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CHAPTER 6Discounted Cash Flow Valuation

I. DEFINITIONS

ANNUITY

a 1. An annuity stream of cash flow payments is a set of:

a. level cash flows occurring each time period for a fixed length of time.

b. level cash flows occurring each time period forever.

c. increasing cash flows occurring each time period for a fixed length of time.

d. increasing cash flows occurring each time period forever.

e. arbitrary cash flows occurring each time period for no more than 10 years.

PRESENT VALUE FACTOR FOR ANNUITIES

b 2. The present value factor for annuities is calculated as:

a. (1 + present value factor) ¸ r.

b. (1 – present value factor) ¸ r.

c. present value factor + (1 ¸ r).

d. (present value factor ´ r) + (1 ¸ r).

e. r ´ (1 + present value factor).

FUTURE VALUE FACTOR FOR ANNUITIES

d 3. The future value factor for annuities is calculated as the:

a. future value factor + r.

b. (1 ¸ r) + (future value factor ´ r).

c. (1 ¸ r) + future value factor.

d. (future value factor –1) ¸ r.

e. (future value factor + 1) ¸ r.

ANNUITIES DUE

e 4. Annuities where the payments occur at the end of each time period are called _____

, whereas _____ refer to annuity streams with payments occurring at the beginning

of each time period.

a. ordinary annuities; early annuities

b. late annuities; straight annuities

c. straight annuities; late annuities

d. annuities due; ordinary annuities

e. ordinary annuities; annuities due

PERPETUITY

c 5. An annuity stream where the payments occur forever is called a(n):

a. annuity due.

b. indemnity.

c. perpetuity.

d. amortized cash flow stream.

e. amortization table.

STATED INTEREST RATES

a 6. The interest rate expressed in terms of the interest payment made each period is

called the _____ rate.

a. stated interest

b. compound interest

c. effective annual

d. periodic interest

e. daily interest

EFFECTIVE ANNUALRATE

c 7. The interest rate expressed as if it were compounded once per year is called the

_____ rate.

a. stated interest

b. compound interest

c. effective annual

d. periodic interest

e. daily interest

ANNUAL PERCENTAGE RATE

b 8. The interest rate charged per period multiplied by the number of periods per year is

called the _____ rate.

a. effective annual

b. annual percentage

c. periodic interest

d. compound interest

e. daily interest

PURE DISCOUNT LOAN

d 9. A loan where the borrower receives money today and repays a single lump sum at

some time in the future is called a(n) _____ loan.

a. amortized

b. continuous

c. balloon

d. pure discount

e. interest-only

INTEREST-ONLY LOAN

e 10. A loan where the borrower pays interest each period and repays the entire principal

of the loan at some point in the future is called a(n) _____ loan.

a. amortized

b. continuous

c. balloon

d. pure discount

e. interest-only

AMORTIZED LOAN

a 11. A loan where the borrower pays interest each period, and repays some or all of the

principal of the loan over time is called a(n) _____ loan.

a. amortized

b. continuous

c. balloon

d. pure discount

e. interest-only

BALLOON LOAN

c 12. A loan where the borrower pays interest each period, repays part of the principal of

the loan over time, and repays the remainder of the principal at the end of the loan,

is called a(n) _____ loan.

a. amortized

b. continuous

c. balloon

d. pure discount

e. interest-only

II. CONCEPTS

ORDINARY ANNUITY VERSUS ANNUITY DUE

c 13. You are comparing two annuities which offer monthly payments for ten years. Both

annuities are identical with the exception of the payment dates. Annuity A pays

on the

first of each month while annuity B pays on the last day of each month. Which one

of

the following statements is correct concerning these two annuities?

a. Both annuities are of equal value today.

b. Annuity B is an annuity due.

c. Annuity A has a higher future value than annuity B.

d. Annuity B has a higher present value than annuity A.

e. Both annuities have the same future value as of ten years from today.

UNEVENCASH FLOWS ANDPRESENT VALUE

b 14. You are comparing two investment options. The cost to invest in either option is

the

same today. Both options will provide you with $20,000 of income. Option A pays

five

annual payments starting with $8,000 the first year followed by four annual

payments of $3,000 each. Option B pays five annual payments of $4,000 each.

Which one of the

following statements is correct given these two investment options?

a. Both options are of equal value given that they both provide $20,000 of income.

b. Option A is the better choice of the two given any positive rate of return.

c. Option B has a higher present value than option A given a positive rate of return.

d. Option B has a lower future value at year 5 than option A given a zero rate of

return.

e. Option A is preferable because it is an annuity due.

UNEVENCASH FLOWS ANDFUTURE VALUE

a 15. You are considering two projects with the following cash flows:

Project AProject B

Year 1 $2,500 $4,000

Year 2 3,000 3,500

Year 3 3,500 3,000

Year 4 4,000 2,500

Which of the following statements are true concerning these two projects?

I. Both projects have the same future value at the end of year 4, given a positive rate

of return.

II. Both projects have the same future value given a zero rate of return.

III. Both projects have the same future value at any point in time, given a positive rate

of

return.

