Principles E120: of Engineering Economics
Final Exam
December 14th, 2004 Instructor: Professor Shmuel Oren
Part 1: Concepts. (20 points)
1. Circle the only correct answer. 1.1 Which of the following statements is FALSE? a. It is never optimal to exercise American call options before the expiration date. b. Buying a call option at the money and selling a put option at the money is equivalent to buying a forward contract. c. It is never optimal to exercise American put options before the expiration date. d. There is an arbitrage opportunity if the put-call parity does not hold. e. An American put option has a higher value than a European put option for the same stock at the same strike price. 1.2 Stock ownership can be replicated by: a. Buying call options on a stock and writing put options on a stock. b. Buying call options on a stock and borrowing at the risk-free interest rate. c. Buying put options on a stock and borrowing at the risk-free interest rate. d. Buying put options on a stock, lending funds at the risk-free interest rate, and writing call options. e. Buying call options on a stock, borrowing (should be lending) funds at the riskfree interest rate, and writing put options. 1.3 The amount of systematic risk present in a particular risky asset, relative to the systematic risk present in an average risky asset, is called the particular assets: a. Beta coefficient b. Reward to risk ratio c. Law of One Price d. Diversifiable risk e. Profitability Index 1.4 Which of the following describes a portfolio that plots above the security market line? a. The security is overvalued. b. The securitys reward to risk ratio is too high. c. The security is providing a return that is less than expected. d. The securitys beta is too high. e. The security provides a return that is less than the average return on the market. 1.5 Which of the following would be considered an example of systematic risk? a. Intel reports record sales. b. Quarterly profit for GM equals expectations. c. Lower quarterly sales for IBM than expected. d. Greater new jobless claims than expected. e. Fed leaves interest rates unchanged, as expected.
1.6 If you exercise a put option prior to expiration, a. You are obligated to buy the asset underlying the option contract at the option strike price. b. You must have been the writer (or provider) of the option when it was created. c. You will always receive more than you would if you let the option run to maturity. d. You have behaved in a rational manner if the market price exceeds the strike price. e. It must be an American option. 1.7 A(n) _____ contract is a legally binding agreement between two parties calling for the purchase/sale of an asset in the future at an agreed-upon price today? a. forward contract b. future contract c. swap contract d. option contract e. cross contract 1.8 In which of the following arrangements, does money NOT change hands (i.e. from one contracting party to another) when the contract is written. I. Future contracts II. Option contracts III. Forward contracts a. I only b. II only c. III only d. I and II only e. I and III only 1.9 A perfect hedge in one that results in a completely flat risk profile. Which of the following describes a perfect hedge? a. On net, the hedger can only make money if prices change. b. On net, the hedger can only lose money if prices change. c. On net, the hedger can either make or lose money if prices change. d. On net, the hedger will neither make nor lose money if prices change. e. None of the above. 1.10 An increase in which of the following, all else the same, leads to an increase in call option value? I. Exercise price II. Stock price III. Time to expiration IV. Volatility a. I and III only b. II and IV only c. I, II, and III only d. I, II and IV only e. II, III and IV only
Part 2: Calculations.
2. (21%) A project requires an initial investment of $5000, straight-line depreciable to zeros over 5 years. The discount rate is 12%. The tax bracket is 35% and you receive a tax credit for negative earnings in the year in which the loss occurs. Additional information for variables with forecast error is shown below. Base lower upper Case bound bound Unit sales 2000 1200 2800 Price/unit $15 $13 $17 Variable cost/unit $10 $8 $12 Annual fixed costs $4000 $3250 $4750 a. What is the base case NPV for the project? Base Case Unit sales 2000 Price/unit $15 Variable cost/unit $10 Annual fixed costs $4000 OCF =[(P-V)*Q-FC](1-T)+DT = [(15-10)*2000-4000](1-0.35)+(5000/5)(0.35) =4250 NPV = -5000+4250[1-1/1.12^5]/0.12 =10320.30 b. What is the best case OCF for the project? Best Case Unit sales 2800 Price/unit $17 Variable cost/unit $8 Annual fixed costs $3250 OCF =[(P-V)*Q-FC](1-T)+DT = [(17-8)*2800-3250](1-0.35)+(5000/5)(0.35) =14617.5 c. Find the sensitivity of NPV to unit price for the base case. Suppose P = $16 in the base case. OCF =[(P-V)*Q-FC](1-T)+DT = [(16-10)*2000-4000](1-0.35)+(5000/5)(0.35) NPV =5550 = -5000+5550[1-1/1.12^5]/0.12 =15006.51 Sensitivity of NPV to unit price change = (15006.51-10320.30/(16-15) =4686.21 d. For the base case, what are the account, cash and financial break-even points? Ignore taxes. Accounting break-even level: NI=0 => OCF = NI+D = D Q=(FC+OCF)/(P-V)=(4000+1000)/(15-10) = 1000 Cash break-even level: OCF=0 Q=(FC+OCF)/(P-V)=4000/(15-10) = 800 Financial break-even level: NPV =0 => -5000+OCF[1-1/1.12^5]/0.12 =0; OCF=1387 Q=(FC+OCF)/(P-V)=(4000+1387)/(15-10) = 1077.4 1078
