Principles of Modern Finance Spring 2013 Sample Midterm February 22, 2012 Instructions • You have 1 hour and 40 minutes. • The exam is out of 25 points. • There are 22 multiple-choice questions. 19 questions are worth one point, 3 questions are worth two points and are marked as such. • If you get stuck, move on and come back later. 1 1. A stock is expected to pay a dividend of $10 next year, and this dividend is expected to grow by 5% each year thereafter. What should the price of the stock be if instruments of similar risk are paying 12%? (a) $83. 33 (b) $142. 86 (c) $150 (d) $200 2. A project has the following cash? ows: Year 0 1 2 Cash? w +12000 ? 7080 ? 6654 The IRR of these cash? ows is 9%. Assets of similar risk pay 5%. Should you accept this project? (a) Yes (b) No 3. I am considering buying a Greek government bond that promises to pay $1210 in two years’ time. However, there is a possibility that the Greek government will default between now and the promised payment. If the government does default, the bond will only pay $500. The probability of default is 0. 5. What should the price of the bond be if instruments of similar risk are paying 10%? (a) $1000 (b) $706. 62 (c) $413. 22 (d) $303. 68 4. I am enrolled in a 2-year MBA program, and have just started classes.
To pay the tuition and living expenses, I borrow $50,000 per year (paid at the start of the year). The interest rate on the loan is 5%. I am certain to get a job at the end of the two years of study. That job will be guaranteed for ten years (from the date I start work), at a constant salary which will be paid at the end of each year of work. There are no taxes. I estimate that I will be able to save 1/4 of my income, whatever my income is. What is the minimum salary the job must have to allow me to pay o? my loans within ten years? (2pts) 2 (a) $43,050 (b) $50,000 (c) $55,752 (d) $61,339 5. A credit card company o? rs me a card with 20% APR, compounded daily. I make purchases of $3,000 on the card, and allow interest to accrue on those purchases for a year. Assuming each year has 365 days, the amount I will have to pay back is: (a) $3,315 (b) $3,600 (c) $3,664 (d) $3,901. 30 Answer the next two questions with reference to this information: Analysts argue that two things can happen over the next year: the economy can continue as it is or it can go into recession. The returns of two stocks: General Electric (GE) and Cisco (CSCO) in each possible state are given below: State Return on GE Continue as-is 15 Recession ? 5 Return on CSCO 5 -1 The analysts estimate the probability of continuing as-is to be 0. 8 , and the probability of a recession to be 0. 2. 6. What is the expected return on a portfolio which is 120% in GE and ? 20% in CSCO? (a) 10. 04% (b) 8% (c) 2. 55% (d) 0% 7. What is the variance of CSCO? (a) 1. 96%2 (b) 5. 76%2 (c) 13%2 (d) 23. 04%2 3 8. Alice can get a one-year loan at 5% at her bank, while no bank is willing to give Brad a one-year loan for less than 10%. Brad has just had surgery, and must pay the hospital $10,000 immediately, but he has no money today, though he will have money in one year. So Alice o? rs Brad a proposal: she will borrow $10,000 from her bank for one year on her own account, and Brad will repay this loan. In addition, he will pay Alice a sum of money today. What is the maximum amount that Brad should be willing to pay Alice up-front under this arrangement? Alice is not willing to consider borrowing more than $10,000. (2pts) (a) $454. 54 (b) $377. 18 (c) $476. 19 (d) $500 9. The risk-free interest rate today is 7%. One year ago, you bought an asset which is risk-free and would pay $100 two years from the date of purchase. The risk-free interest rate on the date of purchase was 10%. You sell the asset today.
What is the rate of return (HPR) that you made? (a) 13% (b) 10% (c) 7% (d) 15% 10. The correlation between Alcoa (AA) and American Express (AXP) is 0. 3. You want to form a portfolio, investing 50% in each stock. What is the variance of your portfolio’s return? You have the following information: AA AXP 10 12 8 16 Expected return Standard deviation of return (a) 85. 76%2 (b) 99. 2%2 (c) 121%2 (d) 144%2 11. If you can get an 8% return (annual e? ective) on a ten year CD from your local bank, would it be wise to invest in a 10 year bond which promises to make a single payment of $1000 at the end of its life? Assume both are equally risky). This bond costs $475 now and will pay $1000 in ten years. 4 (a) Yes, the bond is better. (b) No, the bond is worse. (c) Can’t tell from information given 12. You are given the following information about portfolios of two risky assets, A and B: Weight in A Weight in B Std. dev. of portfolio 0 1 12 0. 5 0. 5 14 1 0 16 What is the covariance between A and B? (a) 192%2 (b) 168%2 (c) 224%2 (d) Cannot be determined 13. A ? rm in a well-functioning capital market has the following projects available. The risk-free rate is 10%. Which should it invest in? NPV IRR X 10 15% Y 0. 3% Z -5 22% OCC 22% 5% 6% (a) X only (b) Z only (c) X and Y (d) X and Z (e) All three 5 14. You are considering investing in a bond. This bond costs $300 now and pays $550 in ten years. What is the IRR of this investment? (a) 1. 06% (b) 6. 25% (c) 8. 33% (d) 9. 01% Answer the next two questions using the following information: A project has the following expected cash ? ows. Year 0 1 2 Expected cash? ow ? 370 814 ? 447. 7 The IRR of these cash ? ows is 10%. 15. Which of the NPV functions on the following page best describes this project? (2pts) (a) Graph A (b) Graph B (c) Graph C (d) Graph D 16.