IV. Project A has a higher future value than project B, given a positive rate of return.

a. II only

b. IV only

c. I and III only

d. II and IV only

e. I, II, and III only

PERPETUITY VERSUS ANNUITY

d 16. A perpetuity differs from an annuity because:

a. perpetuity payments vary with the rate of inflation.

b. perpetuity payments vary with the market rate of interest.

c. perpetuity payments are variable while annuity payments are constant.

d. perpetuity payments never cease.

e. annuity payments never cease.


e 17. Which one of the following statements concerning the annual percentage rate is

correct?

a. The annual percentage rate considers interest on interest.

b. The rate of interest you actually pay on a loan is called the annual percentage rate.

c. The effective annual rate is lower than the annual percentage rate when an interest

rate

is compounded quarterly.

d. When firms advertise the annual percentage rate they are violating U.S. truth-in-

lending laws.

e. The annual percentage rate equals the effective annual rate when the rate on an

account is designated as simple interest.

INTEREST RATES

b 18. Which one of the following statements concerning interest rates is correct?

a. The stated rate is the same as the effective annual rate.

b. An effective annual rate is the rate that applies if interest were charged annually.

c. The annual percentage rate increases as the number of compounding periods per

year

increases.

d. Banks prefer more frequent compounding on their savings accounts.

e. For any positive rate of interest, the effective annual rate will always exceed the

annual

percentage rate.

EFFECTIVE ANNUAL RATE

c 19. Which of the following statements concerning the effective annual rate are correct?

I. When making financial decisions, you should compare effective annual rates rather

than annual percentage rates.

II. The more frequently interest is compounded, the higher the effective annual rate.

III. A quoted rate of 6 percent compounded continuously has a higher effective annual

rate

than if the rate were compounded daily.

IV. When choosing which loan to accept, you should select the offer with the highest

effective annual rate.

a. I and II only

b. I and IV only

c. I, II, and III only

d. II, III, and IV only

e. I, II, III,and IV

CONTINUOUS COMPOUNDING

d 20. The highest effective annual rate that can be derived from an annual percentage rate

of

9 percent is computed as:

a. .09e -1.b. e.09 ´ q.

c. e ´ (1 + .09).

d. e.09 – 1.

e. (1 + .09)q.

PURE DISCOUNT LOAN

a 21. A pure discount loan is a(n):

a. example of a present value problem.

b. loan that is interest-free.

c. loan that gives you a discount if you pay your payments on time.

d. loan that requires all interest to be paid at the time the loan is made.

e. loan that discounts the payments if you pay them in advance.

INTEREST-ONLY LOAN

c 22. The principle amount of an interest-only loan is:

a. never repaid.

b. repaid in equal increments and included in each loan payment.

c. repaid in full at the end of the loan period.

d. repaid in equal annual payments even when the loan interest is repaid monthly.

e. repaid in increasing increments and included in each loan payment.

AMORTIZED LOAN

b 23. An amortized loan:

a. requires the principle amount to be repaid in even increments over the life of the

loan.

b. may have equal or increasing amounts applied to the principle from each loan

payment.

c. requires that all interest be repaid on a monthly basis while the principle is repaid at

the end of the loan term.

d. requires that all payments be equal in amount and include both principle and

interest.

e. is the type of loan that describes most corporate bonds.

III. PROBLEMS

ORDINARY ANNUITY AND PRESENT VALUE

d 24. Your parents are giving you $100 a month for four years while you are in college.

At a

6 percent discount rate, what are these payments worth to you when you first start

college?

a. $3,797.40

b. $4,167.09

c. $4,198.79

d. $4,258.03

e. $4,279.32

ORDINARY ANNUITYAND PRESENT VALUE

b 25. You just won the lottery! As your prize you will receive $1,200 a month for 100

months. If you can earn 8 percent on your money, what is this prize worth to you

today?

a. $87,003.69

b. $87,380.23

c. $87,962.77

d. $88,104.26

e. $90,723.76


b 26. Todd is able to pay $160 a month for five years for a car. If the interest rate is 4.9

percent, how much can Todd afford to borrow to buy a car?

a. $6,961.36

b. $8,499.13

c. $8,533.84

d. $8,686.82

e. $9,588.05


a 27. You are the beneficiary of a life insurance policy. The insurance company informs

you that you have two options for receiving the insurance proceeds. You can

receive a lump sum of $50,000 today or receive payments of $641 a month for ten

years. You can earn 6.5 percent on your money. Which option should you take and

why?

a. You should accept the payments because they are worth $56,451.91 today.

b. You should accept the payments because they are worth $56,523.74 today.

c. You should accept the payments because they are worth $56,737.08 today.

d. You should accept the $50,000 because the payments are only worth $47,757.69

today.

e. You should accept the $50,000 because the payments are only worth $47,808.17

today.


c 28. Your employer contributes $25 a week to your retirement plan. Assume that you

work for your employer for another twenty years and that the applicable discount

rate is 5 percent. Given these assumptions, what is this employee benefit worth to

you today?

a. $13,144.43

b. $15,920.55

c. $16,430.54

d. $16,446.34

e. $16,519.02


a 29. You have a sub-contracting job with a local manufacturing firm. Your agreement

calls for annual payments of $50,000 for the next five years. At a discount rate of

12 percent, what is this job worth to you today?

a. $180,238.81

b. $201,867.47

c. $210,618.19

d. $223,162.58

e. $224,267.10

ANNUITY DUE AND PRESENT VALUE

b 30. The Ajax Co. just decided to save $1,500 a month for the next five years as a safety

net for recessionary periods. The money will be set aside in a separate savings

account which pays 3.25 percent interest compounded monthly. They deposit the

first $1,500 today. If the company had wanted to deposit an equivalent lump sum

today, how much would they have had to deposit?

a. $82,964.59

b. $83,189.29

c. $83,428.87

d. $83,687.23

e. $84,998.01


b 31. You need some money today and the only friend you have that has any is your

