Deck 5: Discounted Cash Flow Valuation

Question 1

Anna pays 1.5 percent interest monthly on her credit card account. When the interest rate on that debt is expressed as if it were compounded only annually, the rate would be referred to as the:

A) annual percentage rate.
B) compounded rate.
C) quoted rate.
D) stated rate.
E) effective annual rate.

Answer 1

effective annual rate.

Question 2

Which one of the following can be classified as an annuity but not as a perpetuity?

A) Increasing monthly payments forever
B) Increasing quarterly payments for 6 years
C) Unequal payments each year for 9 years
D) Equal annual payments for life
E) Equal weekly payments forever

Answer 2

Equal annual payments for life

Question 3

Which one of the following will decrease the present value of an annuity?

A) Increase in the annuity's future value
B) Increase in the payment amount
C) Increase in the time period
D) Decrease in the discount rate
E) Decrease in the annuity payment

Answer 3

Decrease in the annuity payment

Question 4

A perpetuity in Canada is frequently referred to as which one of the following?

A) Consul
B) Infinity
C) Forever cash
D) Dowry
E) Forevermore

Question 5

Christie is buying a new car today and is paying a $500 cash down payment. She will finance the balance at 7.25 percent interest. Her loan requires 36 equal monthly payments of $450 each with the first payment due 30 days from today. Which one of the following statements is correct concerning this purchase?

A) The present value of the car is equal to $500 + (36 * $450).
B) The $500 is the present value of the purchase.
C) The car loan is an annuity due.
D) To compute the initial loan amount, you must use a monthly interest rate.
E) The future value of the loan is equal to 36 * $450.

Question 6

Which one of the following is an ordinary annuity, but not a perpetuity?

A) $75 paid at the beginning of each month period for 50 years
B) $15 paid at the end of each monthly period for an infinite period of time
C) $40 paid quarterly for five years, starting today
D) $50 paid every year for ten years, starting today
E) $25 paid weekly for one year, starting one week from today

Question 7

Which one of the following features distinguishes an ordinary annuity from an annuity due?

A) Number of equal payments
B) Amount of each payment
C) Frequency of the payments
D) Annuity interest rate
E) Timing of the annuity payments

Question 8

Janis just won a scholarship that will pay her $500 a month, starting today, and continuing for the next 48 months. Which one of the following terms best describes these scholarship payments?

A) Ordinary annuity
B) Annuity due
C) Consol
D) Ordinary perpetuity
E) Perpetuity due

Question 9

Which one of the following is an example of a perpetuity?

A) Trust income of $1,200 a year forever
B) Retirement pay of $2,200 a month for 20 years
C) Lottery winnings of $1,000 a month for life
D) Car payment of $260 a month for 60 months
E) Apartment rent payment of $800 a month for one year

Question 10

The stated interest rate is the interest rate expressed:

A) as if it were compounded one time per year.
B) as the quoted rate compounded by 12 periods per year.
C) in terms of the rate charged per day.
D) in terms of the interest payment made each period.
E) in terms of an effective rate.

Question 11

Which one of the following statements concerning annuities is correct?

A) The present value of an annuity is equal to the cash flow amount divided by the discount rate.
B) An annuity due has payments that occur at the beginning of each time period.
C) The future value of an annuity decreases as the interest rate increases.
D) If unspecified, you should assume an annuity is an annuity due.
E) An annuity is an unending stream of equal payments occurring at equal intervals of time.

Question 12

Which one of the following is the annuity present value formula?

A)
B)
C)
D)
E)

Question 13

The Jones Brothers recently established a trust fund that will provide annual scholarships of $12,000 indefinitely. These annual scholarships can best be described by which one of the following terms?

A) Ordinary annuity
B) Annuity due
C) Amortized payment
D) Perpetuity
E) Continuation

Question 14

Lee pays one percent per month interest on his credit card account. When his monthly rate is multiplied by 12, the resulting answer is referred to as the:

A) annual percentage rate.
B) compounded rate.
C) effective annual rate.
D) perpetual rate.
E) simple rate.

Question 15

Which one of the following qualifies as an annuity?

