Deck 4: Discounted Cash Flow Valuation

Question 1

Given a positive rate of return and multiple time periods,compound interest

A)increases in an exponential manner.
B)increases in a linear manner.
C)produces the same future values as simple interest.
D)provides future values that are less than those provided by simple interest.
E)increases at a decreasing rate.

Answer 1

increases in an exponential manner.

Question 2

The selection of an appropriate discount rate for a particular project is primarily dependent upon the project's

A)time to closure.
B)initial cost.
C)level of risk.
D)starting date.
E)expected dollar return.

Answer 2

level of risk.

Question 3

Which one of the following statements concerning the annual percentage rate (APR)is correct?

A)The APR considers interest on interest.
B)The rate of interest you actually pay on a loan is called the APR.
C)The effective annual rate is lower than the APR when an interest rate is compounded quarterly.
D)Lenders are not permitted to disclose or advertise the APR of a loan.
E)The APR equals the effective annual rate when simple interest is applied to a loan.

Answer 3

The APR equals the effective annual rate when simple interest is applied to a loan.

Question 4

Which one of the following statements concerning interest rates is correct?

A)The stated rate is the same as the effective annual rate.
B)Banks are most apt to prefer more frequent compounding on their savings accounts.
C)The annual percentage rate increases as the number of compounding periods per year increases.
D)An effective annual rate is the rate that applies if interest were charged annually.
E)For any positive rate of interest,the effective annual rate will always exceed the annual percentage rate.

Question 5

An interest rate expressed as if it were compounded once per year is called the

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

Question 6

Investment options A and B are equally risky and have identical initial costs.Each investment will produce cash inflows of $20,000.Option A will pay $8,000 the first year followed by four annual payments of $3,000 each.Option B will pay five annual payments,starting in 1 year,of $4,000 each.Which one of the following statements is correct given these two investment options? Assume a positive rate of return.

A)Neither investment should be undertaken.
B)Option A is the better investment.
C)Option B has a higher net present value.
D)Option B has a lower future value at Year 5.
E)Both options are of equal value.

Question 7

The effective annual rate (EAR)of a loan will increase if

A)the frequency of the interest rate compounding is decreased.
B)the interest is changed from compound to simple interest at the same annual percentage rate (APR).
C)the annual percentage rate (APR)is decreased.
D)either the annual percentage rate (APR)or the compounding frequency is increased.
E)the compounding of interest is changed from continuous compounding to daily compounding.

Question 8

Which one of the following would have the greatest value assuming each has a Year 0 cash flow of zero and a Year 1 annual cash flow of $100? Assume a discount rate of 8 percent,compounded annually.Also,assume any growth rate is positive.

A)Perpetuity
B)Annuity
C)Growing perpetuity
D)Growing annuity
E)Growing perpetuity or growing annuity,as they would have equal values

Question 9

Assume a stated rate of interest of 8 percent.Which form of compounding will produce the highest effective rate of interest?

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

Question 10

By federal law,lenders must disclose

A)the APR,excluding fees or other noninterest charges.
B)the EAR,excluding fees or other noninterest charges.
C)the APR,including fees and other noninterest charges.
D)the EAR,including fees and other noninterest charges.
E)both the APR and EAR,excluding fees and other charges.

Question 11

Kate starts saving for retirement today and plans to make annual contributions into this retirement account.Which one of these is most apt to increase the total amount she has saved on the day she retires? Assume she earns a positive rate of return each year.

A)Retiring at age 62 rather than age 66
B)Decreasing the investment's average rate of return
C)Decreasing the amount she saves each year
D)Delaying her retirement by 1 year
E)Delaying any additions to her savings by 1 year

Question 12

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

A)0.09^e - 1
B)e^0.09 × (1 / 0.09)
C)e^0.09 - 1
D)e × (1 + 0.09)
E)(1 + 0.09)^e

Question 13

You are comparing two investments,A and B,with unequal annual cash flows and varying numbers of years.Which one of these statements is correct regarding this comparison?

