Your name and Perm # ______
Econ 134A John Hartman
Test 1, Version A October 27, 2011
Instructions: (First thing: Bubble in your test form; if you do not, this is one way you can lose 3 points.)
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 in the PROBLEMS section. 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 may be assumed to be cheating.
Unless otherwise specified, you can assume the following: Negative internal rates of return are not possible; all interest is to be compounded as directed unless mentioned otherwise.
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 9 multiple-choice questions and 3 problems. 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:
MULTIPLE CHOICE: Answer the following questions on your scantron. Each correct answer is worth 3 points. All incorrect or blank answers are worth 0 points. If there is an answer that does not exactly match the correct answer, choose the closest answer.
For Questions 1-3: Today is October 27, 2011. You invest $2,500 today. Find the future values on the following dates, given the stated annual interest rates and frequency of compounding.
1. July 27, 2013, 14% interest rate, compounded every three months
A. $3,113 B. $3,144 C. $3,168 D. $3,181 E. $3,249
2. October 27, 2041, 2.31% interest rate, compounded continuously
A. $4,850 B. $4,900 C. $4,950 D. $5,000 E. $5,050
3. April 27, 2019, 5% interest rate, compounded every 30 months
A. $3438 B. $3560 C. $3605 D. $3621 E. $3629
4. Adelle Samuelson is set to receive a real payment of $35,000 (in today’s dollars) seven years from now. Inflation will be 3% per year for the first three years, and 4% per year after the first three years. The nominal payment seven years from now will be _____.
A. $27,379 B. $27,645 C. $37,471 D. $44,312 E. $44,742
5. Suppose that Heath Wells deposits $10,000 in a bank, earning 9% yearly interest for five years. How much MORE interest will Heath earn if the interest is compounded monthly, relative to simple interest?
A. $25 B. $275 C. $875 D. $1150 E. $1175
6. Biliana Marks has been named in her grandmother’s will. She is set to receive $3,000 per year forever, starting six months from now. Her effective annual discount rate is 8%. The present value of this stream of payments is _____.
A. $37,500 B. $38,971 C. $39,000 D. $40,500 E. infinite
7. In 1803, the United States made the “Louisiana Purchase” for $15 million. This amount of money would be equivalent to $219 million in 2010, once inflation is factored in. (Note that this comes out to less than 42 cents per acre.) If annual inflation was the same every year over this 207-year period, then the yearly inflation rate would have been _____. (The following information may help you: You need to compound on a yearly basis here. Dollar amounts listed are in nominal dollars.)
A. 1.3% B. 2.6% C. 6.6% D. 7% E. 13,600%
8. Suppose that Rosie buys a robot for $1,000 today and must pay a maintenance cost of $100 one year from today. The machine lasts for two years. The equivalent annual cost of the machine is _____ if the effective annual discount rate is 4%.
A. $509 B. $529 C. $550 D. $559 E. $581
9. If Taeil Smith deposits $500 today at an effective annual interest rate of 8%, how many years will be needed for the $500 to grow to $32,000?
A. 54 B. 62 C. 70 D. 108 E. 788
PROBLEMS: 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.
1. Suppose you invest $500 today in a project. After investing in the project, you would get paid back $214.70 one year from now and $350.30 two years from now.
(a) (2 points) Find the net present value of the project if the effective annual discount rate is 15%. Round your answer to the nearest cent.
(b) (3 points) Based on your answer above, is the annual internal rate of return greater than, equal to, or less than 15%? You will only receive credit if you can justify your answer in 40 words or less.
(c) (6 points) Calculate the annual internal rate of return, to the nearest hundredth of a percent.
(d) (5 points) Suppose that the effective annual discount rate is 20%, and that you not only receive the payments one and two years from now, but also a payment three years from now. Determine what the payment three years from now needs to be in order for the project to have a net present value of $100. Round your answer to the nearest cent.
2. (6 points) You are considering buying a junk bond that promises 4 coupon payments of $500, at the following times: Later today, one year from today, two years from today, and three years from today. You decide that for this bond, the effective annual discount rate for the first two years (from today to two years from today) is 6%. The effective annual discount rate after the first two years (from two years from today onward) is 14%. Based on these assumptions, what is the present value of the four coupon payments? Round your answer to the nearest cent.
3. (10 points) Sammy Waffle has won the Wacky Lottery. The Wacky Lottery pays out its prize of 10 payments as follows:
· $10,000 two years, four years, and six years from today (3 payments)
· $13,000 eight years from today (1 payment)
· Payments made 10 years, 12 years, 14 years, 16 years, 18 years, and 20 years from today: Each of these payments is 3% higher than the previous payment (6 payments)
What is the present value of these payments if the effective annual discount rate is 5%? Round your answer to the nearest dollar.