3. (12%) The manager of GoldenBears Inc. plans to manufacture engine blocks for classic cars from the 60s era. They expect to sell 250 blocks annually for the next 5 years. The necessary foundry and machining equipment will cost a total of $800,000 and will depreciated on a straight-line basis to zero over the projects life. The firm expects to be able to dispose the manufacturing equipment for $150,000 at the end of the project. The project also needs a one-time investment in net working capital of $50,000. Labor and materials costs total $500 per engine block, fixed costs are $125,000 per year. Assume a 35% tax rate and a 12% discount rate. a. What is the expected after-tax cash flow to the firm when the equipment is sold in year 5? After-tax salvage value = 150,000-(150,000-0)(0.35)=150,000(1-0.35)=97,500 b. What is the minimum price the firm should set for the blocks if they dont want to lose money? Find P such that NPV=0. 0= -800,000-50,000+OCF[1-1/1.12^5]/0.12+97,500/1.12^5 +50,000/1.12^5 212,580.34=OCF=[(P-500)(250)-125,000](1-0.35)+(800,000/5)(0.35) P=1,963.57 4. (15%) Using the following information to answer questions Security Expected return Standard deviation Beta A 16% 20% 1.2 B 12% 25% 0.8 a. Which of A and B has least total risk, systematic risk and unsystematic risk? Why? Total risk is measured by the variance. A has the least total risk. Systematic risk is measured by the beta coefficient. B has least systematic risk. Unsystematic risk is the difference between total risk and systematic risk. A has the least unsystematic risk. b. What are the expected market return and the risk-free rate? By CAPM: 0.16 = RF +1.2(RM- RF) 0.12 = RF + 0.8(RM- RF) RM =0.14; RF =0.04 c. What is the portfolio expected return and the portfolio beta if you invest 35% in A, 45% in B and 20% in the risk-free asset? E [RP] = 0.35(0.16)+0.45(0.12)+0.2(0.04) =0.118 Beta= 0.35(1.2)+0.45(0.8)+0.2(0) =0.78 5. (12%) using the following information Orange Juice(CTN) 15,000 lbs.; cents per lb. May 12, 2002 Open High Low Settle change Lifetime High Lifetime Low July 80.00 86.10 79.90 85.20 +4.70 128.50 73.00 Sept 84.75 88.50 84.50 88.00 +3.00 121.30 77.10 Nov 89.25 93.20 89.00 92.75 +3.00 115.50 79.80 Jan03 91.00 94.80 90.80 94.50 +3.00 109.75 82.75
Open interest 37,832 16,379 13,149 5,397
a. Suppose you are interested in purchasing the September futures contract. What is the future price of 15,000 lbs. of orange juice for September delivery? $0.88*15,000 = $13,200 b. Suppose that yesterday you purchased one July futures contract at the settle price. At the close of business today, how much is your contract worth, e.g. the value changed? The settlement price has increased by 4.7 cents per lb. For the long position in futures contract, its a gain since you settled on a lower price yesterday. Value of the contract = $0.047*15,000 = $705 c. How many orange juice futures contracts for delivery in 2002 ONLY were outstanding at the end of the trading day? July 37,832 Sept 16,379 Nov 13,149 Total =37,832+16,379+13,149= 67360 6. (20%) A firm has stock outstanding with a current price of $28 per share. The price in one year is expected to be either $30 or $39. A call option is available with the strike price of $25. The risk-free rate is 10%, a. What will you pay for the call options? The option will finish in the money for sure. C = S-PV(E) = 28-25/1.1=5.27 b. What is the value of a put option with the same strike price? Given an intuition for the value of the put option. The value of the put option with the same strike price should be zero since the put option is worthless at the time the option matures. c. Show that you can be replicated the stock with a bond and call options with a strike price of $36? Suppose we have a portfolio of buying one call (E:36) and investing 30/1.1 in bond ST 30 39 From bond From call Total payoffs (30/1.1)(1.1) =30 0 30 (30/1.1)(1.1) =30 39-36=3 33 Need 3 call options to replicate the stock when ST=39. Therefore, buying 3 call options with strike price of $36 and investing 30/1.1 in bond now can replicate the value of the stock a year from now. d. What is the value of a call option with strike price of $36? What is the value of the put option with the same strike price? From part d, C=(28-30/1.1)/3 = 0.24 From put-call parity, P = C-S+PV(E) = 0.24-28+36/1.1=4.97