‘miserly’ friend. He agrees to loan you the money you need, if you make payments

of $20 a month for the next six month. In keeping with his reputation, he requires

that the first payment be paid today. He also charges you 1.5 percent interest per

month. How much money are you borrowing?

a. $113.94

b. $115.65

c. $119.34

d. $119.63

e. $119.96


c 32. You buy an annuity which will pay you $12,000 a year for ten years. The payments

are paid on the first day of each year. What is the value of this annuity today at a 7

percent discount rate?

a. $84,282.98

b. $87,138.04

c. $90,182.79

d. $96,191.91

e. $116,916.21


a 33. You are scheduled to receive annual payments of $10,000 for each of the next 25

years. Your discount rate is 8.5 percent. What is the difference in the present value

if you receive these payments at the beginning of each year rather than at the end of

each year?

a. $8,699

b. $9,217

c. $9,706

d. $10,000

e. $10,850


d 34. You are comparing two annuities with equal present values. The applicable

discount rate is 7.5 percent. One annuity pays $5,000 on the first day of each year

for twenty years. How much does the second annuity pay each year for twenty

years if it pays at the end of each year?

a. $4,651

b. $5,075

c. $5,000

d. $5,375

e. $5,405


a 35. Martha receives $100 on the first of each month. Stewart receives $100 on the last

day of each month. Both Martha and Stewart will receive payments for five years.

At an 8 percent discount rate, what is the difference in the present value of these

two sets of payments?

a. $32.88

b. $40.00

c. $99.01

d. $108.00

e. $112.50

ORDINARY ANNUITYAND FUTURE VALUE

c 36. What is the future value of $1,000 a year for five years at a 6 percent rate of

interest?

a. $4,212.36

b. $5,075.69

c. $5,637.09

d. $6,001.38

e. $6,801.91


d 37. What is the future value of $2,400 a year for three years at an 8 percent rate of

interest?

a. $6,185.03

b. $6,847.26

c. $7,134.16

d. $7,791.36

e. $8,414.67


c 38. Janet plans on saving $3,000 a year and expects to earn 8.5 percent. How much will

Janet have at the end of twenty-five years if she earns what she expects?

a. $219,317.82

b. $230,702.57

c. $236,003.38

d. $244,868.92

e. $256,063.66

ANNUITY DUE VERSUS ORDINARY ANNUITY

b 39. Toni adds $3,000 to her savings on the first day of each year. Tim adds $3,000 to

his savings on the last day of each year. They both earn a 9 percent rate of return.

What is the difference in their savings account balances at the end of thirty years?

a. $35,822.73

b. $36,803.03

c. $38,911.21

d. $39,803.04

e. $40,115.31

ORDINARY ANNUITY PAYMENTS

d 40. You borrow $5,600 to buy a car. The terms of the loan call for monthly payments

for four years at a 5.9 percent rate of interest. What is the amount of each payment?

a. $103.22

b. $103.73

c. $130.62

d. $131.26

e. $133.04

ORDINARY ANNUITY PAYMENTS AND COST OF INTEREST

c 41. You borrow $149,000 to buy a house. The mortgage rate is 7.5 percent and the loan

period is 30 years. Payments are made monthly. If you pay for the house according

to the loan agreement, how much total interest will you pay?

a. $138,086

b. $218,161

c. $226,059

d. $287,086

e. $375,059

ORDINARY ANNUITY PAYMENTS AND FUTURE VALUE

d 42. The Great Giant Corp. has a management contract with their newly hired president.

The contract requires a lump sum payment of $25 million be paid to the president

upon the completion of her first ten years of service. The company wants to set aside

an

equal amount of funds each year to cover this anticipated cash outflow. The

company

can earn 6.5 percent on these funds. How much must the company set aside each

year for this purpose?

a. $1,775,042.93

b. $1,798,346.17

c. $1,801,033.67

d. $1,852,617.25

e. $1,938,018.22

ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE

e 43. You retire at age 60 and expect to live another 27 years. On the day you retire, you

have $464,900 in your retirement savings account. You are conservative and expect

to earn 4.5 percent on your money during your retirement. How much can you

withdraw from your retirement savings each month if you plan to die on the day

you spend your last penny?

a. $2,001.96

b. $2,092.05

c. $2,398.17

d. $2,472.00

e. $2,481.27


c 44. The McDonald Group purchased a piece of property for $1.2 million. They paid a

down payment of 20 percent in cash and financed the balance. The loan terms

require monthly payments for 15 years at an annual percentage rate of 7.75 percent

compounded monthly. What is the amount of each mortgage payment?

a. $7,440.01

b. $8,978.26

c. $9,036.25

d. $9,399.18

e. $9,413.67


d 45. You estimate that you will have $24,500 in student loans by the time you graduate.

The interest rate is 6.5 percent. If you want to have this debt paid in full within five

years, how much must you pay each month?

a. $471.30

b. $473.65

c. $476.79

d. $479.37

e. $480.40


b 46. You are buying a previously owned car today at a price of $6,890. You are paying

$500 down in cash and financing the balance for 36 months at 7.9 percent. What is

the amount of each loan payment?

a. $198.64

b. $199.94

c. $202.02

d. $214.78

e. $215.09


b 47. The Good Life Insurance Co. wants to sell you an annuity which will pay you $500

per quarter for 25 years. You want to earn a minimum rate of return of 5.5 percent.

