Deck 2: How to Calculate Present Values

Question 1

Present Value of $100,000 that is, expected, to be received 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) None of the above

Answer 1

$80,000

Question 2

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

A) $100
B) $96
C) $108
D) None of the above

Answer 2

$108

Question 3

An initial investment of $400,000 will 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) None of the above

Answer 3

$0 (zero)

Question 4

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

A) Option A
B) Option B
C) Option C
D) Option D

Question 5

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) None of the above

Question 6

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

A) 10%
B) 20%
C) 25%
D) None of the above

Question 7

The net present value formula for one period is:
I. NPV = C0 + [C1/(1 + r)]; II) NPV = PV required investment; and
III. NPV = C0/C1

A) I only
B) I and II only
C) III only
D) None of the above

Question 8

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

A) $372,431.81
B) $450,000
C) $405,950.68
D) None of the above

Question 9

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

A) 1.5
B) 0.5
C) 0.25
D) None of the above

Question 10

If the interest rate is 12%, what is the 2-year discount factor?

A) 0.7972
B) 0.8929
C) 1.2544
D) None of the above

Question 11

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) None of the above

Question 12

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) None of the above

Question 13

The present value formula for one period cash flow is:

A) PV = C1(1 + r)
B) PV = C1/(1 + r)
C) PV = C1/r
D) None of the above

Question 14

The rate of return is also called:
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) None of the given ones

Question 15

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

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

Question 16

Present Value is defined as:

A) Future cash flows discounted to the present at an appropriate discount rate
B) Inverse of future cash flows
C) Present cash flow compounded into the future
D) None of the above

Question 17

One year discount factor at a discount rate of 25% per year is:

A) 1.25
B) 1.0
C) 0.8
D) None of the above

Question 18

Present value of $121,000 expected to be received 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) None of the above

Question 19

The present value of $100 expected in two years from today at a discount rate of 6% is:

A) $116.64
B) $108.00
C) $100.00
D) $89.00

Question 20

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

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

Question 21

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

A) $122,431.81
B) $200,000
C) $155,950.68
D) None of the above

Question 22

You would like to have enough money saved to receive a $50,000 per year perpetuity after retirement so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal (assume that the perpetuity payments starts on the day of retirement. The interest rate is 8%)?

A) $1,000,000
B) $675,000
C) $625,000
D) None of the above

Question 23

The following statements regarding the NPV rule and the rate of return rule are true except:

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 24

An annuity is defined as

A) Equal cash flows at equal intervals of time for a specified period of time
B) Equal cash flows at equal intervals of time forever
C) Unequal cash flows at equal intervals of time forever
D) None of the above

Question 25

If the five-year present value annuity factor is 3.60478 and 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) None of the above

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

You would like to have enough money saved to receive $80,000 per year perpetuity after retirement so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal (assume that the perpetuity payments start one year from the date of your retirement. The interest rate is 8%)?

A) $7,500,000
B) $750,000
C) $1,000,000
D) None of the above

Question 28

If the three-year present value annuity factor is 2.673 and two-year present value annuity factor is 1.833, what is the present value of $1 received at the end of the 3 years?

A) $1.1905
B) $0.84
C) $0.89
D) None of the above

Question 29

What is the present value of the following cash flow at a discount rate of 16% APR?

A) $136,741.97
B) $122,948.87
C) $158,620.69
D) None of the above

Question 30

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 portfolio of securities of similar risks as the project
D) None of the above

Question 31

What is the present value annuity factor at a discount rate of 11% for 8 years?

A) 5.7122
B) 11.8594
C) 5.1461
D) None of the above

Question 32

A perpetuity is defined as:

A) Equal cash flows at equal intervals of time for a specific number of periods
B) Equal cash flows at equal intervals of time forever
C) Unequal cash flows at equal intervals of time forever
D) None of the above

Question 33

You would like to have enough money saved to receive an $80,000 per year perpetuity after retirement so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal (assume that the perpetuity payments starts on the day of retirement. The interest rate is 10%)?

A) $1,500,000
B) $880,000
C) $800,000
D) None of the above

Question 34

Which of the following statements regarding the net present value rule and the rate of return rule is not true?

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 investment in the financial market
D) Reject a project if NPV is negative

Question 35

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

A) 10%
B) 15%
C) 25%
D) none of the above

Question 36

If you receive $1,000 payment at the end each year for the next five years, what type of cash flow do you have?

A) Uneven cash flow stream
B) An annuity
C) An annuity due
D) None of the above

Question 37

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) Consols
D) None of the above

Question 38

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

A) $10,000
B) $100,000
C) $200,000
D) None of the above

Question 39

You would like to have enough money saved to receive $100,000 per year perpetuity after retirement so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal (assume that the perpetuity payments start one year from the date of your retirement. The interest rate is 12.5%)?

A) $1,000,000
B) $10,000,000
C) $800,000
D) None of the above

Question 40

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

A) $69,108.03
B) $231,432.51
C) $80,000
D) None of the above

Question 41

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 the retirement to receive this income, if the interest is 9% per year (assume that the payments start one year after the retirement)?

A) $736,693.47
B) $6,352,567.22
C) $1,875,000
D) None of the above

Question 42

Mr. Hopper is expected to retire in 25 years and he wishes 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 the retirement fund each year in order to achieve this goal? [Assume that the payments are made at the end of each year]

A) $4,559.44
B) $2,500
C) $7,626.05
D) None of the above

Question 43

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 the retirement to receive this income, if the interest is 9% per year (assume that the payments start on the day of retirement)?

