Deck 4: The Time Value of Money

Question 1

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

Answer 1

False

Question 2

What is the PV of an investment that will pay you $1,500 every year,forever,starting in one year's time,if the interest rate is 8%?

A) $18,750
B) $1,500
C) $15,000
D) $25,000
E) $12,000

Answer 2

$18,750

Question 3

When evaluating investment opportunities,we can compare and combine cash flows that occur at different points in time.

Answer 3

False

Question 4

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) Investment Y has half the present value of Investment X.
E) No comparison can be made - we need to know the interest rate to calculate the present value.

Question 5

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) $20,548
D) $34,604
E) $25,000

Question 6

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
E) $19,111

Question 7

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

Question 8

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
E) $220

Question 9

Suppose the current interest rate is 8.5%,what is the future value of a $15 million investment in 10 years?

A) $16.275 million
B) $33.915 million
C) $17.858 million
D) $150 million
E) $15 million

Question 10

Jessica deposits her $2,500 bonus cheque into the bank at the end of 2015.At the end of 2016 ,she deposits another bonus cheque,which is double the amount of last year's cheque.Given that the interest rate is 5%,what is the total future value of these two bonuses at the end of 2017?

A) $7625
B) $8406.56
C) $7875
D) $7,500
E) $8,006.25

Question 11

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) The present value of cash flows in Investment A is half the present value of cash flows in Investment B.
E) No comparison can be made - we need to know the cash flows to calculate the present value.

Question 12

What is the total future value of these cash flows in year 4,given that the interest rate is 10%?

A) $80,000
B) $65,134.35
C) $117,128
D) $95,363.20
E) $75,363.20

Question 13

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
E) $13,605

Question 14

Given that the interest rate is 10% per annum,what is the present value of an investment that has 5 equal payments of $50,000 each year for 5 years,starting today?

A) $250,000
B) $25,000
C) $208,493.27
D) $158,493.27
E) $ 178,493.27

Question 15

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
E) $2007

Question 16

To calculate the future value of an annuity,we divide the annuity formula by the appropriate discount factor.

Question 17

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 18

An investor receives $250,000 at the end of each of the next 5 years.What is the present value of her investment,given that the interest rate is 5%?

A) $1,082,369.17
B) $1,250,000
C) $979,407.71
D) $1,332,369.17
E) $1,000,000

Question 19

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
E) $410

Question 20

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%.
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 21

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) $25,000
E) There is no solution to this problem.

Question 22

You are saving money for the down payment on a house.If you can save $7,500 per year for the next five years at an interest rate of 8%,how much will you have saved at the end of five years?

A) $40,500
B) $37,500
C) $44,000
D) $29,945
E) $93,750

Question 23

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
E) $15,287.27

Question 24

An annuity will pay you $1,000 per year for 30 years.What is the FV of this annuity at the end of 30 years,if your cost of capital is 3%?

A) $47,575
B) $19,600
C) $30,131
D) $30,000
E) $30,900

Question 25

Jason buys a consol (perpetual bond)that pays out a fixed cash flow of $750,000 every year,forever,starting at the end of this year.If the current market rate is 12.5%,what is the present value of the cash flows?

A) $6,000,000
B) $750,000
C) $843,750
D) $600,000
E) $7,500,000

Question 26

An annuity will pay you $12,000 per year for 20 years.What is the PV of this annuity if your cost of capital is 7%?

A) $224,299
B) $240,000
C) $127,128
D) $491,946
E) $238,245

Question 27

Anya finally decides that she will give her cousin,Zen,the loan he requested. He is expected to pay Anya $12,500 each year for the next 5 years,starting at the end of this year.The loan interest rate at the bank is 5% but because he is family,she will only charge him half of this interest rate.What is the current value of this loan,today?

A) $58,072.86
B) $500,000
C) $62,500
D) $54,118.46
E) $55,240.89

Question 28

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
E) $10,016

Question 29

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
E) $50,645

Question 30

Jackie & her husband started a savings account for their twin daughters when they were 2 years old.They have been saving $100,000 a year at an interest rate of 10%,and intend on keeping up with their annual contribution to the fund until the girls are 21.What is the future value of their investment?

A) $864,869.43
B) $836,492.01
C) $5,115,909.05
D) $6,400,249.94
E) $2,090,000

Question 31

James is a law student who wishes to understand how a perpetuity works.His grandfather invested in a perpetual bond 25 years ago,which pays $15,000 annually at a 12% interest rate.What was the present value of the cash flows of this perpetuity when it was purchased?

A) $84,753.35
B) $150,000
C) $125,000
D) $133,928.57
E) $16,800

Question 32

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) $9818
D) $20,000
E) $10,016

Question 33

An annuity will pay you $5,000 per year for 25 years.What is the FV of this annuity at the end of 25 years,if your interest rate is 8%?

A) $126,207
B) $365,530
C) $125,000
D) $135,000
E) $53,374

Question 34

An annuity will pay you $1,000 per year for 75 years.What is the PV of this annuity if your cost of capital is 4%?

