Structure of Finance Chapters 4-5-6
List of Question Codes
Entries below refer to codes for questions appearing on exam 1. All questions exist as ungraded and
unrestricted practice items in the course shell accessible online anytime/anywhere.
Exam 2, Chapters 4-5-6
25 questions = 15 definite ones + 10-from-26
Question & #points
Easy, Medium, Hard
#1
E
5 pts
#2
5
#3
3
#4
E
#5
5
Step 1: Click the topic, watch and
see the gist of the story.
Find balance after crediting of
periodic interest
The cumulative rate of return ;
Periodic components of time
value: interest-on-interest and
interest-on-principal ; Using
the calculator time value keys
to find FV and periodic interest
Streetbite on the discount rate
and the Fed ; Inflation and
time value
Find shortfall given target FV,
target r, and actual r
5
Find actual APR given lumpsum surplus
Find shortfall for mixed cash
flows
115 maximum points = 20@5 points + 5@3 points
2 Click and open to the
Chapter & section cited.
Read/browse the financial
context for the question.
3 Click the code then practice
online; OR(a,b,c)≡ 1/3 chance
question “a” is on exam, 1/3
chance “b” etc.
Ch4.2A #6
LS7a
Ch4.1 #5 #3, 4.2a #4, #5
OR(ROR1, ROR3c, LS4c
LS6a)
OR(BS38, LS24)
Ch4.2b #4
LS10a
Ch4.2c #3 #4
OR(LS14, LS15)
Ch4.3a #7
CY10a
Ch4.5b #3c
MC5c
#6
E
5
#7
M
5
#8
M
5
PV of cheapest cost
Ch4.3a #12
CY21
3
What is a basis point? ;
Present value and PVIFA ;
The difference between the
geometric and arithmatic
average ROR
Ch5.1, 5.3
OR(FF6, TR15, TR33)
5
FV given beginning balance
Ch5.2a #4
FV5
Ch5.2a #2 #5
OR(FV7, FV9)
Ch5.2b #4
FV6
#9
#10
E
#11
#12
5
E
5
Find FV and total interest ; FV
given beginning balance
Annuity sandwiched between
lumpsums
#13
5
Guardian angel initial deposit ;
Ch5.3a #5 #3
OR(PV7, PV9)
#14
3
Work with general time value
Ch4.5 formula 4.11
OR(TR3, TR4, TR5)
Ch 5.3.B #4
TS1b
Ch5.3a #6b
PV10b
Ch5.4a #6
FV17
#15
M
5
#16
E
5
#17
M
5
#18
3
#19
5
Scholarships after savings
plan
With PV FV and PMT find
ROR for counteroffer
Find PMT that adjusts balance
The Rule of 72 finds the length
of a doubling period ; APR v
EAR
Fixed payment, amortized
loans, and payoff amount
OR(TR1, TR2, TR27)
Ch 5.5, #8, #7
OR(AM5a, AM9c)
#20
M
5
Amortization 3
Ch 5.5, #12a
AM3d
#21
M
5
IRR for a bank selling a loan
Ch 6.1, #12
CB8
#22
M
5
Compare ranking
Ch 6.2, #7
CB2a
#23
H
5
Mixed CF with SL
Ch 6.3, #6
CB10a
3
Payback period introduction ;
Relation between NPV and
IRR ; NPV is economic profit
Ch 6.1, 6.2b
OR(FF23, TR32, TR36)
5
Refi NPV
Ch 6.3, #9a
CB3c
#24
#25
H
Exam 2 Questions
Chapters 4-5-6
25 of these 41 questions appear on Exam 2. See the table above
for more details about question selection.
1.
LS7a Find today's FV given today’s periodic interest on a deposit made long ago with
annual compounding VideoSolution
An account was established 6 years ago with an initial deposit. Today the account is
credited with annual interest of $329 . The interest rate is 4.4% compounded annually.
