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Unformatted text preview: Chapter 14 Chapter Options and Corporate Finance Chapter Outline Chapter Options: The Basics Fundamentals of Option Valuation Valuing a Call Option Employee Stock Options Equity as a Call Option on the Firm’s Assets Options and Capital Budgeting Options and Corporate Securities Option Terminology Option Call Put Strike or Exercise price Expiration date Option premium Option writer American Option European Option Option Payoffs – Calls Option The value of the call at The expiration is the intrinsic value value Call Option Payoff Diagram 25 20 Call Value 15 10 5 0 0 10 20 30 40 50 60 Stock Price Max(0, SE) If S<E, then the payoff is 0 If S>E, then the payoff is S – E Assume that the exercise Assume price is $30 price Option Payoffs  Puts Option The value of a put at The expiration is the intrinsic value value Payoff Diagram for Put Options
35 30 25 20 15 10 5 0 0 10 20 30 40 50 60 Stock Price Assume that the exercise Assume price is $30 price Option Value Max(0, ES) If S<E, then the payoff is ES If S>E, then the payoff is 0 Call Option Bounds Call Upper bound Call price must be less than or equal to the stock Call price price Call price must be greater than or equal to the stock Call price minus the exercise price or zero, whichever is greater greater Lower bound If either of these bounds are violated, there is an If arbitrage opportunity arbitrage Figure 14.2 Figure A Simple Model Simple An option is “inthemoney” if the payoff is An greater than zero greater If a call option is sure to finish inthemoney, the option value would be option C0 = S0 – PV(E) If the call is worth something other than this, If then there is an arbitrage opportunity Example 1 Example Suppose we are looking at a call option with one year to Suppose expiration and an exercise price of $105. The stock currently sells for $100, and the riskfree rate is 20%. The value of the stock in one year is uncertain, of course; however we are certain that the option will finish somewhere in the money. What is the value of the call option today? Solution: Call option is certain to finish in the money, so will Call therefore invest the present value of $105 in the risk free asset and buy one call option. asset C0=S0E/(1+Rf)=100105/1.2=12.5 )=100105/1.2=12.5 Example 2 Example Suppose we are looking at a call option with one year to expiration Suppose and an exercise price of $90. The stock currently sells for $100, and it will move either up or down by 20%. The riskfree rate is 5%. What is the value of the call option today? Solution: Stock price will be either $80 or $120. The option is worth zero Stock when the stock is worth $80, and it’s worth 30 when the stock is worth $120. So will therefore invest the present value of $80 in the risk free asset and buy some call option. risk The number of options you need to buy to replicate the value of The stock is always equal to (SuSd)/(CuCd) stock (SuSd)/(CuCd)=40/30 S0=100=(4/3)Co+80/1.05=> Co=17.86 =17.86 What Determines Option Values? Values? Stock price As the stock price increases, the call price increases and the put price As decreases decreases As the exercise price increases, the call price decreases and the put As price increases price Generally, as the time to expiration increases both the call and the put Generally, prices increase prices As the riskfree rate increases, the call price increases and the put price As decreases decreases Exercise price Time to expiration Riskfree rate Variance of return on the underlying asset The greater the variance, the more the call and the put are worth Example 3 Example Suppose we are looking at a call option with one year to Suppose expiration and an exercise price of $120. The stock currently sells for $100, and the riskfree rate is 20%. Suppose the stock price can be $110 or $130 in a year. What is the value of the call option today? S0=100=(20/10)Co+110/1.2=> Co=$4.17 Now suppose the stock price can be $105 or $135 Now instead of $110 or $130 (i.e., stock’s future price more volatile than before) S0=100=(30/15)Co+105/1.2=> Co=$6.25 The greater the variance, the more the call and The the put are worth the More on Variance More If an option finishes outofthemoney, the most you If can lose is your premium, no matter how far out it is (i.e. an increase in the volatility does not affect the option’s value) option’s The more an option is inthemoney, the greater the The gain (i.e., an increase in the volatility increases the possible payoffs) possible The owner of the option gains from volatility on the The upside, but don’t lose anymore from volatility on the downside downside Table 14.2 Table Employee Stock Options Employee Options that are given to employees as part of their Options benefits package benefits Often used as a bonus or incentive
• Designed to align employee interests with stockholder interests and Designed reduce agency problems reduce ESO has no immediate, upfront, outof the pocket cost to the ESO corporation corporation
• In smaller, cashstrapped companies, ESO are simply a substitute In for ordinary wages. for A typical ESO has a longer life than most ordinary typical options options ESOs can not be sold ESOs have a vesting period (i.e., the option can be ESOs exercised after a certain period) Equity: A Call Option Equity: Equity can be viewed as a call option on the company’s Equity assets when the firm is leveraged assets The exercise price is the face value of the debt If the assets are worth more than the debt when it comes If due, the option will be exercised and the stockholders retain ownership retain If the assets are worth less than the debt, the If stockholders will let the option expire and the assets will belong to the bondholders belong Capital Budgeting Options Capital Real options are options that give the right to make Real decisions on a capital investment project decisions A llimitation of traditional investment analysis is that it is imitation static, meaning that it does not do a good job capturing the value of options embedded in a project value One can go as far as arguing that the NPV rule One systematically undervalues every project systematically These options add value to a project and may change a These project’s NPV from negative (under traditional analysis) into positive into Project’s