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

Question 1

A perpetuity will pay $2 500 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 5%?

A)$41 096
B)$42 740
C)$47 429
D)$50 000

Answer 1

$42 740

Question 2

$12 500 is invested in a certain business at the start of a year, in return the investor will receive $3 000 at the end of each of the next five years. What is the net present value of this business opportunity if the interest rate is 5% per year?

A)$137.09
B)$443.88
C)$385.10
D)$488.43

Answer 2

$488.43

Question 3

A business promises to pay the investor of $2 000 today with a payment of $500 in one year's time, $1 000 in two years' time and $1 000 in three years' time. What is the net present value of this business opportunity if the interest rate is 5% per year?

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

Answer 3

$247.06

Question 4

Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 6.75%, then the present value (PV)of this stream of cash flows is closest to:

A)$21 864
B)$21 211
C)$23 474
D)$22 833

Question 5

A homeowner in Queensland has the opportunity to install a solar water heater in her home for a cost of $3 000. 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 8.5% per year.)

A)$255
B)$225
C)$267
D)$287

Question 6

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

Question 7

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

Question 8

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

Question 9

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)$1 626
B)$1 500
C)$1 288
D)$1 723

Question 10

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

A)$3 100
B)$2 909
C)$3 520
D)$3 200

Question 11

A lottery winner will receive $1 million at the end of each of the next ten years. What is the present value (PV)of her winnings at the time of her final payment, given that the interest rate is 8.75% per year?

A)$6.49 million
B)$6.94 million
C)$7.96 million
D)$6.56 million

Question 12

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

Question 13

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 14

Salvatore has the opportunity to invest in a scheme which will pay $5 000 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)$1 248.56
B)-$1 410.67
C)$2 643.73
D)-$112.23

Question 15

Ally wishes to leave a provision in her will that $2 000 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)$3 201.21
B)$42 000.00
C)$21 200.00
D)$33 333.33

Question 16

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)$7 200
B)$8 000
C)$2 400
D)$3 600

Question 17

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)$287
C)$460
D)$600

Question 18

Suppose you invest $1 000 into a managed fund that is expected to earn an annual rate of return of 10%. The amount of money you will 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)$2 594; $45 259
B)$3 138; $ 1 311 892
C)$2 594; $117 391
D)$386; $9

Question 19

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

Question 20

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 equal to the present value of cash flows in Investment B.
C)The present value of cash flows in Investment A is lower than 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 21

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)$31 559
B)$11 941 266
C)$30 774
D)$21 600

Question 22

An annuity pays $10 per year for 50 years. What is the present value (PV)of this annuity, given that the discount rate is 5%?

A)$182.56
B)$2 093.48
C)$185.65
D)$187.22

Question 23

Jasmine wants to fund a scholarship in honour of her parents that will pay $15 000 per year to a deserving student, starting next year. She wants the annual amount paid to the student to grow by 2% per year to keep up with student fee increases. Given that the interest rate she can earn on her investment is 6%, how much does she need to fund this perpetuity?

A)$375 000
B)$385 000
C)$357 850
D)$358 000

Question 24

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 lower growth rate than Investment Y.
B)Investment X has a higher 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 25

A perpetuity will pay $2 500 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 5%?

A)$41 096
B)$42 740
C)$47 429
D)There is no solution to this problem.

Question 26

If the current rate of interest is 8%, then the present value (PV)of an investment that pays $1 000 per year and lasts 20 years is closest to:

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

Question 27

Which of the following is true about perpetuities?

A)A perpetuity does not generate cash flows every period infinitely.
B)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.
C)Since a perpetuity generates cash flows every period infinitely, the cash flow generated equals the PV times the interest rate.
D)Since a perpetuity generates cash flows every period infinitely, each cash flow must be discounted to calculate the present value.

Question 28

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

Question 29

Since your first birthday, your grandparents have been depositing $1 000 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)$12 659
B)$36 465
C)$18 000
D)$25 645

Question 30

An annuity pays $12 per year for 100 years. What is the future value (FV)of this annuity at the end of those 100 years, given that the discount rate is 8%?

