高级公司金融optionsandcorporatefinance(编辑修改稿)

高级公司金融optionsandcorporatefinance(编辑修改稿)内容摘要：

largely determined by the price of copper.  Suppose some of the copper Q1 in the mine will be extracted at date 1 and the remainder Q2 at date 2. The extraction costs are K1 and K2 respectively. The prices of copper in date 1 and date 2 are p1 and p2. The prices are the only unknown variables at the beginning.  What is the value of the mine? The Option to Abandon  The cash flows at date 1 and date 2 of the mine are as the following,  C1 = p1Q1 – K1  C2 = p2Q2 – K2  The value of the mine is,  The value of a mine can be viewed as a derivative with the copper as the underlying assets.  If the forward contract on copper exists, the cash flows of a copper mine are possible to be perfectly tracked and then valued by the no arbitrage rule. 222111 1 )(1 )( rpr CErpr CEPV The Option to Abandon The tracking portfolios are as the follows, (1) A forward contract to purchase Q1 units of copper at date 1 at the current forward price of F1 per unit, and a second forward contract to purchase Q2 units of copper at date 2 at the current forward price of F2 per unit. (2) A riskfree zerocoupon bond paying F1Q1 – K1 in year 1, and a second risk free zerocoupon bond paying F2Q2 – K2 at date 2. The value of the mine is then, 2222111111 rKQFrKQFPVThe Option to Abandon Valuing a mine with abandonment option  The conventional valuation technique implicitly assume that the amount Q to be extracted at date 1 and date 2 are predetermined and fixed at date 0.  Whatever happens to the copper price (low or high) these amounts will be extracted, which makes the mine equivalent to a forward contract to buy Q1 copper with strike price K1 at date 1, and a forward contract to buy Q2 copper with strike price K2 at date 2. The Option to Abandon  The owners of the mine can choose not to extract the copper when price of copper is lower and the cost of extraction is not able to be covered.  In this case the payoff at date 1 and date 2 are Max[p1Q1 – K1, 0] and Max[p2Q2 – K2, 0].  The cash flows from a mine are equivalent to the cash flows of an option to purchase Q1 units of copper at an exercise price of K1. A Simple Binomial Example Valuing the mine with abandonment option  Penny Copper Mining’s Brazilian mine will produce 75 million pounds of copper one year from now if economic conditions are favorable. Penny’s managers forecast two possible outes for copper prices then: $ per pound if demand is low and $ per pound if demand is high. The year 1 forward price is currently $ per pound. The risk free 1 year interest rate is 5 percent. The extraction costs are $ per pound, so if demand turns out to be low, the firm will shut down the mine. What is the value of the mine? The Binomial Tree Year 1 Year 0 Scenario 2 Scenario 1 Cash flow = 75,000,000 ($ $ ) Cash flow = $0 Tracking portfolio: X pounds of copper purchased forward Y dollars invested in zerocoupon bonds today Scenario 1: X( – ) + Y() = 0 Scenario 2: X( – ) + Y() = 75000000 X: 18,750,000 pounds of copper forward Y: $1,785,714 invested in zerocoupon bonds The Option to Delay the Start of a Project  Conventional DCF analysis implicitly assume that any investment project is an takeitorleaveit decision. The project can and only can be undertaken at date 0.  Firms have the option to delay the start of the project.  Undertaking a project is equivalent to exercising an American call option. The initial cost is the strike price. The present value of future cash flows can be viewed as the value of underlying asset.  As long as the underlying economy is uncertain, the generic lesson of American call options applies to the real investment: delay exercising is valuable. An Example Creating Value by Rejecting a “Positive NPV Project”  Acme Industries is considering building a plant which costs $100 initial investment. The firm’s management can immediately invest the $100 million, or wait until next year. If the project is undertaken immediately, the cash flow in the next year will be $10 million, and a perpetual annual cash flow stream of either $15 million or $ million follows thereafter, depending on whether the economic condition is good or bad. If the project is delayed, the $10 million cash flow at the next year will be lost. Only the perpetual cash flow stream will be captured. Assuming that the riskfree interest rate is 5 percent per year and that $1 invested in the market portfolio today will be worth either $ or $. What is the NPV of the project? The Binomial Trees Do not wait Year 1 Year 2 Year 3, 4, 5, … $10 million $10 million $15 million $15 million per year forever $ million $ million per year forever Good Bad $100 million Market portfolio $1 $ $ Risk neutral probability: π = π + (1 π) π = mmmmmmN P V $100$]*) $10($*) 15$10[ ( $ The Binomial Trees Wait Year 1 Year 2 Year 3, 4, 5, … $100 million $100 million $15 million $15 million per year forever $ million $ million per year forever Good Bad $0 NPV = 100 + 15/ = 200 NPV = 100 + The firm will not take the project if bad state occur at year 1 mmN P V *2 0 0$ Creating Value by Rejecting a “Positive NPV Project”  If the project is undertaken immediately, the NPV is positive,  If the firm wait until next period  If the economic condition is good, taking the project generate a positive NPV, $200m at year 1.  If the economic condition is bad, taking the project generate a negative NPV, $50m at year 1. The firm will not take the project.  At year 0, the NPV of the project is, mmmmmm $100$]*) $10($*) 15$10[ ( $ mmm 2 0 0$1 0 0$$ mmm 50$1 0 0$ $ mm *2 0 0$ Creating Value by Rejecting a “Positive NPV Project” 。