What is the most you are willing to pay as a lump sum today to buy this annuity?

a. $26,988.16

b. $27,082.94

c. $27,455.33

d. $28,450.67

e. $28,806.30

ANNUITY DUE PAYMENTSAND PRESENT VALUE

c 48. Your car dealer is willing to lease you a new car for $299 a month for 60 months.

Payments are due on the first day of each month starting with the day you sign the

lease contract. If your cost of money is 4.9 percent, what is the current value of the

lease?

a. $15,882.75

b. $15,906.14

c. $15,947.61

d. $16,235.42

e. $16,289.54

ANNUITY DUE PAYMENTS AND PRESENT VALUE

d 49. Your great-aunt left you an inheritance in the form of a trust. The trust agreement

states that you are to receive $2,500 on the first day of each year, starting

immediately and continuing for fifty years. What is the value of this inheritance

today if the applicable discount rate is 6.35 percent?

a. $36,811.30

b. $37,557.52

c. $39,204.04

d. $39,942.42

e. $40,006.09

ANNUITY DUE PAYMENTS AND PRESENT VALUE

e 50. You recently filed suit against a company. Today, you received three settlement

options as follows:

Option A: $10,000 on the first day of each year for 25 years

Option B: $880 on the first day of each month for 25 years

Option C: $119,830 as a lump sum payment today

You can earn 7.5 percent on your investments. You do not care if you personally

receive the funds or if they are paid to your heirs should you die within the next 25

years. Which one of the following statements is correct given this information?

a. Option C is clearly the best choice since you can earn 7.5 percent on the entire

lump sum starting immediately.

b. Option B is clearly the best choice since it offers the largest number of payments.

c. Option A is clearly the best choice since it has by far the largest future value.

d. Option B is clearly the best choice since it has by far the largest present value.

e. You are relatively indifferent to the three options as they are all approximately

equal in value to you.

ANNUITY DUE PAYMENTSAND FUTURE VALUE

a 51. Your firm wants to save $250,000 to buy some new equipment three years from

now. The plan is to set aside an equal amount of money on the first day of each

year starting today. The firm can earn a 4.7 percent rate of return. How much does

the firm have to save each year to achieve their goal?

a. $75,966.14

b. $76,896.16

c. $78,004.67

d. $81.414.14

e. $83,333.33

ANNUITY DUE PAYMENTSAND FUTURE VALUE

e 52. Today is January 1. Starting today, Sam is going to contribute $140 on the first of

each month to his retirement account. His employer contributes an additional 50

percent of the amount contributed by Sam. If both Sam and his employer continue

to do this and Sam can earn a monthly rate of ½ of 1 percent, how much will he

have in his retirement account 35 years from now?

a. $199,45.944.

b. $200,456.74

c. $249,981.21

d. $299,189.16

e. $300,685.11

ORDINARY ANNUITY TIME PERIODS AND PRESENT VALUE

c 53. You are considering an annuity which costs $100,000 today. The annuity pays

$6,000 a year. The rate of return is 4.5 percent. What is the length of the annuity

time period?

a. 24.96 years

b. 29.48 years

c. 31.49 years

d. 33.08 years

e. 38.00 years

ORDINARY ANNUITY TIME PERIODS AND PRESENT VALUE

d 54. Today, you signed loan papers agreeing to borrow $4,954.85 at 9 percent

compounded monthly. The loan payment is $143.84 a month. How many loan

payments must you make before the loan is paid in full?

a. 29.89

b. 36.00

c. 38.88

d. 40.00

e. 41.03

ORDINARY ANNUITY TIME PERIODS AND FUTURE VALUE

a 55. Winston Enterprises would like to buy some additional land and build a new

factory. The anticipated total cost is $136 million. The owner of the firm is quite

conservative and will only do this when the company has sufficient funds to pay

cash for the entire expansion project. Management has decided to save $450,000 a

month for this purpose. The firm earns 6 percent compounded monthly on the funds

it saves. How long does the company have to wait before expanding its operations?

a. 184.61 months

b. 199.97 months

c. 234.34 months

d. 284.61 months

e. 299.97 months

ANNUITY DUE TIME PERIODS AND PRESENT VALUE

b 56. Today, you are retiring. You have a total of $413,926 in your retirement savings

and have the funds invested such that you expect to earn an average of 3 percent,

compounded monthly, on this money throughout your retirement years. You want

to withdraw $2,500 at the beginning of every month, starting today. How long will

it be until you run out of money?

a. 185.00 months

b. 213.29 months

c. 227.08 months

d. 236.84 months

e. 249.69 months

ANNUITY DUE TIME PERIODS

c 57. The Bad Guys Co. is notoriously known as a slow-payer. They currently need to

borrow $25,000 and only one company will even deal with them. The terms of the

loan

call for daily payments of $30.76. The first payment is due today. The interest rate

is 21 percent compounded daily. What is the time period of this loan?

a. 2.88 years

b. 2.94 years

c. 3.00 years

d. 3.13 years

e. 3.25 years

ORDINARY ANNUITY INTEREST RATE

c 58. The Robertson Firm is considering a project which costs $123,900 to undertake.