A) Weekly grocery bill
B) Clothing purchases
C) Car repairs
D) Auto loan payment
E) Medical bills

Question 16

Travis is buying a car and will finance it with a loan which requires monthly payments of $265 for the next 4 years. His car payments can be described by which one of the following terms?

A) Perpetuity
B) Annuity
C) Consol
D) Lump sum
E) Factor

Question 17

Which one of the following statements is true concerning annuities?

A) All else equal, an ordinary annuity is more valuable than an annuity due.
B) All else equal, a decrease in the number of payments increases the future value of an annuity due.
C) An annuity with payments at the beginning of each period is called an ordinary annuity.
D) All else equal, an increase in the discount rate decreases the present value and increases the future value of an annuity.
E) All else equal, an increase in the number of annuity payments decreases the present value and increases the future value of an annuity.

Question 18

Which of the following will increase the present value of an annuity, all else held constant? I. Increase in the number of payments
II) Increase in the interest rate
III) Decrease in the interest rate
IV) Decrease in the payment amount

A) I and II only
B) I and III only
C) II and IV only
D) I, II, and IV only
E) I, III, and IV only

Question 19

You are comparing two annuities. Annuity A pays $100 at the end of each month for 10 years. Annuity B pays $100 at the beginning of each month for 10 years. The rate of return on both annuities is 8 percent. Which one of the following statements is correct given this information?

A) The present value of Annuity A is equal to the present value of Annuity B.
B) Annuity B will pay one more payment than Annuity A will.
C) The future value of Annuity A is greater than the future value of Annuity B.
D) Annuity B has both a higher present value and a higher future value than Annuity A.
E) Annuity A has a higher future value but a lower present value than Annuity B.

Question 20

Which of the following characteristics apply to a perpetuity? I. Constant cash flow dollar amount
II) Unequal cash flow dollar amount
III) Limited time period
IV) Infinite time period

A) I and III only
B) I and IV only
C) II and III only
D) II and IV only
E) I plus either III or IV

Question 21

Which one of the following has the highest effective annual rate?

A) 6 percent compounded annually
B) 6 percent compounded semi-annually
C) 6 percent compounded quarterly
D) 6 percent compounded monthly
E) All the other answers have the same effective annual rate.

Question 22

Bill just financed a used car through his credit union. His loan requires payments of $275 a month for 5 years. Assuming that all payments are paid timely, his last payment will pay off the loan in full. What type of loan does Bill have?

A) Amortized
B) Complex
C) Pure discount
D) Lump sum
E) Interest-only

Question 23

Capstone Crowns is considering a project that will produce cash inflows of $11,000 in year one, $24,000 in year two, and $36,000 in year three. What is the present value of these cash inflows if the company assigns the project a discount rate of 14 percent?

A) $40,331.89
B) $46,564.28
C) $52,415.32
D) $54,868.15
E) $60,978.35

Question 24

A loan has an APR of 8.5 percent and an EAR of 8.5 percent. Given this, the loan must:

A) have a one-year term.
B) have a zero percent interest rate.
C) charge interest annually.
D) must be an interest-only loan.
E) require the accrued interest be paid in full with each monthly payment.

Question 25

A credit card has an annual percentage rate of 12.9 percent and charges interest monthly. The effective annual rate on this account:

A) will be less than 12.9 percent.
B) can either be less than or equal to 12.9 percent.
C) is 12.9 percent.
D) can either be greater than or equal to 12.9 percent.
E) will be greater than 12.9 percent.

Question 26

Which one of the following can NOT be computed?

A) Future value of an ordinary annuity
B) Future value of a perpetuity
C) Present value of a perpetuity
D) Present value of an annuity due
E) Present value of an ordinary annuity

Question 27

Tom is planning to invest the following amounts at 4 percent interest. How much money will he have saved at the end of year 3?

A) $2,200.00
B) $2,238.47
C) $2,272.80
D) $2,309.16
E) $2,363.71

Question 28

Jodie's Fashions has just signed a $2.2 million contract. The contract calls for a payment of $0.6 million today, $0.8 million one year from today, and $0.8 million two years from today. What is this contract worth today if the firm can earn 7.2 percent on its money?

