Deck 4: The Time Value of Money

Question 1

Use the figure for the question(s)below.
Which of the following statements regarding timelines is FALSE?

A)Timelines are an important first step in organizing and then solving a financial problem.
B)We refer to a series of cash flows lasting several periods as a stream of cash flows.
C)Not every stream of cash flows can be represented on a timeline.
D)A timeline is a linear representation of the timing of the (expected)cash flows.

Answer 1

Not every stream of cash flows can be represented on a timeline.

Question 2

Use the table for the question(s)below.

Draw a timeline detailing the cash flows from investment "A."

Answer 2

Question 3

At an annual interest rate of 7%,the present value of $5000 received in five years is closest to:

A)$3565
B)$6750
C)$7015
D)$7035

Answer 3

$3565

Question 4

Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child's college education.They decide to make deposits into an educational savings account on each of their daughter's birthdays,starting with her first birthday.Assume that the educational savings account will return a constant 7%.The parents deposit $2000 on their daughter's first birthday and plan to increase the size of their deposits by 5% each year.Draw a timeline that details the amount that would be available for the daughter's college expenses on her 18th birthday.

Question 5

The amount of money that your great aunt Matilda originally put in the account is closest to:

A)$600
B)$800
C)$1000
D)$1200

Question 6

Draw a timeline detailing Joe's cash flows from the sale of the family business.

Question 7

Use the figure for the question(s)below.
Which of the following statements regarding the timeline is FALSE?

A)Date 1 is the end of the first year.
B)Date 0 is the beginning of the first year.
C)The space between date 0 and date 1 represents the time period between two specific dates.
D)You will find the timeline most useful in tracking cash flows if you interpret each point on the timeline as a period or interval of time.

Question 8

Use the figure for the question(s)below.
Which of the following statements regarding the timeline is FALSE?

A)Date 1 is one year from now.
B)The $5000 below date 1 is the payment you will receive at the end of the first year.
C)The $5000 below date 2 is the payment you will receive at the beginning of the second year.
D)Date 0 represents today.

Question 9

At an annual interest rate of 7%,the future value of $5000 in five years is closest to:

A)$3565
B)$6750
C)$7015
D)$7035

Question 10

The ranking of the four alternatives from most valuable to least valuable if the interest rate is 7% per year would be:

A)1,2,3,4
B)4,3,2,1
C)3,4,2,1
D)3,1,2,4

Question 11

Which of the following statements is FALSE?

A)Finding the present value and compounding are the same.
B)A dollar today and a dollar in one year are not equivalent.
C)If you want to compare or combine cash flows that occur at different points in time,you first need to convert the cash flows into the same units or move them to the same point in time.
D)The equivalent value of two cash flows at two different points in time is sometimes referred to as the time value of money.

Question 12

Which of the following statements is FALSE?

A)The process of moving a value or cash flow backward in time is known as discounting.
B)FV =
C)The process of moving a value or cash flow forward in time is known as compounding.
D)The value of a cash flow that is moved forward in time is known as its future value.

Question 13

Which of the following statements is FALSE?

A)The process of moving a value or cash flow forward in time is known as compounding.
B)The effect of earning interest on interest is known as compound interest.
C)It is only possible to compare or combine values at the same point in time.
D)A dollar in the future is worth more than a dollar today.

Question 14

Use the figure for the question(s)below.
Which of the following statements regarding the timeline is TRUE?

A)Date 1 is the beginning of the first year.
B)Date 2 is the beginning of the second year.
C)Date 1 is the beginning of the second year.
D)Date 0 is the end of the first year.

Question 15

Consider the following time line: If the current market rate of interest is 8%,then the present value of this timeline is closest to:

A)$1000
B)$857
C)$860
D)$926

Question 16

The ranking of the four alternatives from most valuable to least valuable if the interest rate is 6% per year would be:

A)1,2,3,4
B)1,3,2,4
C)4,3,1,2
D)3,4,2,1

Question 17

Use the table for the question(s)below.

