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

Question 1

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)$10,114
B)$20,227
C)$24,272
D)$32,363

Answer 1

$20,227

Question 2

A perpetuity has a PV of $20,000. If the interest rate is 6%, how much will the perpetuity pay every year?

A)$600
B)$960
C)$1200
D)$720

Answer 2

$1200

Question 3

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

Answer 3

True

Question 4

A business promises to pay the investor of $6000 today for a payment of $1500 in one year's time, $3000 in two years' time, and $3000 in three years' time. What is the present value of this business opportunity if the interest rate is 6% per year?

A)$603.94
B)$301.97
C)$724.73
D)$966.30

Question 5

What is the present value (PV)of an investment that will pay $500 in one year's time, and $500 every year after that, when the interest rate is 10%?

A)$2500
B)$4000
C)$3000
D)$5000

Question 6

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 7

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?

Question 8

An investment pays you $30,000 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 5% per year?

A)$39,614
B)$63,382
C)$79,228
D)$95,074

Question 9

Suppose you invest $1000 into a mutual fund that is expected to earn a rate of return of 11%. 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)$1420; $110,739
B)$2271; $166,109
C)$2839; $184,565
D)$3123; $221,478

Question 10

If $8000 is invested in a certain business at the start of the year, the investor will receive $2400 at the end of each of the next four years. What is the present value of this business opportunity if the interest rate is 6% per year?

A)$158.13
B)$316.25
C)$379.50
D)$506.00

Question 11

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)$1,500
C)$2068
D)$2757

Question 12

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)$242
B)$581
C)$484
D)$774

Question 13

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 14

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)$5850
C)$14,039
D)$18,718

Question 15

A homeowner in a sunny climate has the opportunity to install a solar water heater in his home for a cost of $2900. 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 5% per year.)

A)$145
B)$160
C)$175
D)$190

Question 16

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 17

A lottery winner will receive $6 million at the end of each of the next twelve years. What is the future value (FV)of her winnings at the time of her final payment, given that the interest rate is 8.6% per year?

A)$94.40 million
B)$118.00 million
C)$165.20 million
D)$188.80 million

Question 18

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 3%?

A)-$3189.80
B)-$5907.57
C)5907.57
D)$3189.80

Question 19

A perpetuity will pay $900 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 11%?

A)$2695
B)$4312
C)$5390
D)$3234

Question 20

Ally wishes to leave a provision in her will that $7000 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)$58,334
B)$93,334
C)$116,667
D)$70,000

Question 21

Clarissa wants to fund a growing perpetuity that will pay $10,000 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 9%, how much does she need to fund this perpetuity?

A)$125,000.00
B)$200,000.00
C)$300,000.00
D)$250,000.00

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 9%?

A)$5776
B)$9626
C)$11,551
D)$13,476

Question 23

A perpetuity will pay $1000per year, starting five years after the perpetuity is purchased. What is the future value (FV)of this perpetuity, given that the interest rate is 3%?

A)$1456
B)$19,867
C)$21,320
D)There is no solution to this problem.

Question 24

If the current rate of interest is 7%, then the future value (FV)of an investment that pays $1200 per year and lasts 18 years is closest to ________.

A)$24,479
B)$40,799
C)$48,959
D)$57,119

Question 25

An annuity pays $13 per year for 53 years. What is the future value (FV)of this annuity at the end of that 53 years given that the discount rate is 9%?

A)$8258.91
B)$16,517.82
C)$19,270.79
D)$13,764.85

Question 26

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, initial cash outflow 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 using the present value and the interest rate.
D)Since a perpetuity generates cash flows every period infinitely, its FV is the same as its PV.

Question 27

An annuity pays $47 per year for 22 years. What is the future value (FV)of this annuity at the end of those 22 years, given that the discount rate is 8%?

A)$1563.88
B)$3127.76
C)$3649.06
D)$2606.47

Question 28

Investment X and Investment Y are both growing perpetuities with initial cash flow of $100. Both investments have the same interest rate (r)and cash flows. 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)With the same initial cash flow and the same interest rate, Investment X and Investment Y should have the same present value.

Question 29

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 30

You are saving money to buy a car. If you save $310 per month starting one month from now at an interest rate of 6%, how much will you be able to spend on the car after saving for 4 years?

A)$10,062.20
B)$20,124.40
C)$16,770.33
D)$23,478.46

Question 31

You are borrowing money to buy a car. If you can make payments of $320 per month starting one month from now at an interest rate of 12%, how much will you be able to borrow for the car today if you finance the amount over 4 years?

A)$7291.00
B)$14,582.00
C)$17,012.34
D)$12,151.67

Question 32

An annuity pays $10 per year for 98 years. What is the present value (PV)of this annuity given that the discount rate is 7%?

A)$85.60
B)$171.20
C)$142.67
D)$199.74

Question 33

Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. That bequest will provide $4000 in the first year, and will grow by 7% per year, forever. If the interest rate is 9%, how much must Martin provide to fund this bequest?

