Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng F. Lee Rutgers University Chapter 10 Option Pricing Theory and firm Valuation

Outline  10.1 Introduction  10.2 Basic concepts of Options  10.3 Factors affecting option value  10.4 Determining the value of options  10.5 Option pricing theory and capital structure  10.6 Warrants  10.7 Summary  Appendix 10A. Application of the Binomial Distribution to evaluate call options

10.2 Basic concepts of Options  Option price information

10.2 Basic concepts of Options Exhibit 10-1 Listed Options Quotations Close Price Strike Price CallsPuts SepOctJanSepOctJan JNJ N/A N/A N/A N/A6.40N/A N/A

10.2 Basic concepts of Options Exhibit 10-1 Listed Options Quotations (Cont’d) Close Price Strike Price CallsPuts SepOctJanSepOctJan MRK N/A N/A N/A N/A N/A8.40

10.2 Basic concepts of Options Exhibit 10-1 Listed Options Quotations (Cont’d) Close Price Strike Price Calls Puts SepOctJanSepOctJan PG N/A N/A N/A15.20N/A N/A N/A N/A N/A N/A

10.2 Basic concepts of Options

Figure 10-1 Value of $50 Exercise Price Call Option (a) to Holder, (b) to Seller

10.2 Basic concepts of Options Figure 10-1 Value of $50 Exercise Price Call Option (a) to Holder, (b) to Seller

10.3 Factors affecting option value  Determining the value of a call option before the expiration date

10.3 Factors affecting option value Figure 10-2 Value of Call Option

10.3 Factors affecting option value Figure 10-3 Call Option Value as a Function of Stock Price

10.3 Factors affecting option value TABLE 10-1 Probabilities for Future Prices of Two Stocks Less Volatile StockMore Volatile Stock Future Price($)ProbabilityFuture Price ($)Probability

10.3 Factors affecting option value Figure 10-4 Call-Option Value as Function of Stock Price for High-, Moderate-, and Low-Volatility Stocks

10.3 Factors affecting option value TABLE 10-2 Data for a Hedging Example TABLE 10-3 Possible Expiration-Date Outcomes for Hedging Example Current price per share: $100 Future price per share: $125 with probability.6 $85 with probability.4 Exercise price of call option: $100 Expiration-Date Stock Price Value per Share of Stock Holdings Value per Share of Options Written $125 $85 $125 $85 － $25 $0

10.3 Factors affecting option value

(5)(125) － (8)(25) = $425 (5) (85) ＋ (8) (0) = $425

10.4 Determining the value of options  Expected value estimation  The Black-Scholes option  Pricing model  Taxation of options  American options

10.4 Determining the value of options expected value of share = (.6)(125) + (.4)(85) = $109 expected value of call = (.6)(25) + (.4)(0) = $15

10.4 Determining the value of options Figure 10-5 Put-Option Value

10.4 Determining the value of options (10-1) (10-2A) (10-2B)

10.4 Determining the value of options FIGURE 10-6 Probability Distribution of Stock Prices

10.4 Determining the value of options  Example 10-1

10.4 Determining the value of options  Example 10-1

10.5 Option pricing theory and capital structure  Proportion of debt in capital structure  Riskiness of business operations

10.5 Option pricing theory and capital structure （ 10-3 ） FIGURE 10-7 Option Approach to Capital Structure

10.5 Option pricing theory and capital structure  Example 10-2

10.5 Option pricing theory and capital structure  Example 10-2

10.5 Option pricing theory and capital structure value of debt = 14 － = $3.09 million

10.5 Option pricing theory and capital structure Table 10-4 Effect of Different Levels of Debt on Debt Value Face Value of Debt ($ millions) Actual Value of Debt ($ millions) Actual Value per Dollar Debt Face Value of Debt $.618 $.610

10.5 Option pricing theory and capital structure value of debt = 14 － 8.77 = $5.23 million

10.5 Option pricing theory and capital structure Table 10-5 Effect of Different Levels of Business Risk on the Value of $10 Million Face Value of Debt Variance of Rate of Return Value of Equity ($ millions) Value of Debt ($ millions)

10.6 Warrants old equity = stockholders’ equity + warrants new equity = old equity + exercise money H(new equity) = H (old equity) + H (exercise money)

10.6 Warrants

old equity = 100(lm) + 20(.5m) = $110 million new equity = $110m + $40m = $150 million

10.7 Summary In Chapter 10, we have discussed the basic concepts of call and put options and have examined the factors that determine the value of an option. One procedure used in option valuation is the Black-Scholes model, which allows us to estimate option value as a function of stock price, option-exercise price, time-to-expiration date, and risk-free interest rate. The option pricing approach to investigating capital structure is also discussed, as is the value of warrants.

Appendix 10A: Applications of the Binomial Distribution to Evaluate Call Options  What is an option?  The simple binomial option pricing model  The Generalized Binomial Option Pricing Model

Appendix 10A: Applications of the Binomial Distribution to Evaluate Call Options (10A.1) (10A.2) (10A.3) (10A.4)

Appendix 10A: Applications of the Binomial Distribution to Evaluate Call Options (10A.5) (10A.6) (10A.7) (10A.8)

Appendix 10A: Applications of the Binomial Distribution to Evaluate Call Options Table 10A.1Possible Option Value at Maturity Today Stock (S)Option (C)Next Period (Maturity) uS = $110C u = Max (0,uS – X) = Max (0,110 – 100) =Max (0,10) =$ 10 $100C dS = $ 90C d = Max (0,dS – X) = Max (0,90 – 100) = Max (0, – 10) =$0

Appendix 10A: Applications of the Binomial Distribution to Evaluate Call Options C T = Max [0, S T – X] (10A.9) C u = [pC uu + (1 – p)C ud ] / R (10A.10) C d = [pC du + (1 – p)C dd ] / R (10A.11) (10A.12)

Appendix 10A: Applications of the Binomial Distribution to Evaluate Call Options (10A.13) C 1 = Max [0, (1.1) 3 (.90)0(100) – 100] = C 2 = Max [0, (1.1) 2 (.90) (100) – 100] = 8.90 C 3 = Max [0, (1.1) (.90) 2 (100) – 100] = 0 C 4 = Max [0, (1.1) 0 (.90) 3 (100) – 100] = 0

Appendix 10A: Applications of the Binomial Distribution to Evaluate Call Options

(10A.14) (10A.15)

Appendix 10A: Applications of the Binomial Distribution to Evaluate Call Options

Figure 10A.1 Price Path of Underlying Stock Source: R.J.Rendelman, Jr., and B.J.Bartter (1979), “Two-State Option Pricing,” Journal of Finance 34 (December), $

Appendix 10A: Applications of the Binomial Distribution to Evaluate Call Options