Draw a timeline detailing the cash flows from investment "B."

Question 18

You have been offered the following investment opportunity,if you pay $2500 today,you will receive $1000 at the end of each of the next three years.Draw a timeline detailing this investment opportunity.

Question 19

Assume that college costs continue to increase an average of 4% per year and that all her college savings are invested in an account paying 7% interest.Draw a timeline that details the amount of money she will need to have in the future four each of her four years of her undergraduate education.

Question 20

The amount of money that would be in the account if you left the money there until your 65th birthday is closest to:

A)$29,556
B)$148,780
C)$168,824
D)$748,932

Question 21

Wyatt oil is considering drilling a new self sustaining oil well at a cost of $1,000,000.This well will produce $100,000 worth of oil during the first year,but as oil is removed from the well the amount of oil produced will decline by 2%,per year forever.If the Wyatt oil's appropriate interest rate is 8%,then the NPV of this oil well is closest to:

A)-$250,000
B)$0
C)$250,000
D)$1,000,000

Question 22

Consider the following timeline: If the current market rate of interest is 9%,then the present value of this timeline as of year 0 is closest to:

A)$492
B)$637
C)$600
D)$400

Question 23

In terms of present value,how much will Joe receive for selling the family business?

Question 24

Which of the following statements is FALSE?

A)FV =
B)PV =

C)FV = C_n × (1 + r)ⁿ
D)Most investment opportunities have multiple cash flows that occur at different points in time.

Question 25

At an annual interest rate of 7%,the future value of this timeline in year 3 is closest to:

A)$3295
B)$3600
C)$3770
D)$4035

Question 26

Kampgrounds Inc.is considering purchasing a parcel of wilderness land near a popular historic site.Although this land will cost Kampgrounds $400,000 today,by renting out wilderness campsites on this land,Kampgrounds expects to make $35,000 at the end of every year indefinitely.If the appropriate discount rate is 8%,then the NPV of this new wilderness campsite is closest to:

A)-$50,000
B)-$37,500
C)$37,500
D)$50,000

Question 27

At an annual interest rate of 7%,the future value of this timeline in year 2 is closest to:

A)$3080
B)$3525
C)$3770
D)$4035

Question 28

If the appropriate interest rate is 10%,then Nielson Motors should:

A)invest in this opportunity since the NPV is positive.
B)not invest in this opportunity since the NPV is positive.
C)invest in this opportunity since the NPV is negative.
D)not invest in this opportunity since the NPV is negative.

Question 29

Consider the following timeline: If the current market rate of interest is 7%,then the future value of this timeline as of year 3 is closest to:

A)$1720
B)$1500
C)$1404
D)$1717

Question 30

If the appropriate interest rate is 15%,then Nielson Motors should:

A)invest in this opportunity since the NPV is positive.
B)not invest in this opportunity since the NPV is positive.
C)invest in this opportunity since the NPV is negative.
D)not invest in this opportunity since the NPV is negative.

Question 31

Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 10%,then the present value of this stream of cash flows is closest to:

A)$674
B)$600
C)$460
D)$287

Question 32

Taggart Transcontinental currently has a bank loan outstanding that requires it to make three annual payments at the end of the next three years of $1,000,000 each.The bank has offered to allow Taggart Transcontinental to skip making the next two payments in lieu of making one large payment at the end of the loan's term in three years.If the interest rate on the loan is 6%,then the final payment that the bank will require to make Taggart Transcontinental indifferent between the two forms of payments is closest to:

A)$2,673,000
B)$3,000,000
C)$3,184,000
D)$3,375,000

Question 33

Consider the following timeline: If the current market rate of interest is 10%,then the future value of this timeline is closest to:

A)$666
B)$500
C)$605
D)$650

Question 34

At an annual interest rate of 7%,the present value of this timeline in year 0 is closest to:

A)$3080
B)$3600
C)$3770
D)$4035

Question 35

Consider the following timeline: If the current market rate of interest is 8%,then the value of the cash flows as of year 1 is closest to:

A)$0
B)$1003
C)$540
D)$77

Question 36

Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 8%,then the future value of this stream of cash flows is closest to:

A)$11,699
B)$10,832
C)$12,635
D)$10,339

Question 37

Which of the following statements regarding perpetuities is FALSE?