A)If A has the higher net present value at one discount rate,then A will have the higher net present value at all other discount rates.
B)If B has a higher net present value,then B will have the higher net future value at any point in time,given a stated discount rate.
C)If B has a higher net future value at one discount rate,then B will have the higher net present value given any discount rate.
D)The two projects cannot be compared since their time periods differ in length.
E)The project with the greater number of years will have the higher present value.

Question 14

Which one of the following will increase the present value of a finite stream of even cash flows? Assume a positive rate of return.

A)Moving every cash flow one time period further into the future
B)Decreasing the amount of each cash flow
C)Increasing the Time 2 cash flow by $100 and lowering the Time 3 cash flow by $100
D)Moving the Time 1 cash inflow to Time 2
E)Increasing the discount rate

Question 15

You want to make a one-time deposit today that will increase in value to $100 at the end of this year.Which rate of interest will allow you to deposit the least amount today to reach this goal?

A)3.8%
B)2.6%
C)2.9%
D)3.6%
E)3.4%

Question 16

Which one of these statements related to the time value of money is correct? Assume a positive rate of interest.

A)A dollar increases in value the further into the future it is received.
B)The future value of an invested dollar is inversely related to the rate of interest.
C)The present value of a dollar to be received in 1 year is directly related to the interest rate.
D)A dollar received today is more valuable than a dollar received next month.
E)A dollar invested today will increase in value in a linear manner if interest earned is reinvested.

Question 17

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

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

Question 18

Discounting cash flows involves

A)taking the cash discount offered on trade merchandise.
B)estimating only the cash flows that occur in the first 4 years of a project.
C)adjusting only those cash flows that occur at least 10 years in the future.
D)multiplying expected future cash flows by the cost of capital.
E)adjusting all expected future cash flows to their current value.

Question 19

Which term applies to a set of cash flows that are finite in number and increase in amount at a steady rate?

A)Perpetuity
B)Growing annuity
C)Growing perpetuity
D)Annuity
E)Lump sum payment

Question 20

The net present value of an investment is best defined as the

A)current cost if the investment is made today.
B)net value received at the end of the investment period.
C)present value of the investment's future cash flows minus the investment's cost.
D)net decrease in value caused by waiting to receive the cash benefit from the investment.
E)value received at the end of the investment period minus the investment's cost.

Question 21

Which one of these is the best indicator that acquiring a firm is a good idea?

A)The firm has a positive NPV at an appropriate discount rate.
B)The firm has a negative NPV at all positive discount rates.
C)The firm has a positive NPV at the riskless rate of return.
D)The firm has increasing cash inflows.
E)The firm is growing on an annual basis.

Question 22

Wise University expects to receive $100 next year from a new donor.They also expect this amount to increase by 3 percent annually and to continue forever.Which formula will correctly compute the current value of this donation at a discount rate of 13 percent?

A)$100 / 0.13 + 0.03
B)$100 / (0.13 - 0.03)
C)($100 × 1.03)/ 0.13
D)($100 × 1.03)/ (0.13 - 0.03)
E)$100 + ($100 × 1.03)/ (0.13 - 0.03)

Question 23

Which type(s)of loan repays the interest as an annuity and the principal as a lump sum?

A)Pure discount loans
B)Both amortized and interest-only loans
C)Amortized loans
D)Both interest-only and amortized loans
E)Interest-only loans

Question 24

The future value of an annuity due is computed as

A)C(1 + r)^T
B)C{[(1 + r)^T - 1] / r}
C)C{[(1 + r)^T - 1] / (1 + r)}
D)C(1 + r)^T - 1 / (1 + r)
E)C{[(1 + r)^T - 1] / r}(1 + r)

Question 25

In which type of loan does the borrower initially receive the present value of the future lump sum loan repayment amount?

A)Pure discount loan
B)Both pure discount and interest-only loans
C)Amortized loan
D)Both interest-only and amortized loans
E)Interest-only loan

Question 26

The value of a firm is best defined as the

A)sum of all of the firm's future cash flows.
B)current year's cash flow times (1 + g).
C)current year's cash flow divided by r.
D)total present value of all of the firm's future cash flows.
E)current year's cash flows divided by (g - r).

