Deck 6: Discounted Cash Flows and Valuation

Question 1

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

Answer 1

False

Question 2

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

Answer 2

True

Question 3

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 3

False

Question 4

The APR is the annualised interest rate using compound interest.

Question 5

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 per cent every year forever. This is a growing perpetuity.

Question 6

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

Question 7

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

Question 8

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

Question 9

The EAR is the true cost of borrowing and lending.

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

A fertiliser manufacturing company enters into a contract with a county parks and recreation department that calls for the company to sell 10 per cent 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 18

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

Question 19

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.

Question 20

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

Question 21

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 22

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 23

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 per cent. 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 24

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 per cent 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 25

PV of multiple cash flows: Ferris Ltd has borrowed from their bank at a rate of 8 per cent 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 26

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

Question 27

In Australia, the National Consumer Credit Protection Act requires the bank and other credit providers to disclose to consumers the annual percentage rate (APR) charged on a loan.

Question 28

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 29

PV of multiple cash flows: Jack Stuart has loaned money to his brother at an interest rate of 5.75 per cent. 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 30

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 31

FV of multiple cash flows: Stiglitz Ltd 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 per cent, find the future value of these cash flows. (Round to the nearest dollar.)

A) $799,549
B) $732,114
C) $685,312
D) $900,810

Question 32

FV of multiple cash flows: International Shippers, Ltd, 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 per cent? (Round to the nearest dollar.)

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

Question 33

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

Question 34

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 35

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 36

PV of multiple cash flows: Ajax Company 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 per cent, 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 37

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 per cent 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

Question 38

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

Question 39

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 per cent, 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 40

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 41

Jenny Abel is investing $2,500 today and will do so at the beginning of another six years for a total of seven payments. Her investment can earn 12 per cent per year. i) How much will Jenny have at the end of seven years? (Round to the nearest dollar.)

A) $25,223
B) $28,249
C) $31,127
D) $29,460

Question 42

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

A) Amortisation refers to the way the borrowed amount (principal) is paid down over the life of the loan.
B) With an amortised loan, each loan payment contains some payment of principal and an interest payment.
C) With an amortised loan, a smaller proportion of each month's payment goes toward interest in the early periods.
D) A loan amortisation 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 43

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 44

Which one of the following inputs is not required to calculate the present value of an annuity?

A) level and equally spaced cash flow.
B) discount rate or interest rate.
C) number of periods.
D) all of the above are required.

Question 45

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 per cent, 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 46

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 per cent, 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 47

The annuity transformation method is used to transform

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

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

Which one of the following statements is true about amortisation?

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

Question 50

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

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

Question 51

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 per cent, 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 52

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 53

Present value of an annuity: Myers, Ltd, 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 per cent 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 54

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 per cent 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 55

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 per cent. 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 56

Future value of an annuity: Terri Garner will invest $3,000 in an investment account for the next 30 years. The investment will earn 13 per cent 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 57

Which ONE of the following statements is true about amortisation?

A) Amortisation refers to the way the borrowed amount (principal) is paid down over the life of the loan.
B) With an amortised loan, each loan payment contains some payment of principal and an interest payment.
C) A loan amortisation 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 58

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 per cent 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 59

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 per cent, 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 60

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 per cent 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 61

Perpetuity: Chris Collinge has funded a retirement investment with $250,000 earning a return of 5.75 per cent. What is the value of the payment that he can receive in perpetuity? (Round to the nearest dollar.)

A) $12,150
B) $15,250
C) $14,375
D) $14,900

Question 62

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 63

Growing annuity: Wilbon Company is evaluating whether it should take over the lease of an ethnic restaurant in Manhattan. The current owner had originally signed a 25-year lease, of which 16 years still remain. The restaurant has been growing steadily at a 7 per cent growth for the last several years. Wilbon Company expects the restaurant to continue to grow at the same rate for the remaining lease term. Last year, the restaurant brought in net cash flows of $310,000. If the firm evaluates similar investments at 15 per cent, what is the present value of this investment? (Round to the nearest dollar.)

