Deck 4: Time Value of Money: Valuing Cash Flow Streams

Question 1

If a few intermediate cash flows in valuing a stream of cash flows are zero can we delete those points on the timeline and squeeze the timeline to show only nonzero cash flows?

Answer 1

Every cash flow contains two pieces of information-the nominal value and the time stamp.If we decide to eliminate the zero cash flows from the timeline and concentrate only on the nonzero ones,we will be distorting the time stamp of some nonzero cash flows.Hence,we need to show the timeline in full,including all cash flows zero as well as nonzero.

Question 2

A perpetuity will pay $1000 per year,starting five years after the perpetuity is purchased.What is the present value (PV)of this perpetuity on the date that it is purchased,given that the interest rate is 4%?

A)$1410
B)$20,582
C)$21,370
D)$34,604

Answer 2

C

Question 3

A lottery winner will receive $1 million at the end of each of the next ten years.What is the future value (FV)of her winnings at the time of her final payment,given that the interest rate is 8.5% per year?

A)$13.84 million
B)$14.84 million
C)$18.95 million
D)$19.95 million

Answer 3

B

Question 4

Ally wishes to leave a provision in her will that $2000 will be paid annually in perpetuity to a local charity.How much must she provide in her will for this perpetuity if the interest rate is 6%?

A)$3201.21
B)$21,200.00
C)$33,333.33
D)$42,000.00

Question 5

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

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

Question 6

Which of the following investments has a higher present value,assuming the same (strictly positive)interest rate applies to both investments?

A)Investment X has a higher present value.
B)Investment Y has a higher present value.
C)Investment X and Investment Y have the same present value,since the total of the cash flows is the same for both.
D)No comparison can be made - we need to know the interest rate to calculate the present value.

Question 7

What is the present value (PV)of an investment that will pay $400 in one year's time,and $400 every year after that,when the interest rate is 5%?

A)$2400
B)$3600
C)$7200
D)$8000

Question 8

Salvatore has the opportunity to invest in a scheme which will pay $5000 at the end of each of the next 5 years.He must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first year.What is the present value of this investment if the interest rate is 4%?

A)-$1410.67
B)-$112.23
C)$1248.56
D)$2643.73

Question 9

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

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

Question 10

If $10,000 is invested in a certain business at the start of the year,the investor will receive $3000 at the end of each of the next four years.What is the present value of this business opportunity if the interest rate is 7% per year?

A)$148.53
B)$161.63
C)$172.45
D)$178.88

Question 11

A business promises to pay the investor of $2000 today for a payment of $500 in one year's time,$1000 in two years' time and $1000 in three years' time.What is the present value of this business opportunity if the interest rate is 5% per year?

A)$247.06
B)$253.78
C)$256.88
D)$261.07

Question 12

You are given two choices of investments,Investment A and Investment B.Both investments have the same future cash flows.Investment A has a discount rate of 4%,and Investment B has a discount rate of 5%.Which of the following is true?

A)The present value of cash flows in Investment A is higher than the present value of cash flows in Investment B.
B)The present value of cash flows in Investment A is lower than the present value of cash flows in Investment B.
C)The present value of cash flows in Investment A is equal to the present value of cash flows in Investment B.
D)No comparison can be made - we need to know the cash flows to calculate the present value.

Question 13

The present value (PV)of a stream of cash flows is just the sum of the present values of each individual cash flow.

Question 14

A homeowner in a sunny climate has the opportunity to install a solar water heater in his home for a cost of $2400.After installation the solar water heater will produce a small amount of hot water every day,forever,and will require no maintenance.How much must the homeowner save on water heating costs every year if this is to be a sound investment? (The interest rate is 9% per year. )

A)$216
B)$240
C)$248
D)$262

Question 15

Suppose you invest $1000 into a mutual fund that is expected to earn a rate of return of 10%.The amount of money will you have in ten years is closest to which of the following? The amount you will have in 50 years is closest to which of the following?

A)$386;$9
B)$2594;$45,259
C)$2594;$117,391
D)$3138;$ 1,311,892

Question 16

A perpetuity has a PV of $32,000.If the interest rate is 10%,how much will the perpetuity pay every year?

A)$2909
B)$3100
C)$3200
D)$3520

Question 17

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

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

Question 18

An investment pays you $20,000 at the end of this year,and $10,000 at the end of each of the four following years.What is the present value (PV)of this investment,given that the interest rate is 4% per year?

