Deck 6: Discounted Cash Flow Valuation

Question 1

Annuities where the payments occur at the end of each time period are called annuities due, whereas ordinary annuities refer to annuity streams with payments occurring at the beginning of each time period.

Answer 1

False

Question 2

Endowment fund providing equal annual payments from accrued earnings fit the definition of a perpetuity.

Answer 2

True

Question 3

You are going to invest $500 at the end of each year for 10 years. Given an interest rate, you can find the future value of this investment by finding the present value of each cash flow, adding all of the present values together, then finding the future value at the end of year 10 of this lump sum.

Answer 3

True

Question 4

$100 a quarter for 10 years fits the definition of an annuity.

Question 5

Preferred stock dividends fit the definition of a perpetuity.

Question 6

You are going to invest $500 at the end of each year for 10 years. Given an interest rate, you can find the future value of this investment by adding the cash flows together and finding the future value of the sum using the appropriate future value factor.

Question 7

The future value factor for annuities is calculated as (Future value factor-1)/r:

Question 8

Monthly payments equal to 100% of the income earned by a restaurant fits the definition of a perpetuity.

Question 9

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

Question 10

An annuity stream where the payments occur forever is called an annuity due

Question 11

You are going to invest $500 at the end of each year for 10 years. Given an interest rate, you can find the future value of this investment by applying the proper future value factor to each cash flow, then adding up these future values.

Question 12

You hold a winning ticket from your provincial lottery. It entitles the bearer to receive payments of $50,000 at the end of each of the next 20 years. Given what you know about the time value of money, you should be able to sell this ticket for no less than $1 million in the open market.

Question 13

The interest rate expressed in terms of the interest payment made each period is called the compound interest rate:

Question 14

An annuity stream of cash flow payments is a set of level cash flows occurring each time period for a fixed length of time.

Question 15

The interest rate expressed as if it were compounded once per year is called the effective annual rate:

Question 16

A loan where the borrower pays interest each period and repays some or the entire principal of the loan over time is called an amortized loan.

Question 17

Which one of the following would have the greatest present value, assuming a positive discount rate?

A) $1,000 today plus $100 a month for 2 years.
B) $1,000 today plus $200 a month for a year.
C) $1,000 today plus $400 a month for six months.
D) $2,200 today plus $200 a month for six months.
E) $2,200 today plus $100 a month for a year.

Question 18

$150 a month for 72 months fits the definition of an annuity.

Question 19

You have just won a lottery prize. You can choose to receive $750,000 today or an annual payment of $50,000 at the end of each of the next 20 years. The interest rate that makes you indifferent between the two is 2.91%, and at higher rates you should take the lump sum.

Question 20

What is the future value at the end of year 3 of the following set of cash flows if the interest rate is 14%?

A) -$649.32
B) -$268.88
C) $0
D) $316.72
E) $469.23

Question 21

You would like to establish a trust fund that will provide $50,000 a year forever for your heirs. The trust fund is going to be invested very conservatively so the expected rate of return is only 2.75%. How much money must you deposit today to fund this gift for your heirs?

A) $1,333,333.33
B) $1,375,000.00
C) $1,425,000.00
D) $1,666,666.67
E) $1,818,181.82

Question 22

Calculate the present value of a growing annuity given the following information: annual cash flows = $67,000; cash flow growth rate = 3%; required rate of return = 8%; timeframe = 45years.

A) $1,179,251
B) $1,180,251
C) $1,181,251
D) $1,182,251
E) $1,183,251

Question 23

Your neighbour makes you the following offer. He would like to borrow $10,000 today. He will repay the $10,000 by making 10 yearly payments with the first payment being made at the end of this year. If the payments are to grow by 10% each year and the appropriate discount rate is 12%, how much will your neighbour have to pay at the end of the first year?

A) $108.98
B) $1,212.97
C) $1,627.45
D) $1,769.84
E) $1,867,94

Question 24

What is the total future value six years from now of $50 received in one year, $200 received in two years, and $800 received in six years if the discount rate is 8%?

