Last name of TA
Day and time of your section
__________________________________________________________
Your name and Perm #
Econ 134A
Test 1
John Hartman
July 11, 2013
Instructions:
You have 80 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 10 multiple-choice questions and 4 problems (40 points total). The maximum
possible point total is 73 points. If your test is incomplete, it is your responsibility to notify a proctor to
get a new test.
Grading:
For your reference, an example of a well-labeled graph is below:
Filling in name, perm #, TA name, and day/time of section, &
3/3
(automatic unless something is not done correctly)
having photo ID
Multiple choice
_____/30
Problems
_____/40
Total score
_____/73
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 or best answer.
1. If the effective annual discount rate is 13%, what is the effective discount rate for 8 months?
A. 8.3%
B. 8.4%
C. 8.5%
D. 8.6%
E. 8.7%
(1.13)^(2/3) – 1 = 8.48898 %
2. The Tree Annihilator 5000 can be purchased today for $5,000, and lasts for five years. Annual
maintenance costs must be paid two years from today and four years from today, at $500 each.
What is the equivalent annual cost if the effective annual discount rate is 5%?
A. $1350
B. $1300
C. $1260
D. $1230
E. $1200
PV of costs = 5,000 + 500/(1.05^2) + 500/(1.05^4) = 5,864.87
EAC: 5,864.87 = C/0.05 (1 – 1/1.05^5)
 C = 1,354.64
3. Jack is set to receive $70,000 per year, forever, starting six months from now. What is the
present value of this perpetuity if his effective annual discount rate is 8%?
A. $875,000 B. $909,000 C. $910,000 D. $945,000 E. $946,000
PV = 70,000/0.08 * √1.08 = 909,327
4. Hazel is investing in a household supply company. She knows the following: If she invests
$5,000 today, she will receive $X every year starting one year from now. She will receive these
payments forever. Her effective annual discount rate is 10%. The internal rate of return for this
project is 7%. Find X.
A. $350
B. $400
C. $450
D. $500
E. $550
-5000 + X/0.07 = 0
 X = 350
For the next three questions, use the following information: Barry is ready to buy a car. In order
to do so, he needs to take out a loan today of $50,000. He will pay back the loan over 50
months. The stated annual interest rate being charged to Barry is 9.6%, compounded monthly.
5. If the loan is amortized such that all payments are constant, how much is the first payment?
A. $1,000
B. $1,100
C. $1,200
D. $1,300
E. $1,400
50,000 = C/0.008 (1 – 1/1.008^50)
 C = 1,217.24
6. If the loan is amortized such that the amount of principal reduced each month is constant,
how much is the first payment?
A. $1,000
B. $1,100
C. $1,200
D. $1,300
E. $1,400
Interest = 50,000 * 0.008 = 400
Principal reduction = 50,000/50 = 1,000
Total = 1,400
7. If the loan is amortized such that the amount of principal reduced each month is constant,
how much is the last payment?
A. $1,000
B. $1,100
C. $1,200
D. $1,300
E. $1,400
Interest = 1,000 * 0.008 = 8
Principal reduction = 50,000/50 = 1,000
Total = 1,008
8. Susan invests $10,000 today. She is set to receive $1,200 per year, forever, starting four years
from now. What is the profitability index for this investment if the stated annual interest rate is
10%, compounded continuously?
A. 1.2
B. 1.0
C. 0.9
D. 0.85
E. 0.8
PV of benefits = 1,200/(exp(0.1) – 1) * 1 / exp(0.1 * 3) = 8,452.73
PI = 8,452.73/10,000 = 0.845273
9. Robert has just deposited $50,000 into a bank account but he does not know if he is earning
simple interest or compound interest. If the annual interest rate is 12%, how much more interest
is earned with compound interest (relative to simple interest) over the next 7 years?