A)$42,150
B)$45,913
C)$54,134
D)$58,614

Question 19

Use the information for the question(s)below.
Joe just inherited the family business,and having no desire to run the family business,he has decided to sell it to an entrepreneur.In exchange for the family business,Joe has been offered an immediate payment of $100,000.Joe will also receive payments of $50,000 in one year,$50,000 in two years,and $75,000 in three years.The current market rate of interest for Joe is 6%.
In terms of present value (PV),how much will Joe receive for selling the family business?

Question 20

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

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

Question 21

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 22

An annuity is set up that will pay $1500 per year for ten years.What is the present value (PV)of this annuity given that the discount rate is 6%?

A)$8441
B)$11,040
C)$14,721
D)$19,771

Question 23

Since your first birthday,your grandparents have been depositing $100 into a savings account every month.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)$11,941,266
B)$31,559
C)$30,774
D)$21,600

Question 24

You are borrowing money to buy a car.If you can make payments of $300 per month starting one month from now at an interest rate of 4%,how much will you be able to borrow for the car today if you finance the amount over four years?

A)$6,358.54
B)$13,067.62
C)$15,587.88
D)$13,286.65

Question 25

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

A)$18,519
B)$45,761
C)$9,818
D)$20,000

Question 26

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 27

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

A)$18,519
B)$45,762
C)$9,818
D)$20,000

Question 28

Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest.That bequest will provide $1000 in the first year,and will grow by 7% per year,forever.If the interest rate is 11%,how much must Martin provide to fund this bequest?

A)$9090.90
B)$14,285.71
C)$25,000.00
D)$36,687.45

Question 29

You are saving money to buy a car.If you save $300 per month starting one month from now at an interest rate of 4%,how much will you be able to spend on the car after saving for 4 years?

A)$41,778.96
B)$15,287.27
C)$15,587.88
D)$13,286.65

Question 30

Which of the following is true about perpetuities?

A)All else equal,the value of a perpetuity is higher when the periodic cash flow is higher.
B)All else equal,the value of a perpetuity is higher when the interest rate is lower.
C)If two perpetuities have the same present value and the same interest rate,they must have the same cash flows.
D)All of the above are true statements.

Question 31

An annuity pays $12 per year for 100 years.What is the present value (PV)of this annuity given that the discount rate is 8%?

A)$144.62
B)$146.63
C)$149.93
D)$151.45

Question 32

Which of the following is true about perpetuities?

A)Since a perpetuity generates cash flows every period infinitely,the cash flow generated equals the PV times the interest rate.
B)Since a perpetuity generates cash flows every period infinitely,each cash flow must be discounted to calculate the present value.
C)Since a perpetuity generates cash flows every period infinitely,there is no way to solve for the cash flow given the present value and the interest rate.
D)A perpetuity does not generate cash flows every period infinitely.

Question 33

An annuity pays $10 per year for 50 years.What is the future value (FV)of this annuity at the end of that 50 years given that the discount rate is 5%?

A)$182.56
B)$525.00
C)$845.25
D)$2093.48

Question 34

A perpetuity will pay $1000 per year,starting five years after the perpetuity is purchased.What is the future value (FV)of this perpetuity,given that the interest rate is 4%?

A)$1410
B)$20,582
C)$21,370
D)There is no solution to this problem.

Question 35

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 36

Cash flows from an annuity occur every year in the future.

Question 37

A growing perpetuity where the rate of growth is greater than the discount rate will have an infinitely large present value (PV).

Question 38

An annuity pays $50 per year for 20 years.What is the future value (FV)of this annuity at the end of those 20 years,given that the discount rate is 7%?

A)$326.44
B)$684.76
C)$1524.24
D)$2049.77

Question 39

Investment X and Investment Y are both growing perpetuities with initial cash flow of $100.Both investments have the same interest rate (r).The present value of Investment X is $5,000,while the present value of Investment Y is $4,000.Which of the following is true?

A)Investment X has a higher growth rate than Investment Y.
B)Investment X has a lower growth rate than Investment Y.
C)The answer cannot be determined without knowing the interest rate for both investments.
D)This makes no sense - with the same initial cash flow and the same interest rate Investment X and Investment Y should have the same present value.

