February 22, 2012
• 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. 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 cashﬂows: Year 0 1 2 Cashﬂow +12000 −7080 −6654 The IRR of these cashﬂows 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 oﬀ my loans within ten years? (2pts) 2
(a) $43,050 (b) $50,000 (c) $55,752 (d) $61,339 5. A credit card company oﬀers 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 −15 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 oﬀers 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....