A. $20,000 B. $25,000 C. $30,000 D. $35,000 E. $40,000
Compound interest: 50,000 (1.12^7 - 1) = 60,534.07
Simple interest: 50,000 (0.12 * 7) = 42,000
Difference = 18,534.07
10. Suppose that in the final interview before someone receives a job offer, the interviewees get
the following problem: Use the discounted payback period method, with the cutoff date 10
years, 3 months from now. In other words, the payback period is 10 years, 3 months. The
effective annual discount rate is 12%. Which of the following offers should be picked if
someone uses this method?
A. $800 per year, forever, starting 5 years from now
B. $500 per year, forever, starting 2 years from now
C. $8,000 every 10 years, forever, starting 10 years from now
D. $80,000 every 20 years, forever, starting 12 years from now
E. A one-time payment today of $2,500
A: 800/0.12 (1 – 1/1.12^6) (1/1.12^4) = 2,090.30 B: 500/0.12 (1 – 1/1.12^9) (1/1.12) =2,378.68
C: 8,000/(1.12^10) = 2,575.79
D: 0
E: 2,500
Pick option C because it has the highest PV
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. (9 points) Piper is investing $10,000 today in a project and receives $6,000 one year from
today and $7,000 two years from today in return. What is her annual internal rate of
return if her effective annual discount rate is 14%?
– 10,000 + 6,000/(1 + R) + 7,000/(1 + R)^2 = 0
 10R^2 + 14R – 3 = 0
R = [ – 14 + √( 14^2 – 4 (10) (-3) ) ] / (2 * 10) = 0.188819
2. Wesley is about to take a loan of $36,000 from the Wonderful World of Money Bank. The
stated annual interest rate for the loan is 6%, compounded monthly. The first payment will be
made one month from today.
(a) (6 points) If the loan is amortized over 25 years with monthly payments, and Wesley pays an
equal amount of principal each month of repayment, how much will the 6th payment be?
Principal reduction: 5 * [36,000/(25 * 12)] = 600
6th month interest payment = (36,000 – 600) * 0.06/12 = 177
6th month principal payment = 36,000/(25 * 12) = 120
Total 6th month payment = 297
(b) (7 points) Suppose the loan is amortized with monthly payments made over 100 years, and
the first payment will be $X. Each subsequent payment will be 0.05% higher than the previous
payment. Find X.
36,000 = C/(0.005 – 0.0005) [ 1 – (1.0005/1.005)^(100*12)]
 C = 162.75
3. There are two investments that could go up on an empty lot by the train tracks somewhere in
Goleta. Due to the small size of the lot, only one of the investments can be implemented. This
lot cannot be used for anything else in the next four years. Assume an effective annual discount
rate of 15%.
To implement an investment called “Noisy Train Museum,” $100,000 must be invested
today, and $230,000 will be received three years from now.
To implement an investment called “Here’s a Target for Your Bullseye,” $60,000 must
be invested today, and $120,000 will be received one year from now.
Any money not put into one of the investments above earns 15% per year.
(a) (6 points) What is the internal rate of return of “Noisy Train Museum” and “Here’s a Target
for Your Bullseye?”
IRR Noisy: – 100,000 + 230,000/(1 + R)^3 = 0  R = 0.320006
IRR Bullseye: – 60,000 + 120,000/(1 + R) = 0  R = 1
(b) (4 points) Which investment should be chosen? You must justify your answer in 40 words or
less. Please provide a complete mathematical justification for your answer or you will receive at
most 1 point for this part of the problem.
NPV Noisy = – 100,000 + 230,000/(1.15)^3 = 51,228.73
NPV Bullseye = – 60,000 + 120,000/(1.15)^3 = 44,347.83
Choose Noisy because it has the higher NPV
4. (8 points) Phil has just finalized a loan contract with ZZ Bottom National Bank. He will
receive $111,111 today, and must make equal daily payments to pay off the loan over the next
year. The stated annual interest rate is 18.25%, and interest is compounded daily. How much
will Phil have to pay every day to pay off the loan one year from today? (You can assume the
last payment is made 365 days from today.)
Daily interest rate = 0.1825/365 = 0.0005
111,111 = C/0.0005 [ 1 – 1/1.0005^365]
=> C = 333.11