A) $1,050.00
B) $1,047.93
C) $1,145.56
D) $1,237.21
E) $1,269.15

Question 25

Starting today, Stephen is going to contribute $200 on the first of each month to his retirement account. His employer will contribute an additional 50% of the amount Stephen contributes. If both Stephen and his employer continue to do this and he can earn a monthly rate of 0.75%, how much will Stephen have in his retirement account 40 years from now?

A) $936,264
B) $943,286
C) $1,404,396
D) $1,414,929
E) $1,672,413

Question 26

You are considering two payment options on a $500,000 20-year mortgage having an interest rate of 2.8% compounded monthly. The first option is to make monthly payments at the start of each month, while the second option is to make payments at the end of each month. How much interest will be saved by choosing the first option?

A) $1,521.60
B) $1,721.60
C) $1,921.60
D) $2,121.60
E) $2,321.60

Question 27

Calculate the present value of a growing annuity given the following information: annual cash flows = $120,000; cash flow growth rate = 2%; required rate of return = 9%; timeframe = 20 years.

A) $1,059,762
B) $1,259,762
C) $1,459,762
D) $1,659,762
E) $1,859,762

Question 28

Calculate the present value of a growing annuity given the following information: annual cash flows = $100,000; cash flow growth rate = 2%; required rate of return = 9%; timeframe = 50years.

A) $1,375,860
B) $1,376,860
C) $1,377,860
D) $1,378,860
E) $1,379,860

Question 29

You own a bond issued by the Canadian Pacific railroad that promises to pay the holder $100 annually forever. You plan to sell the bond five years from now. If similar investments yield 8% at that time, how much will the bond be worth?

A) $918.79
B) $1,014.28
C) $1,250.00
D) $1,489.42
E) $1,958.20

Question 30

You just borrowed $12,750 from the bank to use in your business. The loan terms require you to pay the interest annually with the entire principle due in six years. The interest rate is 8.95%. How much will you pay to the bank in year five of the loan?

A) $1,106.67
B) $1,141.13
C) $1,203.17
D) $1,244.98
E) $1,424.58

Question 31

How much will you pay on a 25 year, $400,000 mortgage if you make monthly payment at the beginning of month? Interest is 3.5% compounded annually.

A) $1,968
B) $1,973
C) $1,979
D) $1,985
E) $1,991

Question 32

Howard Melville established a trust fund that provides $125,000 in scholarships each year for worthy students. The trust fund earns a 6.65% rate of return. How much money did Mr. Melville contribute to the fund assuming that only the interest income is distributed?

A) $1,333,125
B) $1,525,000
C) $1,879,699
D) $1,900,000
E) $2,004,699

Question 33

Calculate the present value of a growing annuity given the following information: current cash flows: $90,000; cash flow growth rate = 2%; timeframe = 20 years; required rate of return = 5%.

A) $1,319,886
B) $1,329,886
C) $1,339,886
D) $1,349,886
E) $1,359,886

Question 34

What is the future value at the end of year 3 of the following set of cash flows if the interest rate is 8%?

A) -$64.93
B) $366.89
C) $1,824.64
D) $2,698.13
E) $3,714.21

Question 35

Pat retires at age 58 and expects to live to age 90. On the day she retires, she has $287,409 in her retirement savings account. She is conservative and expects to earn 5.25% on her money during her retirement years. How much can she withdraw from her retirement savings each month if she plans to die on the day she spends her last penny?

A) $1,359.79
B) $1,364.18
C) $1,540.01
D) $1,546.75
E) $1,702.11

Question 36

You are going to loan your friend $1,000 for one year at a 5% rate of interest. How much additional interest can you earn if you compound the rate continuously rather than annually?

A) $0.97
B) $1.09
C) $1.27
D) $1.36
E) $1.49

Question 37

A wealthy benefactor just donated some money to the local college. This gift was established to provide scholarships for worthy students. The first scholarships will be granted one year from now for a total of $50,000. Annually thereafter the scholarship amount will be increased by 5% to help offset the effects of inflation. The scholarship fund will last indefinitely. What is the value of this gift today at a discount rate of 7.5%?

