Financial Management: Core Concepts, 4e (Brooks)
Chapter 4 The Time Value of Money (Part 2)
1) Your employer has agreed to place year-end deposits of $1,000, $2,000 and $3,000 into your
retirement account. The $1,000 deposit will be one year from today, the $2,000 deposit two years
from today, and the $3,000 deposit three years from today. If your account earns 5% per year,
how much money will you have in the account at the end of year three when the last deposit is
made?
A) $5,357.95
B) $6,000
C) $6,202.50
D) $6,727.88
2) Your company just sold a product with the following payment plan: $40,000 today, $35,000
next year, and $30,000 the following year. If your firm places the payments into an account
earning 6% per year, how much money will be in the account after collecting the last payment?
A) $118,767
B) $112,044
C) $94,074
D) $85,000
3) Given the following cash flows, what is the future value at year six when compounded at an
annual interest rate of 8.0%?
Year
0
2
4
6
Cash Flow
$9,000
$7,000
$5,000
$11,000
A) $38,955.39
B) $40,637.29
C) $42,074.42
D) $50,779.98
4) Given the following cash flows, what is the future value at year ten when compounded at an
interest rate of 4.0%?
Year
7
8
9
10
Cash Flow
$4,000
$3,000
$2,000
$1,000
A) $30,000.00
B) $25,267.31
C) $16,864.17
D) $10,824.26
5) The future value of a combination of positive and negative cash flows cannot be determined.
6) When solving for the future value of a stream of unequal cash flows, it is important to add
together the values BEFORE applying the future value formula to determine their future value.
7) When solving for future value, we use the term compounding of cash flows rather than the
term discounting of cash flows.
8) Weston Inc. just agreed to pay $8,000 today, $10,000 in one year, and $15,000 in two years to
a landowner to explore for, but not extract, valuable minerals. If the landowner invests the
money at a rate of 5.5% compounded annually, what is the investment worth two years from
today?
9) Elliot Industries invests a portion of its profits each year into a benefit emergency health care
account for its employees. For the last five years it has invested year-end amounts of $50,000,
$43,000, $26,000, $61,000, and $84,000. If the last deposit ($84,000) was made today and the
account earns an average of 7.3% per year, how much money is currently in the account,
assuming there have been no withdrawals?
4
Copyright © 2019 Pearson Education, Inc.
4.2 Future Value of an Annuity Stream
1) Your department at work places $8,000 every year-end into an account earning 5%. The
money is used when the corporate office fails to fully finance your profitable projects. The
money has not been touched since the first deposit was made exactly six years ago. If the most
recent deposit was made today, how much money is currently in the account?
A) $55,256.31
B) $60,000.00
C) $65,136.07
D) $68,019.13
2) If for the next 35 years you place $4,000 in equal annual year-end-deposits into an account
earning 8% per year, how much money will be in the account at the end of that time period?
A) $689,267.21
B) $777,169.56
C) $839,343.12
D) $2,606,942.58
3) You are saving money for a down payment on a new house. You intend to place $7,500 at the
end of each year for three years into an account earning 5% per year. At the end of the fourth
year, you will place $10,000 into this account. How much money will be in the account at the
end of the fourth year?
A) $26,873.08
B) $34,825.94
C) $37,918.00
D) $39,000.00
4) You just won a lottery—CONGRATULATIONS! Your parents have always told you to plan
for the future, so since you already have a well-paying job you decide to invest rather than spend
your lottery winnings. The payment schedule from the lottery commission is $100,000 after
taxes at the end of year one and 19 more payments of exactly $100,000 after taxes in equal
annual end-of-the-year deposits (i.e., 20 deposits of $100,000 each, the first deposit is one year
from today) into your account paying 8.5% compounded annually. How much money will be in
your account after the last deposit is made?
A) $2,000,000.00
B) $3,637,896.48
C) $4,099,549.23
D) $4,837,701.32
5) A/An ________ is a series of equal end-of-the-period cash flows.
A) ordinary annuity
B) annuity due
C) perpetuity due
D) None of the above
6) Which of the following is NOT an example of annuity cash flows?
A) Regular equal monthly rent payments
B) Equal annual deposits into a retirement account
C) The $50 of gasoline you put into your car every two weeks on pay day
D) All of the examples above are annuity cash flows.
7) Which of the following is NOT an example of annuity cash flows?
A) The university tuition bill you pay every month that is always the same
B) The grocery bill that changes every week
C) The $3.50 you pay every morning for a bagel and coffee as you run to your first morning
class
D) All of the examples above are annuity cash flows.
8) Which of the following is NOT an example of ordinary annuity cash flows?
A) Insurance payments due at the start of the period
B) Car loans due at the end of the period
C) Mortgage payments due at the end of the period
D) All of the examples above are ordinary annuity cash flows.