Given your answer to the previous question, what is the range of discount rates for which you should accept this project? (a) 10% only (b) Greater than 10% (c) Less than 10% (d) Always accept, except at 10% (e) Always reject 6 NPV NPV 10% Discount rate 10% Discount rate Graph A Graph B NPV NPV 10% Discount rate 10% Discount rate Graph C Graph D 7 Answer the next six questions using the following information: Boeing is a very pro? table aeroplane manufacturer. It is considering building a facility to manufacture 747s on 10,000 acres in the Nevada desert. It is not considering any other sites.
To encourage Boeing to set up the facility, the local chamber of commerce has bought the land and has o? ered to rent it to Boeing at a rent of zero dollars per year. Assume that this “gift” has no tax implications for Boeing. If Boeing were to try to rent the land in the open market, the rent would be $1,500 per acre per year, payable at the end of each year. Building the factory will cost Boeing $800M (800 million dollars), of which $200M is payable today and $600M will be need to be paid as soon as the factory begins production. It will take one year to build the factory and start production.
The IRS says that the $800M cost can be depreciated (straight-line to zero) over the ? rst twenty years in which the factory produces aeroplanes. However, Boeing expects that the demand for the 747 will eventually dry up, and so they plan to scrap the plant after the ? rst ten years of production. They expect the scrap will be sold for $100M. Boeing expects the facility to produce and sell three Boeing 747 aeroplanes a year, with the ? rst batch ready by the end of year 2. Raw materials cost $100M per plane, and labour costs will be $120M a year. Labour costs will be paid at the end of the year in which they are incurred.
Raw material will be paid for one year late (i. e. , raw material costs incurred in year 2 will be paid at the end of year 3). Sales will be paid for two years late. Inventory is always 0. The price Boeing will receive for each plane is uncertain. It might be as high as $500M, or as low as $200M. Most likely, the price will be $400M. On average, the price they expect to receive is $350M. Boeing’s corporate o? ce is located in Chicago. Currently the CEO and his sta? make 120 ? ights a year in the corporate jet. Each ? ight costs $200,000. If the Nevada facility is built, the CEO will have to make ten more ? ghts a year, starting in the ? rst year of production, with the cost per ? ight being the same. The cost of the ? ights is incurred at the end of year in which the ? ights are made. The salary of the CEO will remain ? xed at $12m per year. However, the corporate o? ce has decided to allocate $1m per year of this cost to the Nevada project, should it be built, starting at the end of year 2. This allocation has no tax implications. Boeing has another project which they wanted to start today. This project has a single after-tax cash in? ow of $20 million one year after it is started (and no other in? ws or out? ows). Building the factory in Nevada will occupy executive time, and mean that Boeing will have to delay starting this project until the Nevada factory begins production. Taxes are expected to be 30%. The discount rate is 8%. 8 17. When calculating cash ? ows for NPV, the revenue in the income statement at the end of each year of production will be (a) $600M (b) $1050M (c) $1200M (d) $1500M 18. The expected cash ? ow the ? rm obtains from scrapping the plant after ten years of production is (a) $70M (b) $90M (c) $100M (d) $190M (e) $280M 19.
The cost that you will show in the income statement for each year of production will be: (a) $420M (b) $422M (c) $423M (d) $438M 20. What is the working capital at the end of the second year of production? (a) ? $300M (b) $750M (c) $1050M (d) $1800M 21. What is your net cash ? ow two years after the plant has stopped producing, that is, at the end of year 13? (a) $0 (b) $735M (c) $750M (d) $1050M (e) $1800M 9 22. The PV today of the opportunity cost from delaying the other project is: (a) $20M (b) $18. 52M (c) $17. 15M (d) $1. 37M 10