Deck 6: Discounted Cash Flows and Valuation

Question 1

When you pay the same amount every month as your insurance premium for a term life policy for a period of five years, the stream of cash flows is called a perpetuity.

Answer 1

False

Question 2

Calculating the present and future values of multiple cash flows is relevant for businesses only.

Answer 2

False

Question 3

When you pay the same amount every month on your car loan for a period of three years, the stream of cash flows is called an annuity.

Answer 3

True

Question 4

In today's financial markets, the best example of a perpetuity is the common stock issued by firms.

Question 5

The present value of an annuity due is equal to the present value of an ordinary annuity.

Question 6

The present value of a perpetuity is the promised constant cash payment divided by the interest rate (i).

Question 7

In an annuity due, cash flows occur at the beginning of each period.

Question 8

The present value of multiple cash flows is greater than the sum of those cash flows.

Question 9

The future value of an annuity due is equal to the future value of an ordinary annuity.

Question 10

The future value of an annuity due is greater than the future value of an ordinary annuity.

Question 11

A fertilizer manufacturing company enters into a contract with a county parks and recreation department that calls for the company to sell 10 percent more of its best lawn feed every year for the next five years. If they also agree to maintain the total price as constant over the contract period, this growth in revenue is an example of a growing perpetuity.

Question 12

Cash flow streams that increase at a constant rate over time are called growing annuities or growing perpetuities.

Question 13

Calculating the present and future values of multiple cash flows is relevant only for individual investors.

Question 14

You have received news about an inheritance that will pay you $5,000 next year. Beginning the following year, your inheritance will increase by 5 percent every year forever. This is a growing perpetuity.

Question 15

In ordinary annuities, cash flows occur at the beginning of each period.

Question 16

In computing the present and future value of multiple cash flows, each cash flow is discounted or compounded at a different rate.

Question 17

Since the issuers of preferred stock promise to pay investors a fixed dividend, usually quarterly, forever, these are the most important perpetuities in the financial markets.

Question 18

The lease payments by a business on a warehouse rental are an example of an annuity due.

Question 19

The present value of an annuity due is less than the present value of an ordinary annuity.

Question 20

Trey Hughes opened a pizza place last year. He expects to increase his revenue from last year by 7 percent every year for the next 10 years. This is an example of a growing annuity.

Question 21

Which one of the following steps is NOT involved in solving future value problems?

A) First, draw a time line to make sure that each cash flow is placed in the correct time period.
B) Second, discount each cash flow for its time period.
C) Third, add up the values.
D) All of the above are necessary steps.

Question 22

If your investment pays the same amount at the end of each year for a period of six years, the cash flow stream is called

A) a perpetuity.
B) an ordinary annuity.
C) an annuity due.
D) none of the above.

Question 23

The effective annual interest rate (EAR) is defined as the annual growth rate that takes compounding into account.

Question 24

The quoted interest rate is by definition a simple annual interest rate, such as the EAR.

Question 25

Calculating the present and future values of multiple cash flows is relevant

A) for businesses only.
B) for individuals only
C) for both individuals and businesses.
D) none of the above.

Question 26

Which one of the following steps is NOT involved in solving present value problems?

A) First, draw a time line to make sure that each cash flow is placed in the correct time period.
B) Second, compound each cash flow for its time period.
C) Third, add up the values.
D) All of the above are necessary steps.

Question 27

The EAR is the true cost of borrowing and lending.

Question 28

The correct way to annualize an interest rate is to compute the annual percentage rate (APR).

Question 29

The APR is defined as the simple interest charged per period multiplied by the number of periods per year.

Question 30

In computing the present and future value of multiple cash flows,

A) earlier cash flows are discounted at a lower rate.
B) each cash flow is discounted or compounded at the same rate.
C) earlier cash flows are discounted at a higher rate.
D) none of the above.

Question 31

Only the APR or some other quoted rate should be used as the interest rate factor for present or future value calculations.

Question 32

To solve future value problems with multiple cash flows involves which of the following steps?

A) First, draw a time line to make sure that each cash flow is placed in the correct time period.
B) Second, calculate the future value of each cash flow for its time period.
C) Third, add up the future values.
D) All of the above are necessary steps.

Question 33

The future value of multiple cash flows is

A) greater than the sum of the cash flows.
B) equal to the sum of all the cash flows.
C) less than the sum of the cash flows
D) none of the above.

Question 34

To solve present value problems with multiple cash flows involves which of the following steps?

A) First, draw a time line to make sure that each cash flow is placed in the correct time period.
B) Second, calculate the present value of each cash flow for its time period.
C) Third, add up the present values.
D) All of the above are necessary steps.

