Econ 134A John Hartman

Your name and Perm # ______

Test 1, Version B April 28, 2011

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 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 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 10 multiple-choice questions and 3 problems. The maximum possible point total is 60 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 1-2: Assume that you receive $600 annually forever. Assume that the effective annual discount rate is 8%. Determine the present value given the following assumptions.

1. You receive the first payment today.

A. $6,900 B. $6,944 C. $7,500 D. $8,056 E. $8,100

2. You receive the first payment one year from today, but you receive a payment of $300 every six months.

A. $7,275 B. $7,350 C. $7,425 D. $7,500 E. $7,650

3. Suppose Joanne Green invests in a new technology that makes tubeless toilet paper. Her annual discount rate is 8%. Her investment today is $50,000. The only positive cash flow she receives is three years from now, for $58,000. Her annual internal rate of return for this project is

A. 5% B. 6% C. 8% D. 12% E. 16%

4. Billy Bo Bob is set to receive a nominal payment of $100,000 six years from now. There is no inflation over the next year, followed by 5% annual inflation each of the following five years. The real payment six years from now is _____.

A. $74,600 B. $76,900 C. $78,400 D. $80,000 E. $95,200

5. If Treasury bonds have an effective annual inflation rate of 7% and the annual nominal interest rate is 8.9%, then the annual real rate of interest is _____.

A. 1.9% B. 15.9% C. 16.2% D. 16.5% E. 16.8%

6. Liv invests $500 in a project today, and receives $200 one year from today and $250 two years from today. Her NPV from the project is $0, and she receives one final payment four years from today. If her annual discount rate is 7%, then the final payment is _____.

A. $50 B. $79 C. $95 D. $104 E. $124

For Questions 7-8: Today is April 28, 2011. You invest $1,000 today. Find the future values on the following dates, given the stated nominal annual interest rates and frequency of compounding.

7. April 28, 2021, 3% interest rate, compounded monthly

A. $1,300 B. $1,310 C. $1,340 D. $1,350 E. $1,400

8. October 28, 2012, 5.5% interest rate, compounded continuously

A. $1,057 B. $1,083 C. $1,086 D. $1,100 E. $1,116

9. You invest $50,000 today and the future value 12 years from now is $100,000. Interest is compounded twice per year. The stated annual interest rate is _____.

A. 5.86% B. 5.94% C. 6% D. 6.12% E. 8.33%

10. Suppose that I purchase a rare 1909-S VDB one-cent coin today for $2,000. In five years, I sell it for $1,500. If I compound my rate of return annually, what is my annual rate of return on this investment?

A. –5.59% B. –5% C. 5% D. 5.77% E. 5.92%

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. You have been asked to analyze the costs of two different machines. If you buy Machine A, you have to pay $1,000 today (year 0), and maintenance costs of $200 in each of years 2, 3, and 4. If you buy Machine B, you have to pay $1,500 today and $100 maintenance costs in each of years 1, 2, 3, 4, and 5. Machine A lasts 4 years, and Machine B lasts 5 years. The effective annual discount rate is 6%. (Note: All dollar amounts in this problem are in real terms.)

(a) (2 points) What is the NPV of all of the costs of Machine A?

(b) (2 points) What is the NPV of all of the costs of Machine B?

(d) (3 points) What is the equivalent annual cost of Machine B?

(e) (2 points) If both machines can be easily replaced in the future, which machine will you buy? Explain in 15 words or less.

2. Suppose that Aucks, Inc. has formulated a new drink, Super Water. If Super Water is a success, the present value of the payoff is $5 million (when the product is brought to market). If the product fails, the present value of the payoff is $2 million. If the product goes directly to market, there is a 30% chance of success and a 70% chance of failure. Alternatively, Aucks can delay the introduction of Super Water by 2 years and spend $300,000 today to test market the product. Test marketing will improve the product and increase the chance of success to 60%. The appropriate annual discount rate is 5%. (Note: Ignore previous costs in the calculations below.)

(a) (3 points) What is the NPV of going directly to market?

(b) (3 points) What is the NPV of delaying the introduction of Super Water by two years?

(c) (1 points) If you were advising Aucks what to do in 20 words or less, what would you say? Include any justification for your advise.

3. (8 points) Suppose you start a bank account one year from now. If you make annual deposits of $500, into an account that pays an effective annual interest rate of 7.1%, how many years will you have made when your account balance is $41,000? (Round to the nearest number of years.)