problem 2 ----4 , I have solved the first problem.

FIN 361 Spring 2016 Arizona State University W.P. Carey School of Business FIN 361 - Advanced Managerial Finance Spring 2016, Prof. Jessie Jiaxu Wang Problem Set 3 Due: 04/25, Monday, beginning of class. Note: No late homework will be accepted. You should show your work. Your writeup should be stapled. Problem 1 Consider the following projects: Project C0 A -1000 B -2000 C -3000 C1 +1000 +1000 +1000 C2 0 +1000 +1000 C3 C4 C5 0 0 0 +4000 +1000 +1000 0 +1000 +1000 1. If the opportunity cost of capital is 10%, which projects have positive NPVs? 2. Calculate the payback period of each project. 3. Which project(s) would a rm using the payback rule accept if the cuto period were three years? Prof. Jessie Jiaxu Wang 1 This version: April 18, 2016 FIN 361 Spring 2016 Problem 2 Play Doo company is trying to choose between two projects, which both generate perpetual, growing streams of nominal cash ows. The rm must do one or the other, but cannot do both. Project A will generate a net after-tax cash ow of $5 million at the end of the rst year. The cash ow from the project is expected to grow at 6% per year on a nominal basis. Project B will produce an initial net cash ow of only $2 million, but the anticipated growth rate of the cash ows is 8% nominally. Each project costs $150 million dollars to implement. 1. Which project has the higher Internal Rate of Return (IRR)? (Show your calculations.) 2. If you were to use NPV rule, at what costs of capital would you choose to invest in Project A rather than Project B? Recall the rm must do one or the other. Prof. Jessie Jiaxu Wang 2 This version: April 18, 2016 FIN 361 Spring 2016 Problem 3 ABC Co.'s assets consist of $20 thousand in cash and three investment projects. The rm has no debt outstanding. The company can borrow and lend at 8% per year. Each project lasts for only one year. The table below lists the cash ows from the projects at the initial date (t = 0) and at the end of the year (t = 1). Cash outows are listed as negative numbers, while cash inows are listed as positive. All gures are in thousands of dollars. t Project X Project Y Project Z 0 1 -100 +110 +200 -224 -80 +84 1. Calculate the Internal Rate of Return (IRR) of each project. 2. Which projects should the rm invest in and why? 3. How much would you pay today, before any investments have been made, to buy this rm? Prof. Jessie Jiaxu Wang 3 This version: April 18, 2016 FIN 361 Spring 2016 Problem 4 Currently a share of Globex Industries trades for $50 per share. In one year, Globex's share price will be $60 with probability 0.55 or $40 with probability 0.45. A riskless bond also exists with a current price of $95. In one year, this bond pays $100 for certain. You can both lend and borrow using this bond. If you borrow one riskless bond, you will receive $95 today in exchange for the promise to repay $100 in one year. The stock and the bond have no other cash ows over the year. In the problems that follow, you are asked to price by no arbitrage three common derivative securities. Approach these problems exactly like the bond examples we did in class. Start by nding a trading strategy in the stock and the bond that exactly matches the payo of the derivative under all future contingencies (the stock price either rises or fall over the next year). By no arbitrage, the current value of this strategy is the value of the derivative security. 1. Pricing a European Call Option. Consider a European call option on Globex Industries. This security gives the holder the right to buy a share of Globex in one year (the expiration date) for a pre-specied price X called the strike price. Since the holder is given the right (not the obligation), they will only exercise the option (pay X in exchange for a share of stock in one year) when it is protable for them. This implies the cash ow of a European call option in one year is max(S1 X, 0) where S1 is the price of Globex in one year. Consider a European call option which expires in one year and has a strike price of X = 48. What trading strategy in the stock and the bond today will exactly match the payo of this call option in one year? By no arbitrage, what is the price today of this option? 2. Pricing a European Put Option. Consider a European put option on Globex Industries. This security gives the holder the right to sell a share of Globex in one year (the expiration date) for a pre-specied price X called the strike price. Since the holder is given the right (not the obligation), they will only exercise the option (receive X in exchange for selling a share of stock in one year) when it is protable for them. This implies the cash ow of a European put option in one year is max(X S1 , 0) where S1 is the price of Globex in one year. Consider a European put option which expires in one year and has a strike price of X = 48. What trading strategy in the stock and the bond today will exactly match the payo of this put option in one year? By no arbitrage, what is the price today of this option? Prof. Jessie Jiaxu Wang 4 This version: April 18, 2016 FIN 361 Spring 2016 extra page Prof. Jessie Jiaxu Wang 5 This version: April 18, 2016