The project will yield cash flows of $4,894.35 monthly for 30 months. What is the

rate of return on this project?

a. 12.53 percent

b. 13.44 percent

c. 13.59 percent

d. 14.02 percent

e. 14.59 percent


a 59. Your insurance agent is trying to sell you an annuity that costs $100,000 today. By

buying this annuity, your agent promises that you will receive payments of $384.40

a

month for the next 40 years. What is the rate of return on this investment?

a. 3.45 percent

b. 3.47 percent

c. 3.50 percent

d. 3.52 percent

e. 3.55 percent


e 60. You have been investing $120 a month for the last 15 years. Today, your

investment account is worth $47,341.19. What is your average rate of return on

your investments?

a. 9.34 percent

b. 9.37 percent

c. 9.40 percent

d. 9.42 percent

e. 9.46 percent


c 61. Brinker, Inc. has been investing $136,000 a year for the past 4 years into a business

venture. Today, Brinker sold that venture for $685,000. What is their rate of return

on this venture?

a. 9.43 percent

b. 11.06 percent

c. 15.59 percent

d. 16.67 percent

e. 18.71 percent

ANNUITY DUE INTEREST RATE

b 62. Your mother helped you start saving $25 a month beginning on your 10th birthday.

She always made you make your deposit on the first day of each month just to

“start the month out right”. Today, you turn 21 and have $4,482.66 in your account.

What is your rate of return on your savings?

a. 5.25 percent

b. 5.29 percent

c. 5.33 percent

d. 5.36 percent

e. 5.50 percent

ANNUITY DUE INTERESTRATE

a 63. Today, you turn 21. Your birthday wish is that you will be a millionaire by your

40th birthday. In an attempt to reach this goal, you decide to save $25 a day, every

day until you turn 40. You open an investment account and deposit your first $25

today. What rate of return must you earn to achieve your goal?

a. 15.07 percent

b. 15.13 percent

c. 15.17 percent

d. 15.20 percent

e. 15.24 percent

UNEVENCASH FLOWS ANDPRESENT VALUE

b 64. Marko, Inc. is considering the purchase of ABC Co. Marko believes that ABC Co.

can generate cash flows of $5,000, $9,000, and $15,000 over the next three years,

respectively. After that time, they feel the business will be worthless. Marko has

determined that a 14 percent rate of return is applicable to this potential purchase.

What is Marko willing to pay today to buy ABC Co.?

a. $19,201.76

b. $21,435.74

c. $23,457.96

d. $27,808.17

e. $31,758.00

UNEVEN CASH FLOWS ANDPRESENT VALUE

a 65. You are considering two savings options. Both options offer a 4 percent rate of

return. The first option is to save $1,200, $1,500, and $2,000 a year over the next

three years, respectively. The other option is to save one lump sum amount today. If

you want to have the same balance in your savings at the end of the three years,

regardless of the savings method you select, how much do you need to save today if

you select the lump sum option?

a. $4,318.67

b. $4,491.42

c. $4,551.78

d. $4,607.23

e. $4,857.92


b 66. You are considering two insurance settlement offers. The first offer includes annual

payments of $5,000, $7,500, and $10,000 over the next three years, respectively.

The other offer is the payment of one lump sum amount today. You are trying to

decide which offer to accept given the fact that your discount rate is 5 percent.

What is the minimum amount that you will accept today if you are to select the

lump sum offer?

a. $19,877.67

b. $20,203.00

c. $21,213.15

d. $23,387.50

e. $24,556.88


d 67. You are considering a job offer. The job offers an annual salary of $52,000,

$55,000, and $60,000 a year for the next three years, respectively. The offer also

includes a starting bonus of $2,000 payable immediately. What is this offer worth

to you today at a discount rate of 6 percent?

a. $148,283.56

b. $148,383.56

c. $150,283.56

d. $150,383.56

e. $152,983.56


b 68. You are considering a project with the following cash flows:

Year 1 Year 2 Year 3

$1,200 $1,800 $2,900

What is the present value of these cash flows, given a 9 percent discount rate?

a. $4,713.62

b. $4,855.27

c. $5,103.18

d. $5,292.25

e. $6,853.61


d 69. You are considering a project with the following cash flows:


$5,600 $9,000 $2,000

What is the present value of these cash flows, given an 11 percent discount rate?

a. $8,695.61

b. $8,700.89

c. $13,732.41

d. $13,812.03

e. $19,928.16


a 70. You are considering a project with the following cash flows:


$4,200 $5,000 $5,400

What is the present value of these cash flows, given a 3 percent discount rate?

a. $13,732.41

b. $13,812.03

c. $14,308.08

d. $14,941.76

e. $14,987.69


a 71. You have some property for sale and have received two offers. The first offer is for

$189,000 today in cash. The second offer is the payment of $100,000 today and an

additional $100,000 two years from today. If the applicable discount rate is 8.75

percent, which offer should you accept and why?

a. You should accept the $189,000 today because it has the higher net present value.

b. You should accept the $189,000 today because it has the lower future value.

c. You should accept the second offer because you will receive $200,000 total.

d. You should accept the second offer because you will receive an extra $11,000.

e. You should accept the second offer because it has a present value of $194,555.42.


b 72. Your local travel agent is advertising an extravagant global vacation. The package

deal

requires that you pay $5,000 today, $15,000 one year from today, and a final

payment of $25,000 on the day you leave two years from today. What is the cost of

this vacation in today’s dollars if the discount rate is 6 percent?

a. $39,057.41

b. $41,400.85

c. $43,082.39

d. $44,414.14

e. $46,518.00

UNEVEN CASH FLOWS ANDFUTURE VALUE

e 73. One year ago, the Jenkins FamilyFun Centerdeposited $3,600 in an investment

account for the purpose of buying new equipment four years from today. Today,

they are adding another $5,000 to this account. They plan on making a final deposit

of $7,500 to the account next year. How much will be available when they are

ready to buy the equipment, assuming they earn a 7 percent rate of return?

a. $18,159.65

b. $19,430.84

c. $19,683.25

d. $20,194.54

e. $20,790.99


c 74. What is the future value of the following cash flows at the end of year 3 if the

interest rate is 6 percent? The cash flows occur at the end of each year.