A)To find the value of a perpetuity one cash flow at a time would take forever.
B)A perpetuity is a stream of equal cash flows that occurs at regular intervals and lasts forever.
C)PV of a perpetuity =
D)One example of a perpetuity is the British government bond called a consol.

Question 38

If the appropriate interest rate is 10%,then the NPV of this opportunity is closest to:

A)($88,000)
B)$88,000
C)$300,000
D)$1,300,000

Question 39

Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 8%,then the present value of this stream of cash flows is closest to:

A)$22,871
B)$21,211
C)$24,074
D)$26,000

Question 40

Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 6%,then the future value of this stream of cash flows is closest to:

A)$1723
B)$1500
C)$1626
D)$1288

Question 41

Which of the following formulas is INCORRECT?

A)PV of a growing annuity = C ×

B)PV of an annuity = C ×

C)PV of a growing perpetuity =
D)PV of a perpetuity =

Question 42

The future value at retirement (age 65)of your savings is closest to:

A)$497,530
B)$928,895
C)$1,263,236
D)$108,000

Question 43

Assuming that college costs continue to increase an average of 4% per year and that all her college savings are invested in an account paying 7% interest,then the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education is closest to:

A)$97,110
B)$107,532
C)$101,291
D)$50,000

Question 44

Which of the following statements regarding growing annuities is FALSE?

A)A growing annuity is a stream of N growing cash flows,paid at regular intervals.
B)We assume that g < r when using the growing annuity formula.
C)PV of a growing annuity = C ×

D)A growing annuity is like a growing perpetuity that never comes to an end.

Question 45

If the current rate of interest is 8%,then the future value 20 years from now of an investment that pays $1000 per year and lasts 20 years is closest to:

A)$45,762
B)$36,725
C)$9818
D)$93,219

Question 46

Which of the following statements regarding growing perpetuities is FALSE?

A)We assume that r < g for a growing perpetuity.
B)PV of a growing perpetuity =
C)To find the value of a growing perpetuity one cash flow at a time would take forever.
D)A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.

Question 47

You are thinking about investing in a mine that will produce $10,000 worth of ore in the first year.As the ore closest to the surface is removed it will become more difficult to extract the ore.Therefore,the value of the ore that you mine will decline at a rate of 8% per year forever.If the appropriate interest rate is 6%,then the value of this mining operation is closest to:

A)$71,429
B)$500,000
C)$166,667
D)This problem cannot be solved.

Question 48

The British government has a consol bond outstanding that pays ₤100 in interest each year.Assuming that the current interest rate in Great Britain is 5% and that you will receive your first interest payment one year from now,then the value of the consol bond is closest to:

A)₤1000
B)₤1100
C)₤2100
D)₤2000

Question 49

Which of the following statements regarding annuities is FALSE?

A)PV of an annuity = C ×

B)The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments.
C)An annuity is a stream of N equal cash flows paid at regular intervals.
D)Most car loans,mortgages,and some bonds are annuities.

Question 50

The present value (at age 30)of your retirement savings is closest to:

A)$87,000
B)$108,000
C)$46,600
D)$75,230

Question 51

Consider a growing perpetuity that will pay $100 in one year.Each year after that,you will receive a payment on the anniversary of the last payment that is 6% larger than the last payment.This pattern of payments will continue forever.If the interest rate is 11%,then the value of this perpetuity is closest to:

A)$1667
B)$588
C)$2000
D)$909

Question 52

Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child's college education.They decide to make deposits into an educational savings account on each of their daughter's birthdays,starting with her first birthday.Assume that the educational savings account will return a constant 7%.The parents deposit $2000 on their daughter's first birthday and plan to increase the size of their deposits by 5% each year.Assuming that the parents have already made the deposit for their daughter's 18th birthday,then the amount available for the daughter's college expenses on her 18th birthday is closest to:

A)$42,825
B)$97,331
C)$67,998
D)$103,063

Question 53

You work for a pharmaceutical company that has developed a new drug.The patent on the drug will last for 17 years.You expect that the drug will produce cash flows of $10 million in its first year and that this amount will grow at a rate of 4% per year for the next 17 years.Once the patent expires,other pharmaceutical companies will be able to produce generic equivalents of your drug and competition will drive any future profits to zero.If the interest rate is 12% per year,then the present value of producing this drug is closest to:

A)$71 million
B)$90 million
C)$170 million
D)$105 million

Question 54

Since your first birthday,your grandparents have been depositing $1000 into a savings account on every one of your birthdays.The account pays 4% interest annually.Immediately after your grandparents make the deposit on your 18th birthday,the amount of money in your savings account will be closest to:

A)$25,645
B)$36,465
C)$12,659
D)$18,000

Question 55

Assuming that costs continue to increase an average of 4% per year,tuition and other costs for one year for this student in 18 years when she enters college will be closest to:

A)$12,500
B)$21,500
C)$320,568
D)$25,323

Question 56

Your son is about to start kindergarten in a private school.Currently,the tuition is $12,000 per year,payable at the start of the school year.You expect annual tuition increases to average 6% per year over the next 13 years.Assuming that your son remains in this private school through high school and that your current interest rate is 6%,then the present value of your son's private school education is closest to:

A)$106,230
B)$156,000
C)$137,900
D)This problem cannot be solved.

Question 57

Which of the following statements is FALSE?

A)The difference between an annuity and a perpetuity is that an annuity ends after some fixed number of payments.
B)Most car loans,mortgages,and some bonds are annuities.
C)A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.
D)An annuity is a stream of N equal cash flows paid at irregular intervals.

Question 58

Your son is about to start kindergarten in a private school.Currently,the tuition is $12,000 per year,payable at the start of the school year.You expect annual tuition increases to average 6% per year over the next 13 years.Assuming that you son remains in this private school through high school and that your current interest rate is 7%,then the present value of your son's private school education is closest to:

A)$332,300
B)$137,900
C)$155,800
D)$156,000

Question 59

If the current rate of interest is 8%,then the present value of an investment that pays $1000 per year and lasts 20 years is closest to:

A)$18,519
B)$45,761
C)$9818
D)$20,000

Question 60

The British government has a consol bond outstanding that pays ₤100 in interest each year.Assuming that the current interest rate in Great Britain is 5% and that you will receive your first interest payment immediately upon purchasing the consol bond,then the value of the consol bond is closest to:

A)₤2000
B)₤2100
C)₤1000
D)₤1100

Question 61

Assuming that college costs continue to increase an average of 4% per year and that all her college savings are invested in an account paying 7% interest,then the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education is closest to:

Question 62

The future value at retirement (age 65)of your savings is:

Question 63

If the current rate of interest is 8% APR,then the future value of an investment that pays $250 per quarter and lasts 20 years is closest to:

A)$18,519
B)$48,443
C)$9936
D)$20,000

Question 64

Suppose that you deposit $10,000 in an account that pays 6% interest and you want to know how much will be in your account at the end of 10 years.To solve this problem in Microsoft Excel,you would use which of the following Excel formulas?

A)=FV(.06,10000,0,10)
B)=PV(.06,10000,0,10)
C)=FV(.06,10,0,10000)
D)=PV(.06,10,0,10000)

Question 65

If the appropriate interest rate is 8%,then present value of $500 paid at the end of each of the next 40 years is closest to:

A)$23
B)$5962
C)$6439
D)$20,0000

Question 66

Assume that you are 30 years old today,and that you are planning on retiring at age 65.Your current salary is $45,000 and you expect your salary to increase at a rate of 5% per year as long as you work.To save for your retirement,you plan on making annual contributions to a retirement account.Your first contribution will be made on your 31^st birthday and will be 8% of this year's salary.Likewise,you expect to deposit 8% of your salary each year until you reach age 65.At retirement (age 65)you will begin withdrawing equal annual payments to pay for your living expenses during retirement (on your 65th birthday).If you expect to die one day before your 101st birthday (Your last withdraw will be on your 100th birthday)and if the annual rate of return is 7%,then how much money will you have to spend in each of your golden years of retirement?

