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

Question 1

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

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

Answer 1

$11,040

Question 2

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.

Answer 2

Investment X has a higher growth rate than Investment Y.

Question 3

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

Answer 3

$11,699

Question 4

Which of the following statements regarding perpetuities is FALSE?

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

Question 5

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

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

Question 6

Which of the following statements regarding growing perpetuities is FALSE?

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

Question 7

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

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

Question 8

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

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

Question 9

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

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

Question 10

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

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

Question 11

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) $26,000
C) $24,074
D) $21,211

Question 12

Which of the following investments has a higher present value, assuming the same (strictlypositive) interest rate applies to both investments? $$\begin{array} { | c | c | c | } \hline \text { Year } & \text { Investment } \mathrm { X } & \text { Investment } \mathrm { Y } \\\hline 1 & \$ 5,000 & \$ 11,000 \\\hline 2 & \$ 7,000 & \$ 9,000 \\\hline 3 & \$ 9,000 & \$ 7,000 \\\hline 4 & \$ 11,000 & \$ 5,000 \\\hline\end{array}$$

A) Investment X and Investment Y have the same present value, since the total of the cash flows is the same for both.
B) Investment X has a higher present value.
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

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

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

Which of the following statements regarding annuities is FALSE?

A) Most car loans, mortgages, and some bonds are annuities.
B) An annuity is a stream of N equal cash flows paid at regular intervals.
C) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments.
$$\text { Di PV of an annuity } = C \times \frac { 1 } { r } \left( 1 - \frac { 1 } { ( 1 + r ) ^ { \mathrm { N } } } \right)$$

Question 19

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 equal to the present value of cash flows in Investment B.
B) The present value of cash flows in Investment A is higher than 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 20

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

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

Question 21

35? of this investment, given that the interest rate is 4% per year?

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

Question 22

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

Question 23

A homeowner in Queensland 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) $262
B) $240
C) $248
D) $216

Question 24

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) $151.45
C) $146.63
D) $149.93

Question 25

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

Question 26

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) $3200
C) $3100
D) $3520

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) $20,000
B) $18,519
C) $45,762
D) $9818

Question 28

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) $1626
C) $1288
D) $1500

Question 29

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

Question 30

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

Question 31

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

Question 32

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) 11%
C) 5%
D) 7%

Question 33

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 net present value of this business opportunity if the interest rate is 7% per year?

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

Question 34

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

Question 35

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

Question 36

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

Question 37

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) $1390
B) $660
C) $2585
D) $2536

Question 38

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

Question 39

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, each cash flow must be discounted to calculate the present value.
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, there is no way to solve for the cash flow given the present value and the interest rate.

Question 40

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

Question 41

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) $25,000.00
C) $14,285.71
D) $36,687.45

Question 42

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

Question 43

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

Question 44

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 45

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

Question 46

Suppose you invest $1000 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) $3138; $ 1,311,892
B) $2594; $45,259
C) $2594; $117,391
D) $386; $9

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

Question 48

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) $2093.48
C) $525.00
D) $845.25

Question 49

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

Question 50

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) If two perpetuities have the same present value and the same interest rate, they must have the same cash flows.
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 51

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 52

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

Question 53

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 university education. Currently, 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 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 54

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

Question 55

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

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

You are offered an investment opportunity that costs you $28,000, has a net present value (NPV) of $2278, 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) $10,000
B) $12,000
C) $12,500
D) $13,000

Question 58

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

Question 59

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) $18,000
C) $36,465
D) $12,659