Deck 6: Discounted Cash Flows and Valuation

Question 1

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

Answer 1

True

Question 2

The future value of the annuity due exceeds the future value of the ordinary annuity, but the present value of the annuity due is less than the present value of the ordinary annuity.

Answer 2

False

Question 3

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

Answer 3

True

Question 4

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

Question 5

Jacob Oram pays the same amount every month as insurance premium for a term life policy for a period of five years. The stream of cash flows is called a perpetuity.

Question 6

The present value of a perpetuity exceeds the present value of a 100-year ordinary annuity as long as the discount rate is positive.

Question 7

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

Question 8

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

Question 9

Allen Bell pays the same amount every month on a car loan for a period of three years. The stream of cash flows is called an annuity.

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

In calculating the present value or the future value of a cash flow stream one must either discount or compound the cash flows to the same point in time

Question 15

The future value of multiple cash flows is greater than the sum of those cash flows when the discount rate is zero.

Question 16

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

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

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

Question 19

Each cash flow is discounted or compounded at a same rate when calculating the present or future values of multiple cash flows.

Question 20

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

Question 21

The annual percentage rate (APR) is the annualized interest rate using compound interest.

Question 22

Credit card issuers are required to disclose the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 23.50%, with interest compounded monthly, the Effective Annual Interest Rate (EAR) is less than 23.50%.

Question 23

A growing annuity for an infinite number of periods is called a growing perpetuity.

Question 24

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

Question 25

Growing perpetuity is widely used in the valuation of common stock of firms that have a policy and history of paying dividends that grow at a constant rate.

Question 26

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

Question 27

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

Question 28

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

Question 29

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

Question 30

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 31

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 32

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

Question 33

Only the annual percentage rate (APR) or some other quoted rate should be used as the discount rate for present or future value calculations.

Question 34

For computation of the present value of growing annuity with n periods, the cash flow for the current period is used and not the cash flow to be received in the next period.

Question 35

The annual percentage rate (APR) is defined as the simple interest charged per period multiplied by the number of periods per year.

Question 36

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

Question 37

A car manufacturer enters into a contract for 25-years lease of warehouse rental that adjusts annually for the expected rate of inflation over the life of the contract. This is an example of growing perpetuity.

Question 38

The effective annual interest rate (EAR) is the true cost of borrowing and lending.

Question 39

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

Question 40

Natalia Greenberg opened a pizza place last year. She expects to increase her revenue from last year by 7 percent every year for the next 10 years. This is an example of a growing annuity.

Question 41

A "growing annuity" is a series of cash flows that grow at a constant rate for a specified number of periods.

Question 42

The present value of future cash flows are computed by multiplying future value with the:

A) discounting factor.
B) compound factor.
C) interest rate.
D) number of periods.

Question 43

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) higher or lower than the cash flows depending on the interest rate.

Question 44

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) higher or lower than the cash flows depending on the interest rate.

Question 45

Which of the following is true of the discounting factor?

A) The discounting factor is the reciprocal of compounding factor.
B) The discounting factor is the sum of 1 and the rate of interest.
C) The discounting factor is period n times the rate of interest.
D) The discounting factor is computed by dividing period n by the sum of 1 and the rate of interest.

Question 46

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) a growing perpetuity.

Question 47

Cash flows associated with annuities are considered to be:

A) an uneven cash flow stream.
B) a constant cash flow stream.
C) a mix of constant and uneven cash flow streams.
D) a cash flow stream with decreasing trend.

Question 48

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 49

A preferred stock would be an example of:

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

Question 50

The present value of a growing perpetuity is computed as the cash flow occurring at the end of the first period divided by the difference between the interest or discount rate and the growth rate.

Question 51

William deposited $25,000 today that would earn an interest at the rate of 3% for a period of 2 years. The amount of $25,000 represents the:

A) present value of an annuity
B) future value of an annuity
C) present value
D) future value

Question 52

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) a growing perpetuity.

Question 53

Which of the following is used as the denominator while calculating the present value for a growing perpetuity that begins next period (PVP)?

A) The difference between i (the discount or interest rate) and g (the constant rate of growth of the cash flow)
B) i (the discount or interest rate)
C) g (the constant rate of growth of the cash flow)
D) The addition of i (the discount or interest rate) and g (the constant rate of growth of the cash flow)

Question 54

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 55

Which of the following statements is true of amortization?