Question 27

The growing perpetuity present value formula assumes that

A)g = r and the time periods are limited in number.
B)g < r and the time periods are regular and discrete.
C)the growth rate increases as time progresses.
D)the first cash flow occurs at Time 0.
E)g < r and the time periods are finite.

Question 28

An annuity stream where the payments occur forever is called a(n)

A)annuity due.
B)indemnity.
C)perpetuity.
D)amortized cash flow stream.
E)ordinary annuity.

Question 29

Given a firm with positive annual cash flows,which one of the following will increase the current value of that firm?

A)Increasing the annual growth rate of the cash flows
B)Increasing the discount rate
C)Decreasing the amount of each cash flow
D)Decreasing the life of the firm
E)Increasing either the growth rate of the cash flows or the discount rate

Question 30

A 10-year,$600 annuity pays its first payment at Date 3.If you compute the present value of this annuity,the computed value will be as of Date

A)0
B)1
C)2
D)3
E)4

Question 31

Annuities with payments occurring at the end of each time period are called ________,whereas annuities with payments occurring at the beginning of each time period are called ________.

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

Question 32

Later on today,you will receive an annual dividend of $2.50 a share on ABC stock.The dividend is expected to increase by 2 percent annually thereafter.Which formula should be used to compute the value of the stock today if the discount rate is 14 percent?

A)$2.50 + $2.50 / 0.14
B)($2.50 × 1.02)/ (0.14 - 0.02)
C)($2.50 × 1.02)/ 0.14
D)$2.50 + ($2.50 × 1.02)/ (0.14 - 0.02)
E)$2.50 + ($2.50 × 1.02)/ 0.14

Question 33

The present value of an ordinary annuity formula is

A)(C / r)(1 / (1 + r)^T(1 + r)
B)C({1 - [1 / (1 + r)^T]}/ r)
C)[C(1 + r)^T/ r] / (1 + r)
D)(C / r)(1 / (1 + r)^T
E)C(1 + r)^T/ r(1 + r)

Question 34

Which statement applies to an amortized loan that requires fixed principal payments?

A)The loan payments will be either an ordinary annuity or an annuity due.
B)The final loan payment will equal the required principal payment amount.
C)The interest is paid only at loan maturity.
D)The loan payments are an annuity due.
E)The loan payments will decrease over time.

Question 35

A growing annuity is a set of

A)arbitrary cash flows occurring each time period for no more than 10 years.
B)level cash flows occurring each time period forever.
C)steadily increasing cash flows occurring each time period for a fixed number of periods.
D)increasing cash flows occurring each time period forever.
E)level cash flows occurring each time period for a fixed period of time.

Question 36

Which statement is correct regarding amortized loans with equal payments?

A)If you pay more than the scheduled amount,the additional payment will reduce the total interest paid over the life of the loan.
B)The final loan payment will all be applied to the outstanding principal balance.
C)The interest is paid only at loan maturity.
D)If you pay more than the scheduled amount,the additional payment will increase the remaining principal balance.
E)The principal portion of each payment will decrease over time.

Question 37

An annuity

A)has greater value than a comparable perpetuity.
B)is either an equal or an unequal stream of payments that occur in equal time periods for a finite period of time.
C)is a stream of payments that fluctuate with current market interest rates.
D)is a stream of equal payments that occur in equal periods of time for a finite period.
E)has a longer life span than a perpetuity.

Question 38

An investment will pay $3,000 every 3 years with the first payment occurring 3 years from today.The investment has a 12-year life.To compute the present value of this investment you need to calculate the

A)present value of a $3,000,12-year annuity,and divide the result by 4.
B)present value of a $1,000 annuity with 12 time periods.
C)rate of growth for each 3-year period.
D)present value of a $3,000 annual annuity with four payments and discount that value for 3 years.
E)interest rate for the 3-year period.

Question 39

Which type(s)of loan can be repaid with annuity payments?

