Deck 5: Discounted Cash Flow Valuation

Question 1

Christie is buying a new car today and is paying a $500 cash down payment.She will finance the balance at 6.3 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.

Answer 1

To compute the initial loan amount, you must use a monthly interest 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 six years
C)Unequal payments each year for nine years
D)Equal annual payments for life
E)Equal weekly payments forever

Answer 2

Equal annual payments for life

Question 3

Perpetuities have:

A)irregular payments but constant payment periods.
B)equal payments and an infinite life.
C)equal payments and a set number of equal payment periods.
D)less value than comparable annuities.
E)no application in today's world.

Answer 3

equal payments and an infinite life.

Question 4

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

A)C × ({1 - [1/(1 + r)t]}/r)
B)C × ({1 - [1/(1 + r)t]} -r)
C)C × ({1 - [r/(1 + r)t]}/r)
D)C × ({1 - [1/(1 × r)t]} × r)
E)C × ({1 - [r/(1 × r)t]} × r)

Question 5

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 6

Which one of these is 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)Rental payment of $800 a month for one year

Question 7

The Jones Brothers recently established a trust fund that will provide annual scholarships of $12,000 indefinitely.These annual scholarships are:

A)an ordinary annuity.
B)an annuity due.
C)amortized payments.
D)a perpetuity.
E)a perpetuity due.

Question 8

All else held constant, the present value of an annuity will decrease if you:

A)increase the annuity's future value.
B)increase the payment amount.
C)increase the time period.
D)decrease the discount rate.
E)decrease the annuity payment.

Question 9

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 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

Anna pays .85 percent interest monthly on her credit card account.When the interest rate on that debt is expressed as if it were compounded annually, the rate would be referred to as the:

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

Question 12

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

A)Perpetuity
B)Annuity
C)Consol
D)Lump sum
E)Present value

Question 13

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 14

All else held constant, the future value of an annuity will increase if you:

A)decrease both the interest rate and the time period.
B)increase the time period.
C)decrease the present value.
D)decrease the payment amount.
E)decrease the interest rate.

Question 15

A perpetuity in Canada is frequently referred to as:

A)a consul.
B)an infinity.
C)forever cash.
D)a dowry.
E)a forevermore.

Question 16

Which statement is true?

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 17

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

A)$75 paid at the beginning of each monthly 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 5 years, starting today
D)$50 paid every year for ten years, starting today
E)$25 paid weekly for 1 year, starting one week from today

Question 18

Lee pays 1 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 19

A 30-year home mortgage is a classic example of:

A)a set of unequal cash flows.
B)an ordinary annuity.
C)a perpetuity.
D)an annuity due.
E)a consol.

Question 20

Which one of the following qualifies as an annuity payment?

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

Question 21

Scott borrowed $2,500 today at an APR of 7.4 percent.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 22

Assume all else is equal.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 23

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 six years.Project 2 will produce cash flows of $48,000 a year for eight 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 by $4,000 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 $72,000 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 24

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

A)6 percent compounded annually
B)6 percent compounded semiannually
C)6 percent compounded quarterly
D)6 percent compounded daily
E)6 percent compounded every 2 years

Question 25

Krystal plans to save $500 at the end of Year 1, $600 at the end of Year 2, and $800 at the end of Year 3.If she earns 2.8 percent on her savings, how much money will she have saved at the end of Year 3?

A)$1,676.51
B)$1,714.97
C)$1,945.19
D)$1,785.66
E)$1,878.69

Question 26

Moonlight Industries just signed a sales contract with a new customer.JK will receive annual payments in the amount of $50,000, $96,000, $123,000, and $138,000 at the end of Years 1 to 4, respectively.What is this contract worth at the end of Year 4 if the firm earns 3.75 percent on its savings?

A)$ 443,571.88
B)$ 348,457.72
C)$ 431,417.66
D)$ 412,264.53
E)$ 424,786.07

Question 27

Letitia borrowed $6,000 from her bank two years ago.The loan term is four 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 28

Tiger Trucking Company is considering a project that will produce cash inflows of $18,000 at the end of Year 1, $32,000 in Year 2, and $45,000 in Year 3.What is the present value of these cash inflows at a discount rate of 9 percent?

