Deck 2: How to Calculate Present Values

Question 1

The one-year discount factor,at a discount rate of 25% per year,is:

A)1.25.
B)1.0.
C)0.8.
D)0.75.

Answer 1

0.8.

Question 2

If the present value of $250 expected one year from today is $200,what is the one-year discount rate?

A)10%
B)20%
C)25%
D)30%

Answer 2

25%

Question 3

What is the present value of the following cash flows at a discount rate of 9%?

A)$372,431.81
B)$450,000.00
C)$405,950.68
D)$412,844.04

Answer 3

$372,431.81

Question 4

If the present value of $480 to be paid at the end of one year is $400,what is the one-year discount factor?

A)0.8333
B)1.20
C)0.20
D)1.00

Question 5

An initial investment of $400,000 is expected to produce an end-of-year cash flow of $480,000.What is the NPV of the project at a discount rate of 20%?

A)$176,000
B)$80,000
C)$0 (zero)
D)$64,000

Question 6

The present value of $100,000 expected at the end of one year,at a discount rate of 25% per year,is:

A)$80,000.
B)$125,000.
C)$100,000.
D)$75,000.

Question 7

Present value is defined as:

A)future cash flows discounted to the present by an appropriate discount rate.
B)inverse of future cash flows.
C)present cash flows compounded into the future.
D)future cash flows multiplied by the factor (1 + r)^t.

Question 8

If the one-year discount factor is 0.8333,what is the discount rate (interest rate)per year?

A)10%
B)20%
C)30%
D)40%

Question 9

If the present value of a cash flow generated by an initial investment of $200,000 is $250,000,what is the NPV of the project?

A)$250,000
B)$50,000
C)$200,000
D)-$50,000

Question 10

The present value formula for a cash flow expected one period from now is:

A)PV = C₁ × (1 + r).
B)PV = C₁/(1 + r).
C)PV = C₁/r.
D)PV = (1 + r)/C₁.

Question 11

The net present value formula for one period is:

A)NPV = C₀ + [C₁/(1 + r)].
B)NPV = PV required investment.
C)NPV = C₀/C₁.
D)NPV = C₁/C₀.

Question 12

The rate of return is also called the: I)
Discount rate; II)hurdle rate; III)opportunity cost of capital

A)I only.
B)I and II only.
C)I,II,and III.
D)I and III only.

Question 13

The present value of $121,000 expected one year from today at an interest rate (discount rate)of 10% per year is:

A)$121,000.
B)$100,000.
C)$110,000.
D)$108,900.

Question 14

The present value of $100.00 expected two years from today at a discount rate of 6% is:

A)$112.36.
B)$106.00.
C)$100.00.
D)$89.00.

Question 15

At an interest rate of 10%,which of the following sequences of cash flows should you prefer?

A)option A
B)option B
C)option C
D)option D

Question 16

If the present value of cash flow X is $240,and the present value of cash flow Y is $160,then the present value of the combined cash flows is:

A)$240.
B)$160.
C)$80.
D)$400.

Question 17

If the annual interest rate is 12.00%,what is the two-year discount factor?

A)0.7972
B)0.8929
C)1.2544
D)0.8065

Question 18

The one-year discount factor,at an interest rate of 100% per year,is:

A)1.50.
B)0.50.
C)0.25.
D)1.00.

Question 19

If the present value of $600,expected one year from today,is $400,what is the one-year discount rate?

A)15%
B)20%
C)25%
D)50%

Question 20

If the one-year discount factor is 0.90,what is the present value of $120 expected one year from today?

A)$100
B)$96
C)$108
D)$133

Question 21

Which of the following statements regarding the net present value rule and the rate of return rule is false?

A)Accept a project if NPV > cost of investment.
B)Accept a project if NPV is positive.
C)Accept a project if return on investment exceeds the rate of return on an equivalent-risk investment in the financial market.
D)Reject a project if NPV is negative.

Question 22

What is the net present value of the following cash flow sequence at a discount rate of 11%?

A)$69,108.03
B)$231,432.51
C)$80,000.00
D)$88,000.00

Question 23

You would like to have enough money saved to receive a $50,000 per year perpetuity after retirement.How much would you need to have saved in your retirement fund to achieve this goal? (Assume that the perpetuity payments start on the day of your retirement.The annual interest rate is 8%.)

A)$1,000,000
B)$675,000
C)$625,000
D)$500,000

Question 24

Which of the following is generally considered an example of a perpetuity?