A) $1,500,000
B) $1,666,667
C) $1,750,000
D) $1,885,000
E) $2,000,000

Question 38

Calculate the present value of a growing annuity given the following information: current cash flows: $100,000; cash flow growth rate = 2%; timeframe = 25 years; required rate of return = 5%.

A) $1,708,415
B) $1,718,415
C) $1,728,415
D) $1,738,415
E) $1,748,415

Question 39

The Frank Trust would like to gift some money to their local university so that the money gifted will provide $100,000 to the university each year from now on. The funds are expected to earn an 8% rate of return. How much money does the Frank Trust have to gift to the university today?

A) $1,000,000
B) $1,250,000
C) $1,500,000
D) $2,000,000
E) $2,500,000

Question 40

You plan on withdrawing monthly payments for the next ten years and have deposited $100,000 in an account. If the rate of return is 8% compounded monthly, determine the value of the monthly withdrawals.

A) $2,013.28
B) $1,813.28
C) $1,613.28
D) $1,413.28
E) $1,213.28

Question 41

You are considering a job offer. The job offers an annual salary of $42,000, $45,000, and $48,000 a year for the next three years, respectively. The offer also includes a starting bonus of $1,000 payable immediately. What is this offer worth to you today at a discount rate of 5.5%?

A) $121,616,06
B) $121,866.67
C) $122,118.24
D) $122,333.33
E) $122,609.14

Question 42

You are considering investing $750 in a 10 year annuity. The rate of return you require is 6.5%. What annual cash flow from the annuity will provide the required return?

A) $70.77
B) $102.96
C) $104.33
D) $114.31
E) $129.27

Question 43

On the day you enter college you borrow $12,000 from your local bank. The terms of the loan include an interest rate of 5.45%. The terms stipulate that the principle is due in full one year after you graduate. Interest is to be paid annually at the end of each year. Assume that you complete college in four years. How much will you pay the bank one year after you graduate?

A) $2,806.27
B) $3,419.59
C) $12,000.00
D) $12,654.00
E) $15,646.39

Question 44

Analysts expect Marble Comics to pay shareholders $1.00 per share annually for the next five years. After that, the dividend will be $1.50 annually forever. Given a discount rate of 10%, what is the value of the stock today?

A) $6.55
B) $9.87
C) $12.37
D) $13.10
E) $21.88

Question 45

What is the future value in 10 years of $1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.625%.

A) $12,259.63
B) $12,949.23
C) $13,679.45
D) $14,495.48
E) $14,782.15

Question 46

What is the future value of the following cash flows at the end of year 3 if the interest rate is 7.25%? The cash flows occur at the end of each year.

A) $8,758.04
B) $8,806.39
C) $10,073.99
D) $10,314.00
E) $10,804.36

Question 47

Your car dealer is willing to lease you a new car for $199 a month for 72 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 5.45%, what is the current value of the lease?

A) $11,708.18
B) $11,297.60
C) $12,197.74
D) $12,253.14
E) $13,008.31

Question 48

Your uncle left you an inheritance in the form of a trust. The trust agreement states that you are to receive $750 each year, starting today and continuing for 25 years. What is the value of this inheritance today if the applicable discount rate is 5.8%?

A) $9,772.46
B) $9,989.82
C) $10,339.26
D) $10,623.33
E) $11,004.28

Question 49

You are considering a project with the following cash flows: What is the present value of these cash flows, given an 11% discount rate?

A) $8,695.61
B) $8,700.89
C) $13,732.41
D) $13,812.03
E) $19,928.16

Question 50

You have a 25-year $400,000 mortgage with a 3.5% rate of interest (compounded monthly) that you make monthly payments on. What is the balance of the loan at the end of year 20?

A) $90,077
B) $100,077
C) $110,077
D) $120,077
E) $130,077

Question 51

You are buying a previously owned car today at a price of $4,950. You are paying $750 down in cash and financing the balance for 42 months at 8.45%. What is the amount of each loan payment?

A) $108.54
B) $115.05
C) $115.86
D) $135.60
E) $136.55

Question 52

You plan on withdrawing quarterly payments for the next ten years and have deposited $350,000 in an account. If the rate of return is 5% compounded quarterly, determine the value of the quarterly withdrawals.

