Deck 4: Discounted Cash Flow Valuation

Question 1

The interest rate charged per period multiplied by the number of periods per year is called the ________ rate.

A)effective annual
B)annual percentage
C)periodic interest
D)compound interest
E)daily interest

Answer 1

annual percentage

Question 2

A flow of unending annual payments that increase by a set percentage each year and occur at regular intervals of time is called a(n):

A)annuity due.
B)growing annuity.
C)growing perpetuity.
D)variable annuity.
E)variable perpetuity.

Answer 2

growing perpetuity.

Question 3

The highest effective annual rate that can be derived from an annual percentage rate of 9 percent is computed as:

A)(1 + .09/365)(365).
B)e.⁰⁹q.
C)1.09e.
D)e.⁰⁹ − 1.
E)(1 + .09/365)³⁶⁵ − 1.

Answer 3

e.⁰⁹ − 1.

Question 4

Given a stated interest rate,which form of compounding will yield the highest effective rate of interest?

A)Annual compounding
B)Monthly compounding
C)Daily compounding
D)Continuous compounding
E)Semiannual compounding

Question 5

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

A)ordinary annuities; early annuities
B)late annuities; straight annuities
C)straight annuities; late annuities
D)annuities due; ordinary annuities
E)ordinary annuities; annuities due

Question 6

An annuity stream of cash flow payments is a set of:

A)equal cash flows occurring at equal periods of time over a fixed length of time.
B)equal cash flows occurring each time period forever.
C)either equal or varying cash flows occurring at set intervals of time for a fixed period.
D)increasing cash flows occurring at set intervals of time that go on forever.
E)arbitrary cash flows occurring each time period for no more than 10 years.

Question 7

Martha left an inheritance to her grandson that will pay him $1,500 on the first day of every other year.When computing the PV of this inheritance,the grandson should use:

A)simple interest.
B)a semiannually compounded discount rate.
C)an effective annual rate.
D)a 2-year discount rate.
E)a semiannual discount rate.

Question 8

Ted purchased an annuity today that will pay $1,000 a month for five years.He received his first monthly payment today.Allison purchased an annuity today that will pay $1,000 a month for five years.She will receive her first payment one month from today.Which one of the following statements is correct concerning these two annuities?

A)Both annuities are of equal value today.
B)Allison's annuity is an annuity due.
C)Ted's annuity has a higher present value than Allison's.
D)Allison's annuity has a higher present value than Ted's.
E)Ted's annuity is an ordinary annuity.

Question 9

At a discount rate of 5 percent,which one of the following is the correct formula for computing the PV of $1 to be received one year from today?

A)$1/1.05
B)$1
C)$1 × 1.05
D)$1 × 1.05²
E)$1/1.05²

Question 10

The annual percentage rate:

A)considers interest on interest.
B)is the actual cost of a loan with monthly payments.
C)is higher than the effective annual rate when interest is compounded quarterly.
D)is the interest rate charged per period divided by (1 + n),when n is the number of periods per year.
E)equals the effective annual rate when the interest on an account is designated as simple interest.

Question 11

What effect will an increase in the discount rate have on the present value of a project that has an initial cash outflow followed by five years of cash inflows?

A)There will be no effect on the PV.
B)The PV will change but the direction of the change is unknown.
C)The PV will remain the same as the timing of the cash flows must change also.
D)The PV will increase.
E)The PV will decrease.

Question 12

A perpetuity differs from an annuity because:

A)perpetuity cash flows vary with the rate of inflation.
B)perpetuity cash flows vary with the market rate of interest.
C)perpetuity cash flows are variable while annuity payments are constant.
D)perpetuity cash flows never cease.
E)annuity cash flows occur at irregular intervals of time.

Question 13

An interest rate that is compounded monthly,but is expressed as if the rate were compounded annually,is called the ________ rate.

A)stated interest
B)compound interest
C)effective annual
D)periodic interest
E)daily interest

Question 14

Which one of these statements is correct concerning the time value of money?