A)$65,615.21
B)$70,181.89
C)$78.195.78
D)$78,485.76
E)$87,112.15

Question 29

You are comparing three investments, all of which pay $100 a month and have an interest rate of 8 percent.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 30

Oakville Trucking just signed a $5.0 million contract.The contract calls for a payment of $1.25 million today, $1.75 million one year from today, and $2.0 million two years from today.What is this contract worth today at a discount rate of 7.25 percent?

A)$4,923,275.74
B)$4,620,444.63
C)$3,247,628.58
D)$4.341,851.15
E)$4,342,468.17

Question 31

Jorge is considering an investment that will pay $4,650 a year for five years, starting one year from today.What is the maximum amount he should pay for this investment if he desires a rate of return of 9.0 percent?

A)$17,736.81
B)$18,566.10
C)$15,064.70
D)$18,086.88
E)$20,859.52

Question 32

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 33

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 34

How much money does Yvette need to have in her retirement savings account today if she wishes to withdraw $36,000 a year for 30 years? She expects to earn an average rate of return of 8.25 percent.(

A)$393,388.77
B)$405,280.20
C)$339,752,80
D)$354,049.89
E)$395,904.99

Question 35

The manager of Steve's Audio has approved Daisy's application for 24 months of credit with maximum monthly payments of $45.If the APR is 19.2 percent, what is the maximum initial purchase that Daisy can buy on credit?

A)$501.36
B)$1,024.35
C)$890.99
D)$980.99
E)$1,134.57

Question 36

Travis borrowed $10,000 four years ago at an annual interest rate of 7 percent.The loan term is six 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 37

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

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

Question 38

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 partially amortized with each loan payment.
E)require the accrued interest be paid in full with each monthly payment.

Question 39

Bill just financed a used car through his credit union.His loan requires payments of $275 a month for five years.Assuming that all payments are paid on time, 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 40

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 three years.What type of loan did you obtain?

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

Question 41

Postal Express is considering the purchase of a new sorting machine.The sales quote consists of quarterly payments of $37,200 for five years at 7.6 percent interest.What is the purchase price?

A)$621,380.92
B)$614,184.40
C)$687,418.22
D)$774,311.28
E)$836,267.35

Question 42

Janice plans to save $80 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, Janice will have approximately _____ more than Janice.

A)$159.73
B)$66.67
C)$0
D)$78.14
E)$189.12

Question 43

Karley's setting aside $32,000 each quarter, starting today, for the next three years for an expansion project.How much money will the firm have at the end of the three years if it can earn an average of 5.45 percent on its savings?

A)$428,409.29
B)$414,123.86
C)$390,411.20
D)$419,766.30
E)$362,009.14

Question 44

Max's Kennels spent $220,000 to refurbish its current facility.The firm borrowed 60 percent of the refurbishment cost at 5.95 percent interest for six years.What is the amount of each monthly payment?

A)$1,985.25
B)$2,205.36
C)$2,356.23
D)$2,184.51
E)$1,895.32

Question 45

London Motors will sell a $24,000 car for $335 per month for 60 months.What is the interest rate?

A)8.95percent
B)7.15 percent
C)6.90 percent
D)9.17.59percent
E)6.77 percent

Question 46

Forni's Furniture is offering a bedroom suite for $2,700.The credit terms are 60 months at $73.00 per month.What is the interest rate on this offer?

A)20.97 percent
B)20.05 percent
C)19.26 percent
D)21.75 percent
E)1.75 percent

Question 47

RB Farworth will pay you $2,500 a year for 15 years in exchange for $25,000 today.What interest rate will you earn on this annuity?

A)6.23 percent
B)35.56percent
C)7.46 percent
D)4.23 percent
E)4.56 percent

Question 48

You owe $6,800on a car loan that has an interest rate of 6.75 percent and monthly payments of $310.You lost your job and your new job pays less, so your lender just agreed to lower the monthly payments to $225 while keeping the interest rate at 6.75 percent.How much longer will it take you to repay this loan than you had originally planned?

A)10.50 months
B)11.47 months
C)9.74 months
D)12.19 months
E)18.90 months

Question 49

Industrial Tools owes you $38,600.This amount is seriously delinquent so you have offered to accept weekly payments for one year at an interest rate of 3 percent to settle this debt in full.What is the amount of each payment?

