Lecture 3

1. Lecture 3 Derivatives in Corporate Finance By Wei Jiang, Professor of Finance and Economics Columbia Business School Prepared for 2013 CITIC Program in Advanced Corporate Finance

2. An option is a security that gives its owner the right to purchase(call) or to sell (put) a given asset on (or before) a given date for a predetermined price (strike) European options and American options. Options are just “side bets” between investors. They do not involve the firms on which the “bets” are based! (The CEO of Overstock.com begs to disagree…) Why do we talk about them in Corporate Finance? Options - Reminder Wei Jiang

3. Option theory has three main applications in Corporate Finance: Valuation of convertible/callable securities Warrants – entitle owners to buy shares from the firm. Convertible bonds – bonds that can be converted to shares. Executive compensation involves more and more options (actually warrants). Real options in decision making. Options and Corporate Finance Wei Jiang

4. Intrinsic value: value if exercising today Time value: always positive before maturity because you don’t have to exercise today. If you need cash, sell the option (rather than exercising and sell the stock!). Option Pricing:CT = Max {ST - X, 0} Wei Jiang

5. The price of a call option is affected by the following factors: The stock price, St (+). The strike price, X (-). The volatility of the stock price,  (+). The risk-free interest rate, r (+). The maturity of the option, T (+). Dividends, (-). Factors that Affect Option Price Wei Jiang

6. Tools available for computing the price of the option without being familiar with the quantitative aspects of the formula. I have prepared an option pricer spreadsheet. Inputs: Current stock price (in $); Option exercise price (in $); Dividend yield (in %); Annual interest rate to maturity of the option (in %); Volatility (in %); Time to expiration (in days). Output: Call price; Put price; etc. Option Pricer Wei Jiang

7. Very common in executive compensation. Similar to a call option. However, warrants are issued by corporations. Upon exercise, the writing corporation issues new shares to the warrant holders. This leads to: Infusion of cash to firm. Dilution of value of existing shares. Need to adjust the B&S formula for these two effects. Warrants - Introduction Wei Jiang

8. Let us define: m = number of shares outstanding. n = number of new shares created by exercise.  = n / (n + m) = the fraction of the firm that the warrant holders own after they exercise. 1 - is the dilution factor. Pricing Warrants Wei Jiang

9. The value of a share after warrants are exercised is: ST=(VT + n XW)/(m + n). Warrant holders choose to exercise if ST - XW > 0. Thus, the value of the warrant upon maturity is WT = Max {ST – XW , 0}. Manipulating this formula, we can see that WT = ( 1 - ) * Max { ( VT / m ) - XW , 0 }. Thus, the value of a warrant is equal to ( 1 - ) times the value of a call option on a share of a firm that has: value of VT, m shares, no warrants. Pricing Warrants Wei Jiang

10. Real example: Warren Buffett and Goldman Sachs in 2008 • In September 23, 2008, Buffett paid $5 billion for $5 billion of preferred at 10% dividend yield plus the warrants to buy $5 billion of GS stock at $115 in five years. • After the announcement, the stock price was $133. • The annual dividend yield is about 1%, the long-term treasury yields about 3%, and the annual volatility is about 51%. Shares outstanding amounted to 428 million. • In May 1st, 2010 (stock price close to $150), “I’d absolutely do it again.” Wei Jiang

11. Options (warrants) issued as executive compensation are call options on the firm shares. Dividends reduce the value of call options. FASB rules make it inconvenient to adjust strike price for dividends. How would executive option compensation affect firms’ payout policies? Dividends, Warrants and Exec Compensation Wei Jiang

12. Composition of CEO Compensation (S&P 1500 companies average) Wei Jiang

13. Stock or option? Wei Jiang

14. Compensation and payout policy Dividend Increase Repurchase Executive options outstanding Shares outstanding Executive options exercisable Shares outstanding 1.3% 2.4% 0.73% 1.36% How does this affect investors? Wei Jiang