A)Increasing the initial cost of a project increases the project's NPV.
B)Increasing the discount rate,increases the PV of a project.
C)Increasing the FV decreases the PV.
D)Decreasing the PV decreases the FV.
E)Decreasing the discount rate increases the FV.

Question 15

Assume an annuity will pay $1,000 a year for five years with the first payment occurring in Year 4,that is,four years from today.When you compute the present value of that annuity using the PV formula,the PV will be as of which point in time?

A)Today,Year 0
B)Year 1
C)Year 3
D)Year 4
E)Year 2

Question 16

You would be making a wise decision if you chose to:

A)base decisions regarding investments on effective rates and base decisions regarding loans on annual percentage rates.
B)assume all loans and investments are based on simple interest.
C)accept the loan with the lower effective annual rate rather than the loan with the lower annual percentage rate.
D)invest in an account paying 6 percent,compounded quarterly,rather than an account paying 6 percent,compounded monthly.
E)ignore the effective rates and concentrate on the annual percentage rates for all transactions.

Question 17

Binder and Sons borrowed $138,000 for three years from their local bank and now they are paying monthly payments that include both principal and interest.Paying off debt by making instalment payments,such as this firm is doing,is referred to as:

A)foreclosing on the debt.
B)amortizing the debt.
C)funding the debt.
D)calling the debt.
E)refunding the debt.

Question 18

You are considering two projects.Project A has projected cash flows of $6,500,$4,500,and $2,500 for the next three years,respectively.Project B has projected cash flows of $2,500,$4,500,and $6,500 for the next three years,respectively.Assuming both projects have the same initial cost,you know that:

A)there are no conditions under which the projects can have equal values.
B)Project B has a higher net present value than Project A.
C)Project A is more valuable than Project B given a positive discount rate.
D)both projects offer the same rate of return.
E)both projects have equal net present values at any discount rate.

Question 19

The net present value of a project is equal to the:

A)present value of the future cash flows.
B)present value of the future cash flows minus the initial cost.
C)future value of the future cash flows minus the initial cost.
D)future value of the future cash flows minus the present value of the initial cost.
E)sum of the project's anticipated cash inflows.

Question 20

You are comparing two investment options,each of which will provide $15,000 of total income.Option A pays five annual payments starting with $5,000 the first year followed by four annual payments of $2,500 each.Option B pays five annual payments of $3,000 each.Which one of the following statements is correct given these two investment options?

A)Both options are of equal value today.
B)Given a positive rate of return,Option A is worth more today than Option B.
C)Option B has a higher present value than Option A given a positive rate of return.
D)Option B has a lower present value than Option A given a zero rate of return.
E)Option A is preferable because it is an annuity due.

Question 21

Over the next three years,Marti plans to save $2,000,$2,500,and $3,000,respectively,starting one year from today.You want to have as much money as Marti does three years from now but you plan to make one lump sum investment today.What amount must you save today if you both earn 4.65 annually?

A)$6,811.50
B)$6,791.42
C)$7,128.23
D)$6,607.23
E)$7,500.00

Question 22

You have been offered a job that pays an annual salary of $48,000,$51,000,and $55,000 over the next three years,respectively.The offer also includes a starting bonus of $2,500 payable immediately.What is this offer worth to you today at a discount rate of 6.5 percent?

A)$129,640.14
B)$134,383.56
C)$132,283.56
D)$138,066.75
E)$130,983.56

Question 23

You are considering a project with projected annual cash flows of $32,200,$41,800,and $22,900 for the next three years,respectively.What is the present value of these cash flows at a discount rate of 14 percent?

A)$86,487.47
B)$75,866.20
C)$77,103.18
D)$81,292.25
E)$66,549.30

Question 24

Beatrice invests $1,000 in an account that pays 5 percent simple interest.How much more could she have earned over a period of 10 years if the interest had compounded annually?

A)$132.45
B)$135.97
C)$128.89
D)$117.09
E)$121.67

Question 25

Anna has $38,654 in a savings account that pays 2.3 percent interest.Assume she withdraws $10,000 today and another $10,000 one year from today.If she waits and withdraws the remaining entire balance four years from today,what will be the amount of that withdrawal?