A) $11,172.50
B) $12,172.50
C) $13,172.50
D) $14,172.50
E) $15,172.50

Question 53

On the day you enter college, you work out a deal with your local bank such that you borrow $9,600 for four years. The terms of the loan include an interest rate of 5.9%. The terms also stipulate that the principle is due in full one year after you graduate. Interest is to be paid annually at the end of each year. Assume that you complete college in four years. How much will you pay the bank one year after you graduate?

A) $566.40
B) $2,265.60
C) $10,166.40
D) $11,865.60
E) $12,432.00

Question 54

You need some money today and the only friend you have that has any is your miserly friend. He agrees to loan you the money you need, if you make payments of $15 a month for the next nine months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 2% interest per month. How much money are you borrowing?

A) $120.67
B) $122.43
C) $124.88
D) $126.49
E) $135.00

Question 55

You are expecting annual cash flows of $80,000 in years 1-5; $95,000 in years 6-20; and $105,000 in years 21-50. If the rate of interest is 10% compounded annually, calculate the future value of this cash flow stream.

A) $103.54 million.
B) $104.54 million.
C) $105.54 million.
D) $106.54 million.
E) $107.54 million.

Question 56

Your recently departed rich, eccentric uncle has left for you in his will a large sum of money. Unfortunately, rather than giving you this sum of money immediately, he has instructed the executor of the will to pay you $10,000 in one year. This payment is to grow by 9% each year and to be made each year forever. If the appropriate discount rate is 10%, how much have you actually inherited?

A) $100,000
B) $1,000,000
C) $11,111.11
D) $9,090.90
E) $10,000,000

Question 57

You just won the lottery! As your prize you will receive $1,500 a month for ten years. If you can earn 9.3% on your money, what is this prize worth to you today?

A) $110,757.83
B) $111,616.20
C) $112,001.73
D) $116,908.87
E) $117,814.92

Question 58

Angela is able to pay $230 a month for 6 years on a car loan. If the interest rate is 7.9%, how much can she afford to borrow to buy a car?

A) $13,154.54
B) $13,408.17
C) $13,528.28
D) $13,666.67
E) $13,809.19

Question 59

You need some money today and the only friend you have that has any is your 'miserly' friend. He agrees to loan you the money you need, if you make payments of $20 a month for the next six months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 1.5% interest per month. How much money are you borrowing?

A) $113.94
B) $115.65
C) $118.34
D) $119.63
E) $121.96

Question 60

Mr. Dubofsky just won a "Name That Tune" contest with a grand prize of $250,001. However, the contest stipulates that the winner will receive $100,000 immediately, and $15,000 at the end of each of the next 10 years. Assuming that he can earn 5% on his money, how much has he actually won?

A) $92,156.46
B) $98,225.11
C) $115,826.02
D) $215,826.02
E) $250,000.00

Question 61

You borrow $7,900 to buy a car. The terms of the loan call for monthly payments for five years at a 6.5% rate of interest. What is the amount of each payment?

A) $153.74
B) $153.80
C) $154.39
D) $154.57
E) $154.68

Question 62

What is the future value at the end of year 4 of the following set of cash flows? Assume an interest rate of 8%.

A) $50.00
B) $127.38
C) $173.31
D) $379.41
E) $3,312.13

Question 63

What is the future value of the following cash flows at the end of year 3 if the interest rate is 9%? The cash flows occur at the end of each year.

A) $15,213.80
B) $15,619.70
C) $15,916.78
D) $16,177.14
E) $17,633.08

Question 64

Sun Woo wants to purchase an annuity that will pay him $1,000 a month for fifteen years. If he can negotiate a 4.5% rate of return, how much will he have to pay today in order to purchase this annuity?

A) $96,489
B) $123,185
C) $130,720
D) $154,327
E) $185,171

Question 65

What is the future value of the following cash flows at the end of year 3 if the interest rate is 6%? The cash flows occur at the end of each year.

A) $15,916.78
B) $18,109.08
C) $18,246.25
D) $19,341.02
E) $19,608.07

Question 66

Priestly Engineers wants to save $145,000 to buy some new equipment two years from now. The plan is to set aside an equal amount of money on the first day of each quarter starting today. The firm can earn a 5.5% rate of return. How much does the firm have to save each quarter to achieve their goal?