15. Convertible bonds are bonds that can be converted to stocks. Effectively, a convertible bond is a bond with non-detachable warrants. Valuation principle: Value straight bond portion. Add option value (account for dilution). Convertible bond contract specifies: Standard provisions (face value, coupon rate, maturity). Conversion price. Conversion period. Convertible Bonds - Introduction Wei Jiang

16. Normally, the face value of a bond is set to $1,000. The conversion price is often translated into a conversion ratio - the number of shares a bondholder is entitled to buy. Since stock dividends and stock splits can make any conversion option worthless, conversion prices are usually protected against stock splits and stock dividends. Convertible Bonds – Conversion Ratio Wei Jiang

17. Valuing the straight bond portion is a straightforward valuation exercise. You can calculate the expected payments and discount them with the risk-adjusted cost of capital. Assess the risk of the bond (e.g., with ratios). Estimate the appropriate rating (e.g., by comparing ratios). Estimate the appropriate risk-adjusted yield to maturity (i.e., the average YTM of bonds in the estimated rating). Discount the promised payments (coupon and principal) at the estimated risk-adjusted YTM. The value of the bond portion is often called the straight bond floor. You can then follow the same steps as in the valuation of warrants. Convertible Bonds –Straight Bond plus warrants Wei Jiang

18. Many convertible bonds are callable. The issuing firm has the right to call the bond at a predetermined price during a predetermined period. Issuers benefit by calling outstanding debt When interest rates are lower than they were at the issue time. When call can force conversion of the bond (when the conversion option is in the money). Callable bonds are worth less than otherwise identical non-callable bonds. The difference is the value of the call option (accrued to the issuer). Convertible Bonds – Other Issues Wei Jiang

19. “Back-door equity issuance.” By largely giving up the timing option, convertibles mostly avoid the negative signaling effect associated with straight equity issues. (But less so today than before.) The high volatility and growth potential translates high value of the convertibility option and a large discount off the straight debt interest rate (for a given conversion premium), making convertible debt appear cheap (it’s still fairly priced). Seems that it is the better of both worlds, is there a downside? Reasons for Convertible Bonds Wei Jiang

20. Real options are pervasive in real life. The art is in identifying those options that are “significant:” A decision that is discretionary, contingent and irreversible (within some period of time). Check list: Growth/expand option. Timing option. Abandonment option. Option to switch (inputs, outputs, processes, etc.). Identifying Real Options Wei Jiang

21. An investment includes a growth option if there is: a possible follow-on investment, to be decided later based on new information. Examples: R&D  Developing applications if R&D is successful. Establishing a brand name. Movie Production  Sequel. Real option #1: Growth Options Wei Jiang

22. Option to switch • The hybrid car. • Combination of an American call and put. Abandonment Options • Like a put option: you can get rid of something and sometimes receive a payment (the liquidation value). • Examples: • Non-recourse mortgage loan. • Divesting: Business Week Wei Jiang

23. Example: non-recourse mortgage • Underlying price (property value): 100. • Exercise price: LTV = 100 (Alt-A); = 80 (conforming). • Maturity: 5 years (during which principal repayment is negligible). • Risk free rate: 2%. • Mortgage yield: 6% • Volatility: 5% (low) or 10% (high). Wei Jiang

24. How serious? Option value as % of face value of mortgage What could make it worse: Housing price drop: lower the underlying value. Negative amortization loans (“pick-your-payment” loans): increase the strike price. Wei Jiang

25. Case of option to abandon: Fund incubation • A fund management company can incubate/seed 10 funds for two years before open to outside investors. • Fund flows follow past performance (a big myth!). • A successful track record will raise enough outside capital to be profitable. • A mediocre/poor track record will not grow into economically viable size, and will suffer losses. • But, it seems nearly impossible to predict future performance of funds—the same for the sponsor/seeder! So it might not be worth doing. • The answer changes with the option to abandon. • The “incubation bias.” Wei Jiang

26. Now you can explain the fun fact Source: Census Wei Jiang