$5,180 $9,600 $2,250

a. $15,916.78

b. $18,109.08

c. $18,246.25

d. $19,341.02

e. $19,608.07


d 75. What is the future value of the following cash flows at the end of year 3 if the

interest rate is 9 percent? The cash flows occur at the end of each year.


$9,820 $0 $4,510

a. $15,213.80

b. $15,619.70

c. $15,916.78

d. $16,177.14

e. $17,633.08


c 76. What is the future value of the following cash flows at the end of year 3 if the

interest rate is 7.25 percent? The cash flows occur at the end of each year.


$6,800 $2,100 $0

a. $8,758.04

b. $8,806.39

c. $10,073.99

d. $10,314.00

e. $10,804.36


e 77. Suzette is going to receive $10,000 today as the result of an insurance settlement. In

addition, she will receive $15,000 one year from today and $25,000 two years from

today. She plans on saving all of this money and investing it for her retirement. If

Suzette can earn an average of 11 percent on her investments, how much will she

have in her account if she retires 25 years from today?

a. $536,124.93

b. $541,414.14

c. $546,072.91

d. $570,008.77

e. $595,098.67

PRESENT VALUE, PAYMENTS AND FUTURE VALUE

b 78. The Bluebird Company has a $10,000 liability they must pay three years from

today.

The company is opening a savings account so that the entire amount will be

available when this debt needs to be paid. The plan is to make an initial deposit

today and then deposit an additional $2,500 a year for the next three years, starting

one year from today. The account pays a 3 percent rate of return. How much does

the Bluebird Company need to deposit today?

a. $1,867.74

b. $2,079.89

c. $3,108.09

d. $4,276.34

e. $4,642.28


c 79. The government has imposed a fine on the Not-So-Legal Company. The fine calls

for annual payments of $100,000, $250,000, and $250,000, respectively over the

next three years. The first payment is due one year from today. The government

plans to invest the funds until the final payment is collected and then donate the

entire amount, including investment earnings, to a national health center. The

government will earn 3.5 percent on the funds held. How much will the national

health center receive three years from today?

a. $613,590.00

b. $614,622.50

c. $615,872.50

d. $616,006.00

e. $619,050.05

PERPETUITY PRESENT VALUE

b 80. George Jefferson established a trust fund that provides $150,000 in scholarships

each year for worthy students. The trust fund earns a 4.25 percent rate of return.

How much money did Mr. Jefferson contribute to the fund assuming that only the

interest income is distributed?

a. $3,291,613.13

b. $3,529,411.77

c. $3,750,000.00

d. $4,328,970.44

e. $6,375,000.00


e 81. A 9 percent preferred stock pays an annual dividend of $4.50. What is one share of

this stock worth today?

a. $.41

b. $4.50

c. $5.00

d. $45.00

e. $50.00


e 82. You would like to establish a trust fund that will provide $50,000 a year forever for

your heirs. The trust fund is going to be invested very conservatively so the

expected rate of return is only 2.75 percent. How much money must you deposit

today to fund this gift for your heirs?

a. $1,333,333.33

b. $1,375,000.00

c. $1,425,000.00

d. $1,666,666.67

e. $1,818,181.82

PERPETUITY DISCOUNT RATE

c 83. You just paid $350,000 for a policy that will pay you and your heirs $12,000 a year

forever. What rate of return are you earning on this policy?

a. 3.25 percent

b. 3.33 percent

c. 3.43 percent

d. 3.50 percent

e. 3.67 percent

PERPETUITY DISCOUNT RATE

d 84. The Eternal Gift Insurance Company is offering you a policy that will pay you and

your heirs $10,000 a year forever. The cost of the policy is $285,000. What is the

rate of return on this policy?

a. 2.85 percent

b. 3.25 percent

c. 3.46 percent

d. 3.51 percent

e. 3.60 percent

PERPETUITY PAYMENT

e 85. Your rich uncle establishes a trust in your name and deposits $150,000 in it. The

trust pays a guaranteed 4 percent rate of return. How much will you receive each

year

if the trust is required to pay you all of the interest earnings on an annual basis?

a. $3,750

b. $4,000

c. $4,500

d. $5,400

e. $6,000

PERPETUITY PAYMENT

b 86. The preferred stock of ABC Co. offers an 8.4 percent rate of return. The stock is

currently priced at $50.00 per share. What is the amount of the annual dividend?

a. $2.10

b. $4.20

c. $5.00

d. $6.40

e. $8.60


d 87. Your credit card company charges you 1.5 percent per month. What is the annual

percentage rate on your account?

a. 12.00 percent

b. 15.00 percent

c. 15.39 percent

d. 18.00 percent

e. 19.56 percent


d 88. What is the annual percentage rate on a loan with a stated rate of 2 percent per

quarter?

a. 2.00 percent

b. 2.71 percent

c. 4.04 percent

d. 8.00 percent

e. 8.24 percent


c 89. You are paying an effective annual rate of 13.8 percent on your credit card. The

interest is compounded monthly. What is the annual percentage rate on your

account?

