Deck 4: The Time Value of Money Part 2

Question 1

A/An ________ is a series of equal end-of-the-period cash flows.

A) annuity
B) annuity due
C) perpetuity due
D) None of the above

Answer 1

A

Question 2

Elliot Industries invests a portion of its profits each year into a benefit emergency health care account for its employees. For the last five years it has invested year-end amounts of $50,000, $43,000, $26,000, $61,000, and $84,000. If the last deposit ($84,000) was made today and the account earns an average of 7.3% per year, how much money is currently in the account, assuming there have been no withdrawals?

Answer 2

Question 3

Johnson has an annuity due that pays $600 per year for 15 years. (Note: There are 15 annual cash flows with the first cash flow occurring today.) What is the value of the cash flows 14 years from today (immediately after the last deposit is made) if they are placed in an account that earns 7.50%?

A) $9,000.00
B) $9,675.00
C) $15,671.02
D) $16,846.35

Answer 3

C

Question 4

The future value three years from today of a $100 three-year annuity due compounded at a rate of 10% is equal to ________.

A) $300.00
B) $331.00
C) $364.10
D) $133.10

Question 5

The future value of a combination of positive and negative cash flows cannot be determined.

Question 6

Johnson has an annuity due that pays $600 per year for 15 years. What is the value of the cash flows 15 years from today if they are placed in an account that earns 7.50%? Note: You are asked to find the FV one year after the last cash flow is realized.

A) $9,000.00
B) $9,675.00
C) $15,671.02
D) $16,846.35

Question 7

You just won a lottery - CONGRATULATIONS! Your parents have always told you to plan for the future, so since you already have a well-paying job you decide to invest rather than spend your lottery winnings. The payment schedule from the lottery commission is $100,000 after taxes at end of year one and 19 more payments of exactly $100,000 after taxes in equal annual end-of-the-year deposits (i.e., the first of the next 19 deposits is one year from today) into your account paying 7% compounded annually. How much money will be in your account after the last deposit is made?

A) $2,000,000.00
B) $3,637,896.48
C) $4,099,549.23
D) $4,486,517.68

Question 8

Your department at work places $10,000 every year-end into an account earning 5%. The money is used when the corporate office fails to fully finance your profitable projects. The money has not been touched since a deposit was made exactly five years ago. If the most recent deposit was made today, how much money is currently in the account?

A) $55,256.31
B) $60,000
C) $65,256.31
D) $68,019.13

Question 9

Your employer has agreed to place year-end deposits of $1,000, $2,000 and $3,000 into your retirement account. The $1,000 deposit will be one year from today, the $2,000 deposit two years from today, and the $3,000 deposit three years from today. If your account earns 5% per year, how much money will you have in the account at the end of year three when the last deposit is made?

A) $5,357.95
B) $6,000
C) $6,202.50
D) $6,727.88

Question 10

Eastinghome Inc. just agreed to pay $8,000 today, $10,000 in one year, and $15,000 in two years to a landowner to explore for but not extract valuable minerals. If the landowner invests the money at a rate of 5.5% compounded annually, what is the investment worth two years from today?

Question 11

Your company just sold a product with the following payment plan: $50,000 today, $25,000 next year, and $10,000 the following year. If your firm places the payments into an account earning 10% per year, how much money will be in the account after collecting the last payment?

A) $99,000
B) $98,000
C) $88,500
D) $85,000

Question 12

When solving for the future value of a stream of unequal cash flows, it is important to add the values together BEFORE applying the future value formula to determine their future value.

Question 13

If for the next 40 years you place $3,000 in equal year-end-deposits into an account earning 8% per year, how much money will be in the account at the end of that time period?

A) $120,000.00
B) $777,169.56
C) $839,343.12
D) $2,606,942.58

Question 14

Given the following cash flows, what is the future value at year six when compounded at an interest rate of 8.0%?

A) $38,955.39
B) $56,687.43
C) $42,074.42
D) $$32,000.00

Question 15

Which of the following is NOT an example of annuity cash flows?

A) The university tuition bill you pay every month that is always the same
B) The grocery bill that changes every week
C) The $3.50 you pay every morning for a bagel and coffee as you run to your first morning class
D) All of the examples above are annuity cash flows.

Question 16

Which of the following is NOT an example of ordinary annuity cash flows?

A) Insurance payments due at the start of the period
B) Car loans due at the end of the period
C) Mortgage payments due at the end of the period
D) All of the examples above are ordinary annuity cash flows.