A)$829.90
B)$818.11
C)$609.18
D)$599.04
E)$753.71

Question 50

Cromwell is acquiring some land for $1,200,000 in exchange for semiannual payments of $75,000 at an interest rate of 6.35 percent.How many years will it take Cromwell to pay for this purchase?

A)11.00 years
B)12.00 years
C)11.35 years
D)10.47 years
E)11.80 years

Question 51

So you can retire early, you have decided to start saving $500 a month starting one month from now.You plan to retire as soon as you can accumulate $1 million.If you can earn 5 percent on your savings, how many years will it be before you can retire?

A)33.39 years
B)42.87 years
C)44.76 years
D)44.71 years
E)33.87 years

Question 52

Recently, you needed money and agreed to sell a car you had inherited at a price of $55,000, to be paid in monthly payments of $1,500 for 42 months.What interest rate did you charge for financing the sale?

A)7.25 percent
B)6.50 percent
C)6.84 percent
D)7.78 percent
E)8.33 percent

Question 53

Your grandfather started his own business 52 years ago.He opened an investment 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 5.73 percent annually.Today, his account is valued at $289,209.11.How much did your grandfather save every three months assuming he saved the same amount each time?

A)$284.02
B)$328.67
C)$331.09
D)$226.78
E)$262.25

Question 54

Varian wants to have $500,000 in an investment account six years from now.The account will pay .58 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)$5,614.90
B)$6,049.86
C)$5,391.05
D)$5,053.86
E)$5,360.94

Question 55

What is the future value of $25 a week for 40 years at 8.5 percent interest? Assume the first payment occurs at the end of this week.

A)$441,710.03
B)$414,361.08
C)$469,727.15
D)$350,003.14
E)$335,221.18

Question 56

Lionheart Trucking recently purchased a new truck costing $178,000.The firm financed this purchase at 6.6 percent interest with monthly payments of $2,400.How many years will it take the firm to pay off this debt?

A)8.95 years
B)6.89 years
C)9.26 years
D)8.83years
E)7.96 years

Question 57

You have just won the lottery! You can either receive $183,555 per year for 20 years or $2,300,000 as a lump sum payment today.What is the interest rate on the annuity option?

A)4.94 percent
B)3.98 percent
C)5.50 percent
D)4.75percent
E)4.25 percent

Question 58

Jake owes $3,990 on a credit card with an APR of 13.9 percent.How much more will it cost him to pay off this balance if he makes monthly payments of $50 rather than $60? Assume he does not charge any further purchases.

A)$2,409
B)$2,811
C)$1,648
D)$1,018
E)$3,545

Question 59

You want to purchase a new condominium that costs $325,000.Your plan is to pay 20 percent down in cash and finance the balance over 15 years at 4.1 percent.What will be your monthly mortgage payment including principal and interest?

A)$1,936.24
B)$2,185.56
C)$2,560.39
D)$2,420.30
E)$2,258.34

Question 60

Today, you are purchasing a 15-year, 6.5 percent annuity at a cost of $36,500.The annuity will pay annual payments starting one year from today.What is the amount of each payment?

A)$4,177.59
B)$3,881.88
C)$2,420.91
D)$3,679.71
E)$4,874.70

Question 61

A preferred stock offers a rate of return of 5.45 percent and sells for $78.20? What is the annual dividend amount?

A)$4.26
B)$4.09
C)$3.53
D)$4.50
E)$3.87

Question 62

Standards Life Insurance offers a perpetuity that pays annual payments of $12,000.This contract sells for $250,000 today.What is the interest rate?

A)4.80 percent
B)3.87 percent
C)4.10 percent
D)4.21 percent
E)4.39 percent

Question 63

Round House Furniture offers credit to its customers at a rate of 1.15 percent per month.What is the effective annual rate of this credit offer?

A)14.13 percent
B)13.80 percent
C)14.41 percent
D)15.04 percent
E)14.71 percent

Question 64

At the end of this month, Les will start saving $200 a month for retirement through his company's retirement plan.His employer will contribute an additional $.50 for every $1.00 that he saves.If he is employed by this firm for 30 more years and earns an average of 8.25 percent on his retirement savings, how much will he have in his retirement account 30 years from now?

A)$589,406.19
B)$401,005.25
C)$540,311.67
D)$470,465.70
E)$503,289.01

Question 65

What is the value today of $3,600 received at the end of each year for eight years if the first payment is paid at the end of Year 4 and the discount rate is 12 percent?