A) $2,038,616.67
B) $2,042,414.79
C) $2,108,001.32
D) $2,124,339.07
E) $2,202,840.91

Question 29

Webster Industrial Products just signed a sales contract with a new customer. What is this contract worth as of the end of year 4 if the following payments will be received and the firm earns 5 percent on its savings?

A) $397,425.35
B) $402,311.19
C) $460,000.00
D) $478,887.78
E) $483,073.00

Question 30

Letitia borrowed $6,000 from her bank 2 years ago. The loan term is 4 years. Each year, she must repay the bank $1,500 plus the annual interest. Which type of loan does she have?

A) Amortized
B) Blended discount
C) Interest-only
D) Pure discount
E) Complex

Question 31

You are comparing three investments, all of which pay $100 a month and have an 8 percent interest rate. One is ordinary annuity, one is an annuity due, and the third investment is a perpetuity. Which one of the following statements is correct given these three investment options?

A) To be the perpetuity, the payments must occur on the first day of each monthly period.
B) The ordinary annuity would be more valuable than the annuity due if both had a life of 10 years.
C) The present value of the perpetuity has to be higher than the present value of either the ordinary annuity or the annuity due.
D) The future value of all three investments must be equal.
E) The present value of all three investments must be equal.

Question 32

Cindy is taking out a loan today. The cash amount that she will receive today is equal to the present value of the lump sum payment which she will be required to pay 2 years from today. Which type of loan is this?

A) Principal-only
B) Amortized
C) Interest-only
D) Compound
E) Pure discount

Question 33

Chandler Tire Co. is trying to decide which one of two projects it should accept. Both projects have the same start-up costs. Project 1 will produce annual cash flows of $52,000 a year for 6 years. Project 2 will produce cash flows of $48,000 a year for 8 years. The company requires a 15 percent rate of return. Which project should the company select and why?

A) Project 1; because the annual cash flows are greater than those of Project 2
B) Project 1; because the present value of its cash inflows exceeds those of Project 2 by $14,211.62
C) Project 2; because the total cash inflows are $70,000 greater than those of Project 1
D) Project 2; because the present value of the cash inflows exceeds those of Project 1 by $18,598.33
E) It does not matter as both projects have almost identical present values.

Question 34

Travis borrowed $10,000 four years ago at an annual interest rate of 7 percent. The loan term is 6 years. Since he borrowed the money, Travis has been making annual payments of $700 to the bank. Which type of loan does he have?

A) Interest-only
B) Pure discount
C) Compound
D) Amortized
E) Complex

Question 35

Kristi is considering an investment that will pay $5,000 a year for 7 years, starting one year from today. How much should she pay for this investment if she wishes to earn a 12 percent rate of return?

A) $17,899.08
B) $18,023.88
C) $20,186.75
D) $22,818.78
E) $24,507.19

Question 36

When comparing savings accounts, you should select the account that has the:

A) lowest annual percentage rate.
B) highest annual percent rate.
C) highest stated rate.
D) lowest effective annual rate.
E) highest effective annual rate.

Question 37

Scott borrowed $2,500 today. The loan agreement requires him to repay $2,685 in one lump sum payment one year from now. This type of loan is referred to as a(n):

A) interest-only loan.
B) pure discount loan.
C) quoted rate loan.
D) compound interest loan.
E) amortized loan.

Question 38

Which one of the following statements is correct?

A) The APR is equal to the EAR for a loan that charges interest monthly.
B) The EAR is always greater than the APR.
C) The APR on a monthly loan is equal to (1 + monthly interest rate)¹² - 1.
D) The APR is the best measure of the actual rate you are paying on a loan.
E) The EAR, rather than the APR, should be used to compare both investment and loan options.

Question 39

You just borrowed $3,000 from your bank and agreed to repay the interest on an annual basis and the principal at the end of 3 years. What type of loan did you obtain?

A) Interest-only
B) Amortized
C) Perpetual
D) Pure discount
E) Lump sum

Question 40

Dressler Engine Tuning just decided to save money each year for the next 4 years to help fund a new building. If it earns 5.5 percent on its savings, how much will the firm have saved at the end of year 4?

A) $107,525.40
B) $108,392.69
C) $110,414.14
D) $111,737.43
E) $117,882.99

Question 41

Today is your 21^st birthday and you just decided to start saving money so you can retire early. Thus, you are going to save $500 a month starting one month from now. You plan to retire as soon as you can accumulate $1 million. If you can earn an average of 8 percent on your savings, how old will you be when you retire?