A) Amortization solely refers to the total value to be paid by the borrower at the end of maturity.
B) The amortization schedule represents only the interest portion of the loan.
C) The computation of loan amortization is wholly based on the computation of simple interest.
D) The amortization schedule provides principal, interest, and unpaid principal balance for each month.

Question 56

Which of the following statements is true of amortization?

A) With an amortized loan, a larger proportion of each month's payment goes toward interest in the early periods.
B) With an amortized loan, a larger 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) With an amortized loan, the interest portion of each month's payment remains unchanged.

Question 57

Nick invested $2,000 in a bank savings account today and another $2000 a year from now. If the bank pays interest of 10 percent per year, how much money will Nick have at the end of two years?

A) $4,210
B) $4,200
C) $4,000
D) $4,620

Question 58

Which of the following statements is true of amortization?

A) With an amortized loan, a periodic payment of principal portion gradually decreases over a period.
B) Amortization schedule represents only the interest portion of the loan.
C) With an amortized loan, a larger proportion of each month's payment goes toward interest in the early periods.
D) The computation of loan amortization is wholly based on the computation of simple interest.

Question 59

Anna will receive $15,000 from a bank deposit in 2 years which has an interest rate of 3.5%. The amount of $15,000 represents the:

A) present value of an annuity
B) future value of an annuity
C) present value
D) future value

Question 60

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 61

Which 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 rates that do not take compounding into account.
B) The EAR is the annualized interest rate using simple interest. It ignores the interest earned on interest associated with compounding periods of less than one year.
C) The EAR is the simple interest charged per period multiplied by the number of periods per year.
D) The EAR is the interest rate actually paid (or earned) after accounting for compounding.

Question 62

Helen Ashley 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) $414,454
C) $412,372
D) $434,599

Question 63

Global Shippers Inc. has forecasted earnings of $1,233,600, $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) 4,551,701
C) $3,900,865
D) $4,362,428

Question 64

Phosfranc Inc., is expecting the following cash flows starting at the end of the year-$133,245, $152,709, $161,554, and $200,760. If their opportunity cost of capital is 9.4 percent, find the future value of these cash flows. (Round to the nearest dollar.)

A) $734,731
B) $756,525
C) $734,231
D) $776,252

Question 65

Moore's 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 66

David Stephens 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 offer a return of 14 percent. What is the present value of these cash flows? (Round to the nearest dollar.)

A) $37,712
B) $36,022
C) $41,675
D) $39,208

Question 67

Ransport 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 68

Graciela Treadwell 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 least 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 69

Newship Inc. has borrowed from its bank at a rate of 8 percent and will repay the loan with interest over the next five years. Its 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) $2,989,351
C) $2,431,224
D) $2,815,885

Question 70

The true cost of borrowing is the:

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

Question 71

Robert White will receive cash flows of $4,450, $4,775, and $5,125from his investment. If he can earn 7 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) $15,329
B) $15,427
C) $16,427
D) $14,427

Question 72

Which of the following statements is true of annual percentage rate (APR)?

A) The APR is similar to the quoted interest rate, which is a simple annual rate.
B) The APR calculation adjusts for the effects of compounding and, hence, the time value of money.
C) The APR is the true cost of borrowing and lending.
D) The APR takes compounding into account.

Question 73

Nutech 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 of capital is 15 percent, what is the present value of these cash flows? (Round to the nearest dollar.)

A) $429,560
B) $485,097
C) $480,906
D) $477,235

Question 74

Which of the following statements is true of annual percentage rate (APR)?

A) The Truth-in-Savings Act was passed by Congress to ensure that the true cost of credit was disclosed to consumers.
B) The Truth-in-Lending Act was passed to provide consumers an accurate estimate of the return they would earn on an investment.
C) The Truth-in-Savings Act and Truth-in-Lending Act require by law that the APR be disclosed on all consumer loans and savings plans.
D) The annual percentage rate (APR), and not the effective annual interest rate (EAR), represents the true economic interest rate.

Question 75

What is the appropriate interest rate to use when making future value or present value calculations?

A) The effective annual interest rate (EAR)
B) The annual percentage rate (APR)
C) The quoted interest rate
D) The simple interest

Question 76

Scottie Barnes has an investment that will pay him $6,400, $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) $32,020
C) $30,455
D) $31,770

Question 77

The true cost of lending is the:

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

Question 78

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 79

Damien McCoy has loaned money to his brother at an interest rate of 5.85 percent. He expects to receive $987, $1,012, $1,062, and $1,162 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) $3,785
B) $3,757
C) $3,657
D) $3,685

Question 80

Ryan Campbell 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