A)Pure discount loan
B)Both pure discount and interest-only loans
C)Amortized loan
D)Both interest-only and amortized loans
E)Interest-only loan

Question 40

Assume two annuities will each provide $500 annual cash flows for 5 years.One is an ordinary annuity and the other is an annuity due.Which statement concerning these annuities is correct?

A)The ordinary annuity will pay on the first day of each time period.
B)The annuity due is more valuable than the ordinary annuity.
C)The annuity due will pay one more payment than the ordinary annuity.
D)The ordinary annuity will have the highest value at the end of Year 4.
E)Both annuities are of equal value given any positive discount rate.

Question 41

You are considering two insurance settlement offers.The first offer includes annual payments of $25,000,$17,500,and $12,500,with the first payment being paid 1 year from now.The other offer is a lump sum amount today.What is the minimum amount you will accept today in lieu of the annual payments if you require a discount rate of 6.2 percent?

A)$50,877.67
B)$49,492.88
C)$52,213.15
D)$55,000.00
E)$54,556.88

Question 42

Erickson's is considering a project with an initial cost of $623,000.The project will produce cash inflows of $33,500 monthly for 21 months.What is the annual rate of return on this project?

A)11.57%
B)13.59%
C)16.59%
D)17.47%
E)18.44%

Question 43

A project is expected to produce cash flows of $12,800,$15,900,and $18,000 over the next 3 years,respectively.After 3 years,the project will be discontinued.What is this project worth today at a discount rate of 12.5 percent?

A)$35,201.76
B)$34,435.74
C)$36,582.72
D)$36,808.17
E)$35,758.00

Question 44

1 year ago,the Jenkins Center opened an investment account and deposited $5,000.Today,it is depositing an additional $6,000 and will make a final deposit of $7,500 1 year from now.How much will the firm have saved 3 years from now if it earns an average annual return of 6.5 percent?

A)$19,159.67
B)$22,430.84
C)$23,628.86
D)$20,832.60
E)$22,186.72

Question 45

You are considering a job that offers a starting bonus of $2,500,paid immediately,and an annual salary of $44,000,$47,000,and $50,000 for the next 3 years,respectively.The annual salary is paid at the end of each year.What is this offer worth today at a discount rate of 5.6 percent?

A)$158,283.49
B)$154,383.50
C)$139,283.56
D)$128,773.82
E)$142,983.33

Question 46

What is the annual percentage rate on a loan with a stated rate of 2.109 percent per quarter?

A)8.717%
B)9.174%
C)8.036%
D)8.707%
E)8.436%

Question 47

Rita plans to save $1,500,$1,500,and $2,500 a year over the next 3 years,respectively.How much would you need to deposit in one lump sum today to have the same amount as Rita 3 years from now if you both earn 3.5 percent,compounded annually?

A)$4,857.92
B)$5,104.40
C)$5,491.42
D)$6,097.95
E)$4,434.87

Question 48

What is the effective annual rate if a firm charges you 7.75 percent,compounded daily,based on a 360-day year?

A)7.928%
B)7.994%
C)8.057%
D)7.582%
E)8.109%

Question 49

Cast Out Co.invested $37,900 in a project.At the end of three years,the company sold the project for $62,500.What annual rate of return did the firm earn on this project?

A)16.91%
B)19.20%
C)18.14%
D)18.67%
E)17.47%

Question 50

What is the effective annual rate on a loan with an APR of 10.6 percent if interest is compounded daily? Assume a 365-day year.

A)10.08%
B)11.02%
C)10.72%
D)10.16%
E)11.18%

Question 51

What is the effective annual rate if the APR is 5.25 percent,compounded semiannually?

A)5.278%
B)5.299%
C)5.306%
D)5.313%
E)5.319%

Question 52

Antonio is going to receive $25,000 today as an insurance settlement.In addition,he will receive $12,000 1 year from today and $10,000 2 years from today.If he invests these funds,how much will he have saved when he retires 32 years from now if he earns an average annual return of 6.7 percent?

A)$456,124.93
B)$461,414.14
C)$395,072.90
D)$407,008.77
E)$358,726.88

Question 53

This morning,you invested your tax refund of $638 at an interest rate of 3.1 percent,compounded annually.How much will this investment be worth 7 years from now?