A) 33.39 years old
B) 42.87 years old
C) 54.39 years old
D) 64.71 years old
E) 63.87 years old

Question 42

You have just won a contest! You can either receive $10,000 a year for 15 years or $100,000 as a lump sum payment today. What is the interest rate on the annuity option?

A) 5.56 percent
B) 5.68 percent
C) 6.20 percent
D) 6.39 percent
E) 6.50 percent

Question 43

Turntable Industrial, Inc. owes your firm $138,600. This amount is seriously delinquent so your firm has offered to arrange a payment plan in the hopes that it might at least collect a portion of this receivable. Your firm's offer consists of weekly payments for one year at an interest rate of 3 percent. What is the amount of each payment?

A) $2,229.90
B) $2,318.11
C) $2,409.18
D) $2,599.04
E) $2,706.33

Question 44

You just received a loan offer from Friendly Loans. The company is offering you $5,000 at 14.3 percent interest. The monthly payment is only $100. If you accept this offer, how long will it take you to pay off the loan?

A) 5.84 years
B) 6.37 years
C) 6.80 years
D) 7.33 years
E) 7.59 years

Question 45

Used Motors will sell you a $13,000 car for $380 a month for 48 months. What is the interest rate?

A) 16.55 percent
B) 16.67 percent
C) 16.99 percent
D) 17.58 percent
E) 17.72 percent

Question 46

The manager of Gloria's Boutique has approved Carla's application for credit. The maximum payment that has been approved is $65 a month for 24 months. The APR is 15.7 percent. What is the maximum initial purchase that Carla can make given this credit approval?

A) $1,288.90
B) $1,300.00
C) $1,331.42
D) $1,350.00
E) $1,428.46

Question 47

Karl can afford car payments of $235 a month for 48 months. The bank will lend him money to buy a car at 7.75 percent interest. How much money can he afford to borrow?

A) $9,672.48
B) $9,734.95
C) $9,899.60
D) $10,022.15
E) $10,422.09

Question 48

Your grandfather started his own business 52 years ago. He opened a savings account at the end of his third month of business and contributed $x. Every three months since then, he faithfully saved another $x. His savings account has earned an average rate of 4.5 percent annually. Today, his account is valued at $364,209.11. How much did your grandfather save every 3 months?

A) $425.15
B) $428.67
C) $431.09
D) $443.13
E) $462.25

Question 49

Stanley Enterprises is acquiring Berkley, Inc. for $899,000. Berkley has agreed to accept annual payments of $210,000 at an interest rate of 7.5 percent. How many years will it take Stanley Enterprises to pay for this purchase?

A) 5.00 years
B) 5.14 years
C) 5.35 years
D) 5.47 years
E) 5.60 years

Question 50

Kurt wants to have $25,000 in an investment account 4 years from now. The account will pay 0.2 percent interest per month. If he saves money every month, starting one month from now, how much will he have to save each month to reach his goal?

A) $496.75
B) $497.03
C) $497.75
D) $501.03
E) $502.14

Question 51

You recently sold an antique car you owned and valued greatly. However, you needed money and agreed to sell the car at a price of $48,000, to be paid in monthly payments of $1,200 each for 48 months. What interest rate did you charge for financing the sale?

A) 8.65 percent
B) 8.75 percent
C) 8.88 percent
D) 9.24 percent
E) 9.49 percent

Question 52

The Solvent Insurance Co. will pay you $2,500 a year for 20 years in exchange for $30,000 today. What interest rate will you earn on this annuity?

A) 5.40 percent
B) 5.45 percent
C) 5.50 percent
D) 5.55 percent
E) 5.60 percent

Question 53

Today, you are purchasing a 20-year, 6 percent annuity at a cost of $120,000. The annuity will pay annual payments starting one year from today. What is the amount of each payment?

A) $9,511.08
B) $10,462.15
C) $10,754.40
D) $11,013.20
E) $12,208.19

Question 54

Jake owes $3,400 on his credit card. He is not charging any additional purchases because he wants to get this debt paid in full. The card has an APR of 13.9 percent. How much longer will it take him to pay off this balance if he makes monthly payments of $50 rather than $60?