A)Interest payments on a 10-year bond
B)Interest payments on a 30-year bond
C)Interest payments on a consol
D)Interest payments on government bonds

Question 25

You would like to have enough money saved to receive an $80,000 per year perpetuity after retirement.How much would you need to have saved in your retirement fund to achieve this goal? (Assume that the perpetuity payments start on the day of your retirement.The annual interest rate is 10%.)

A)$1,500,000
B)$880,000
C)$800,000
D)$80,000

Question 26

According to the net present value rule,an investment in a project should be made if the:

A)net present value is greater than the cost of investment.
B)net present value is greater than the present value of cash flows.
C)net present value is positive.
D)net present value is negative.

Question 27

An annuity is defined as a set of:

A)equal cash flows occurring at equal intervals of time for a specified period.
B)equal cash flows occurring at equal intervals of time forever.
C)unequal cash flows occurring at equal intervals of time forever.
D)unequal cash flows occurring at equal intervals of time for a specified period.

Question 28

You would like to have enough money saved to receive $80,000 per year in perpetuity after retirement for you and your heirs.How much would you need to have saved in your retirement fund to achieve this goal? (Assume that the perpetuity payments start one year from the date of your retirement.The annual interest rate is 8%.)

A)$7,500,000
B)$750,000
C)$1,000,000
D)$800,000

Question 29

If you are paid $1,000 at the end of each year for the next five years,what type of cash flow did you receive?

A)uneven cash flow stream
B)an annuity
C)an annuity due
D)a perpetuity

Question 30

A perpetuity is defined as a sequence of:

A)equal cash flows occurring at equal intervals of time for a specific number of periods.
B)equal cash flows occurring at equal intervals of time forever.
C)unequal cash flows occurring at equal intervals of time forever.
D)unequal cash flows occurring at equal intervals of time for a specific number of periods.

Question 31

What is the eight-year present value annuity factor at a discount rate of 11%?

A)5.7122
B)11.8594
C)5.1461
D)6.9158

Question 32

You would like to have enough money saved after your retirement such that you and your heirs can receive $100,000 per year in perpetuity.How much would you need to have saved at the time of your retirement in order to achieve this goal? (Assume that the perpetuity payments start one year after the date of your retirement.The annual interest rate is 12.5%.)

A)$1,000,000
B)$10,000,000
C)$800,000
D)$1,125,000

Question 33

An initial investment of $500 produces a cash flow of $550 one year from today.Calculate the rate of return on the project.

A)10%
B)15%
C)20%
D)25%

Question 34

What is the present value of $10,000 per year in perpetuity at an interest rate of 10%?

A)$10,000
B)$100,000
C)$200,000
D)$1,000

Question 35

What is the net present value (NPV)of the following sequence of cash flows at a discount rate of 9%?

A)$122,431.81
B)$200,000.00
C)$155,950.68
D)$177,483.77

Question 36

If the five-year present value annuity factor is 3.60478 and the four-year present value annuity factor is 3.03735,what is the present value at the $1 received at the end of five years?

A)$0.63552
B)$1.76233
C)$0.56743
D)$1.2132

Question 37

Which of the following statements regarding the NPV rule and the rate of return rule is false?

A)Accept a project if its NPV > 0.
B)Reject a project if the NPV < 0.
C)Accept a project if its rate of return > 0.
D)Accept a project if its rate of return > opportunity cost of capital.

Question 38

The opportunity cost of capital for a risky project is:

A)the expected rate of return on a government security having the same maturity as the project.
B)the expected rate of return on a well-diversified portfolio of common stocks.
C)the expected rate of return on a security of similar risk as the project.
D)The expected rate of return on a typical bond portfolio.

Question 39

If the three-year present value annuity factor is 2.673 and the two-year present value annuity factor is 1.833,what is the present value of $1 received at the end of the three years?

A)$1.19
B)$0.84
C)$0.89
D)$0.92

Question 40

What is the net present value of the following sequence of annual cash flows at a discount rate of 16% APR?

A)$136,741.97
B)$122,948.87
C)$158,620.69
D)$139,418.23

Question 41

If the present value annuity factor at 12% for five years is 3.6048,what is the equivalent future value annuity factor?

A)2.0455
B)6.3529
C)1.7623
D)5.1237

Question 42

If the present value annuity factor for 10 years at 10% interest rate is 6.1446,what is the present value annuity factor for an equivalent annuity due?

A)6.1446
B)7.3800
C)6.7590
D)5.7321

Question 43

John House has taken a 20-year,$250,000 mortgage on his house at an interest rate of 6% per year.What is the value of the mortgage after the payment of the fifth annual installment?