A) $25,000
B) $72,115
C) $75,000
D) $23,680
E) $24,038

Question 35

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
E) $15,939.84

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) $11,941,266
B) $31,559
C) $30,774
D) $21,600
E) $31,764

Question 37

JJ & Co has decided to donate money to a cancer research fund every year for the next 25 years.They will make annual payments of $3.5 million.What is the present value of their donation if the current market rate is 7.5%?

A) $87.5 million
B) $14.3 million
C) $33.33 million
D) $46.7 million
E) $39.0 million

Question 38

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
E) $20,000

Question 39

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.
E) Since a perpetuity generate cash flows every period infinitely, the cash flow generated equals the PV divided by the interest rate.

Question 40

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 lower.
B) All else equal, the value of a perpetuity is higher when the interest rate is higher.
C) If two perpetuities have the same present value and the same interest rate, they must have the same cash flows.
D) All else equal, the value of a perpetuity is lower when the interest rate is lower.
E) If two perpetuities have the same cash flows, they must have the same present value.

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

What is the difference between a perpetuity and an annuity?

Question 43

The timeline below shows a $10,000 dollar investment that is being compounded at a set rate per year.What is that rate?

A) 11.25%
B) 12.50%
C) 15.00%
D) 18.50%
E) 16.25%

Question 44

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
E) $14,000

Question 45

The present value of an annuity that pays $1 million per year for n years,is $9 million.If the interest rate is 5% per annum,n is approximately equal to how many years?

A) 45 years
B) 8 years
C) 11 years
D) 16.5 years
E) 12.25 years

Question 46

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 47

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
E) $1868

Question 48

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
E) $5,184.00

Question 49

Can we apply the annuity or perpetuity equations to cash flows that do not arrive at regular intervals?

Question 50

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%
E) 8%

Question 51

What is the interest rate of an investment that pays $65 million next year with a current value of $58 million?

A) 15.07%
B) 10.77%
C) 1.207%
D) 1.12%
E) 12.07%

Question 52

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) years
B) 3 years
C) years
D) 5 years
E) 4 years

Question 53

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%
E) 9%

Question 54

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
E) 4.75 years

Question 55

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%
E) 33%

Question 56

Joey buys a bond for $10,000 that will mature in 25 years.He will receive a single payment of $150,000 when the bond reaches maturity.What is the interest rate?

A) 15%
B) 11.44%
C) 114.4%
D) 6.67%
E) 10%

Question 57

A consol bond (perpetual bond)pays $27,500 every year.If its present value is $3,000,000,what is the interest rate?

A) 9.17%
B) 3%
C) 0.275%
D) 0.917%
E) 2.75%

Question 58

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
E) $789

Question 59

An investor receives X dollars at the end of each of the next 3 years.If the present value of her investment is $10 million,what is her yearly cash flow,given that the interest rate is 5%?

A) $3.672 million
B) $3.33 million
C) $2.5 million
D) $2.879 million
E) $3.472 million

Question 60

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
E) $13,250.00

Question 61

AB Company has decided to donate to the children's hospital every year.The company 's first payment will be $1 million and it will grow at a constant rate of 3% forever.What is the present value of this growing perpetuity if the current market rate is 5%?

A) $150 million
B) $20 million
C) $33.33 million
D) $53.33 million
E) $50 million

Question 62

What is the future value of this annuity?

A) $243,145.35
B) $200,000
C) $181,692.35
D) $168,494.55
E) $238,301.70

Question 63

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
E) $100,000.00

Question 64

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

Question 65

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) $87,003
B) $108,000
C) $46,600
D) $75,230
E) $88,741

Question 66

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) Investment X has the same growth rate as Investment Y.
D) The answer cannot be determined without knowing the interest rate for both investments.
E) 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 67

A growing perpetuity' with a first payment of $17,500 grows at a constant rate,g.If the present value of this perpetuity is $1,000,000,what is the growth rate of the cash flows,given that the interest rate is 6%?

A) 1.75%
B) 6%
C) 6.75%
D) 4.25%
E) 10.75%

Question 68

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
E) $1,120,727.79

Question 69

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
E) $85,790

Question 70

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

Question 71

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) $41,667
E) This problem cannot be solved.

Question 72

Mark invests in a 10-year annuity with an initial payment of $20,000,that grows at 4% per year. What is the future value of this annuity,if the interest rate is 8%?

A) $200,000
B) $339,340.36
C) $157,180.24
D) $162,217.92
E) $350,216.31

Question 73

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 74

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

Question 75

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) $9090.91
B) $14,285.71
C) $25,000.00
D) $36,687.45
E) $5555.56

Question 76

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
E) $1,013,783

Question 77

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

Question 78

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

Question 79

A perpetuity with a first payment of $500 grows at a constant rate of 5%.If the interest rate is 7%,what is the Present Value of this perpetuity?

A) $10,000
B) $25,000
C) $7,142.86
D) $4,166.67
E) $50,000

Question 80

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.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
E) $50,000