A) $2,966.350
B) $2,838,182
C) $3,109,460
D) $2,709,124

Question 64

Annuity due: Mark Holcomb has a five-year loan on which he will make annual payments of $2,235, beginning now. If the interest rate on the loan is 8.3 per cent, what is the present value of this annuity? (Round to the nearest dollar.)

A) $9,588
B) $8,854
C) $8,612
D) $9,122

Question 65

Perpetuity: Jeff Conway wants to receive $25,000 in perpetuity and will invest his money in an investment that will earn a return of 13.5 per cent annually. What is the value of the investment that he needs to make today to receive his perpetual cash flow stream? (Round to the nearest dollar.)

A) $640,225
B) $252,325
C) $144,350
D) $185,185

Question 66

Perpetuity: A lottery winner was given a perpetual payment of $11, 444. She could invest the cash flows at 7 per cent. What is the present value of this perpetuity? (Round to the nearest dollar.)

A) $112,344
B) $163,486
C) $191,708
D) $201,356

Question 67

Your investment in a small business venture will produce cash flows that increase by 15 per cent 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 68

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 per cent, 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 69

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 investment account earning 8 per cent 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 per cent on any investment he makes. (Round to the nearest dollar.)

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

Question 70

Growing perpetuity: Norwood Investments is putting out a new product. The product will pay out $25,000 in the first year, and after that the payouts will grow by an annual rate of 2.5 per cent forever. If you can invest the cash flows at 7.5 per cent, how much will you be willing to pay for this perpetuity? (Round to the nearest dollar.)

A) $312,000
B) $233,000
C) $250,000
D) $500,000

Question 71

Annuity due: Your inheritance will pay you $100,000 a year for five years beginning now. You can invest it in a bank account that will pay 7.75 per cent annually. What is the present value of your inheritance? (Round to the nearest dollar.)

A) $399,356
B) $401,916
C) $433,064
D) $467,812

Question 72

Annuity due: You plan to save $1,400 for the next four years, beginning now, to pay for a vacation. If you can invest it at 6 per cent, how much will you have at the end of four years? Round to the nearest dollar.

A) $6,124
B) $5,618
C) $4,019
D) $6,492

Question 73

A firm receives a cash flow from an investment that will increase by 10 per cent 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 74

Computing annuity payment: Jackson Electricals has borrowed $27,850 from its bank at an annual rate of 8.5 per cent. It plans to repay the loan in eight equal instalments, beginning at the end of next 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 75

Growing annuity: Hill Enterprises is expecting tremendous growth from its newest boutique store. Next year the store is expected to bring in net cash flows of $675,000. The company expects its earnings to grow annually at a rate of 13 per cent for the next 15 years. What is the present value of this growing annuity if the firm uses a discount rate of 18 per cent on its investments? (Round to the nearest dollar.)

A) $6,448,519
B) $6,750,000
C) $7,115,449
D) $5,478,320

Question 76

Perpetuity: Roger Barkley wants to set up a scholarship at his alma mater. He is willing to invest $500,000 in an account earning 10 per cent. What will be the annual scholarship that can be given from this investment? (Round to the nearest dollar.)

A) $5,000
B) $500,000
C) $50,000
D) None of the above

Question 77

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 per cent 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 78

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 annualised 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 79

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 per cent, and the loan needs to be repaid in four years. 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 80

Growing perpetuity: Jack Benny is planning to invest in an insurance company product. The product will pay $10,000 at the end of this year. Thereafter, the payments will grow annually at a 3 per cent rate forever. Jack will be able to invest his cash flows at a rate of 6.5 per cent. What is the present value of this investment cash flow stream? (Round to the nearest dollar.)

A) $326,908
B) $312,766
C) $285,714
D) $258,133