9) Johnson has an annuity due that pays $600 per year for 15 years. (Note: There are 15 annual
cash flows with the first cash flow occurring today.) What is the value of the cash flows 14 years
from today (immediately after the last deposit is made) if they are placed in an account that earns
7.50%?
A) $9,000.00
B) $9,675.00
C) $15,671.02
D) $16,846.35
10) On your first through fifth birthdays your parents placed $2,000 into your college fund (five
total deposits of $2,000 each). The account has earned an average of 8.5% per year until today,
your twenty-first birthday. How much money is in the account today?
A) $11,733.20
B) $37,219.70
C) $43,714.09
D) $42,383.41
11) Which of the following choices will result in a greater future value at age 65? Choice number
1 is to invest $3,000 per year from ages 20 through 26 (a total of seven investments) into an
account and then leave it untouched until you are 65 (another 39 years). Choice number 2 is to
begin at age 27 and make $3,000 deposits into an investment account every year until you are 65
years old (a total of 39 investments). Each account earns an average of 10% per year. (The
investments are end-of-year payments.)
A) Choice 1 is better than choice 2 because it has a FV of $1,304,146.89, which is greater than
choice 2 FV of $1,204,343.33.
B) Choice 2 is better than choice 1 because it has a FV of $1,304,146.89, which is greater than
choice 1 FV of $1,204,343.33.
C) Choice 2 is better than choice 1 because it has a FV of $1,204,343.33, which is greater than
choice 1 FV of $1,171,042.63.
D) Choice 1 is better than choice 2 because it has a FV of $1,288,146.89, which is greater than
choice 2 FV of $1,204,343.33.
12) What is the future value in year four of an ordinary annuity cash flow of $6,000 per year at
an interest rate of 12.00% per year?
A) $90,154.83
B) $93,761.02
C) $28,675.97
D) $32,117.08
13) What is the future value in year thirty-five of an ordinary annuity cash flow of $4,000 per
year at an interest rate of 11.0% per year?
A) $1,366,358.22
B) $555,000.32
C) $196,694.12
D) $140,000.00
14) Even with an interest rate of 0.0%, the future value of a 5-year $800 annual annuity will be
greater than the present value of the same annuity.
15) Given positive equal annual cash flows and a positive interest rate, the future value of an
annuity will be greater than the sum of the cash flows.
16) Given positive equal annual cash flows and a positive interest rate, the present value of an
annuity will be greater than the sum of the cash flows.
17) A trend among universities is to guarantee tuition to incoming freshmen for a four-year
period. Further, the annual amount due is collected in equal payments collected every three
months. Although the payments are equal as well as equally spaced, this is NOT an example of
an annuity because the payments are made every three months rather than on a monthly or
annual basis.
18) The formula for the Future Value Interest Factor of an Annuity (FVIFA) is .
19) Autorola plans to invest $5,000 per year in equal end-of-the-year amounts at an interest rate
of 6% compounded annually. How much will the firm have at the end of four years?
20) Amy Plisko is 23 years old and plans to retire in 32 years when she is 55 years old. Amy just
graduated from a university in the West. Upon graduation, she took a job with a starting annual
salary of $50,000. Amy asks you to answer the following two questions:
1. If her salary increases at a rate roughly equal to the U.S. long-run average annual rate of
inflation over the past 80 years (about 3% per year), how large will her annual salary be in her
last year before retirement? (Use 32 years.)
2. If her salary increases at a rate roughly equal to the U.S. long-run average annual rate of return
on common stocks over the past 80 years (about 10.5% per year), how large will her annual
salary be in her last year before retirement? (Use 32 years.)
After hearing your answers, Amy says, “WOW! That’s quite a difference.” She decides that she
would like an income of $500,000 per year each year in retirement, provided in equal annual
end-of-the-year cash flows. These cash flows need to last for 40 years, and her investments
would earn an annual rate of return of 7% during her retirement.
Amy’s final question to you is how much money must she save in equal annual end-of-the-year
cash flows for the next 32 years to provide for her desired retirement, if her investments earn
roughly the same rate of return as those earned by U.S. small stocks over the last 80 years
(geometric average is about 12% per year).
Use a calculator to determine the answers to the different parts of the problem.
12
Copyright © 2019 Pearson Education, Inc.
4. Calculator solution for the PMTs needed to get to the FV of $6,665,854.42 at T = 32:
MODE = END
INPUT 32 12.0 0 ? 6,665,854.42
KEY N I/Y PV PMT FV
CPT 21,866.18
Diff: 3
Topic: 4.2 Future Value of an Annuity Stream
AACSB: Analytical Thinking
LO: 4.2 Determine the future value of an annuity.
4.3 Present Value of an Annuity
1) The furniture store offers you no-money-down on a new set of living room furniture. Further,
you may pay for the furniture in three equal annual end-of-the-year payments of $750 each with
the first payment to be made one year from today. If the discount rate is 5%, what is the present
value of the furniture payments?