A)$20,916.78
B)$20,109.08
C)$20,676.53
D)$19,341.02
E)$19,608.07

Question 26

Assume you borrow $12,000 for 5 years with equal annual repayments.If the interest rate on the actual loan turns out to be higher than you anticipated,then the:

A)total principal repaid will be less than anticipated.
B)loan will still have a balance due at the end of the 5-year amortization period.
C)first annual payment will repay more of the principal than anticipated.
D)anticipated amortization schedule will still apply as the loan is still a 5-year loan.
E)annual payments will be higher than you anticipated.

Question 27

Shawn has $2,500 invested at a guaranteed rate of 4.35 percent,compounded annually.What will his investment be worth after five years?

A)$2,997.04
B)$3,288.00
C)$3,321.32
D)$3,093.16
E)$2,857.59

Question 28

You expect an investment to return $11,300,$14,600,$21,900,and $38,400 annually over the next four years,respectively.What is this investment worth to you today if you desire a rate of return of 16.5 percent?

A)$64,253.91
B)$58,700.89
C)$63,732.41
D)$55,153.57
E)$59,928.16

Question 29

For a proposed purchase to be acceptable,the PV of the future cash flows must:

A)be positive at the relevant discount rate.
B)be less than the cost of the purchase.
C)equal or exceed the cost of the purchase.
D)equal the purchase price.
E)be positive at all discount rates.

Question 30

U Do It Centers deposited $3,200 in an account two years ago and is depositing another $5,000 today.A final deposit of $3,500 will be made one year from now.What will the account balance be three years from now if the account pays 4.85 percent interest,compounded annually?

A)$13,033.95
B)$13,430.84
C)$12,431.05
D)$14,328.90
E)$13,666.10

Question 31

What is the present value of $6,811 to be received in one year if the discount rate is 6.5 percent?

A)$6,395.31
B)$6,023.58
C)$6,643.29
D)$6,671.13
E)$7,253.72

Question 32

An insurance settlement offer includes annual payments of $36,000,$42,000,and $50,000 over the next three years,respectively,with the first payment being made one year from today.What is the minimum amount you should accept today as a lump sum settlement if your discount rate is 7 percent?

A)$119,877.67
B)$111,144.18
C)$105,000.10
D)$118,924.27
E)$114,556.88

Question 33

A project is expected to produce cash flows of $48,000,$39,000,and $15,000 over the next three years,respectively.After three years,the project will be worthless.What is the net present value of this project if the applicable discount rate is 15.25 percent and the initial cost is $78,500?

A)−$1,201.76
B)$2,309.09
C)−$3,457.96
D)$1,808.17
E)$3,132.48

Question 34

Stu can purchase a house today for $110,000,including the cost of some minor repairs.He expects to be able to resell it in one year for $129,000 after cleaning up the property.At a discount rate of 5.5 percent,what is the expected net present value of this purchase opportunity?

A)$13,001.61
B)$12,487.43
C)$12,274.88
D)$9,208.18
E)$11,311.02

Question 35

Theo is depositing $1,300 today in an account with an expected rate of return of 8.1 percent.If he deposits an additional $3,200 two years from today,and $4,000 three years from today,what will his account balance be ten years from today?

A)$14,044.89
B)$16,412.31
C)$15,182.53
D)$15,699.54
E)$17,741.71

Question 36

You plan to invest $6,500 for three years at 4 percent simple interest.What will your investment be worth at the end of the three years?

A)$7,280.00
B)$7,311.62
C)$7,250.00
D)$6,924.32
E)$6,760.00

Question 37

Assume a cash flow of $82,400 in the first year and $148,600 in the second year.Also assume a present value of $303,764.34 at a discount rate of 12.75 percent.What is the cash flow in the third year if that is the only other cash flow?

A)$163,100
B)$163,800
C)$164,900
D)$164,400
E)$163,700

Question 38

What rate of return should be used to compute the NPV of a proposed purchase of Smiley's,an operating business?

