Options in Corporate Finance

Transcription

1 FIN 614 Corporate Applications of Option Theory Professor Robert B.H. Hauswald Kogod School of Business, AU Options in Corporate Finance The value of financial and managerial flexibility: everybody values it but nobody knows how to value strategic aspects options theory to the rescue: business strategies are just portfolios of real and strategic options Applications of options financial strategy: warrants corporate strategy: bankruptcy investment strategy: capital budgeting Further applications: VC, default risk, etc. 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 2

2 Warrants Warrants: rights to buy shares at a set strike price direct application of option theory usually issued in conjunction with underwritings and private placement of bonds commonly given to underwriters as partial payment for services Warrant analysis: payoff identical to call option warrant on a stock with no dividends can be valued with the standard Black - Scholes formula to value warrant: Black - Scholes with adjustments 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 3 Valuing Warrants Two complications in valuing warrants 1. dilution: upon exercise more shares exist 2. change in the risk of equity Standard dev. of fictitious (no warrants) firm's equity is different from the real firm s (warrants) Analyze the two effects one at a time 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 4

3 Dilution V + NqK Note share price after exercise S' V value of equity N + Nq N Number of shares outstanding q % of warrants outstanding per share of stock K exercise price on the warrant Value at exercise: same as a call option, but with the new share price: warrant value max{s - K, 0} 1/(1+q) * max{v/n - K, 0} Value expression using Black Scholes formula on a firm without any warrants outstanding 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 5 Change in Equity Risk To find the new standard deviation of equity, use the following formula: std.dev. of assets proportion * new std.dev. (assume constant) of equity after of equity issue ("new firm") The first item (s.d. of assets) we get by unlevering the standard deviation of the leveraged firm o E std. dev. of assets σ ( assets ) σ ( old common stock ) and E V o o o pre-warrant equity value V / pre-warrant firm value. The second item in the formula is the equity to value ratio after the warrant has been exercised 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 6

4 Final Complication: Dividends The warrant may be on a dividend paying stock: valued using adjustments to the Black-Scholes formula for constant proportional dividends generally, you have to compare the value of exercising at each point in time and getting the dividends with the value of holding the option or warrant numerical techniques exist to value the dividend paying feature: exact formulae exist for special cases Having found the warrant s value you may want to compute its required return and Beta so asto include it in the cost of capital for the firm 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 7 Equity and Leverage Call Levered Equity is a Call Option. The underlying asset comprise the assets of the firm. The strike price is the payoff of the bond. If at the maturity of their debt, the assets of the firm are greater in value than the debt, the shareholders have an in-the-money call: they will pay the bondholders and call in the assets of the firm. If at the maturity of the debt the shareholders have an out-of-the-money call, they will not pay the bondholders (i.e. the shareholders will declare bankruptcy) and let the call expire. 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 8

5 Equity and Leverage Put Levered Equity is a Put Option. The underlying asset comprise the assets of the firm. The strike price is the payoff of the bond. If at the maturity of their debt, the assets of the firm are less in value than the debt: shareholders hold an in-the-money put. they will put the firm to the bondholders. If at the maturity of the debt the shareholders have an out-of-the-money put, they will not exercise the option and let the put expire, i.e. NOT declare bankruptcy. 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 9 Equity as a Put and Call: PCP Again! Recall risky borrowing and put-call parity: S t c Value of a call on the firm t r( T t ( F ) V + p ( F ) e ) F t Value of a put on the firm Value of the firm + t Value of a risk-free bond Shareholder s position in terms of the ownership (call) option Shareholder s position in terms of the bankruptcy (abandonment) option 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 10

6 Debt Payoff and Firm Value At maturity T, the debtholders receive F if V T exceeds the debt s face value F and V T otherwise: bankruptcy They get F - max[f - V T, 0]: the payoff of riskless debt minus the payoff of a put on V T with exercise price F: what is this put? risky lending corresponds to riskless debt plus selling a put option: D t e -r(t-t) F p t (F) Shareholder get max[v T - F, 0], the payoff of a call on the firm 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 11 Capital-Structure Policy Revisited Recall some of the agency costs of debt: they can all be seen in terms of options. for example, the incentive shareholders in a levered firm have to take large risks. Use option theory to price such risks better understanding of default risks of debt option pricing provides models to extract default probability from observed market prices 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 12

7 Balance Sheet for a Company in Distress Assets BV MV Liabilities BV MV Cash $200 $200 LT bonds $300? Fixed Asset $400 $0 Equity $300? Total $600 $200 Total $600 $200 What happens if the firm is liquidated today? The bondholders get $200; the shareholders get nothing. 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 13 Gambling for Resurrection: Take Large Risks The Gamble Probability Payoff Win Big 10% $1,000 Lose Big 90% $0 Cost of investment is $200 (all the firm s cash) Required return is 50% Expected CF from the Gamble $ $0 $100 $100 NPV $ NPV $133 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 14