No other deposits or withdrawals have been made. How much is the end-of-day
balance?
a. $7,086
b. $10,375
c. $9,432
d. $7,795
e. $8,574
2. 1-of-4
ROR1 Find AND(cumulative, geometric average) ROR for venture capitalist
A venture capitalists provides a company equity financing of $15.0 million. After 7 years
the company repurchases the equity for $47.5 million. There are no other cash flows
between the two. Find the average annual geometric rate of return, and also find the
cumulative rate of return.
a. the average annual geometric ror is 17.9% and the cumulative ror is 249.2%
b. the average annual geometric ror is 23.7% and the cumulative ror is 249.2%
c. the average annual geometric ror is 23.7% and the cumulative ror is 216.7%
d. the average annual geometric ror is 17.9% and the cumulative ror is 216.7%
e. the average annual geometric ror is 20.6% and the cumulative ror is 216.7%
2. 2-of-4
ROR3c What is AND(geometric,arithmetic) average ROR given 3 prices
Two years ago you purchased a stock for $44 . One year ago the price had moved to
$11 . Today it is at $59 . Which one statement about the annual average rate of return
is correct?
a. The geometric average return is 18.2% and the arithmetic average return is 180.7%.
b. The geometric average return is 13.7% and the arithmetic average return is 180.7%.
c. The geometric average return is 13.7% and the arithmetic average return is 157.1%.
d. The geometric average return is 15.8% and the arithmetic average return is 157.1%.
e. The geometric average return is 15.8% and the arithmetic average return is 180.7%.
2. 3-of-4
LS4c Find total interest-on-principal of a deposit long ago given annual compounding
A deposit exactly 10 years ago of $1,400 earns 7.5% annual interest compounded
annually. There have been no other deposits or withdrawals. As of today, how much
total interest-on-principal has accumulated?
a. $1,398
b. $955
c. $1,050
d. $1,155
e. $1,271
2. 4-of-4
LS6a Find today’s periodic interest of a deposit long ago given annual compounding
A savings account was established with $50,000 exactly 4 years ago. The account
earns 6.0% compounded annually. Otherwise, the account has been left alone. When
the annual interest is credited to the account today, how much interest is credited?
a. $3,248
b. $3,573
c. $2,440
d. $2,684
e. $2,953
3. 1-of-2
BS38 Describe the three tools of the Fed
The Federal Reserve Board of Directors uses three significant tools to influence market
activity. Which of these statements is the most accurate description of one of these Fed
tools?
a. The official government “federal funds rate” is the interest rate charged by Federal
Reserve District banks to member public and private banks.
b. The reserve requirement on member bank accounts regulates the amount of loans
that banks may lend to business and individual borrowers.
c. Buying and selling currencies and government securities in the global financial
marketplace causes widespread panic and capital flight.
d. Two choices, B and C, are correct
e. None of the A-B-C choices are correct
3. 2-of-2
LS24 Inflation and verbal description of proper discounting
You wish to purchase in 10 years an item that today costs $1,000 . The cost is
expected to inflate at an annual rate of 4.7%. You make a deposit today that perfectly
finances the future purchase. The observed interest rate that your savings earns is
9.2%. Describe the relation between your deposit, inflation, and the discount rate.
a. the deposit equals the real cost of $1000 discounted at the nominal rate 9.2%
b. the deposit equals the nominal cost of $1583 discounted at the real rate 4.3%
c. the real interest rate is 4.3%
d. Two choices, B and C, are correct
e. None of the A-B-C choices are correct
4.
LS10a Find actual FV given target FV, N, target r, and actual r VideoSolution
In exactly 16 months a bill of $13,540 is due. Today you deposit money such that if the
account earns a target rate of return of 1.12% per month, the bill is perfectly financed.
Unfortunately, your account earns 30 basis points less than your target. When the bill is
due, how much money do you lack?
a. $629
b. $472
c. $571
d. $429
e. $520
5. 1-of-2
LS14 Find N given this year's periodic interest, long ago's PV, and r
Today your account was credited with its annual interest of $16,650 . The account was
established some time ago with a $31,800 initial deposit. No other deposits or
withdrawals have been made. The account earns 12.0% annual interest. How many
years ago was the account established?
a. 15 b. 14 c. 18 d. 16 e. 17
5. 2-of-2
LS15 Find N given lifetime accumulated interest, long ago's PV, and r
Some time ago a $109,800 initial deposit opened an account. No other deposits or
withdrawals have been made. Today the annual interest was credited to the account.
Total lifetime interest now equals $176,525 . The account earns 5.8% annual interest.
How many years ago was the account established?
a. 13 b. 17 c. 14 d. 15 e. 16
6.