Question 67

Suppose that you are considering an investment that will pay you $4000 per year for the next five years.The appropriate rate of interest is 5%.You want to know the present value of the cash flows from this investment.To solve this problem in Microsoft Excel,you would use which of the following excel formulas?

A)=PV(.05,5,4000,0,0)
B)=PV(.05,5,4000,0,1)
C)=PV(5,.05,4000,0)
D)=PV(5,5,4000,0)

Question 68

Henry Rearden is saving for retirement and has determined that to live comfortably he must save $3 million by his 65th birthday.Henry just turned 30 today,and he has decided that starting today and continuing on every birthday up to and including his 65th birthday,he will deposit the same amount into an individual retirement account (IRA).If Henry can earn 8% on his IRA,then the amount he must set aside each year to make sure that he will have $3 million in his account on his 65th birthday is closest to:

A)$16,035
B)$17,410
C)$83,335
D)$85,715

Question 69

Which of the following is NOT a valid time value of money function in Excel?

A)PMT
B)NPER
C)I
D)FV

Question 70

You are considering purchasing a new home.You will need to borrow $250,000 to purchase the home.A mortgage company offers you a 15 year fixed rate mortgage (180 months)at 9% APR (0.75% month).If you borrow the money from this mortgage company,your monthly mortgage payment will be closest to:

A)$2585
B)$660
C)$2535
D)$1390

Question 71

If the current rate of interest is 8% APR,then the present value of an investment that pays $250 per quarter and lasts 20 years is closest to:

A)$18,519
B)$48,443
C)$9936
D)$20,000

Question 72

Define the following terms:
(a)perpetuity
(b)annuity
(c)growing perpetuity
(d)growing annuity

Question 73

If the current rate of interest is 8% APR,then the future value of an investment that pays $500 every two years and lasts 20 years is closest to:

A)$11,000
B)$10,661
C)$22,881
D)$20,000

Question 74

You are offered an investment opportunity that costs you $28,000,has an NPV of $2278,lasts for three years,has interest rate of 10%,and produces the following cash flows: The missing cash flow from year 2 is closest to:

A)$12,500
B)$12,000
C)$13,000
D)$10,000

Question 75

How do you calculate (mathematically)the present value of a(n):
(a)perpetuity
(b)annuity
(c)growing perpetuity
(d)growing annuity

Question 76

If the appropriate interest rate is 8%,then present value of $500 paid at the beginning of each of the next 40 years is closest to:

A)$23
B)$5962
C)$6439
D)$20,000

Question 77

The British government has just issued a new consol bond that sells for £1000 and pays interest of 8%.The annual interest payment on this bond must be:

A)£80
B)£8
C)£1000
D)£12,500

Question 78

You are interested in purchasing a new automobile that costs $35,000.The dealership offers you a special financing rate of 6% APR (0.5%)per month for 48 months.Assuming that you do not make a down payment on the auto and you take the dealer's financing deal,then your monthly car payments would be closest to:

A)$729
B)$822
C)$842
D)$647

Question 79

Dagny Taggart is a graduating college senior and she is considering the costs of going to medical school.Beginning next fall,Dagny expects medical school tuition to run $45,000 for the first year and she estimates that tuition will increase by 6% each year.If Dagny is able to invest her money in an account paying 8% interest per year,then the present value to Dagny of four years of medical school tuition is closest to:

A)$149,045
B)$155,930
C)$162,095
D)$180,000

Question 80

Francisco d'Anconia is considering an investment opportunity that costs $10,000 today and will pay $11,500 in two years.The IRR of this opportunity is closest to:

A)7.25%
B)7.50%
C)10.00%
D)15.00%