Corporate Finance FINC-UB.0007- New York University_ Practice Midterm 1 Problems and Solutions:

Which of the following investment rules may not use all possible cash flows in its calculations? a. NPV b. Internal Rate of Return c. Discounted payback d. Real options 2. The real interest rate is 3% and the inflation rate is 5%. What is the nominal interest rate? a. 3% b. 5% c. 8% d. 8.15% 3. Net working capital is the: (I) Shor-term assets, (II) Short-term liabilities, (III) Longterm assets, (IV) Long-term liabilities a. I only b. I and II c. I and III d. III and-IV 4. The naïve IRR rule (invest if the opportunity cost of capital is lower than the IRR) makes the correct investment decision for a. Borrowing projects b. Lending projects c. All projects with one IRR d. All projects 5. You are considering investing $1,000 today in a project that will pay $500 a year from now and $8,000 in two years with certainty. There is another project that requires $1,000 initial investment that has a yearly return of 8%. The risk free rate is 5%. Should you invest? a. Yes b. No c. I don’t have enough information to answer the question 6. You are managing a team in charge of a merger. In their valuation calculations, your team forgot to include the possibility of geographically expanding that arises only if the merger occurs. The NPV of the merger is a. Higher than the one your team computed b. Lower than the one your team computed c. At least as high as the one your team computed7. Winning the lottery gives $1,500,000 divided in equal installments over 5 years. The risk-free rate is 4%. The value of winning the lottery is a. $1,500,000 b. Greater than $1,500,000 c. Lower than $1,500,000 8. One of your friends in considering investing in a project. The project’s initial cash flow is 100 dollars. The cash flows from period 1 onwards (starting at the end of period 1) represent a perpetuity paying -20 dollars each period. Based on this information only, what recommendation would you give your friend? a. Invest if the discount rate is less than the IRR b. Invest if the discount rate is greater than the IRR c. Invest if the discount rate is equal to the IRR d. I don’t have enough information to give a recommendation 9. An investor offers you a $1M loan with an IRR of 3%. The investor, who breaks even, offers you the following repayment plan: one initial payment of $0.5M at the end of year 1 and 3 equal annual installments at the end of years 2, 3 and 4. What is the annual repayment in years 2, 3 and 4? (rounded to the nearest 2 decimals) a. $0.19 b. $0.17 c. $0.51 d. None of the aboveNumerical problems Problem 1. You have a total budget of 500. You can carry out the following projects. Your cost of capital is 10%. The projects are ranged by internal rate of return. What is the optimal project mix in order to maximize the total net present value? Problem 2. Dean Henry is expected to retire in 30 years and he wishes to accumulate $800,000 in his retirement fund by that time (t=30). If the interest rate is 12% per year, how much should Dean Henry put into the retirement fund each year (at the end of each year, from t=1 to t=30) in order to achieve this goal? Problem 3. You just graduated from Stern and got hired at your dream job. You are tired of living in a small apartment with 4 roommates and are considering purchasing your own place. However, real estate in your area is expensive and you do not have enough savings for a down payment yet. You need $200,000 more than what you already have. Your savings account has a return of 5%. a) How much should you save each year to be able to buy an apartment 6 years from now (you would pay for the apartment at the end of year 6). Problem 4. Imagine that you are the producer of James Bond movies. You are trying to decide whether to film the next two James Bond movies at the same time. If you film them both at once, you can save money on production costs, but you could lose a lot of money if the first one flops and no one goes to see the second one. Specifically, if you film them both at once, it will cost a total of $300 million today (t=0), but if you film them separately, they will cost $200 million each (at t=0 and t=1). If the first one is successful, it will have revenues of $1 billion one year from now (t=1) and the second one will have revenues of$1.5 billion two years from now t=2). If the first one fails, it will only have revenues of $150 million (t=1) and the second one will have revenues of only 50 million (t=2). If you decide to film them separately and the first one flops, you don't have to film the second one. The first film has 50% chance of succeeding and 50% chance of failing. Assume the cost of capital is 0%and ignore taxes. Problem 5. You are thinking of buying a chain of coffee shops and operating it for exactly one year. The purchase price is $70M. The end-of-year cash flows, which include both operating profits and resale value, depend on how successful you are at establishing your brand, which in turn depends on consumers’ tastes. With probability 0.5 consumers love your brand, inwhich case the cash flow is $75M. However, with probability 0.5 consumers merely like your brand, in which case the cash flow is only $40M. The opportunity cost of capital is 5%. a) Should you buy the coffee shops? b) Due to your established brand name you have the opportunity to expand into the sale of muffins one year from now. By that time, you will know the consumers’ attitude towards your brand. The expansion costs $10M and generates $60M if consumers love your brand and $5M if they merely like it. Given that you have already invested in the coffee shop, should you expand into the muffin business? Problem 6. Assume you are thinking about the following decision at the beginning of year t=0: Your firm bought six buses ten years ago for a total of $2M. At that time, IRS rules prescribed that the buses be fully depreciated over 20 years in a straight line. The IRS has recently changed its depreciation rule for buses. The new rule prescribes that buses be fully depreciated over six years in a straight line. However, this new rule is not retroactive. It only applies to buses purchased after the new rule became effective. The current market value of the six busses is $1.7M. Your firm expects to use the busses forever. Maintenance costs for the busses are $0.1M per year. A bank approaches you and suggests the following deal: It will buy the buses from you at their current market value and then immediately sell them back to you at the same price. Since you would be selling and buying buses today, you would be eligible for the new depreciation rule already this year, i.e., the depreciation tax shield at this year’s end would be based on the new dep Problem 7. You are considering leaving your current job to set up a restaurant. Your current (after tax) salary is $70,000 and, if you do not go ahead with the restaurant project, you will work 4 more years. In that case, you will receive your salary at t=1,2,3,4. If you go ahead with the restaurant project, you plan to be in business forever (i.e., either you expect to live forever or you expect the restaurant will be in your family for many generations). You have come up with the following information: • The locale for the restaurant will cost $500,000 today (t=0) and will be fully depreciated in a straight line over 5 years according to the IRS rules. • The main cost will be the chef’s salary. Her salary will be $100,000 annually (paid at the end of each year). • The revenues of the restaurant are expected to be $250,000 per year and other costs (not including depreciation or the chef’s salary) are expected to be $50,000 annually. Revenues and costs are paid at the end of each year. The tax rate is 35% and the discount rate is 10% (both constant over time). Compute the cash flows for the first five years separately (t=0,1,2,3,4,5). What is the NPV of your restaurant? Here is the cash-flow table (only add up the numbers in bold):