A) $2,042.44
B) $2,214.27
C) $2,333.39
D) $2,673.01
2) You have an annuity of equal annual end-of-the-year cash flows of $500 that begin three years
from today and last for a total of ten cash flows. Using a discount rate of 4%, what are those cash
flows worth in today’s dollars?
A) $3,899.47
B) $4,055.45
C) $3,749.49
D) $3,957.61
3) What is the present value of a stream of annual end-of-the-year annuity cash flows if the
discount rate is 0%, and the cash flows of $50 last for 25 years?
A) Less than $1,000
B) Exactly $1,250
C) Exactly $1,000
D) This question cannot be answered because we have an interest rate of 0.0%.
4) Which is greater, the present value of a five-year ordinary annuity of $300 discounted at 10%,
or the present value of a five-year ordinary annuity of $300 discounted at 0% that has its first
cash flow six years from today?
A) The first annuity because the cash flows occur sooner.
B) The second annuity because the cash flows are discounted at a 0% interest rate.
C) The two annuities are of equal value.
D) The answer to this question cannot be determined.
5) Which of the following is greater (answers rounded to the nearest cent)?
A) An ordinary annuity of $100.00 per year for three years discounted at 10% per year
B) A present value of $248.69
C) A future value of $331.00 three years from today, given an interest rate of 10% per year
D) You would be indifferent to the three choices since they all have the same present value when
using an interest rate of 10% per year.
6) You have the opportunity to purchase mineral rights to a property in Wyoming with expected
annual cash flows of $8,000 per year for ten years. If you discount these cash flows at a rate of
12% per year, what are these cash flows worth today if the cash flows occur at the end of each
period?
A) $45,201.78
B) $49,676.40
C) $80,000.00
D) $122,996.93
7) Five years ago, you paid for the right to receive twelve $25,000 annual end-of-the-year cash
flows. If discounting the cash flows at an annual rate of 8%, what did you pay for these cash
flows back then?
A) $474,428.16
B) $300,000.00
C) $128,223.20
D) $188,401.95
8) You estimate that the drive-through coffee kiosk you own will generate ordinary annuity after-
tax cash flows of $120,000 per year for the next ten years. If you discount these cash flows at an
annual rate of 11%, what is the present value of your expected cash flows?
A) $706,707.84
B) $782,417.35
C) $1,200,000.00
D) $2,900,594.27
9) You are paid to teach graduate-level classes for the university and want to determine how
much money the university makes from your graduate-level classes. Based on historical data,
you estimate that your graduate classes for the next six years will generate an average annual
revenue of $99,850. If you discount these cash flows at an annual rate of 7.30%, what is the
present value of the expected cash flows?
A) $895,133.52
B) $483,644.36
C) $471,562.95
D) $423,786.85
10) You are presented with two cash flow options: Option Near, a $5,000 annuity for three years,
with the first cash flow one year from today, or Option Far, a $5,000 annuity for six years with
the first cash flow ten years from today. Assuming an interest rate of 7.0%, which set of cash
flows has a greater present value?
A) Option Near has a greater PV of $13,121.58 vs. Option Far PV of $12,963.41.
B) Option Far has a greater PV of $13,121.58 vs. Option Near PV of $12,963.41.
C) Option Far has a greater PV of $30,000 vs. Option Near PV of $15,000.
D) Option Near and Option Far have the same PV of $12,963.41.
11) What is the present value today of an ordinary annuity cash flow of $4,000 per year for thirty
years at an interest rate of 6.0% per year?
A) $120,000.00
B) $55,059.32
C) $45,139.89
D) $32,270.87
12) What is the present value today of an ordinary annuity cash flow of $4,000 per year for thirty
years at an interest rate of 6.0% per year if the first cash flow is six years from today?
A) $120,000.00
B) $55,059.32
C) $45,138.89
D) $41,143.53
13) The formula for the Present Value Interest Factor of an Annuity (PVIFA) is .
14) Given positive equal annual cash flows and a positive interest rate, the present value of an
annuity will be greater than the sum of the cash flows.
15) When solving for present value, we use the term compounding of cash flows rather than the
term discounting of cash flows.
16) Your firm wishes to purchase a financial contract that provides equal end-of-the-year cash
flows of $18,000 per year for the next seven years. What is the present value of these cash flows
if you choose to discount them at a rate of 8% per year?
17) By choosing to attend college today, you have agreed to pay $17,000 per year in tuition and
fees for the next five years. (What… you really thought that you would graduate in four years?)
In addition to the tuition and fees, you have also given up the ability to work full time and earn
$23,000 per year for the next five years. If your required rate of return is 5% (the U.S. long-run
average rate of inflation plus an average real rate of return), what is the total cost in today’s
dollars of your college degree, assuming that all of the aforementioned cash flows are ordinary
annuities?
1) A series of equal periodic finite cash flows that occur at the beginning of the period are known
as a/an ________.
A) ordinary annuity
B) annuity due
C) perpetuity
D) amortization