CY10a Find r given target FV, actual FV, and N (intraperiod compounding
VideoSolution
In exactly 14 years a bill of $26,040 is due. Today you deposit money such that if the
account earns a target rate of return of 6.00% per annum, compounded quarterly, the
bill is perfectly financed. No other deposits or withdrawals have been made. Your
account actually accumulates $22,154 . What was the actual average annual
percentage rate?
a. 3.99% b. 4.83% c. 5.31% d. 5.84% e. 4.39%
7.
MC5c Find the shortfall given 2 irregular and different future expenses, target r and
actual r Video Solution
Here are two future expenses that you want to save for today: $3,000 payable in 6
years, and $6,200 payable in 9 years. You make an investment today that perfectly
finances the future expenses if the investment earns a target 9.8% average annual rate
of return (compounded annually).
The investment indeed grows sufficiently to finance your first expense. Unfortunately,
for the entire investment horizon your actual annual rate of return falls short of the target
by 180 basis points per year. When it is time to pay the second expense, how much
money do you lack?
a. $1,003
b. $829
c. $1,214
d. $1,103
e. $912
8.
CY21 Supplier’s discount and best deal (boolean choices w/o numbers)
9. 1-of-3
FF6 What is a basis point
By how many basis points does 4.2% differ from 9.4% ?
a. 690 b. 790 c. 450 d. 520 e. 600
9. 2-of-3
TR15 explain discount rate, pvifa, and fvifa
9. 3-of-3
TR33 T/F Geometric versus arithmetic average ROR ranking
From a series of periodic rates of return there are two procedures for computing the
average rate of return per period: the arithmetic average and the geometric average. Is
the following statement about these two statistics TRUE or FALSE: The geometric
average periodic rate of return always is greater than or equal to the arithmetic average
periodic rate of return.
a. True
b. False
10.
FV5 Find FV given PV and withdrawal history (annual compounding) VideoSolution
An account is today credited with its annual interest thereby bringing the account
balance to $7,490 . The interest rate is 9.10% compounded annually. You plan to
make annual withdrawals of $700 each. The first withdrawal is in exactly one year and
the last in exactly 18 years. Find the account balance immediately after the last
withdrawal.
a. $6,722 b. $4,591 c. $5,555 d. $5,050 e. $6,111
11. 1-of-2
FV7 Find FV for a simple annuity
Your parents contribute $130 monthly to a college savings plan for you that earns
9.90% compounded monthly. The first deposit was exactly 15 years ago. Find the
account balance after today’s monthly deposit and crediting of monthly interest.
a. $44,595
b. $49,054
c. $59,355
d. $53,959
e. $40,541
11. 2-of-2
FV9 Find FV given PV and withdrawal history (monthly compounding)
An account is today credited with its monthly interest thereby bringing the account
balance to $6,660 . The interest rate is 6.60% compounded monthly. You plan to make
monthly withdrawals of $55 each. The first withdrawal is in exactly one month and the
last in exactly 12 years. Find the account balance immediately after the last withdrawal.
a. $3,516
b. $3,197
c. $2,906
d. $2,642
e. $2,402
12.
FV6 Find FV Given an initial endowment and later deposit stream VideoSolution
Today you inherit an account with a balance of $7,400 . For a while you don’t do
anything with the account but it continues to accrue interest. Exactly 20 months from
today you start an ambitious savings plan and deposit $200 into the account. You plan
to deposit that much each month. Exactly 40 months from today you reconsider your
plan, make your last deposit, and make no additional deposits. You nonetheless leave
the account alone and it continues to accrue interest at a rate of 8.6% compounded
monthly. You finally close the account exactly 7 years from today. How much is the
total accumulation?
a. $16,251 b. $19,664 c. $21,630 d. $23,793 e. $17,876
13. 1-of-2
PV7 Find PV given withdrawal history, today's balance, and rate (quarterly
compounding)
A friend received an inheritance 6 years ago and put all funds into an account earning
6.10% compounded quarterly. Exactly one quarter after establishing the account the
friend started withdrawing $1,350 per quarter. Today she’ll make another quarterly
withdrawal, and quarterly interest will be credited to the account, and then the balance
will be $15,687 . How much was the friend’s inheritance?
a. $45,825
b. $41,659
c. $37,872
d. $55,448
e. $50,407
13. 2-of-2
PV9 Find PV given CF, FV and r (annual compounding)
You might invest in a security that will return after-tax cash flow to you of $1,300 per
year for 6 years (first cash flow one year from now), after which the security likely can
be sold immediately for $7,700 . You make an offer to buy the security so that you’ll get
a 8.60% rate of return (compounded annually). Find the offer price.