A) $17,084.43
B) $17,036.35
C) $17,270.60
D) $17,308.67
E) $17,421.18

Question 67

You are buying a pre-owned car today at a price of $9,200. You are paying $1,500 down in cash and financing the balance for 60 months at 7.25%. What is the amount of each loan payment?

A) $152.46
B) $153.38
C) $153.27
D) $154.06
E) $154.89

Question 68

What is the future value of the following cash flows at the end of year 3 if the interest rate is 12%?

A) $16,819.73
B) $18,194.56
C) $18,488.56
D) $19,942.07
E) $20,015.03

Question 69

You just won the lottery! As your prize you will receive $1,500 a month for twenty years. If you can earn 9% on your money, what is this prize worth to you today?

A) $152,087.19
B) $156,098.29
C) $157,408.16
D) $164,313.82
E) $166,717.43

Question 70

A company has just sold a product with the following payment plan:

$75,000 today, $50,000 at the end of year 1, and $25,000 at the end of year two. If the payments are deposited into an account earning 4.5% per year, calculate the present value for the cash flow.

A) $145,740
B) $165,323
C) $175,536
D) $185,643
E) $193,466

Question 71

Your employer contributes $25 a week to your retirement plan. Assume that you work for your employer for another twenty years and that the applicable discount rate is 5%. Given these assumptions, what is this employee benefit worth to you today?

A) $13,144.43
B) $15,920.55
C) $16,430.54
D) $16,446.34
E) $16,519.02

Question 72

You borrow $110,000 from the bank to be paid monthly over the next 25 years. If interest is 7.5% compounded monthly, how much interest will you pay (in dollars) over the life of the loan? (Assume you make each of the required 300 payments on time.)

A) $133,867
B) $145,583
C) $170,457
D) $190,457
E) $270,457

Question 73

Master Meter is planning on constructing a new $20 million facility. The company plans to pay 20% of the cost in cash and finance the balance. How much will each monthly loan payment be if they can borrow the necessary funds for 30 years at 9% compounded monthly?

A) $128,740
B) $133,667
C) $141,982
D) $148,016
E) $160,925

Question 74

What is the present value of the following set of cash flows if the discount rate is 11.5%?

A) -$50.44
B) -$16.98
C) $16.81
D) $268.37
E) $425.93

Question 75

You are considering a job offer. The job offers an annual salary of $52,000, $55,000, and $60,000 a year for the next three years, respectively. The offer also includes a starting bonus of $2,000 payable immediately. What is this offer worth to you today at a discount rate of 6%?

A) $148,283.56
B) $148,383.56
C) $150,283.56
D) $150,383.56
E) $152,983.56

Question 76

Determine the difference between the present value of a $51,000 twenty-year annuity earning 6% interest compounded annually versus a $51,000 twenty-year growing annuity earning 6% interest compounded annually and having a 3% annuity growth rate.

A) $137,672.18
B) $147,672.18
C) $157,672.18
D) $167,672.18
E) $177,672.18

Question 77

What is the present value of the following set of cash flows at an 8% discount rate?

A) $50.00
B) $127.39
C) $173.31
D) $379.41
E) $3,312.13

Question 78

You have a 25-year $800,000 mortgage with a 4.5% rate of interest (compounded monthly) that you make monthly payments on. What is the balance of the loan at the end of year 22?

A) $141,483
B) $145,483
C) $149,483
D) $153,483
E) $156,483

Question 79

You just settled an insurance claim. The settlement calls for increasing payments over a 5-year period. The first payment will be paid one year from now in the amount of $30,000. The following payments will increase by 6% annually. What is the value of this settlement to you today if you can earn 8.5% on your investments?

A) $126,408.28
B) $129,417.11
C) $132,023.05
D) $141,414.14
E) $152,008.16

Question 80

You are considering a project with the following cash flows: What is the present value of these cash flows, given a 3% discount rate?

A) $15,750.54
B) $13,812.03
C) $14,308.08
D) $14,941.76
E) $14,987.69