A)A discount rate equal to Smiley's current return on equity
B)The discount rate applicable to other investments with similar risks
C)A discount rate equal to Smiley's net profit percentage
D)The rate of interest charged by a bank for a loan similar in size to the cost of the purchase
E)A discount rate that makes the NPV of the proposed purchase positive

Question 39

Assume you borrow $6,600 for three years.How much will you still owe after the three years if you pay all of the payments as set forth in the loan's amortization schedule?

A)$6,500
B)$0
C)$2,200
D)$3,150
E)$2,650

Question 40

You have been awarded an insurance settlement of $250,000 that is payable one year from today.What is the minimum amount you should accept today in exchange for this settlement if you can earn 6.7 percent on your investments?

A)$232,866.67
B)$234,301.78
C)$242,408.19
D)$250,000.00
E)$238,079.19

Question 41

You have $2,500 to deposit into a savings account.The five banks in your area offer the following rates.In which bank should you deposit your savings?

A)Bank A: 3.75%,compounded annually
B)Bank B: 3.69%,compounded monthly
C)Bank C: 3.70% compounded semiannually
D)Bank D: 3.67% compounded continuously
E)Bank E: 3.65% compounded quarterly

Question 42

Suzette is receiving $10,000 today,$15,000 one year from today,and $25,000 four years from today.If she invests these funds immediately and earns 9.6 percent annually,how much will she have in savings 30 years from today?

A)$586,124.93
B)$591,414.14
C)$646,072.91
D)$620,008.77
E)$641,547.39

Question 43

The pawn shop adds 2 percent to loan balances for every two weeks a loan is outstanding.What is the effective annual rate of interest?

A)79.97 percent
B)73.08 percent
C)51.21 percent
D)67.34 percent
E)83.43 percent

Question 44

You would like to have $50,000 saved at the end of Year 5.At the end of Year 2,you can deposit $7,500 for this purpose.If you earn 4.5 percent,how much must you deposit today to reach your goal assuming no other deposits are made?

A)$33,254.58
B)$33,108.09
C)$34,276.34
D)$34,642.28
E)$34,912.63

Question 45

Fred purchased a city lot for $39,900.That lot has appreciated at 6.5 percent annually and is now valued at $287,400.How long has Fred owned this lot?

A)26.87 years
B)37.97 years
C)33.09 years
D)31.35 years
E)29.11 years

Question 46

Taylor's Hardware offers credit at an APR of 14.9 percent and compounds interest monthly.What actual rate of interest are they charging?

A)13.97 percent
B)14.90 percent
C)15.48 percent
D)15.96 percent
E)16.10 percent

Question 47

What is the annual percentage rate on a loan that charges interest of 1.65 percent per quarter?

A)6.50 percent
B)6.45 percent
C)6.54 percent
D)6.60 percent
E)6.72 percent

Question 48

Leo received $7,500 today and will receive another $5,000 two years from today.If he invests these funds immediately at 11.5 percent,what will his investments be worth five years from now?

A)$18,758.04
B)$18,806.39
C)$19,856.13
D)$20,314.00
E)$19,904.36

Question 49

Eleven years ago,a guitar cost $1,800.Today,that same guitar costs $3,650.What has been the inflation rate on this instrument?

A)6.64 percent
B)6.32 percent
C)6.57 percent
D)6.81 percent
E)6.49 percent

Question 50

A credit card compounds interest monthly and has an effective annual rate of 12.67 percent.What is the annual percentage rate?

A)12.35 percent
B)12.00 percent
C)11.99 percent
D)11.87 percent
E)11.93 percent

Question 51

The Smart Bank wants to be competitive based on quoted loan rates and thus must offer loans at an annual percentage rate of 7.9 percent.What is the maximum rate the bank can actually earn based on this quoted rate?