Question 17

You are saving money for a down payment on a new house. You intend to place $5,000 at the end of each year for three years into an account earning 6% per year. At the end of the fourth year, you will place $10,000 into this account. How much money will be in the account at the end of the fourth year?

A) $26,873.08
B) $26,518.17
C) $25,918.00
D) $25,000.00

Question 18

Which of the following is NOT an example of annuity cash flows?

A) Regular equal monthly rent payments
B) Equal annual deposits into a retirement account
C) The $50 of gasoline you put into your car every two weeks on pay day
D) All of the examples above are annuity cash flows.

Question 19

When solving for future value, we use the term compounding of cash flows rather than the term discounting of cash flows.

Question 20

Given the following cash flows, what is the future value at year ten when compounded at an interest rate of 12.0%?

A) $10,000.00
B) $25,267.31
C) $31,864.17
D) $11,948.32

Question 21

Which of the following is greater (answers rounded to the nearest cent)?

A) An ordinary annuity of $100.00 per year for three years discounted at 10% per year
B) A present value of $248.69
C) A future value of $331.00 three years from today, given an interest rate of 10% per year
D) You would be indifferent to the three choices since they all have the same present value when using an interest rate of 10% per year.

Question 22

Autorola plans to invest $5,000 per year in equal annual end-of-the-year amounts at an interest rate of 6% compounded annually. How much will the firm have at the end of four years?

Question 23

You estimate that the little drive-through coffee kiosk you own will generate ordinary annuity after-tax cash flows of $150,000 per year for the next ten years. If you discount these cash flows at an annual rate of 14%, what is the present value of your expected cash flows?

A) $782,417.35
B) $891,955.78
C) $1,500,000
D) $2,900,594.27

Question 24

A trend among universities is to guarantee tuition to incoming freshmen for a four-year period. Further, the annual amount due is collected in equal payments collected every three months. Although the payments are equal as well as equally spaced, this is NOT an example of an annuity because the payments are made every three months rather than on a monthly or annual basis.

Question 25

Which of the following choices will result in a greater future value at age 65? Choice number 1 is to invest $3,000 per year from ages 20 through 26 (a total of seven investments) into an account and then leave it untouched until you are 65 (another 39 years). Choice number 2 is to begin at age 27 and make $3,000 deposits into an investment account every year until you are 65 years old (a total of 39 investments). Each account earns an average of 10% per year. (The investments are end-of-year payments.)

A) Choice 1 is better than choice 2 because it has a FV of $1,304,146.89, which is greater than choice 2 FV of $1,204,343.33.
B) Choice 2 is better than choice 1 because it has a FV of $1,304,146.89, which is greater than choice 1 FV of $1,204,343.33.
C) Choice 2 is better than choice 1 because it has a FV of $1,204,343.33, which is greater than choice 1 FV of $1,171,042.63.
D) Choice 1 is better than choice 2 because it has a FV of $1,288,146.89, which is greater than choice 2 FV of $1,204,343.33.

Question 26

Even with an interest rate of 0.0%, the future value of a 5-year $800 annual annuity will be greater than the present value of the same annuity.

Question 27

Which is greater, the present value of a five-year ordinary annuity of $300 discounted at 10%, or the present value of a five-year ordinary annuity of $300 discounted at 0% that has its first cash flow six years from today?

A) The first annuity because the cash flows occur sooner.
B) The second annuity because the cash flows are discounted at a lower interest rate.
C) The two annuities are of equal value.
D) The answer to this question cannot be determined.

Question 28

The formula for the Future Value Interest Factor of an Annuity (FVIFA) is .

Question 29

What is the future value in year twelve of an ordinary annuity cash flow of $6,000 per year at an interest rate of 4.00% per year?

A) $90,154.83
B) $93,761.02
C) $28,675.97
D) $32,117.08

Question 30

Which is greater, the present value of a $1,000 five-year ordinary annuity discounted at 10%, or the present value of a $1,000 five-year annuity due discounted at 10%?

A) The ordinary annuity is worth more with a present value of $3,790.79.
B) The annuity due is worth more with a present value of $4,169.87.
C) The ordinary annuity is worth more with a present value of $4,169.87.
D) The annuity due is worth more with a present value of $4,586.85.

Question 31

You have the opportunity to purchase mineral rights to a property in North Dakota with expected annual cash flows of $10,000 per year for eight years. If you discount these cash flows at a rate of 12% per year, what are these cash flows worth today if the cash flows occur at the end of each period?