A)$818.40
B)$775.57
C)$894.15
D)$790.01
E)$921.60

Question 54

Beatrice is investing $5,000 in an account that pays 4 percent simple interest.How much more could she have earned over a period of 10 years if the interest had compounded annually?

A)$414.79
B)$0
C)$385.65
D)$401.22
E)$390.70

Question 55

You will be receiving $11,500 one year from now.What is the present value of this amount at a discount rate of 7.83 percent?

A)$10,664.94
B)$9,747.41
C)$11,201.16
D)$11,414.32
E)$10,015.89

Question 56

What is the effective annual rate if the APR is 6.35 percent,compounded continuously?

A)6.427%
B)6.447%
C)6.539%
D)6.602%
E)6.556%

Question 57

You expect to receive $5,400 2 years from now,$6,300 3 years from now,and $10,900 6 years from now.What is the future value of these cash flows 7 years from now if the interest rate is 7.4 percent,compounded annually?

A)$25,916.78
B)$28,109.08
C)$27,805.20
D)$29,341.02
E)$25,889.39

Question 58

You expect to receive $1,800 at the end of 5 years.What is the present value of this payment if the interest rate is 7.12 percent,compounded continuously?

A)$1,271.64
B)$1,276.20
C)$1,269.41
D)$1,257.78
E)$1,260.85

Question 59

You are paying an effective annual rate of 18.87 percent on your credit card.The interest is compounded monthly.What is the annual percentage rate?

A)18.50%
B)17.41%
C)17.79%
D)17.91%
E)18.31%

Question 60

A proposed 3-year project has expected annual cash inflows of $5,600,$7,900,and $11,200,for Years 1 to 3,respectively.What is the net present value of this project at a discount rate of 16 percent if the initial cost is $7,800?

A)$10,713.62
B)$10,073.94
C)$14,103.18
D)$12,292.25
E)$9,899.36

Question 61

Jensen's Shipping wants to expand as soon as it can save $112 million.Towards that goal,the firm started saving 3 years ago and currently has $38.2 million saved.Starting today,the firm will add $15,000 a month to this savings account.The rate of return is 7.1 percent,compounded monthly.How long will it be from now before the company can expand?

A)14.60 years
B)16.52 years
C)15.67 years
D)16.08 years
E)15.39 years

Question 62

Your credit card company quotes you a rate of 17.9 percent,compounded daily.What actual rate of interest you are paying? Assume a 365-day year.

A)18.97%
B)19.81%
C)18.48%
D)19.60%
E)18.79%

Question 63

You desperately need some money and only your "miserly" friend has any.He agrees to loan you the money you need if you make payments of $25 a month for the next 6 months.In keeping with his reputation,he requires that the first payment be paid today.He also charges you 1.65 percent interest per month.How much money are you borrowing?

A)$144.04
B)$140.98
C)$113.94
D)$141.70
E)$114.96

Question 64

Martha receives $200 on the first of each month.Stewart receives $200 on the last day of each month.Both Martha and Stewart will receive payments for 30 years.The discount rate is 9 percent,compounded monthly.What is the difference in the present value of these two sets of payments?

A)$186.43
B)$194.29
C)$192.60
D)$188.05
E)$191.13

Question 65

An investment will pay $1,200 per quarter for 15 years.You require a return of 12 percent,compounded quarterly,for this type of investment.How much is this investment worth to you today?

A)$33,210.68
B)$28,409.08
C)$31,152.59
D)$28,395.10
E)$30,806.30

Question 66

Rodget's is saving $2,500 a month,starting today,and continuing for 4 years.The firm expects to earn 5.6 percent,compounded monthly.If the firm had wanted to deposit an equivalent lump sum today,how much would it have had to deposit?

A)$107,286.58
B)$108,601.95
C)$105,330.60
D)$107,787.25
E)$108,998.01

Question 67

Angela expects to save $500 a year and earn an average annual return of 5.2 percent.How much will her savings be worth 35 years from now?