A)7.90 percent
B)8.18 percent
C)8.20 percent
D)8.22 percent
E)8.39 percent

Question 52

The government imposed a fine on a firm that requires a payment of $100,000 today,$150,000 one year from today,and $200,000 two years from today.The government will hold the funds until the final payment is collected and then donate the entire amount to charity.How much will be donated if the government pays 3 percent interest on the held funds?

A)$475,000
B)$460,590
C)$447,174
D)$451,050
E)$474,407

Question 53

Several years ago,Sara invested $4,208.Today,that investment is worth $28,406 and has earned an average annual rate of return of 7.38 percent.How long ago did Sara make her investment?

A)31.09 years
B)26.82 years
C)18.98 years
D)14.97 years
E)23.03 years

Question 54

You want to save an equal amount each year for the next 38 years,at which time you will retire.What amount of annual savings are needed if you desire a retirement income of $55,000 a year for 25 years and earn 7.5 percent,compounded annually?

A)$3,333.33
B)$2,640.85
C)$3,146.32
D)$2,889.04
E)$3,406.16

Question 55

What is the effective annual rate if your credit card charges you 10.64 percent compounded daily? (Assume a 365-day year.)

A)10.79 percent
B)11.22 percent
C)11.95 percent
D)11.48 percent
E)12.01 percent

Question 56

What is the effective annual rate of 10.25 percent compounded continuously?

A)10.98 percent
B)11.11 percent
C)10.79 percent
D)11.04 percent
E)10.86 percent

Question 57

Thirty-five years ago,your father invested $2,000.Today that investment is worth $98,407.What annual rate of return has been earned on this investment?

A)10.94 percent
B)11.33 percent
C)10.50 percent
D)11.77 percent
E)9.99 percent

Question 58

Marcos will receive an annuity payment of $2,500,payable every two years,for the next ten years.The next payment is due two years from today.What is the present value of this annuity at a discount rate of 5 percent?

A)$10,466.67
B)$11,221.08
C)$9,416.75
D)$10,052.48
E)$8,949.60

Question 59

Your credit card company charges you 1.35 percent per month.What is the annual percentage rate on your account?

A)16.45 percent
B)16.30 percent
C)16.39 percent
D)16.20 percent
E)16.56 percent

Question 60

If you invest $2,500 today,an investment guarantees you will have $3,600 four years from today.What rate of interest will you earn?

A)8.72 percent
B)9.03 percent
C)8.68 percent
D)9.39 percent
E)9.54 percent

Question 61

Scott has been offered an employment contract for ten years at a starting salary of $65,000 with guaranteed annual raises of 5 percent.What is the current value of this offer at a discount rate of 7 percent?

A)$638,724.17
B)$602,409.91
C)$558,845.85
D)$630,500.00
E)$525,000.00

Question 62

Assume you could invest $25,000 at a continuously compounded rate of 10 percent.What would your investment be worth at the end of 50 years?

A)$2,933,054
B)$3,500,824
C)$3,911,215
D)$3,710,329
E)$3,648,029

Question 63

Anna's grandmother established a trust and deposited $250,000 into it.The trust pays a guaranteed 4.25 percent rate of return.Anna will receive all the interest earnings on an annual basis and a charity will receive the principal amount at Anna's passing.How much income will Anna receive each year?

A)$10,000
B)$8,500
C)$12,400
D)$10,625
E)$12,750

Question 64

What is the future value of investing $5,650 for 14 years at a continuously compounded rate of 8.6 percent?

A)$17,933.54
B)$16,685.44
C)$19,369.83
D)$18,833.85
E)$13,183.85

Question 65

Uptown Industries just decided to save $3,000 a quarter for the next three years.The money will earn 2.75 percent,compounded quarterly,and the first deposit will be made today.If the company had wanted to deposit one lump sum today,rather than make quarterly deposits,how much would it have had to deposit to have the same amount saved at the end of the three years?

A)$34,441.56
B)$34,678.35
C)$33,428.87
D)$33,687.23
E)$34,998.01

Question 66

The preferred stock of ABC Co.offers a rate of return of 7.87 percent.The stock is currently priced at $63.53 per share.What is the amount of the annual dividend?