Question 35

The APR is the annualized interest rate using compound interest.

Question 36

The present value of multiple cash flows is

A) greater than the sum of the cash flows.
B) equal to the sum of all the cash flows.
C) less than the sum of the cash flows.
D) none of the above.

Question 37

The Truth-in-Lending Act and the Truth-in-Savings Act require by law that the APR be disclosed on all consumer loans and savings plans and that it be prominently displayed on advertising and contractual documents.

Question 38

The quoted interest rate is by convention a simple annual interest rate, such as the APR.

Question 39

In computing the present and future value of multiple cash flows,

A) each cash flow is discounted or compounded at the same rate.
B) each cash flow is discounted or compounded at a different rate.
C) earlier cash flows are discounted at a higher rate.
D) later cash flows are discounted at a higher rate.

Question 40

The correct way to annualize an interest rate is to compute the effective annual interest rate.

Question 41

The true cost of lending is the

A) annual percentage rate.
B) effective annual rate.
C) quoted interest rate.
D) none of the above.

Question 42

Which one of the following statements is NOT true?

A) The Truth-in-Lending Act was passed by Congress to ensure that the true cost of credit was disclosed to consumers.
B) The Truth-in-Savings Act was passed to provide consumers an accurate estimate of the return they would earn on an investment.
C) The above two pieces of legislation require by law that the APR be disclosed on all consumer loans and savings plans.
D) All of the above are true statements.

Question 43

Cash flows associated with annuities are considered to be

A) an uneven cash flow stream.
B) a cash flow stream of the same amount (a constant cash flow stream).
C) a mix of constant and uneven cash flow streams.
D) none of the above.

Question 44

A firm receives a cash flow from an investment that will increase by 10 percent annually for an infinite number of years. This cash flow stream is called

A) an annuity due.
B) a growing perpetuity.
C) an ordinary annuity.
D) a growing annuity.

Question 45

The true cost of borrowing is the

A) annual percentage rate.
B) effective annual rate.
C) quoted interest rate.
D) periodic rate.

Question 46

The annuity transformation method is used to transform

A) a present value annuity to a future value annuity.
B) a present value annuity to an annuity due.
C) an ordinary annuity to an annuity due.
D) a perpetuity to an annuity.

Question 47

Which one of the following statements is TRUE about the effective annual rate (EAR)?

A) The effective annual interest rate (EAR) is defined as the annual growth rate that takes compounding into account.
B) The EAR conversion formula accounts for the number of compounding periods and, thus, effectively adjusts the annualized interest rate for the time value of money.
C) The EAR is the true cost of borrowing and lending.
D) All of the above are true.

Question 48

If your investment pays the same amount at the beginning of each year for a period of 10 years, the cash flow stream is called

A) a perpetuity.
B) an ordinary annuity.
C) an annuity due.
D) none of the above.

Question 49

PV of multiple cash flows: Jack Stuart has loaned money to his brother at an interest rate of 5.75 percent. He expects to receive $625, $650, $700, and $800 at the end of the next four years as complete repayment of the loan with interest. How much did he loan out to his brother? (Round to the nearest dollar.)

A) $2,713
B) $2,250
C) $2,404
D) $2,545

Question 50

Which one of the following statements is NOT true?

A) The APR is the appropriate rate to do present and future value calculations.
B) The EAR is the appropriate rate to do present and future value calculations.
C) The EAR is the true cost of borrowing and lending.
D) The EAR takes compounding into account.

Question 51

If your investment pays the same amount at the end of each year forever, the cash flow stream is called

A) a perpetuity.
B) an ordinary annuity.
C) an annuity due.
D) none of the above.

Question 52

Which ONE of the following statements is true about amortization?

A) Amortization refers to the way the borrowed amount (principal) is paid down over the life of the loan.
B) With an amortized loan, each loan payment contains some payment of principal and an interest payment.
C) A loan amortization schedule is just a table that shows the loan balance at the beginning and end of each period, the payment made during that period, and how much of that payment represents interest and how much represents repayment of principal.
D) All of the above are true.

Question 53

FV of multiple cash flows: Shane Matthews has invested in an investment that will pay him $6,200, $6,450, $7,225, and $7,500 over the next four years. If his opportunity cost is 10 percent, what is the future value of the cash flows he will receive? (Round to the nearest dollar.)