A) $55,637.57
B) $49,676.40
C) $80,000.00
D) $122,996.93

Question 32

You have an annuity of equal annual end-of-the-year cash flows of $500 that begin two years from today and last for a total of ten cash flows. Using a discount rate of 4%, what are those cash flows worth in today's dollars?

A) $3,899.47
B) $4,055.45
C) $4,380.24
D) $5,000.00

Question 33

The furniture store offers you no-money-down on a new set of living room furniture. Further, you may pay for the furniture in three equal annual end-of-the-year payments of $1,000 each with the first payment to be made one year from today. If the discount rate is 6%, what is the present value of the furniture payments?

A) $3,183.60
B) $3,000.00
C) $2,833.39
D) $2,673.01

Question 34

Twelve years ago, you paid for the right to twelve $25,000 annual end-of-the-year cash flows. If discounting the cash flows at an annual rate of 8%, what did you pay for these cash flows back then?

A) $$474,428.16
B) $300,000.00
C) $203,474.11
D) $188,401.95

Question 35

On your first through fifth birthdays your parents placed $2,000 into your college fund (five total deposits of $2,000 each). The account has earned an average of 8.0% per year until today, your twentieth birthday. How much money is in the account today?

A) $11,733.20
B) $37,219.70
C) $12,671.86
D) $25,383.41

Question 36

What is the future value in year twenty five of an ordinary annuity cash flow of $2,000 per year at an interest rate of 10.0% per year?

A) $66,505.81
B) $55,000.00
C) $196,694.12
D) $216,363.53

Question 37

Given positive equal annual cash flows and a positive interest rate, the future value of an annuity will be greater than the sum of the cash flows.

Question 38

Amy Plisko is 23 years old and plans to retire in 32 years when she is 55 years old. Amy just graduated from a university in the West. Upon graduation, she took a job with a starting annual salary of $50,000. Amy asks you to answer the following two questions:
1. If her salary increases at a rate roughly equal to the U.S. long-run average annual rate of inflation over the past 80 years (about 3% per year), how large will her annual salary be in her last year before retirement? (Use 32 years.)
2. If her salary increases at a rate roughly equal to the U.S. long-run average annual rate of return on common stocks over the past 80 years (about 10.5% per year), how large will her annual salary be in her last year before retirement? (Use 32 years.)
After hearing your answers, Amy says, "WOW ! That's quite a difference." She decides that she would like an income of $500,000 per year each year in retirement, provided in equal annual end-of-the-year cash flows. These cash flows need to last for 40 years, and her investments would earn an annual rate of return of 7% during her retirement.
Amy's final question to you is how much money must she save in equal annual end-of-the-year cash flows for the next 32 years to provide for her desired retirement, if her investments earn roughly the same rate of return as those earned by U.S. small stocks over the last 80 years (geometric average is about 12% per year).
Use a calculator to determine the answers to the different parts of the problem.

Question 39

Given positive equal annual cash flows and a positive interest rate, the present value of an annuity will be greater than the sum of the cash flows.

Question 40

What is the present value of a stream of annual end-of-the-year annuity cash flows if the discount rate is 0%, and the cash flows of $50 last for 20 years?

A) Less than $1,000
B) Exactly $1,000
C) More than $1,000
D) This question cannot be answered because we have an interest rate of 0.0%.

Question 41

What is the present value today of an ordinary annuity cash flow of $3,000 per year for forty years at an interest rate of 6.0% per year?

A) $120,000.00
B) $1,327,777.67
C) $45,139.89
D) $32,270.87

Question 42

What is the present value of a lottery paid as an annuity due for twenty years if the cash flows are $250,000 per year and the appropriate discount rate is 7.50%?

A) $5,000,000.00
B) $3,186,045.39
C) $2,739,769.55
D) $2,548,622.84

Question 43

You are paid to teach classes for the university and wonder how much money the university makes from your graduate-level classes. Based on historical data, you determine that your summer classes for the next seven years will generate an average annual revenue of $93,850. If you discount these cash flows at an annual rate of 8.30%, what is the present value of the expected cash flows?

A) $656,950.00
B) $845,133.52
C) $483,644.36
D) $523,786.85

Question 44

You are presented with two cash flow options: Option Near, a $5,000 annuity for three years, with the first cash flow one year from today, or Option Far, a $5,000 annuity for six years with the first cash flow ten years from today. Assuming an interest rate of 7.0%, which set of cash flows has a greater present value?