8 Negative NPV Project Selection! Expected cash flow from the Gamble To Bondholders $ $0 $30 To Stockholders ($ $300) $0 $70 PV of Bonds Without the Gamble $200 PV of Stocks Without the Gamble $0 PV of Bonds With the Gamble $30 / 1.5 $20 PV of Stocks With the Gamble $70 / 1.5 $47 The stocks are worth more with the high risk project because the call option that the shareholders of the levered firm hold is worth more when the volatility is increased. 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 15 Investment Projects and Options NPV is mechanical: management has no value all decisions taken up-front, no room for flexibility blatantly untrue: firms value flexibility and options However, firms have options that should be considered in project valuation. The Option to Expand: has value if demand turns out to be higher than expected. The Option to Abandon: Has value if demand turns out to be lower than expected. The Option to Delay: Has value if the underlying variables are changing with a favorable trend. 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 16

9 The Option to Delay: Example Year Cost PV NPV t NPV 0 0 $ 20,000 $ 25,000 $ 5,000 $ 5,000 1 $ 18,000 $ 25,000 $ 7,000 $ 6,364 2 $ 17,100 $ 25,000 $ 7,900 $ 6,529 $7,900 $ 6,529 2 (1.10) 3 $ 16,929 $ 25,000 $ 8,071 $ 6,064 4 $ 16,760 $ 25,000 $ 8,240 $ 5,628 Consider the above project, which can be undertaken in any of the next 4 years. The discount rate is 10 percent. The present value of the benefits at the time the project is launched remain constant at $25,000, but since costs are declining the NPV at the time of launch steadily rises. The best time to launch the project is in year 2 this schedule yields the highest NPV when judged today. 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 17 Discounted Cash Flows and Real Options We can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial ( real) options implicit in the project. M NPV + Opt A good example would be comparing the desirability of a specialized machine versus a more versatile machine. If they both cost about the same and last the same amount of time the more versatile machine is more valuable because it comes with options. 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 18

10 The Option to Abandon: Example Suppose that we are drilling an oil well. The drilling rig costs $300 today and in one year the well is either a success or a failure. The outcomes are equally likely. The discount rate is 10%. The PV of the successful payoff at time one is $575. The PV of the unsuccessful payoff at time one is $0. 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 19 The Option to Abandon: NPV Traditional NPV analysis would indicate rejection of the project. Expected Prob. Payoff Prob. Payoff + payoff sucess given success failure given failure Expected payoff $ NPV $ $38.64 t (1.10) ( 0.5 $575) + ( 0.5 0) $ /5/2011 Corporate Applications of Options - Robert B.H. Hauswald 20

11 The Option to Abandon: Decisions Traditional NPV analysis overlooks the option to abandon. Success: PV $500 Drill $500 Failure Sit on rig; stare at empty hole: PV $0. Do not drill NPV $0 Sell the rig; salvage value $250 The firm has two decisions to make: drill or not, abandon or stay. 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 21 The Option to Abandon: Solution When we include the value of the option to abandon, the drilling project should proceed: Expected Prob. Payoff Prob. Payoff + payoff sucess given success failure given failure Expected payoff NPV ( 0.5 $575) + ( ) $ $ $ $75.00 (1.10) t 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 22

12 Valuation of the Option to Abandon Recall that we can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project. M NPV + Opt $ Opt $ Opt Opt $ /5/2011 Corporate Applications of Options - Robert B.H. Hauswald 23 Lattices: Binomial Call Option Pricing C3( U, U, U) max[$38.02 $25,0] $ (1 3) $3.10 C2( U, U ) 2/ (1.05) C1( U ) C3( U, U ) $ (1 3) $1.97 C3( U, U ) C3( U, U, D) 2/ (1.05) 1/3 max[$28.10 $25,0] C ( 2 U, D) C2( U ) /3 2 3 $ (1 3) $ / C1( D) 1/3 (1.05) C (,, ) $25 3 U D D 2 3 $ (1 3) $ C3( U, D) C3( U ) 4.52 (1.05) 2/ /3 1/3 max[$20.77 $25,0] C2( D) $0 + (1 3) $ /3 0 (1.05) 1/3 C,, ) ( D D D 2 3 $ (1 3) $1.25 max[$15.35 $25,0] 0 C0 1/3 (1.05) /5/2011 Corporate Applications of Options - Robert B.H. Hauswald 24 0

13 Stock Options Binomial lattices required to analyze complex applications such as executive stock options 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 25 Conclusions Option theory highlights the following principles valuable to wait to exercise (resolution of uncertainty): the longer the time to expiration, the higher the value you only exercise in good states, you save your exercise money if you wait and the bad (low price) state results the cost of waiting on a stock option is the lost profits (dividends) that would be yours from owning the stock Results hold independent of distributional assumptions (continuous, binomial, jump process) Equity is a call option: implications for risk taking behavior by stockholders 4/5/2011 Corporate Applications of Options - Robert B.H. Hauswald 26