A)$329 814
B)$356 211
C)$389 241
D)$328 491

Question 31

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

Question 32

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

Question 33

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)$13 286.65
C)$13 067.62
D)$15 587.88

Question 34

An annuity is set up that will pay $1 500 per year for ten years. What is the present value (PV)of this annuity given that the discount rate is 6%?

A)$11 040
B)$8 441
C)$19 771
D)$14 721

Question 35

If the current rate of interest is 8%, then the future value (FV)of an investment that pays $1 000 per year and lasts 20 years is closest to:

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

Question 36

Which of the following statements regarding perpetuities is FALSE?

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

Question 37

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)$2 049.77
B)$1 524.24
C)$684.76
D)$326.44

Question 38

Which of the following is true about perpetuities?

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

Question 39

Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. That bequest will provide $1 000 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)$9 090.90
B)$25 000.00
C)$14 285.71
D)$36 687.45

Question 40

Which of the following statements regarding annuities is FALSE?

A)The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments.
B)Most car loans, mortgages, and some bonds are annuities.
C)PV of an annuity = C ×

D)An annuity is a stream of N equal cash flows paid at regular intervals.

Question 41

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

Question 42

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

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 university 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 $2 000 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 university expenses on her 18th birthday is closest to:

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

Question 44

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

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

Question 45

Assuming that university costs continue to increase an average of 4% per year and that all her university 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)$101 291
C)$107 532
D)$50 000

Question 46

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

Question 47

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

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

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

Question 51

A bank offers a home buyer a 30-year mortgage at 7% per year. If the home buyer borrows $225 000 from the bank, how much must be repaid every year?

A)$18 131.94
B)$19 307.27
C)$18 311.49
D)$13 907.72

Question 52

The present value (PV)(at age 30)of your superannuation investment is closest to:

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

Question 53

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

Question 54

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

Question 55

Which of the following formulas is INCORRECT?

A)PV of a growing annuity = C ×

B)PV of a growing perpetuity =
C)PV of an annuity = C ×

D)PV of a perpetuity =

Question 56

Matthew wants to take out a loan to buy a car. He calculates that he can make repayments of $4 000 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)$20 324
B)$21 674
C)$18 243
D)$16 184

Question 57

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 58

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 59

Assuming that university costs continue to increase at an average of 4% per year and that all her university 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 60

Which of the following statements regarding growing perpetuities is FALSE?

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

Question 61

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

A)$660
B)$2 536
C)$1 390
D)$2 585

Question 62

Faisal has $15 000 in his savings account and can save an additional $5 000 per year. If interest rates are 12%, how long will it take his savings to grow to $50 000?

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

Question 63

How long will it take $50 000 placed in a term deposit at 8% interest to double?

A)9.55 years
B)9.59 years
C)10.90 years
D)9.01 years

Question 64

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 three years' time?

A)11.87%
B)12.01%
C)11.78%%
D)10.02%

Question 65

You just took out a mortgage for $285 600. Your monthly payments are $1 279.29, you are being charged a rate of 0.29% on the outstanding balance per month, and you expect to pay everything back in 30 years. 5 years from now you will have the opportunity to renegotiate your mortgage, what will be the balance you owe at that time?

A)$244 899.25
B)$266 086.72
C)$257 085.22
D)$256 086.72

Question 66

You are offered an investment opportunity that costs you $28 000, has a net present value (NPV)of $2 278, lasts for three years, has an interest rate of 10%, and produces the following cash flows: The missing cash flow from year 2 is closest to:

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

Question 67

You recently bought a house for $357 000. You put 20% of your own money into it, and borrowed the rest. Assuming interest is charged at 0.29% per month and you plan to take 30 years to pay off the mortgage, your monthly mortgage payment is closest to:

A)$1 299.22
B)$1 279.29
C)$319.82
D)$1 599.11

Question 68

You are considering investing in a zero-coupon bond that will pay you its face value of $1 000 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)8.0%
B)7.5%
C)12%
D)10%

Question 69

You are interested in purchasing a new car 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 car and you take the dealer's financing deal, then your monthly car payments would be closest to:

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