A) Option Near has a greater PV of $13,121.58 vs. Option Far PV of $12,963.41.
B) Option Far has a greater PV of $13,121.58 vs. Option Near PV of $12,963.41.
C) Option Far has a greater PV of $30,000 vs. Option Near PV of $15,000.
D) Option Near and Option Far have the same PV of $12,963.41.

Question 45

A series of equal periodic finite cash flows that occur at the beginning of the period are known as a/an ________.

A) ordinary annuity
B) annuity due
C) perpetuity
D) amortization

Question 46

By choosing to attend college today, you have agreed to pay $17,000 per year in tuition and fees for the next five years. (What… you really thought that you would graduate in four years?) In addition to the tuition and fees, you have also given up the ability to work full time and earn $23,000 per year for the next five years. If your required rate of return is 5% (the U.S. long-run average rate of inflation plus an average real rate of return), what is the total cost in today's dollars of your college degree, assuming that all of the aforementioned cash flows are ordinary annuities?

Question 47

You dream of endowing a chair in finance at the local university that will provide a salary of $150,000 per year forever, with the first cash flow to be one year from today. If the university promises to invest the money at a rate of 5% per year, how much money must you give the university today to make your dream a reality?

A) $3,000,000
B) $15,000,000
C) $2,857,143
D) This question cannot be answered.

Question 48

You have just won the Reader's Digest lottery of $5,000 per year for twenty years, with the first payment today followed by nineteen more start-of-the-year cash flows. At an interest rate of 5%, what is the present value of your winnings?

A) $100,000.00
B) $65,426.60
C) $62,311.05
D) $47,641.18

Question 49

What is the present value today of an ordinary annuity cash flow of $3,000 per year for forty years at an interest rate of 10.0% per year if the first cash flow is six years from today?

A) $120,000.00
B) $1,327,777.67
C) $45,138.89
D) $33,730.40

Question 50

Johnson has an annuity due that pays $600 per year for 15 years. What is the present value of the cash flows if they are discounted at an annual rate of 7.50%?

A) $5,296.27
B) $5,693.49
C) $9,000.00
D) $9,675.00

Question 51

Your neighbor owns a perpetuity of $100 per year that has a discount rate of 6% per year. He offers to sell to you all but the next 20 cash flows (the first to be received one year from today) for $500. In other words, he keeps the first 20 cash flows of his perpetuity and you get all of the rest. Is this a good price for you if the appropriate discount rate is 6%?

A) No, because the entire perpetuity is worth only $1,666.67 and your neighbor is taking the best cash flows worth more than $1,200 in present value terms
B) Yes, because the present value of the remaining cash flows is $519.68 and you are buying them for only $500.
C) No, because the cash flows you receive are only worth $482.16 and that is less than the $500 your neighbor is asking for the cash flows.
D) This question cannot be answered.

Question 52

When solving for present value, we use the term compounding of cash flows rather than the term discounting of cash flows.

Question 53

Your firm wishes to purchase a financial contract that provides equal end-of-the-year cash flows of $18,000 per year for the next seven years. What is the present value of these cash flows if you choose to discount them at a rate of 8% per year?

Question 54

The present value of a $100 three-year annuity due (first cash flow occurs today) discounted at a rate of 10% is equal to ________.

A) $248.69
B) $273.55
C) $135.17
D) $300.00

Question 55

You have just turned 25 and may now spend a portion of the trust fund your parents established for you. The terms of the trust fund allow you to withdraw 60 beginning-of-the-year cash flows of $100,000 each. An investment firm has offered to pay you cash for all of the fund today. If the rate they use to discount the cash flows is 16% per year, what is their offer price today for your pension fund?

A) $4,605,750,853
B) $6,000,000.00
C) $624,915.20
D) $724,901.63

Question 56

You have accumulated $800,000 for your retirement. How much money can you withdraw in equal annual beginning-of-the-year cash flows if you invest the money at a rate of 7% for thirty years?

A) $64,469.12
B) $60,251.52
C) $8,469.12
D) $9,061.96

Question 57

Given positive equal annual cash flows and a positive interest rate, the present value of an annuity will be greater than the sum of the cash flows.

Question 58

The formula for the Present Value Interest Factor of an Annuity (PVIFA) is .

Question 59

Which of the following is NOT a form of perpetuity?