A)$128,958.41
B)$211,689.53
C)$141,019.50

Question 44

After retirement,you expect to live for 25 years.You would like to have $75,000 income each year.How much should you have saved in your retirement account to receive this income,if the interest rate is 9% per year? (Assume that the payments start on the day of your retirement.)

A)$736,693.47
B)$802,995.88
C)$2,043,750.21
D)$1,427,831.93

Question 45

What is the present value of a six-year,$5,000 per year annuity at a discount rate of 10%?

A)$21,776.30
B)$3,371.91
C)$16,760.78
D)$18,327.82

Question 46

John House has taken a $250,000 mortgage on his house at an interest rate of 6% per year.If the mortgage calls for 20 equal,annual payments,what is the amount of each payment?

A)$21,796.14
B)$10,500.00
C)$16,882.43
D)$24,327.18

Question 47

After retirement,you expect to live for 25 years.You would like to have $75,000 income each year.How much should you have saved in your retirement account to receive this income if the interest rate is 9% per year? (Assume that the payments start one year after your retirement.)

A)$736,693.47
B)$83,431.17
C)$1,875,000
D)$1,213,487.12

Question 48

Mr.Hopper expects to retire in 25 years,and he wishes to accumulate $750,000 in his retirement fund by that time.If the interest rate is 10% per year,how much should Mr.Hopper put into his retirement fund each year in order to achieve this goal? (Assume that he makes payments at the end of each year.)

A)$4,559.44
B)$2,500
C)$7,626.05

Question 49

What is the present value of a $1,000 per year annuity for five years at an interest rate of 12%?

A)$6,352.85
B)$3,604.78
C)$567.43
D)$2,743.28

Question 50

For $10,000,you can purchase a five-year annuity that will pay $2,504.57 per year for five years.The payments occur at the end of each year.Calculate the effective annual interest rate implied by this arrangement.

A)8%
B)9%
C)10%

Question 51

If the present value of $1.00 received n years from today at an interest rate of r is 0.3855,then what is the future value of $1.00 invested today at an interest rate of r% for n years?

A)$1.3855
B)$2.594
C)$1.701
D)not enough information is given to solve the problem

Question 52

For $10,000,you can purchase a five-year annuity that will pay $2,358.65 per year for five years.The payments occur at the beginning of each year.Calculate the effective annual interest rate implied by this arrangement.

A)8%
B)9%
C)10%

Question 53

What is the six-year present value annuity factor at an interest rate of 9%?

A)7.5233
B)4.4859
C)1.6771
D)3.1432

Question 54

If the present value annuity factor at 8% for 10 years is 6.71,what is the equivalent future value annuity factor?

A)3.108
B)14.486
C)2.159
D)5.384

Question 55

If the present value of $1.00 received n years from today at an interest rate of r is 0.621,then what is the future value of $1.00 invested today at an interest rate of r% for n years?

A)$1.000
B)$1.610
C)$1.621
D)not enough information is given to solve the problem

Question 56

If the future value of $1 invested today at an interest rate of r% for n years is 9.6463,what is the present value of $1 to be received in n years at r% interest rate?

A)$9.6463
B)$1.0000
C)$0.1037
D)$0.4132

Question 57

If the future value annuity factor at 10% and five years is 6.1051,calculate the equivalent present value annuity factor:

A)6.1051
B)3.7908
C)6.7156
D)4.8127

Question 58

If the present value annuity factor at 10% for 10 years is 6.1446,what is the equivalent future value annuity factor?

A)3.1080
B)15.9375
C)2.5937
D)8.4132

Question 59

If the present value annuity factor is 3.8896,what is the present value annuity factor for an equivalent annuity due if the interest rate is 9%?

A)3.5684
B)4.2397
C)3.8896
D)5.3127

Question 60

You are considering investing in a retirement fund that requires you to deposit $5,000 per year,and you want to know how much the fund will be worth when you retire.What financial technique should you use to calculate this value?

A)Future value of a single payment
B)Future value of an annuity
C)Present value of an annuity
D)Present value of a perpetuity

Question 61

Which of the following statements is true?

A)The process of discounting is the inverse of the process of compounding.
B)Ending balances using simple interest are always greater than ending balances using compound interest at positive interest rates.
C)The present value of an annuity due is always less than the present value of an equivalent ordinary annuity at positive interest rates.
D)The future value of an annuity due is always less than the present value of an equivalent ordinary annuity at positive interest rates.

