Econ 134A John Hartman
Test 1, Form A October 29, 2014
Instructions:
YOU WILL TURN IN YOUR SCANTRON AND THE PROBLEMS PAGE. MAKE SURE ALL WORK AND ANSWERS ARE PROVIDED ON THESE.
You have 40 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.
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.
· Equivalent annual cost problems are in real dollars.
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 5 multiple choice questions (10 points) and 2 problems (13 points). The maximum possible point total is 24 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 2 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.
1. A stated annual interest rate of 3.65%, compounded daily, is equivalent to an effective annual interest rate of _____.
A. 3.71% B. 3.68% C. 3.65% D. 3.62% E. 3.59%
EAR = EAR=1+3.65%365365-1=3.717%
2. Janet has just borrowed $2,000 from the Interplanetary Bank. This loan has negative amortization. She will pay 0.5% each month over the next year (starting one month from today), but the stated annual interest rate for the loan is 12%, compounded monthly. How much will Janet owe two months from today immediately after her second monthly payment is made?
A. $2,050 B. $2,030 B. $2,020 C. $2,010 D. $2,005
Month / Beginning balance / Payment / Interest / New balance1 / $2,000 / $10 = 2,000*.005 / 20=2,000*(0.01) / 2,010 = 2,000 - 10 + 20
2 / $2,010 / $10.05=2010*.005 / 20.10=2,010*(0.01) / 2,020.05 = 2010 -10.05 + 20.10
Note: monthly interest rate = 12%/12 = .01
3. Bill is a retired politician who has just inherited a school bus business. The business will earn $5,000 later today, and will earn an additional 8% each subsequent year forever. What is the present value of this business if the effective annual interest rate is 13%?
A. $100,000 B. $104,000 C. $108,000 D. $112,000 E. $116,000
PV=5000+5000*(1.08).13-.08=113000
4. Lolly is boldly investing in the stock market and wants to know exactly the real rate of return for an investment. If the annual inflation rate is 50% and the annual rate of return in the stock market is 90%, what is the real rate of return?
A. 25% B. 40% C. 90% D. 140% E. 185%
1+real1+inflation=1+nominal
1+real1.5=1.9
real=26.667%
5. Rufus Xavier is considering buying a new teaching computer. He knows that it will cost $1,000 to purchase and it will last for 8 years. He will have to make maintenance payments of $500 3 years from today and $200 6 years from today. What is the equivalent annual cost of this machine if his effective annual interest rate is 10%?
A. $220 B. $240 C. $280 D. $310 E. $340
PVcost=1000+5001.13+2001.16=1488.53
EAC:1488.55=c.11-11.18 à c=279.02
Name______Perm #______Day/time of section______
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. 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.
6. (6 points) Rocky is considering an investment which requires a $500 payment today and a $499 payment four years from now. In return, she will receive $1000 two years from today. What is the annual internal rate of return for this investment?
-500+10001+r2+4991+r4 = 0
let x=(1+r)2
è 500x2-1000x+499=0
è 1000±-10002-4500(499)2(500)=x
è 1.04472 or 0.955279
è Rule out 0.955279 because it must be that X ≥ 1 in order for r ≥ 0.
è 1.04472=(1+r)2 à r=2.212%
7. (7 points) Mr. Morton is retired and is investing $1,000,000 today in order to receive monthly payments of $6,000, starting in one year. These monthly payments will continue forever after. If his effective annual interest rate is 5%, what is the profitability index of this investment?
monthly rate=121.05-1=0.407%
PV of positive cash flow=6000.0040711.0040711=1408295
PI=14082951000000=1.408