A) A British consol bond
B) Preferred stock that pays the same dividend forever
C) A philanthropic endowment fund that pays the same charitable amount every year forever
D) All are examples of perpetuities.

Question 60

A never-ending stream of equal periodic, end-of-the-period cash flows is called a/an ________.

A) annuity
B) annuity due
C) perpetuity
D) amortization

Question 61

Home mortgage loans are commonly paid off by making equal monthly payments consisting of both interest and principal. This is an example of an amortized loan.

Question 62

Given a positive interest rate and a positive cash flow, an annuity due always has a greater present value than an ordinary annuity of the same size and number of cash flows.

Question 63

You sign a contract to pay back all of the interest and principal of a loan at the maturity date. This is an example of an interest-only loan.

Question 64

If you borrow $100,000 at an annual rate of 8.00% for a 10-year period and repay with 10 equal annual end-of-the-year payments of $14,902.95, then you have just repaid what type of loan?

A) Amortized loan
B) Interest-only loan
C) Discount loan
D) Compound loan

Question 65

A wealthy woman just died and left her pet cats the following estate: $50,000 per year for the next 15 years with the first cash flow today. At a discount rate of 3.2%, what is the feline estate worth in today's dollars?

A) $588,352.84
B) $607,180.14
C) $750,000.00
D) $774,000.00

Question 66

If you borrow $100,000 at an annual rate of 8.00% for a 10-year period and repay the total amount of principal and interest due of $215,892.50 at the end of 10 years, what type of loan did you have?

A) Amortized loan
B) Interest-only loan
C) Discount loan
D) Compound loan

Question 67

When you pay off the principal and all of the interest at one time at the maturity date of the loan, we call this type of loan a(n) ________.

A) amortized loan
B) interest-only loan
C) discount loan
D) compound loan

Question 68

Ordinary annuity payments occur at the beginning of the period, whereas annuity due payments occur at the end of the period.

Question 69

If you borrow $100,000 at an annual rate of 8.00% for a 10-year period and repay the interest of $8,000 at the end of each year prior to maturity and the final payment of $108,000 at the end of 10 years, then you have just repaid what type of loan?

A) Amortized loan
B) Interest-only loan
C) Discount loan
D) Compound loan

Question 70

Assume that you are 23 years old and that you place $3,000 year-end deposits each year into a stock index fund that earns an average of 9.5% per year for the next 17 years. How much money will be in the account at the end of 17 years? How much money will you have in the account 15 years later at age 55 if the account continues to earn 9.5% per year but you discontinue making new contributions? How much money would you have at the end of 17 years if you had made the same number of deposits but at the beginning of the year instead of at the end of the year? How much money will you have in the account 15 years later at age 55 if the account continues to earn 9.5% per year but you discontinued making new contributions?

Question 71

You have decided to endow the insert your name here Chair in Finance at the State University. How much money must you deposit into the endowment account today if the Chair pays $125,000 per year forever (first payment one year from today) and is invested at a rate that pays out 4.50% per year forever?

Question 72

What type of loan requires both principal and interest payments as you go by making equal payments each period?

A) Amortized loan
B) Interest-only loan
C) Discount loan
D) Compound loan

Question 73

What type of loan makes interest payments throughout the life of the loan and then pays the principal and final interest payment at the maturity date?

A) Amortized loan
B) Interest-only loan
C) Discount loan
D) Compound loan

Question 74

If you borrow $50,000 at an annual interest rate of 12% for six years, what is the annual payment (prior to maturity) on a discount loan?

A) $0.00
B) $6,000.00
C) $8,333.33
D) $12,161.29

Question 75

If you borrow $50,000 at an annual interest rate of 12% for six years, what is the annual payment (prior to maturity) on an interest-only type of loan?

A) $0.00
B) $6,000.00
C) $8,333.33
D) $12,161.29

Question 76

Given a positive interest rate and a positive cash flow, an ordinary annuity always has a greater present value than an annuity due of the same size and number of cash flows.

Question 77

You sign a contract to pay back all of the interest and principal of a loan at the maturity date. This is an example of a discount loan.

Question 78

If you borrow $50,000 at an annual interest rate of 12% for six years, what is the annual payment (prior to maturity) on a fully amortized loan?

A) $0.00
B) $6,000.00
C) $8,333.33
D) $12,161.29

Question 79

Given a positive interest rate and a positive cash flow, an ordinary annuity always has a greater future value than an annuity due of the same size and number of cash flows.

Question 80

A British consol bond can be considered a type of perpetuity.