a. $8,757
b. $7,961
c. $10,596
d. $9,632
e. $11,655
14. 1-of-3
TR3 For which stream is the present value the smallest
Suppose two alternative investments promise cash flow streams that possess equal
lives. Further, suppose the simple sum of the cash flows for each investment is the
same amount. Given a positive interest rate, which investment has the smallest present
value?
a. there is no reliable relationship between the distribution of cash flows and present
value.
b. an investment which generates equal cash flows each period.
c. an investment that is being discounted by a small discount rate.
d. an investment which generates most cash flows at the end of its life.
e. an investment which generates most cash flows at the beginning of its life.
14. 2-of-3
TR4 For which stream is the present value the biggest
Suppose two alternative investments promise cash flow streams that possess equal
lives. Further, suppose the simple sum of the cash flows for each investment is the
same amount. Given a positive interest rate, which investment has the biggest present
value?
a. an investment which generates equal cash flows each period.
b. an investment which generates most cash flows at the end of its life.
c. there is no reliable relationship between the distribution of cash flows and present
value.
d. an investment which generates most cash flows at the beginning of its life.
e. an investment that is being discounted by a large discount rate.
14. 3-of-3
TR5 For which stream is the present value the OR(smallest, biggest)
Suppose two equal-cost alternative investments promise cash flow streams that
possess equal lives. Further, suppose the simple sum of the after-tax cash flows for
each investment is the same amount. Given a positive interest rate, which investment
has the biggest present value?
a. an investment that has relatively high sales revenues.
b. an investment which generates equal cash flows each period.
c. there is no reliable relationship between the distribution of cash flows and present
value.
d. an investment that is being discounted by a large discount rate.
e. an investment which generates most cash flows at the beginning of its service life.
E is true.
15.
TS1b Find each withdrawal for a perpetual endowment given the deposit history
16.
PV10b Find actual ROR for annuity given CF, FV, target r, and counteroffer (CF>0)
VideoSolution
You might invest in an asset that will return after-tax cash flow to you of $2,200 per
month for 40 months (first cash flow one month from now), and after receiving the last
cash flow you’ll immediately receive after-tax net proceeds from liquidation equal to
$82,500 . You make an offer to buy the asset so that you’ll get your “target” annual rate
of return of 16.80% (compounded monthly). The seller makes a counteroffer that is
$8,300 higher than your offer. Find your annual rate of return if you buy at the
counteroffer price and receive the expected cash flows.
a. 13.7% b. 15.1% c. 20.1% d. 16.6% e. 18.3%
17.
FV17 Find OR(deposit,withdrawal) given PV, FV, r, and N (annual compounding)
Today you open an account with a $20,800 deposit that earns 5.50% compounded
annually. You’ve set a target for the account so that in exactly 9 years its balance will
be $44,100 . To reach the target you’ll adjust the balance annually; each year’s
adjustment will be exactly the same amount and the first adjustment occurs exactly one
year from now. After the last annual adjustment in exactly 9 years, and crediting of that
year’s interest, the account balance exactly equals the target. Describe the annual
adjustment that you make each year.
a. Each year you make a deposit of $1,065 .
b. Each year you make a withdrawal of $1,065 .
c. Each year you make a withdrawal of $926 .
d. Each year you make a deposit of $926 .
e. Each year you make a deposit of $805 .
18. 1-of-3
TR1 Rule of 72 VideoSolution
Which statement describes the “rule of 72”?
a. The number of months required for a deposit to double equals the decimal interest
rate divided by 72.
b. The approximate number of years required for a deposit to double equals 72 divided
by the percentage interest rate.
c. The simple sum of cash flows required for an investment to earn a positive rate of
return equals the investment cost divided by 72.
d. The simple sum of cash flows required for an investment to earn a positive rate of
return equals the investment cost times 72.
e. The number of months required for a deposit to double equals the decimal interest
rate times 72.
18. 2-of-3
TR2 Sensitivity of total interest to doubling of variables
18. 3-of-3
TR27 Compare EAR and APR wrt bank advertisements VideoSolution
Banks advertise loans so that you’ll borrow money from them and pay them interest.