A) 28.24 months
B) 31.33 months
C) 36.74 months
D) 39.20 months
E) 41.79 months

Question 55

Webster Mining is considering the purchase of a new sorting machine. The quote consists of a quarterly payment of $29,600 for 7 years at 8 percent interest. What is the purchase price of the equipment?

A) $621,380.92
B) $629,925.66
C) $687,418.22
D) $774,311.28
E) $836,267.35

Question 56

The Furniture Hut is offering a bedroom suite for $1,999. The credit terms are 60 months at $50 per month. What is the interest rate on this offer?

A) 16.33 percent
B) 16.50 percent
C) 16.65 percent
D) 17.15 percent
E) 17.30 percent

Question 57

You want to purchase a new condominium which costs $329,000. Your plan is to pay 20 percent down in cash and finance the balance over 25 years at 6.25 percent. What will be your monthly mortgage payment?

A) $1,736.25
B) $1,833.33
C) $1,908.16
D) $2,221.43
E) $2,406.11

Question 58

How much money does Suzie need to have in her retirement savings account today if she wishes to withdraw $25,000 a year for 30 years? She expects to earn an average rate of return of 6 percent.

A) $324,642.24
B) $331,288.67
C) $333,333.33
D) $340,025.00
E) $344,120.78

Question 59

Berkley Trucking recently purchased a new truck costing $147,800. The firm financed this purchase at 7.6 percent interest with monthly payments of $2,100. How many years will it take the firm to pay off this debt?

A) 6.50 years
B) 6.67 years
C) 7.48 years
D) 7.60 years
E) 7.79 years

Question 60

Katie's Dinor spent $84,000 to refurbish its current facility. The firm borrowed 80 percent of the refurbishment cost at 9.2 percent interest for 5 years. What is the amount of each monthly payment?

A) $1,108.91
B) $1,282.16
C) $1,333.33
D) $1,401.49
E) $1,487.06

Question 61

Steve is considering investing $3,600 a year for 40 years. How much will this investment be worth at the end of the 40 years if he earns an average annual rate of return of 11.6 percent? Assume Steve invests his first payment of the end of this year.

A) $1,887,411.26
B) $1,919,200.08
C) $2,103,018.90
D) $2,311,416.67
E) $2,471,685.70

Question 62

Eastern Shore Builders is offering preferred stock for sale with a 7.75 percent rate of return. What is the amount of the annual dividend on this stock if the current market price per share is $83.87?

A) $6.33
B) $6.50
C) $7.00
D) $7.50
E) $7.75

Question 63

A preferred stock pays an annual dividend of $7. What is one share of this stock worth to you today if you require a 14 percent rate of return?

A) $6.14
B) $7.98
C) $43.00
D) $50.00
E) $98.00

Question 64

You will receive annual payments of $2,400 at the end of each year for 15 years. The first payment will be received in year 6. What is the present value of these payments if the discount rate is 7 percent?

A) $11,465.20
B) $12,018.52
C) $13,299.80
D) $15,585.16
E) $16,856.60

Question 65

Kristina started setting aside funds 3 years ago to save for a down payment on a house. She has saved $900 each quarter and earned an average rate of return of 4.8 percent. How much money does she currently have saved for her down payment?

A) $11,542.10
B) $12,388.19
C) $15,209.80
D) $15,366.67
E) $16,023.13

Question 66

At the end of this month, Les will start saving $150 a month for retirement through his company's retirement plan. His employer will contribute an additional $0.50 for every $1.00 that he saves. If he is employed by this firm for 30 more years and earns an average of 10.5 percent on his retirement savings, how much will Les have in his retirement account 30 years from now?

A) $389,406.19
B) $401,005.25
C) $540,311.67
D) $566,190.22
E) $603,289.01

Question 67

Western States Life Insurance offers a perpetuity that pays annual payments of $10,000. This contract sells for $275,000 today. What is the interest rate?

A) 3.64 percent
B) 3.87 percent
C) 4.10 percent
D) 4.21 percent
E) 4.39 percent

Question 68

Anne plans to save $40 a week for the next 5 years. She expects to earn 3 percent for the first 2 years and 5 percent for the last 3 years. How much will her savings be worth at the end of the 5 years?