a. 11.50 percent

b. 12.00 percent

c. 13.00 percent

d. 13.80 percent

e. 14.71 percent


b 90. What is the effective annual rate if a bank charges you 7.64 percent compounded

quarterly?

a. 7.79 percent

b. 7.86 percent

c. 7.95 percent

d. 7.98 percent

e. 8.01 percent


d 91. Your credit card company quotes you a rate of 14.9 percent. Interest is billed

monthly. What is the actual rate of interest you are paying?

a. 13.97 percent

b. 14.90 percent

c. 15.48 percent

d. 15.96 percent

e. 16.10 percent


d 92. Mr. Miser loans money at an annual rate of 21 percent. Interest is compounded

daily. What is the actual rate Mr. Miser is charging on his loans?

a. 22.97 percent

b. 23.08 percent

c. 23.21 percent

d. 23.36 percent

e. 23.43 percent


e 93. You are considering two loans. The terms of the two loans are equivalent with the

exception of the interest rates. Loan A offers a rate of 7.45 percent compounded

daily. Loan B offers a rate of 7.5 percent compounded semi-annually. Loan _____

is the better offer because______:

a. A; you will pay less interest.

b. A; the annual percentage rate is 7.45 percent.

c. B; the annual percentage rate is 7.64 percent.

d. B; the interest is compounded less frequently.

e. B; the effective annual rate is 7.64 percent.


b 94. You have $2,500 that you want to use to open a savings account. You have found

five different accounts that are acceptable to you. All you have to do now is

determine which account you want to use such that you can earn the highest rate of

interest possible. Which account should you use based upon the annual percentage

rates quoted by each bank?

account A: 3.75 percent, compounded annually

account B: 3.70 percent, compounded monthly

account C: 3.70 percent, compounded semi-annually

account D: 3.65 percent, compounded continuously

account E: 3.66 percent, compounded quarterly

a. account A

b. account B

c. account C

d. account D

e. account E


d 95. What is the effective annual rate of 14.9 percent compounded continuously?

a. 15.96 percent

b. 16.01 percent

c. 16.05 percent

d. 16.07 percent

e. 16.17 percent


c 96. What is the effective annual rate of 9.75 percent compounded continuously?

a. 9.99 percent

b. 10.11 percent

c. 10.24 percent

d. 10.28 percent

e. 10.30 percent


d 97. The Smart Bank wants to appear competitive based on quoted loan rates and thus

must offer a 7.9 percent annual percentage rate. What is the maximum rate the bank

can actually earn based on the quoted rate?

a. 7.90 percent

b. 8.18 percent

c. 8.20 percent

d. 8.22 percent

e. 8.39 percent

CONTINUOUS COMPOUNDING VERSUS ANNUAL COMPOUNDING

c 98. You are going to loan your friend $1,000 for one year at a 5 percent rate of interest.

How much additional interest can you earn if you compound the rate continuously

rather than annually?

a. $.97

b. $1.09

c. $1.27

d. $1.36

e. $1.49

PURE DISCOUNT LOAN

b 99. You are borrowing money today at an 8 percent interest rate. You will repay the

principle plus all the interest in one lump sum of $6,500 three years from today.

How much are you borrowing?

a. $5,000.00

b. $5,159.91

c. $5,204.16

d. $5,572.70

e. $6,018.52

PURE DISCOUNT LOAN

e 100. This morning you borrowed $3,900 at 7.75 percent interest. You are to repay the

loan principle plus all of the loan interest in one lump sum two years from today.

How much will you have to pay in two years?

a. $4,202.25

b. $4,241.41

c. $4,404.19

d. $4,465.11

e. $4,527.92

PURE DISCOUNT LOAN

b 101. On this date last year you borrowed $7,450. You have to repay the loan principle

plus all of the interest four years from today. The payment that is required at that

time is $11,426. What is the interest rate on this loan?

a. 7.67 percent

b. 8.93 percent

c. 10.67 percent

d. 11.28 percent

e. 13.34 percent

INTEREST ONLY LOAN

b 102. You just borrowed $12,750 from the bank to use in your business. The loan terms

require you to pay the interest annually with the entire principle due in six years.

The interest rate is 8.95 percent. How much will you pay to the bank in year five of

the loan?

a. $1,106.67

b. $1,141.13

c. $1,203.17

d. $1,244.98

e. $1,424.58

INTEREST ONLY LOAN

c 103. On the day you enter college, you work out a deal with your local bank such that

you borrow $9,600 for four years. The terms of the loan include an interest rate of

5.9 percent. The terms also stipulate that the principle is due in full one year after

you graduate. Interest is to be paid annually at the end of each year. Assume that

you complete college in four years. How much will you pay the bank one year after

you graduate?

a. $566.40

b. $2,265.60

c. $10,166.40

d. $11,865.60

e. $12,432.00

INTEREST ONLY LOAN

d 104. As a college student, you work out a deal with your local bank such that you

borrow

$12,000 on the day you start college. The terms of the loan include an interest rate

of 5 percent. The terms also stipulate that the principle is due in full one year after

you graduate. Interest is to be paid annually at the end of each year. If you complete

college in four years, how much total interest will you pay to the bank?

a. $600

b. $2,410

c. $2,586

d. $3,000

e. $3,315

AMORTIZED LOAN

b 105. On June 1, you take out a mortgage in the amount of $124,900 at a 6 percent rate

compounded monthly. Payments are to be made at the end of each month for thirty

years. How much of the first loan payment is interest? (Assume that each month is

equal to 1/12 of a year.)