A)$11,694.21
B)$12,484.57
C)$12,729.12
D)$15,089.23
E)$14,429.52

Question 66

A local magazine is offering a $5,000 grand prize to one lucky winner.The prize will be paid in five annual payments of $1,000 each, starting one year after the drawing.How much would this prize be worth to you if you can earn 8 percent on your money?

A)$ 4,823.45
B)$ 4,622.88
C)$ 3,992.71
D)$ 4,312.13
E)$ 3,312.13

Question 67

You plan to save $200 a month for the next 24 years and hope to earn an average rate of return of 10.6 percent.How much more will you have at the end of the 24 years if you invest your money at the beginning rather than the end of each month?

A)$1,911.29
B)$1,807.70
C)$2,238.87
D)$2,317.82
E)$2,707.27

Question 68

Anne plans to save $40 a week, starting next week, for ten years and earn a rate of return of 4.6 percent, compounded weekly.After the ten years, she will discontinue saving and invest her account at 6.5 percent, compounded annually.How long from now will it be before she has accumulated a total of $50,000?

A)10.32 years
B)21.14 years
C)15.08 years
D)11.14 years
E)20.32 years

Question 69

A preferred stock pays an annual dividend of $2.95.What is one share of this stock worth to you today if you require a rate of return of 8.2 percent?

A)$ 51.21
B)$ 33.03
C)$ 38.00
D)$ 35.98
E)$ 33.49

Question 70

Kristina started setting aside funds three 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?

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

Question 71

First Bank offers personal loans at 7.7 percent compounded monthly.Second Bank offers similar loans at 7.4percent compounded daily.Which one of the following statements is correct concerning these loans? Assume a 365-day year.

A)The First Bank loan has an effective rate of 7.98 percent.
B)The Second Bank loan has an effective rate of 8.01 percent.
C)The annual percentage rate for the Second Bank loans is 7.68 percent.
D)Borrowers should prefer the loans offered by First Bank.
E)Both banks offer the same effective rate.

Question 72

Uptown Insurance offers an annuity due with semiannual 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 73

Freya plans to invest $3,200 a year for 25 years starting at the end of this year.How much will this investment be worth at the end of the 25years if she earns an average annual rate of return of 8.2 percent?

A)$2 63,837.69
B)$ 381,324.92
C)$ 245,897,34
D)$ 219,672.01
E)$ 240,885.11

Question 74

You will receive annual payments of $800 at the end of each year for 12 years.The first payment will be received in Year 3.What is the present value of these payments if the discount rate is 7 percent?

A)$5,465.20
B)$6,018.52
C)$6,299.80
D)$5,549.96
E)$6,856.60

Question 75

You would like to establish a trust fund that would provide annual scholarships of $100,000 forever.How much would you have to deposit today in one lump sum to achieve this goal if you can earn a guaranteed 4.5 percent rate of return?

A)$1,678,342
B)$1,800,000
C)$2,413,435
D)$1,620,975
E)$2,222,222

Question 76

Assume your university earns an average rate of return of 5.65 percent on its endowment funds.If a new gift permanently increases annual scholarships by $32,000, what was the amount of the gift?

A)$784,090.91
B)$485,293.05
C)$615,384.62
D)$658,929.38
E)$566,371.68

Question 77

Kurt will receive $1,200 a month for five years from an insurance settlement.The first payment was received today.If he invests the full amount of each payment at a guaranteed 6.15 percent rate, how much will he have saved at the end of the five years?

A)$76,003.18
B)$88,219.97
C)$91,388.71
D)$84,478.33
E)$95,115.16

Question 78

What is the effective annual rate of 8.25 percent compounded quarterly?

A)8.25 percent
B)8.49 percent
C)8.38 percent
D)8.51 percent
E)8.56 percent

Question 79

What is the effective annual rate of 9.6 percent compounded semiannually?

A)9.71 percent
B)9.83 percent
C)9.79 percent
D)9.68 percent
E)9.92 percent

Question 80

Leann will receive $ 95,000 a year for 7years, starting today.If the rate of return is 6.8 percent, what are these payments worth today?

A)$568,346.72
B)$531,019.80
C)$ 550,630.68
D)$564,009.27
E)$518,571,80