Question 62

A dollar today is worth more than a dollar tomorrow if the interest rate is positive.

Question 63

Ms.Colonial has just taken out a $150,000 mortgage at an interest rate of 6% per year.If the mortgage calls for equal monthly payments for 20 years,what is the amount of each payment? (Assume monthly compounding or discounting.)

A)$1,254.70
B)$1,625.00
C)$1,263.06
D)$1,074.65

Question 64

The rate of return,discount rate,hurdle rate,and opportunity cost of capital all have the same meaning.

Question 65

You would like to have enough money saved to receive a growing annuity for 20 years,growing at a rate of 5% per year,with the first payment of $50,000 occurring exactly one year after retirement.How much would you need to save in your retirement fund to achieve this goal? (The interest rate is 10%.)

A)$1,000,000.00
B)$425,678.19
C)$605,604.20
D)$827,431.28

Question 66

If you invest $100 at 12% APR for three years,how much would you have at the end of three years using compound interest?

A)$136
B)$140.49
C)$240.18
D)$173.18

Question 67

The managers of a firm can maximize stockholder wealth by:

A)taking all projects with positive NPVs.
B)taking all projects with NPVs greater than the cost of investment.
C)taking all projects with NPVs greater than the present value of cash flows.
D)taking only the highest NPV project each year.

Question 68

Mr.Williams expects to retire in 30 years and would like to accumulate $1 million in his pension fund.If the annual interest rate is 12% APR,how much should Mr.Williams put into his pension fund each month in order to achieve his goal? (Assume that Mr.Williams will deposit the same amount each month into his pension fund,using monthly compounding.)

A)$286.13
B)$771.60
C)$345.30
D)$437.13

Question 69

You just inherited a trust that will pay you $100,000 per year in perpetuity.However,the first payment will not occur for exactly four more years.Assuming an 8% annual interest rate,what is the value of this trust?

A)$918,787
B)$992,290
C)$1,000,000
D)$1,250,000

Question 70

You just inherited a trust that will pay you $100,000 per year in perpetuity.However,the first payment will not occur for exactly five more years.Assuming an 8% annual interest rate,what is the value of this trust?

A)$850,729
B)$918,787
C)$1,000,000
D)$1,250,000

Question 71

You would like to have enough money saved to receive a growing annuity for 25 years,growing at a rate of 4% per year,with the first payment of $60,000 occurring exactly one year after retirement.How much would you need to save in your retirement fund to achieve this goal? (The interest rate is 12%.)

A)$1,500,000.00
B)$632,390
C)$452,165
D)$1,043,287

Question 72

An investment at 10% compounded continuously has an equivalent annual rate of:

A)10.250%.
B)10.517%.
C)10.381%.
D)none of the options.

Question 73

An investment at 12% APR compounded monthly is equal to an effective annual rate of:

A)12.68%
B)12.36%
C)12.00%
D)11.87%

Question 74

Mr.Hopper expects to retire in 30 years,and he wishes to accumulate $1,000,000 in his retirement fund by that time.If the interest rate is 12% per year,how much should Mr.Hopper put into his retirement fund at the end of each year in order to achieve this goal?

A)$4,143.66
B)$8,287.32
C)$4,000.00

Question 75

You just inherited a trust that will pay you $100,000 per year in perpetuity.However,the first payment will not occur for exactly five more years.Assuming a 10% annual interest rate,what is the value of this trust?

A)$620,921
B)$683,013
C)$1,000,000
D)$1,100,000

Question 76

If you invest $100 at 12% APR for three years,how much would you have at the end of three years using simple interest?

A)$136.00
B)$140.49
C)$240.18
D)$187.13

Question 77

The present value of a $100 per year perpetuity at 10% per year interest rate is $1000.What would be the present value of this perpetuity if the payments were compounded continuously?

A)$1000.00
B)$1049.21
C)$1024.40
D)$986.14

Question 78

You just inherited a trust that will pay you $100,000 per year in perpetuity.However,the first payment will not occur for exactly four more years.Assuming a 10% annual interest rate,what is the value of this trust?

A)$683,013
B)$751,315
C)$1,000,000
D)$1,100,000

Question 79

The concept of compound interest is best described as:

A)interest earned on an investment.
B)the total amount of interest earned over the life of an investment.
C)interest earned on interest.
D)the inverse of simple interest.

Question 80

An investment having a 10.47% effective annual rate (EAR)has what APR? (Assume monthly compounding.)

A)10.99%
B)9.57%
C)10.00%
D)8.87%