A) $27,150
B) $29,900
C) $30,455
D) $31,504

Question 54

FV of multiple cash flows: Tariq Aziz will receive from his investment cash flows of $3,125, $3,450, and $3, 800. If he can earn 7.5 percent on any investment that he makes, what is the future value of his investment cash flows at the end of three years? (Round to the nearest dollar.)

A) $11,120
B) $10,944
C) $10,812
D) $12,770

Question 55

Which one of the following statements is NOT true?

A) The correct way to annualize an interest rate is to compute the effective annual interest rate (EAR).
B) The APR is the annualized interest rate using simple interest.
C) The correct way to annualize an interest rate is to compute the annual percentage rate (APR).
D) You can find the interest rate per period by dividing the quoted annual rate by the number of compounding periods.

Question 56

Which one of the following statements is NOT true about amortization?

A) Amortization refers to the way the borrowed amount (principal) is paid down over the life of the loan.
B) With an amortized loan, each loan payment contains some payment of principal and an interest payment.
C) With an amortized loan, a smaller proportion of each month's payment goes toward interest in the early periods.
D) A loan amortization schedule is just a table that shows the loan balance at the beginning and end of each period, the payment made during that period, and how much of that payment represents interest and how much represents repayment of principal.

Question 57

FV of multiple cash flows: Stiglitz, Inc., is expecting the following cash flows starting at the end of the year-$113,245, $132,709, $141,554, and $180,760. If their opportunity cost is 9.6 percent, find the future value of these cash flows. (Round to the nearest dollar.)

A) $644,406.10
B) $732,114
C) $685,312
D) $900,810

Question 58

FV of multiple cash flows: International Shippers, Inc., have forecast earnings of $1, 233,400, $1,345,900, and $1,455,650 for the next three years. What is the future value of these earnings if the firm's opportunity cost is 13 percent? (Round to the nearest dollar.)

A) $4,214,360
B) $4,551,446
C) $3,900,865
D) $4,875,212

Question 59

Which one of the following statements is true about amortization?

A) With an amortized loan, a bigger proportion of each month's payment goes toward interest in the early periods.
B) With an amortized loan, a bigger proportion of each month's payment goes toward interest in the later periods.
C) With an amortized loan, a smaller proportion of each month's payment goes toward interest in the early periods.
D) None of the above.

Question 60

Your investment in a small business venture will produce cash flows that increase by 15 percent every year for the next 25 years. This cash flow stream is called

A) an annuity due.
B) a growing perpetuity.
C) an ordinary annuity.
D) a growing annuity.

Question 61

PV of multiple cash flows: Hassan Ali has made an investment that will pay him $11,455, $16,376, and $19,812 at the end of the next three years. His investment was to fetch him a return of 14 percent. What is the present value of these cash flows? (Round to the nearest dollar.)

A) $33,124
B) $36,022
C) $41,675
D) $39,208

Question 62

Computing annuity payment: Jackson Electricals has borrowed $27,850 from its bank at an annual rate of 8.5 percent. It plans to repay the loan in eight equal installments, beginning in a year. What is its annual loan payment? (Round to the nearest dollar.)

A) $4,708
B) $5,134
C) $4,939
D) $4,748

Question 63

Present value of an annuity: Lorraine Jackson won a lottery. She will have a choice of receiving $25,000 at the end of each year for the next 30 years, or a lump sum today. If she can earn a return of 10 percent on any investment she makes, what is the minimum amount she should be willing to accept today as a lump-sum payment? (Round to the nearest hundred dollars.)

A) $750,000
B) $334,600
C) $212,400
D) $235,700

Question 64

PV of multiple cash flows: Ferris, Inc., has borrowed from their bank at a rate of 8 percent and will repay the loan with interest over the next five years. Their scheduled payments, starting at the end of the year are as follows-$450,000, $560,000, $750,000, $875,000, and $1,000,000. What is the present value of these payments? (Round to the nearest dollar.)

A) $2,735,200
B) $2,615,432
C) $2431,224
D) $2,815,885

Question 65

Computing annuity payment: Jane Ogden wants to save for a trip to Australia. She will need $12,000 at the end of four years. She can invest a certain amount at the beginning of each of the next four years in a bank account that will pay her 6.8 percent annually. How much will she have to invest annually to reach her target? (Round to the nearest dollar.)

A) $3,000
B) $2,980
C) $2,538
D) $2,711

Question 66

Perpetuity: Your father is 60 years old and wants to set up a cash flow stream that would be forever. He would like to receive $20,000 every year, beginning at the end of this year. If he could invest in account earning 9 percent, how much would he have to invest today to receive his perpetual cash flow? (Round to the nearest dollar.)