Question 40

Clarissa wants to fund a growing perpetuity that will pay $5000 per year to a local museum,starting next year.She wants the annual amount paid to the museum to grow by 5% per year.Given that the interest rate is 8%,how much does she need to fund this perpetuity?

A)$62,500.00
B)$102,112.33
C)$143,445.65
D)$166,666.67

Question 41

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 42

Matthew wants to take out a loan to buy a car.He calculates that he can make repayments of $4000 per year.If he can get a five-year loan with an interest rate of 7.5%,what is the maximum price he can pay for the car?

A)$16,184
B)$18,243
C)$20,324
D)$21,674

Question 43

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

Question 44

Use the information for the question(s)below.
Assume that you are 30 years old today,and that you are planning on retirement 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 31st 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.Assume that the rate of interest is 7%.
The future value (FV)at retirement (age 65)of your savings is closest to:

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

Question 45

Use the information for the question(s)below.
Assume that you are 30 years old today,and that you are planning on retirement 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 31st 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.Assume that the rate of interest is 7%.
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 46

Use the information for the question(s)below.
Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child's college education.Currently,college tuition,books,fees,and other costs average $12,500 per year.On average,tuition and other costs have historically increased at a rate of 4% per year.
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 what is the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education?

Question 47

Trial and error is the only way to compute the internal rate of return (IRR)when interest is calculated over five or more periods.

Question 48

Use the information for the question(s)below.
Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child's college education.Currently,college tuition,books,fees,and other costs average $12,500 per year.On average,tuition and other costs have historically increased at a rate of 4% per year.
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 49

A bank is negotiating a loan.The loan can either be paid off as a lump sum of $100,000 at the end of five years,or as equal annual payments at the end of each of the next five years.If the interest rate on the loan is 10%,what annual payments should be made so that both forms of payment are equivalent?

A)$12,000
B)$16,380
C)$19,588
D)$20,000

Question 50

How do the growth perpetuity results differ with negative and positive growths of similar magnitude assuming everything else remains unchanged?

Question 51

Use the information for the question(s)below.
Assume that you are 30 years old today,and that you are planning on retirement 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 31st 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.Assume that the rate of interest is 7%.
The present value (PV)(at age 30)of your retirement savings is closest to:

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

Question 52

Can we apply the growth perpetuity equation for negative growth as well?

Question 53

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 54

A bank offers a home buyer a 25-year loan at 8% per year.If the home buyer borrows $120,000 from the bank,how much must be repaid every year?

A)$7896.45
B)$9845.89
C)$10,786.66
D)$11,241.45

Question 55

A rich donor gives a hospital $100,000 one year from today.Each year after that,the hospital will receive a payment 5% larger than the previous payment,with the last payment occurring in ten years' time.What is the present value (PV)of this donation,given that the interest rate is 9%?

A)$467,922.22
B)$585,987.27
C)$772,173.49
D)$779,843.27

Question 56

The internal rate of return (IRR)is the interest rate that sets the net present value (NPV)of the cash flows equal to zero

Question 57

Dan buys a property for $250,000.He is offered a 20-year loan by the bank,at an interest rate of 6% per year.What is the annual loan payment Dan must make?

A)$21,796.14
B)$24,864.98
C)$32,684.66
D)$64,486.34

Question 58

A businessman wants to buy a truck.The dealer offers to sell the truck for either $120,000 now,or six yearly payments of $25,000.Which of the following is closest to the interest rate being offered by the dealer?

A)5%
B)7%
C)9%
D)11%

Question 59

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 60

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

Question 61

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 62

What is the internal rate of return (IRR)of an investment that requires an initial investment of $10,000 today and pays $14,000 in one year's time?

A)4%
B)14%
C)24%
D)40%

Question 63

How long will it take $50,000 placed in a savings account at 10% interest to grow into $75,000?

A)4.25 years
B)5.00 years
C)5.25 years
D)5.50 years

Question 64

You are considering investing in a zero-coupon bond that will pay you its face value of $1000 in ten years.If the bond is currently selling for $485.20,then the internal rate of return (IRR)for investing in this bond is closest to:

A)12%
B)8.0%
C)7.5%
D)10%

Question 65

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 66

You are offered an investment opportunity that costs you $28,000,has a net present value (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 67

Faisal has $15,000 in his savings account and can save an additional $5000 per year.If interest rates are 12%,how long will it take his savings to grow to $50,000?

A)2 years
B)3 years
C)4 years
D)5 years