A)$100,000.00
B)$160,000.00
C)$200,000.00
D)$240,000.00

Question 34

If the current rate of interest is 8%, then the present value (PV)of an investment that pays $1200 per year and lasts 24 years is closest to ________.

A)$7581
B)$15,162
C)$12,635
D)$17,689

Question 35

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

Question 36

Which of the following is true about perpetuities?

A)All else equal, the present value of a perpetuity is higher when the periodic cash flow is higher.
B)All else equal, the present 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 37

Since your first birthday, your grandparents have been depositing $100 into a savings account every month. The account pays 9% 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)$32,181
B)$53,635
C)$64,362
D)$75,089

Question 38

Which of the following statements regarding perpetuities is FALSE?

A)To find the value of a perpetuity by discounting 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 39

Since your first birthday, your grandparents have been depositing $1200 into a savings account on every one of your birthdays. The account pays 6% 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)$37,086.78
B)$22,252.07
C)$44,504.14
D)$51,921.49

Question 40

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

Question 41

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 42

A bank is negotiating a loan. The loan can either be paid off as a lump sum of $80,000 at the end of four years, or as equal annual payments at the end of each of the next four years. If the interest rate on the loan is 6%, what annual payments should be made so that both forms of payment are equivalent?

A)$14,630
B)$18,287
C)$25,602
D)$29,259

Question 43

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 44

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 45

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 46

Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $40,000 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 10%. The future value (FV)at retirement (age 65)of your savings is closest to ________.

A)$722,766
B)$1,445,531
C)$1,011,872
D)$1,590,084

Question 47

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 9%. The parents deposit $2400 on their daughter's first birthday and plan to increase the size of their deposits by 7% 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)$80,232
B)$160,463
C)$112,324
D)$176,509

Question 48

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

Question 49

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

Question 50

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

Question 51

Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $42,000 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 9%. The present value (PV)(at age 30)of your retirement savings is closest to ________.

A)$61,303
B)$30,652
C)$42,912
D)$67,433

Question 52

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)5.8%
B)6.8%
C)7.8%
D)9.8%

Question 53

Matthew wants to take out a loan to buy a car. He calculates that he can make repayments of $5000 per year. If he can get a four-year loan with an interest rate of 7.9%, what is the maximum price he can pay for the car?

A)$16,598
B)$19,918
C)$23,237
D)$26,557

Question 54

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 55

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 7% per year forever. If the appropriate interest rate is 3%, then the value of this mining operation is closest to ________.

A)$100,000
B)$500,000
C)$250,000
D)This problem cannot be solved.

Question 56

A bank offers a home buyer a 20-year loan at 8% per year. If the home buyer borrows $130,000 from the bank, how much must be repaid every year?

A)$15,888.95
B)$18,537.11
C)$21,185.26
D)$13,240.79

Question 57

A rich donor gives a hospital $1,040,000 one year from today. Each year after that, the hospital will receive a payment 6% 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 11%?

A)$3,840,628.87
B)$5,376,880.42
C)$6,913,131.97
D)$7,681,257.74

Question 58

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

Question 59

Dan buys a property for $210,000. He is offered a 30-year loan by the bank, at an interest rate of 8% per year. What is the annual loan payment Dan must make?

A)$18,653.76
B)$22,384.51
C)$26,115.26
D)$29,846.02

Question 60

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 $12,000 per year. On average, tuition and other costs have historically increased at a rate of 5% per year. Assuming that college costs continue to increase an average of 5% per year and that all her college savings are invested in an account paying 8% 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)$110,793
B)$55,397
C)$77,555
D)$132,952

Question 61

You are considering purchasing a new home. You will need to borrow $290,000 to purchase the home. A mortgage company offers you a 20-year fixed rate mortgage (240 months)at (1% month). If you borrow the money from this mortgage company, your monthly mortgage payment will be closest to ________.

A)$2554
B)$4470
C)$3193
D)$5109

Question 62

You are interested in purchasing a new automobile that costs $33,000. The dealership offers you a special financing rate of (0.75% per month)for 60 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)$548
B)$685
C)$959
D)$1096

Question 63

You are considering investing in a zero-coupon bond that will pay you its face value of $1000 in twelve years. If the bond is currently selling for $496.97, then the internal rate of return (IRR)for investing in this bond is closest to ________.

A)5.0%
B)7.1%
C)6.0%
D)8.2%

Question 64

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)3.25 years
C)5.25 years
D)6.25 years

Question 65

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 66

Faisal has $12,000 in his savings account and can save an additional $3600 per year. If interest rates are 12%, how long will it take his savings to grow to $47,000?

A)4.3 years
B)6.3 years
C)5.3 years
D)7.3 years

Question 67

What is the internal rate of return (IRR)of an investment that requires an initial investment of $11,000 today and pays $15,400 in one year's time?

A)37%
B)44%
C)43%
D)40%