A)$5.20
B)$5.00
C)$4.60
D)$5.50
E)$6.00

Question 67

Lucas invested $4,500 at 6.2 percent,compounded continuously.What will his investment be worth after 15 years?

A)$15,557.78
B)$9,240.03
C)$11,405.29
D)$12,308.84
E)$8,685.00

Question 68

You want to establish a trust fund that will provide $50,000 a year forever for your heirs.If the fund can earn a guaranteed rate of return of 4.5 percent,how much must you deposit in a solitary lump sum to establish this trust?

A)$1,333,333
B)$2,250,000
C)$1,250,000
D)$1,666,667
E)$1,111,111

Question 69

Lois is purchasing an annuity that will pay $5,000 annually for 20 years,with the first annuity payment made on the date of purchase.What is the value of the annuity on the purchase date given a discount rate of 7 percent?

A)$54,282.98
B)$52,970.07
C)$56,677.98
D)$56,191.91
E)$66,916.21

Question 70

Assume your employer will contribute $50 a week for twenty years to your retirement plan.At a discount rate of 5 percent,compounded weekly,what is this employee benefit worth to you today?

A)$29,144.43
B)$35,920.55
C)$32,861.08
D)$26,446.34
E)$36,519.02

Question 71

You are comparing two annuities with equal present values.The applicable discount rate is 6.5 percent.One annuity will pay $2,000 annually,starting today,for 20 years.The second annuity will pay annually,starting one year from today,for 20 years.What is the annual payment for the second annuity?

A)$2,225
B)$2,075
C)$2,000
D)$2,130
E)$2,405

Question 72

Denise will receive annual payments of $10,000 for the next 25 years.The discount rate is 6.8 percent.What is the difference in the present value of these payments if they are paid at the beginning of each year rather than at the end of each year?

A)$8,069.29
B)$9,216.67
C)$9,706.67
D)$8,382.04
E)$8,850.00

Question 73

Wilt has a consulting contract that calls for annual payments of $50,000 a year for five years with the first payment due today.What is the current value of this contract if the discount rate is 8.4 percent?

A)$214,142.50
B)$201,867.47
C)$195,618.19
D)$197,548.43
E)$224,267.10

Question 74

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 percent interest per month.How much total interest does he expect to earn?

A)$3.94
B)$4.35
C)$1.34
D)$3.63
E)$5.96

Question 75

A trust has been established to fund scholarships in perpetuity.The next annual distribution will be $1,200 and future payments will increase by 3 percent per year.What is the value of this trust at a discount rate of 7.4 percent?

A)$17,189.19
B)$19,960.00
C)$27,272.73
D)$24,609.11
E)$30,388.18

Question 76

You just paid $525,000 for a security that will pay you and your heirs $25,000 a year forever.What rate of return will you earn?

A)4.95 percent
B)4.39 percent
C)4.76 percent
D)5.00 percent
E)4.50 percent

Question 77

Tracie will receive payments of $550 a month for ten years.What are these payments worth today at a discount rate of 6 percent,compounded monthly?

A)$49,540.40
B)$51,523.74
C)$53,737.08
D)$49,757.69
E)$48,808.17

Question 78

Olivia is willing to pay $185 a month for four years for a car payment.If the interest rate is 4.9 percent,compounded monthly,and she has a cash down payment of $2,500,what price car can she afford to purchase?

A)$10,961.36
B)$10,549.07
C)$8,533.84
D)$8,686.82
E)$8,342.05

Question 79

Benson's established a trust fund that provides $125,000 in college scholarships each year.The trust fund earns 6.15 percent and distributes only its annual income.How much money did Benson's contribute to establish this fund?

A)$2,291,613
B)$2,032,520
C)$2,150,000
D)$2,018,970
E)$1,987,408

Question 80

A preferred stock pays an annual dividend of $6.50 a share and has an annual rate of return of 7.35 percent.What is the stock price?

A)$74.50
B)$71.78
C)$92.09
D)$88.44
E)$77.78