a. $600.00

b. $624.50

c. $633.33

d. $644.20

e. $648.84

AMORTIZED LOAN

c 106. On August 1, you borrow $160,000 to buy a house. The mortgage rate is 7.5

percent. The loan is to be repaid in equal monthly payments over 15 years. The first

payment is due on September 1. How much of the third payment applies to the

principle balance? (Assume that each month is equal to 1/12 of a year.)

a. $483.22

b. $486.24

c. $489.28

d. $492.30

e. $495.32

AMORTIZED LOAN

a 107. On December 1, you borrow $210,000 to buy a house. The mortgage rate is 8.25

percent. The loan is to be repaid in equal monthly payments over 20 years. The first

payment is due on January 1. Which one of the following statements is true

assuming that you repay the loan as agreed?

a. The total amount paid is about $429,442.

b. The monthly payment is $2,037.30.

c. The total interest paid is $278,952.

d. The monthly interest rate is .75 percent.

e. The first payment reduces the principle balance by $1,443.75.

IV. ESSAYS

EFFECTIVE ANNUAL RATE VERSUS ANNUAL PERCENTAGE RATE

108. Using the example of a savings account, explain the difference between the effective

annual

rate and the annual percentage rate.

The effective annual rate is what you actually earn, the annual percentage rate is a

quoted rate. If interest is compounded during the year, the ending balance of a

savings account cannot be calculated directly using the annual percentage rate.

Also, in the case of the savings account, the effective annual rate will always be

higher than the annual percentage rate as long as the account is compounded more

than once a year and the interest rate is greater than zero.

EFFECTIVE ANNUAL RATE VERSUS ANNUAL PERCENTAGE RATE

109. If you ran a bank, which rate would you rather advertise on monthly-compounded loans,

the effective annual rate or the annual percentage rate? Which rate would you rather

advertise on quarterly-compounded savings accounts, the effective annual rate or the

annual percentage rate? Explain. As a consumer, which would you prefer to see and

why?

A bank would rather advertise the annual percentage rate on loans since this rate is lower

and the effective annual rate on savings accounts since this rate is higher. As a

consumer, the effective annual rate is the more important rate since it represents the rate

actually paid or earned.

COMPARING ANNUITIES

110. You are considering two annuities, both of which make total annuity payments of

$10,000 over their life. Which would be worth more today: annuity A, which pays

$1,000 at the end of each year for the next 10 years, or annuity B, which pays $775 at

the end of the first year, but the annuity payment grows by $50 each year, reaching

$1,225 at the end of year 10? Are there any circumstances in which the two would be

equal? Explain.

The second annuity weights its payments more toward the back of the period, rather than

the front, making it less valuable unless the discount rate is zero. Some students may get

tripped up by the fact that the two annuities have the same total payments. This would

clearly demonstrate a lack of understanding of the time value of money.

PRESENT VALUE OF AN ANNUITY

111. There are three factors that affect the present value of an annuity. Explain what these

three factors are and discuss how an increase in each will impact the present value of the

annuity.

The factors are the interest rate, payment amount, and number of payments. An increase

in the payment and number of payments will increase the present value, while an

increase in the interest rate will decrease the present value.

FUTURE VALUE OF AN ANNUITY

112. There are three factors that affect the future value of an annuity. Explain what these

three factors are and discuss how an increase in each will impact the future value of the

annuity.

The factors are the interest rate, payment amount, and number of payments. An increase

in any of these three will increase the future value of the annuity.

EFFECTIVE ANNUAL RATE VERSUS ANNUAL PERCENTAGERATE

113. Should lending laws be changed to require lenders to report the effective annual rate

rather than the annual percentage rate? Explain the reasoning for your answer.

It would be more meaningful for consumers to know the effective annual rate rather than

the annual percentage rate. The effective annual rate is slightly more difficult to

calculate and also more difficult to explain, and may add confusion to the loan process.

However, regardless of the costs, it would appear that consumers would benefit from

learning what the effective annual rate is as opposed to the annual percentage rate.

COMPARING ANNUITIES AND PERPETUITIES

114. Annuity A makes annual payments of $813.73 for each of the next 10 years, while

annuity B makes annual payments of $500 per year forever. At what interest rate would

you be indifferent between the two? At interest rates above this break-even rate, which

annuity would you choose? How about at interest rates below the break-even rate?

This requires the students to actually use the present value formulas, setting the present

value annuity equal to the present value of a perpetuity and solving for the interest rate

that makes the two equivalent. The first step is recognizing that the indifference point

occurs when the two present values are equal. The break-even rate is 10 percent: below

that rate, the perpetuity is better, while above that rate, the 10-year annuity is preferred.

PERPETUITY PAYMENTS

115. A friend who owns a perpetuity that promises to pay $1,000 at the end of each year,

forever, comes to you and offers to sell you all of the payments to be received after the

25th year for a price of $1,000. At an interest rate of 10 percent, should you pay the

$1,000 today to receive payment numbers 26 and onwards? What does this suggest to

you about the value of perpetual payments?

The present value of the perpetuity is $10,000, and the present value of the first 25

payments is $9,077.04, thus you should be willing to pay only $922.96 for payments 26

and onwards. This suggests that the value of a perpetuity is derived primarily from the

payments received early in its life, and the payments to be received later have little

worth today.

²ÆÎñ¹ÜÀí_chapter_6

Documents

ordinary annuities annuities

time period

r future value factor

present value factor

annuities b2

annuities d3

balloon d

loan e10