They also advertise deposits so that you’ll open an account with them and they’ll pay
you interest. Which statement below most likely describes the relation between the
effective annual rate (“EAR”) and annual percentage rate (“APR”).
a. The APR generally is bigger than the EAR.
b. When banks advertise for loans they likely quote the EAR.
c. When banks advertise for deposits they likely quote the APR.
d. Two choices, A and C, are correct
e. None of the A-B-C choices are correct
19. 1-of-2
AM5a How long to reduce principal by half
Your friend is taking out a mortgage for $170,000 at 9.20% repayable with monthly
payments over 15 years. She respects your financial expertise and asks “how many
payments will I have to make before I reduce the principal balance by half its original
amount.” You pull out your calculator, and tell her the number of payments she’ll make
to reduce the balance by half is:
a. 108 b. 81 c. 89 d. 98 e. 119
19. 2-of-2
AM9c How much OR(Principal, Interest) is in the last payment?
You have just bought a house by borrowing $190,000 at a 10.50% annual interest rate
(compounded monthly) repayable with fixed payments over 30 years. When finally in
the far-off future you make your last payment, how much of that last payment will be
interest?
a. $15.08
b. $11.33
c. $16.58
d. $12.46
e. $13.71
20.
AM3d Find interest-to-date VideoSolution
The Company borrowed $174,000 at 9.60% to be repaid monthly over 15 years. They
just remitted payment number 83. How much interest-to date has been paid?
a. $110,718 b. $100,653 c. $91,503 d. $121,790 e. $133,969
21.
CB8 Find irr for bank selling mortgage after n payments
The bank issued a $121,000 30-year mortgage (monthly payments) with an annual
interest rate of 10.20%. They just received payment number 141 and have decided to
sell the loan. The buyer of the loan expects to receive an annual rate of return equal to
8.80%. For the original bank that issued the loan, what was the internal rate of return?
a. 10.58% b. 9.62% c. 7.95% d. 8.75% e. 7.23%
22.
CB2a Given alternative investment’s cash flows, find which alternative is better at x%
Consider the following cash flows for two mutually exclusive investments:
A
B
t=0
($900)
($1,060)
t=1
$657
$122
t=2
$399
$350
t=3
$162
$1,048
Which statement is true?
a. if the financing rate is 15% then project B is the better of the two
b. if the financing rate is 7.52% then projects A and B create the same amount of
wealth
c. if the financing rate is 7.5% then project A is the better of the two
d. if the financing rate is 18.3% then project A is the better of the two
e. if the financing rate is 21.6% then project B is the better of the two
23.
CB10a IRR&NPV w/ straight-line, no salvage value, 3-year stream VideoSolution
Your company is analyzing purchase of a machine costing $8,700 today. The
investment promises to add $9,000 to sales one year from today, $12,500 two years
from today, and $15,000 three years from today. Incremental cash costs should
consume 50% of the incremental sales. The tax rate is 35% and the company's
financing rate is 15.8%. The investment cost is depreciated to zero over a 3-year
straight-line schedule. Find the project's net present value and internal rate of return.
a. NPV and IRR equal $2,282 and 30.1%
b. NPV and IRR equal $1,725 and 34.6%
c. NPV and IRR equal $1,725 and 30.1%
d. NPV and IRR equal $1,984 and 34.6%
e. NPV and IRR equal $2,282 and 34.6%
24. 1-of-3
FF23 Payback period disadvantages
24. 2-of-3
TR32 Short versus long-term loan advantages
24. 3-of-3
TR36 Describe NPV VideoSolution
Which statement is most consistent with the Net present value (NPV) and Internal rate
of return concepts?
a. The NPV for a project is the financing rate at which the project’s IRR is zero.
b. The NPV for a project is the amount of capitalized economic profit that a project
creates.
c. When the project’s actual financing rate is less than the IRR then the NPV is positive.
d. Two choices, B and C, are correct
e. The three A-B-C choices are all correct
25.
CB3c Refinancing example, PREPAY fees, find NPV
You took out a 30-year mortgage (monthly payments) for $105,000 at 8.70% and
payment number 32 is due today. You are deciding whether you should refinance the
outstanding principal by borrowing at today’s lower rate of 7.40% an amount that pays
off the old loan. The new loan is for 30 years as of today. The total fees for getting the
new loan equal 4.3% of the original loan’s outstanding principal. The first payment for
the new loan would be due one month from today.
Suppose you pay the fees today with funds from your savings account. What is the net
present value of the refinancing venture if your “personal discount rate” is 12%?
a. $5,459
b. $4,963
c. $4,102
d. $4,512
e. $3,729