A) $736,693.47
B) $802,995.88
C) $2,043,750
D) None of the above

Question 44

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

A) 3.108
B) 14.487
C) 2.159
D) None of the above

Question 45

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
D) None of the above

Question 46

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) 7.38
C) 6.759
D) None of the above

Question 47

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

A) $21,796.14
B) $10,500.00
C) $16,882.43
D) None of the above

Question 48

If the future value annuity factor at 10% and 5 years is 6.1051, calculate the equivalent present value annuity factor

A) 6.1051
B) 3.7908
C) 6.7156
D) None of the given ones

Question 49

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

A) 3.108
B) 15.9374
C) 2.5937
D) None of the above

Question 50

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) $1.00
B) $1.61
C) $1.621
D) Not enough information to solve the problem

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) $1.70
D) Not enough information to solve the problem

Question 52

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) $1.00
C) $0.1037
D) None of the above

Question 53

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) None of the above

Question 54

For $10,000 you can purchase a 5-year annuity that will pay $2504.57 per year for five years. The payments are made at the end of each year. Calculate the effective annual interest rate implied by this arrangement: (approximately)

A) 8%
B) 9%
C) 10%
D) None of the above

Question 55

What is the present value annuity factor at an interest rate of 9% for 6 years?

A) 7.5233
B) 4.4859
C) 1.6771
D) None of the above

Question 56

What is the present value of $1000 per year annuity for five years at an interest rate of
12%?

A) $6,352.85
B) $3,604.78
C) $567.43
D) None of the above

Question 57

For $10,000 you can purchase a 5-year annuity that will pay $2358.65 per year for five years. The payments are made at the beginning of each year. Calculate the effective annual interest rate implied by this arrangement: (approximately)

A) 8%
B) 9%
C) 10%
D) none of the above

Question 58

If the present value annuity factor at 12% APR for 5 years is 3.6048, what is the equivalent future value annuity factor?

A) 2.0455
B) 6.3529
C) 1.7623
D) None of the above

Question 59

What is the present value of $5000 per year annuity at a discount rate of 10% for 6 years?

A) $21,776.30
B) $3,371.91
C) $16,760.78
D) None of the above

Question 60

If the present 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) None of the above.

Question 61

The opportunity cost of capital is higher for safe investments than for risky ones.

Question 62

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

A) 12.68%
B) 12.36%
C) 12%
D) None of the above

Question 63

If you invest $100 at 12% APR for three years, how much would you have at the end of 3 years using simple interest?

A) $136
B) $140.49
C) $240.18
D) None of the above

Question 64

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

Question 65

You would like to have enough money saved to receive a growing annuity for 25 years, growing
At a rate of 4% per year, the first payment being $60,000 after retirement, so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal? (assume that the growing perpetuity payments start one year from the date of
Your retirement. The interest rate is 12%)?

A) $1,500,000
B) $632,390
C) $452,165
D) None of the above

Question 66

Mr. William expects to retire in 30 years and would like to accumulate $1 million in the pension fund. If the annual interest rate is 12% per year, how much should Mr. Williams put into the 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 and also use monthly compounding.

A) $286.13
B) $771.60
C) $345.30
D) None of the above

Question 67

The rate of return, discount rate, hurdle rate or opportunity cost of capital all means the same.

Question 68

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 is always greater than the ending balance using compound interest at positive interest rates.
C) Present value of an annuity due is always less than the present value of an equivalent annuity at positive interest rates.
D) All of the above are true.

Question 69

The discount rate is used for calculating the NPV is:

A) Determined by the financial markets
B) Found by the government
C) Found by the CEO
D) None of the above

Question 70

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 twenty years, what is the amount of each payment? (Assume monthly compounding or discounting.)

A) $1254.70
B) $1625.00
C) $1263.06
D) None of the above are true

Question 71

An investment at 10% nominal rate compounded continuously is equal to an equivalent annual rate of:

A) 10.250%
B) 10.517%
C) 10.381%
D) None of the above

Question 72

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 present value of cash flow
D) All of the above

Question 73

Mr. Hopper is expected to retire in 30 years and he wishes 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 the retirement fund each year in order to achieve this goal?

A) $4,143.66
B) $8,287.32
C) $4,000
D) None of the above

Question 74

An investment at 10.47% effective rate compounded monthly is equal to a nominal
(annual) rate of:

A) 10.99%
B) 9.57%
C) 10%
D) None of the above

Question 75

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

A) $1000.00
B) $1049.21
C) $1024.40
D) None of the above

Question 76

The concept of compound interest is most appropriately 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) None of the above

Question 77

If you invest $100 at 12% APR for three years, how much would you have at the end of 3 years using compound interest?

A) $136
B) $140.49
C) $240.18
D) None of the above

Question 78

Net present value is found by subtracting the required investment from the present value of future cash flows.

Question 79

You would like to have enough money saved to receive a growing annuity for 20 years, growing at a rate of 5% per year, the first payment being $50,000 after retirement. That way, you hope that you and your family can lead a good life after retirement. How much would you need to save in your retirement fund to achieve this goal.(assume that the growing annuity payments start one year from the date of your retirement. The interest rate is 10%)?

A) $1,000,000
B) $425,678.19
C) $605,604.20
D) None of the above

Question 80

The present value of a future cash flow can be found by dividing it by an appropriate discount factor.