A) $10,215.60
B) $10,684.29
C) $10,983.58
D) $11,014.88
E) $11,708.15

Question 69

You want to save $200 a month for the next 24 years and hope to earn an average rate of return of 11 percent. How much more will you have at the end of the 24 years if you invest your money at the beginning of each month rather than the end of each month?

A) $1,611.29
B) $1,807.70
C) $2,238.87
D) $2,569.14
E) $2,707.27

Question 70

A local magazine is offering a $2,500 grand prize to one lucky winner. $1,000 will be paid on the day of the drawing. The remaining $1,500 will be paid in three annual payments of $500 each, starting one year after the drawing. How much would this prize be worth to you if you can earn 9 percent on your money?

A) $2,048.18
B) $2,164.29
C) $2,265.65
D) $2,450.14
E) $2,545.54

Question 71

The Food Store is planning a major expansion for 4 years from today. In preparation for this, the company is setting aside $35,000 each quarter, starting today, for the next 4 years. How much money will the firm have when it is ready to expand if it can earn an average of 6.25 percent on its savings?

A) $528,409.29
B) $540,288.16
C) $610,411.20
D) $640,516.63
E) $662,009.14

Question 72

Your parents would like to establish a trust fund that would pay annual payments to you and your heirs of $100,000 a year forever. How much do your parents need to deposit into this trust fund today to achieve their goal if the fund can earn 7 percent interest?

A) $678,342
B) $700,000
C) $1,211,516
D) $1,389,407
E) $1,428,571

Question 73

Currently, you owe the bank $9,800 for a car loan. The loan has an interest rate of 7.75 percent and monthly payments of $310. Your financial situation recently changed such that you can no longer afford these payments. After talking with your banker and explaining the situation, he has agreed to lower the monthly payments to $225 while keeping the interest rate at 7.75 percent. How much longer will it take you to repay this loan than you had originally planned?

A) 12.29 months
B) 14.47 months
C) 15.84 months
D) 17.19 months
E) 19.90 months

Question 74

Janice plans to save $75 a month, starting today, for 20 years. Kate plans to save $80 a month for 20 years, starting one month from today. Both Janice and Kate expect to earn an average return of 5.5 percent on their savings. At the end of the 20 years, Kate will have approximately _____ more than Janice.

A) $2,028.39
B) $2,066.67
C) $2,091.50
D) $2,178.14
E) $2,189.12

Question 75

What is the future value of $20 a week for 10 years at 6 percent interest? Assume the first payment occurs at the end of this week.

A) $14,239.14
B) $14,361.08
C) $14,727.15
D) $15,003.14
E) $15,221.80

Question 76

What is the value today of $3,600 received at the end of each year for 7 years if the first payment is paid at the end of year 3 and the discount rate is 12 percent?

A) $11,694.21
B) $12,484.57
C) $13,097.52
D) $15,089.23
E) $16,429.52

Question 77

Uptown Insurance offers an annuity due with semi-annual payments for 25 years at 6 percent interest. The annuity costs $200,000 today. What is the amount of each annuity payment?

A) $7,546.70
B) $7,600.00
C) $7,773.10
D) $7,800.00
E) $7,856.25

Question 78

A recent alumnus of your university gifted money to the school to fund annual scholarships for needy students. The school expects to earn an average rate of return of 6.5 percent and distribute $40,000 annually in scholarships. What was the amount of the gift?

A) $260,000.00
B) $328,500.00
C) $615,384.62
D) $658,929.38
E) $661,423.33

Question 79

You just won a contest! You will receive $100,000 a year for 20 years, starting today. If you can earn 12 percent on your investments, what are your winnings worth today?

A) $750,000.00
B) $833,333.33
C) $836,577.69
D) $850,000.00
E) $887,450.72

Question 80

Kris will receive $800 a month for the next 5 years from an insurance settlement. The interest rate is 4 percent, compounded monthly, for the first 2 years and 5 percent, compounded monthly, for the final 3 years. What is this settlement worth to him today?

A) $36,003.18
B) $38,219.97
C) $41,388.71
D) $43,066.22
E) $45,115.16