value = NPV + Value of option Timing Options Timing We normally assume that a project must be taken today We or forgone completely or Almost all projects have the embedded option to wait A good project may be worth more if we wait A seemingly bad project may actually have a positive NPV if we seemingly wait due to changing economic conditions wait We should examine the NPV of taking an investment We now, or in future years, and plan to invest at the time that the project produces the highest NPV the Example: Timing Options Example: Consider a project that costs $5,000 and has an Consider expected future cash flow of $700 per year forever. If we wait one year, the cost will increase to $5,500 and the expected future cash flow will increase to $800. If the required return is 13%, should we accept the project? If so, when should we begin? so, NPV starting today = 5,000 + 700/.13 = 384.62 NPV waiting one year = (5,500 + 800/.13)/(1.13) = 578.62 It is a good project either way, but we should wait until next year Managerial Options Managerial Managers often have options after a project has been Managers implemented that can add value implemented It is important to do some contingency planning ahead It of time to determine what will cause the options to be exercised exercised Some examples include The option to expand a project if it goes well The option to abandon a project if it goes poorly The option to suspend or contract operations particularly in the The manufacturing industries manufacturing Strategic options – look at how taking this project opens up Strategic other opportunities that would be otherwise unavailable other Example: Abandoning a project Example:
Suppose a clothing company is considering introducing a Suppose new line of fashion. The project has a 2 year life. An initial investment of $50000 is required to fund a yearlong development phase. At the end of a year, a further $50000 is required for production and cash inflows from sales (net of selling expenses) will occur at the end of the second year. There is some uncertainty about the amount of the cash There inflows since it is unclear whether the market will embrace the new line. The firm currently believes that there is a 70% chance that the new line will be a winner. They also believe that the direction of fashions will become more apparent over the next year. In particular, there is an 80% chance that the direction over the next year will continue over the subsequent year. Suppose also that the required return on projects of this type Suppose is 10%. Example: Abandoning a project cont. Example: Example: Abandoning a project cont. Example: Standard capital budgeting techniques involve Standard computing the expected net present value (NPV) as: (NPV) Example: Abandoning a project Example: Consider, however, the case where the firm has Consider, the option to abandon the project after the first year. the second phase of the project would only proceed if the the market direction was favorable over the first year. Therefore, when the option is considered, the Therefore, expected NPV is: expected and the project should proceed. Warrants Warrants A warrant is a corporate security that looks like a call warrant option option Differences between warrants and traditional call Differences options options Warrants are generally very long term They are written by the company and warrant exercise results They in additional shares outstanding in The exercise price is paid to the company, generates cash for The the firm, and alters the capital structure the Warrants are often issued in combination with privately placed Warrants loans or bonds loans Warrants can normally be detached from the original securities Warrants and sold separately and Exercise of warrants reduces EPS, so warrants are included Exercise when a firm reports “diluted EPS” when Convertibles Convertibles Convertible bonds (or preferred stock) may be converted Convertible into a specified number of common shares (anytime up to and including the maturity date of the bond) at the option of the bondholder option The conversion price is the effective price paid for the The stock stock The conversion ratio is the number of shares received The when the bond is converted when The conversion premium is the difference between The conversion price and the current stock price, divided by the current stock price The conversion value is what the bond would be worth if The it were immediately converted into common stock (i.e., current price x conversion ratio) Convertible bonds will be worth the straight bond value Convertible or the conversion value, whichever is greater or Example Example A convertible bond has a straight bond value of convertible $1,050. The conversion ratio is 24, and the stock price is $49 per share. How much does convertible bond sell for? What is the value of the option to convert? option Conversion value = 24 x $49 = $1,176 convertible bond sell for $1176 Value of the option to convert = $1,176 Value $1,050 = $126 $1,050 Valuing Convertibles Valuing Suppose you have a 10% bond that pays semiannual Suppose coupons and will mature in 15 years. The face value is $1,000 and the yield to maturity on similar bonds is 9%. The bond is also convertible with a conversion price of $100. The stock is currently selling for $110. What is the minimum price of the bond? minimum Straight bond value Straight N = 15*2 = 30; YTM = 9/2 = 4.5; Coupon= .1(1000)/2 = 50; F = 15*2 1000; Straight bond valu= 1,081.44 1000; Conversion ratio = 1,000/100 = 10 Conversion value = 10*110 = 1,100 Min Price of the convertible= Max{1081.44, 1100}=$1,100 Other Options Other Call provision on a bond Allows the company to repurchase the bond prior to maturity at Allows a specified price that is generally higher than the face value specified Allows the bondholder to require the company to repurchase Allows the bond prior to maturity at a fixed price the These are essentially put options Put bond Insurance and Loan Guarantees ...
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This note was uploaded on 04/13/2010 for the course BUSINESS engl 102 taught by Professor Seyhanözmenek during the Spring '10 term at Middle East Technical University.
 Spring '10
 SeyhanÖzmenek
 Corporate Finance, Options, Valuation

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