A)$51,317.82
B)$57,702.57
C)$47,076.06
D)$44,868.92
E)$56,063.66

Question 68

You are comparing two annuities with equal present values.The applicable discount rate is 6.65 percent,compounded annually.One annuity pays $4,500 on the first day of each year for 25 years.How much does the second annuity pay each year for 25 years if it pays at the end of each year?

A)$4,708.03
B)$4,623.87
C)$4,608.51
D)$4,799.25
E)$4,747.50

Question 69

An investment will pay $5,500 every 2 years for the next 40 years.The annual rate of interest is 12 percent.What is the value of this investment at the end of Year 40?

A)$1,630,590.34
B)$1,096,222.20
C)$1,206,504.11
D)$1,353,997.81
E)$1,990,095.67

Question 70

Today,you are retiring.You have a total of $387,419 in your retirement savings and have the funds invested at a guaranteed 3.68 percent,compounded monthly.You want to withdraw $1,500 at the beginning of every month,starting today.You also want the withdrawals to stop when your account balance declines to $100,000.For how many years can you make withdrawals?

A)36.52 years
B)34.43 years
C)34.22 years
D)35.24 years
E)36.22 years

Question 71

Theo just won a prize that will pay him $10,000 a year for 10 years,starting at the end of Year 10.What is the current value of this prize if the discount rate is 7 percent,compounded annually?

A)$37,982.98
B)$35,704.33
C)$38,203.63
D)$36,191.91
E)$35,928.70

Question 72

A bank is loaning $5,000 for 3 years at an interest rate of 7.5 percent.How much additional interest can the bank earn if it compounds interest continuously rather than annually?

A)$61.65
B)$56.67
C)$51.78
D)$50.13
E)$48.89

Question 73

An annuity costs $185,000 today and provides monthly payments of $950 for 40 years.The first payment occurs 1 month from today.What annual rate of return does this annuity offer?

A)5.33%
B)5.47%
C)5.16%
D)4.79%
E)4.56%

Question 74

Today,the Future Trust Co.purchased an investment that will pay $6,000 at the end of 5 years.Every year thereafter,the payment will increase by 1.6 percent.What is the value of this investment today if the required rate of return is 7.4 percent?

A)$62,300.00
B)$73,894.23
C)$65,647.81
D)$77,751.03
E)$83,984.23

Question 75

Clint just won a prize that will pay him $15,000 a year for 15 years,starting at the end of Year 5.What is the current value of this prize if the discount rate is 7 percent,compounded annually?

A)$102,655.52
B)$98,550.64
C)$104,225.76
D)$116,191.91
E)$108,806.61

Question 76

Walt can afford monthly car payments of $140 for 3 years,starting 1 month from now.The interest rate is 4.6 percent,compounded monthly.How much can he afford to borrow to buy a car?

A)$4,961.36
B)$4,717.32
C)$4,533.80
D)$5,333.88
E)$4,699.31

Question 77

Suzie just won the lottery! As her prize,she will receive $2,500 a month for 10 years.The first payment will be paid today.At 6 percent,compounded monthly,what is this prize worth to her today?

A)$224,647.53
B)$223,940.48
C)$224,953.46
D)$225,183.63
E)$226,309.55

Question 78

Your parents have been investing $25 a week for the past 18 years into an account for you.Today,this investment account is worth $60,762.53.Interest is compounded weekly.What is the annual rate of return?

A)8.80%
B)8.47%
C)8.16%
D)9.62%
E)9.34%

Question 79

East Coast Investors invested $28,000 a year into a project for the past 7 years.Today,the project was sold for a net of $324,000.What is the rate of return,ignoring taxes?

A)17.43%
B)17.06%
C)15.59%
D)16.67%
E)16.44%

Question 80

The Life Trust Co.purchased an investment that will pay $5,000 next year.Every year thereafter,the payment will increase by 1.25 percent.What is the value of this investment if the required rate of return is 8.3 percent?

A)$62,300.00
B)$60,993.98
C)$65,647.81
D)$70,921.99
E)$73,984.23