A) $222,222
B) $200,000
C) $189,000
D) $235,200

Question 67

Present value of an annuity: Craymore Tech is expecting cash flows of $67,000 at the end of each year for the next five years. If the firm's discount rate is 17 percent, what is the present value of this annuity? (Round to the nearest dollar.)

A) $214,356
B) $241,653
C) $278,900
D) $197,776

Question 68

Computing annuity payment: Maricela Sanchez needs to have $25,000 in five years. If she can earn 8 percent on any investment, what is the amount that she will have to invest every year at the end of each year for the next five years? (Round to the nearest dollar.)

A) $5,000
B) $4,261
C) $4,640
D) $4,445

Question 69

Future value of an annuity: You plan to save $1,250 at the end of each of the next three years to pay for a vacation. If you can invest it at 7 percent, how much will you have at the end of three years? (Round to the nearest dollar.)

A) $3,750
B) $3,918
C) $4,019
D) $4,589

Question 70

Future value of an annuity: Carlos Menendez is planning to invest $3,500 every year for the next six years in an investment paying 12 percent annually. What will be the amount he will have at the end of the six years? (Round to the nearest dollar.)

A) $21,000
B) $28,403
C) $24,670
D) $26,124

Question 71

PV of multiple cash flows: Ajax Corp. is expecting the following cash flows-$79,000, $112,000, $164,000, $84,000, and $242,000-over the next five years. If the company's opportunity cost is 15 percent, what is the present value of these cash flows? (Round to the nearest dollar.)

A) $429,560
B) $414,322
C) $480,906
D) $477,235

Question 72

Computing annuity payment: John Harper has borrowed $17,400 to pay for his new truck. The annual interest rate on the loan is 9.4 percent, and the loan needs to be repaid in four payments. What will be his annual payment if he begins his payment beginning now? (Round to the nearest dollar.)

A) $5,229
B) $5,450
C) $4,850
D) $4,953

Question 73

Present value of an annuity: Myers, Inc., will be making lease payments of $3,895.50 for a 10-year period, starting at the end of this year. If the firm uses a 9 percent discount rate, what is the present value of this annuity? (Round to the nearest dollar.)

A) $23,250
B) $29,000
C) $25,000
D) $20,000

Question 74

Present value of an annuity: Herm Mueller has invested in a fund that will provide him a cash flow of $11,700 for the next 20 years. If his opportunity cost is 8.5 percent, what is the present value of this cash flow stream? (Round to the nearest dollar.)

A) $234,000
B) $132,455
C) $110,721
D) $167,884

Question 75

Future value of an annuity: Zhijie Jiang is saving to buy a new car in four years. She will save $5,500 at the end of each of the next four years. If she invests her savings at 6.75 percent, how much will she have after four years? (Round to the nearest dollar.)

A) $22,000
B) $23,345
C) $27,556
D) $24,329

Question 76

Future value of an annuity: Jayadev Athreya has started on his first job. He plans to start saving for retirement early. He will invest $5,000 at the end of each year for the next 45 years in a fund that will earn a return of 10 percent. How much will Jayadev have at the end of 45 years? (Round to the nearest dollar.)

A) $2,667,904
B) $3,594,524
C) $1,745,600
D) $5,233,442

Question 77

Computing annuity payment: Trevor Smith wants to have a million dollars at retirement, which is 15 years away. He already has $200,000 in an IRA earning 8 percent annually. How much does he need to save each year, beginning at the end of this year to reach his target? Assume he could earn 8 percent on any investment he makes. (Round to the nearest dollar.)

A) $13,464
B) $14,273
C) $10,900
D) $16,110

Question 78

Present value of an annuity: Transit Insurance Company has made an investment in another company that will guarantee it a cash flow of $37,250 each year for the next five years. If the company uses a discount rate of 15 percent on its investments, what is the present value of this investment? (Round to the nearest dollar.)

A) $101,766
B) $124,868
C) $251,154
D) $186,250

Question 79

Future value of an annuity: Terri Garner will invest $3,000 in an IRA for the next 30 years starting at the end of this year. The investment will earn 13 percent annually. How much will she have at the end of 30 years? (Round to the nearest dollar.)

A) $897,598
B) $912,334
C) $748,212
D) $1,233,450

Question 80

PV of multiple cash flows: Pam Gregg is expecting cash flows of $50,000, $75,000, $125,000, and $250,000 from an inheritance over the next four years. If she can earn 11 percent on any investment that she makes, what is the present value of her inheritance? (Round to the nearest dollar.)

A) $361,998
B) $309,432
C) $412,372
D) $434,599