call price. From the shareholder s perspective, the optimal call policy is to call the bod he its is equal to the call price. I the real orld, most firms ait to call util the bod is substatially above the call price. Perhaps the firm is afraid of the risk of a sharp drop i stock prices durig the 3-day ido.