________________________________________________________________
Your name and Perm #
Econ 134A (9:30 am lecture) John Hartman
Test 1, Version A February 13, 2013
Instructions:
You have 65 minutes to complete this test, unless you arrive late. Late arrival will lower the time available to you, and you must finish at the same time as all other students.
Each question shows how many points it is worth. Show all work in order to receive credit. You will receive partial credit for incorrect solutions in some instances. Clearly circle your answer(s) or else you may not receive full credit for a complete and correct solution.
Cheating will not be tolerated during any test. Any suspected cheating will be reported to the relevant authorities on this issue.
You are allowed to use a nonprogrammable four-function or scientific calculator that is NOT a communication device. You are NOT allowed to have a calculator that stores formulas, buttons that automatically calculate IRR, NPV, or any other concept covered in this class. You are NOT allowed to have a calculator that has the ability to produce graphs. If you use a calculator that does not meet these requirements, you will be assumed to be cheating.
Unless otherwise specified, you can assume the following:
· Negative internal rates of return are not possible.
You are allowed to turn in your test early if there are at least 10 minutes remaining. As a courtesy to your classmates, you will not be allowed to leave during the final 10 minutes of the test.
Your test should have 6 problems, some with multiple parts. The maximum possible point total is 62 points. If your test is incomplete, it is your responsibility to notify a proctor to get a new test.
For your reference, an example of a well-labeled graph is below:
For the following problems, you will need to write out the solution. You must show all work to receive credit. Each problem (or part of problem) shows the maximum point value. Provide at least four significant digits to each answer or you may not receive full credit for a correct solution.
1. (11 points) Eber Extravagant has just purchased $50,000 in furnishings for his living room. To do so, he charged all $50,000 spent on his American Slowpoke credit card, which charges 21% stated annual interest, compounded monthly. After getting home, he finds he has just been approved for a new Uncover credit card, which charges 18% stated annual interest, compounded monthly. The Uncover card charges a 4% fee for any balances that are transferred. If Eber is planning on making monthly payments of $1,500 per month to pay off his furnishings, should he pay off his American Slowpoke credit card, or transfer his balance to the Uncover card today and pay off the higher balance? Assume the first $1,500 payment will be one month from today.
You need to completely justify your answer to get full credit.
2. Solve each of the following:
(a) (4 points) The stated annual interest is r%, compounded continuously. How many years will it take to double an initial deposit made today? Assume that any interest earned gets re-invested.
(b) (6 points) Dan deposits $600 into a bank account today, and will receive $800 three years from today. What is the stated annual interest rate if interest is compounded daily? You can assume there are 365 days per year.
(c) (3 points) Danielle invests $600,000 into a new superconductor project today. She will receive $500,000 one year from now and $300,000 eight years from now. The effective annual discount rate is 9%. What is the profitability index of this project?
3. (7 points) Investment P offers to pay $500 per year forever, starting today. Investment GP offers to pay $400 today, followed by 4% annual growth every year forever. For what effective annual discount rate would you be indifferent between the two investments?
4. (10 points) Club 4321, Inc. pays quarterly dividends. The corporation will pay $4 in dividends per share over the next year. It will pay out $1 every quarter starting three months from now. The annual dividend will increase to $4.60 the following year, and remain there forever. (Remember that the $4.60 annual dividend also gets divided up into four quarterly payments.) The appropriate effective annual discount rate for this stock is 43.21%. What is the present value of Club 4321 stock?
5. (8 points) Rain Rain Rain, Inc. specializes in umbrella production. In anticipation of a rainy season ahead, the executives decide to sell bonds to help fund additional umbrella production. Bonds sell today for $45 each, but the face value of the bond is $50. A 9% coupon is promised twice: One year from today and two years from today. The bond also matures two years from today. What is the yield to maturity, expressed as an effective annual rate?
6. Mountaintop Paving, Inc. needs to buy a new machine that paves roads in rural areas. If the company buys a machine today, the immediate cost is $60,000, and a one-time maintenance cost of $7,000 is required five years from today. The machine lasts for 8 years. The effective annual discount rate is 4%.
(a) (6 points) What is the equivalent annual cost of the machine?
(b) (6 points) Suppose instead that the executives at Mountaintop Paving decide to finance the machine so that the present value of the payments are the same as the present value of all costs of the machine (including maintenance) if purchased. The effective annual interest rate for the loan is 4%. Five payments will be made to pay back the loan. The first will be made today, and the remaining payments will be made 2 years, 4 years, 6 years, and 8 years from today. How much will each payment be?