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Corporate Finance: Core Principles & Apps, 5e (Ross)
Chapter 4 Discounted Cash Flow Valuation
1) 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.
2) 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%
3) 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.
4) The selection of an appropriate discount rate for a particular project is primarily dependent upon
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the project’s
A) time to closure.
B) initial cost.
C) level of risk.
D) starting date.
E) expected dollar return.
5) 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.
6) 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.
7) 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
8) 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
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9) 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.
10) 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.
11) 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.
12) 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.
13) 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.
14) 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.
15) 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
16) 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.
17) The highest effective annual rate that can be derived from an annual percentage rate of 9
percent is computed as
A) 0.09e – 1
B) e0.09 × (1 / 0.09)
C) e0.09 – 1
D) e × (1 + 0.09)
E) (1 + 0.09)e
18) 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.
19) 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
20) 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
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21) 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)
22) 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
23) 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.
24) 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.
25) 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
26) 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.
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27) 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.
28) 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.
29) 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.
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
31) 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)
32) 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)
33) 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
34) 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
35) 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
36) 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.
37) 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.
38) 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).
39) 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
40) 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.
41) 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
42) 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
43) 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%
44) 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
45) 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
46) 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
47) 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