COPYRIGHT AND DISCLAIMER NOTICE:
Copyright, 2012. This document is the sole, Copyrighted property of Dr. Michael R. Williams.
Unauthorized republication, redistribution, storage, and/or transmission, by or on any means, electronic, mechanical, photocopying, recording, and so on, for any
reason, educational or otherwise, of any of Dr. Williams’ material, including this Document, in part or in whole, is strictly prohibited without the prior written consent of
Dr. Williams. Additionally, Dr. Williams makes no guarantee, representation, or warranty regarding the information and/or data provided in this Document. The
information provided and/or opinions expressed within this Document are subject to change without notice or liability to any party. Dr. Williams expressly disclaims
any liability arising from or in reliance upon any part of this Document or any other information provided by Dr. Williams or Governors State University. Dr. Williams
is not responsible or liable, directly or indirectly, for any damage, loss, or liability caused or alleged to be caused by or in connection with any use of or reliance on any
content.
Chapter 5 Homework Problems
P1 Using a Time Line
The finance manager at Starbucks is considering an investment that requires an initial outlay of $25,000 and is
expected to receive cash inflows of $3,000, $6,000, $0, $10,000, $8,000, and $7,000 at the end of years 1
through six, respectively.
a.) Draw and label a timeline depicting the cash inflows and outflows associated with the investment.
b.) Use arrows on the timeline to demonstrate how compounding the cash flows leads to the future value
of the project at the end of year six.
c.) Use arrows on the timeline to demonstrate how discounting the cash flows leads to the present value
of the project back to year zero.
P2 Future Value Calculation
Without referring to the preprogrammed function on your financial calculator, use the basic formula for future
value along with the given interest rate, r, and the number of periods, n, to calculate the future value of $1 in
each of the cases shown in the following table.
Case Interest rate, r Number of periods, n
A 12% 2
B 6% 3
C 9% 4
D 3% 5
P3 Future Value
You have $100 to invest. If you can earn 12% interest, about how long does it take for your $100 investment to
grow to $200? Suppose the interest rate is just half that, at 6%. At half the interest rate, does it take twice as
long to double your money? Why or why not? How long does it take?
COPYRIGHT AND DISCLAIMER NOTICE:
Copyright, 2012. This document is the sole, Copyrighted property of Dr. Michael R. Williams.
Unauthorized republication, redistribution, storage, and/or transmission, by or on any means, electronic, mechanical, photocopying, recording, and so on, for any
reason, educational or otherwise, of any of Dr. Williams’ material, including this Document, in part or in whole, is strictly prohibited without the prior written consent of
Dr. Williams. Additionally, Dr. Williams makes no guarantee, representation, or warranty regarding the information and/or data provided in this Document. The
information provided and/or opinions expressed within this Document are subject to change without notice or liability to any party. Dr. Williams expressly disclaims
any liability arising from or in reliance upon any part of this Document or any other information provided by Dr. Williams or Governors State University. Dr. Williams
is not responsible or liable, directly or indirectly, for any damage, loss, or liability caused or alleged to be caused by or in connection with any use of or reliance on any
content.
P4 Future Values
For each of the cases shown in the following table, calculate the future value of the single cash flow deposited
today at the end of the deposit period if the interest is compounded annually at the rate specified.
Case Single cash flow Interest rate Deposit period (years)
A $ 200 5% 20
B $ 4,500 8% 7
C $ 10,000 9% 10
D $ 25,000 10% 12
E $ 37,000 11% 5
F $ 40,000 12% 9
P5 Time Value
As part of your financial planning, you wish to purchase a new car exactly 5 years from today. The car you wish
to purchase costs $14,000 today, and your research indicates that its price will increase by 2% to 4% per year
over the next 5 years.
a.) Estimate the price of the car at the end of 5 years if inflation is (1) 2% per year and (2) 4% per year.
b.) How much more expensive will the car be if the rate of inflation is 4% rather than 2%?
c.) Estimate the price of the car if inflation is 2% for the next 2 years and 4% for 3 years after that.
P6 Time Value
Misty needs to have $15,000 at the end of 5 years to fulfill her goal of purchasing a small sailboat. She is
willing to invest a lump sum today and leave the money untouched for 5 years until it grows to $15,000, but she
wonders what sort of investment return she will need to earn to reach her goal. Use your calculator or
spreadsheet to figure out the approximate annually compounded rate of return needed in each of these cases:
a.) Misty can invest $10,200 today.
b.) Misty can invest $8,150 today.
c.) Misty can invest $7,150 today.
COPYRIGHT AND DISCLAIMER NOTICE:
Copyright, 2012. This document is the sole, Copyrighted property of Dr. Michael R. Williams.
Unauthorized republication, redistribution, storage, and/or transmission, by or on any means, electronic, mechanical, photocopying, recording, and so on, for any
reason, educational or otherwise, of any of Dr. Williams’ material, including this Document, in part or in whole, is strictly prohibited without the prior written consent of
Dr. Williams. Additionally, Dr. Williams makes no guarantee, representation, or warranty regarding the information and/or data provided in this Document. The
information provided and/or opinions expressed within this Document are subject to change without notice or liability to any party. Dr. Williams expressly disclaims
any liability arising from or in reliance upon any part of this Document or any other information provided by Dr. Williams or Governors State University. Dr. Williams
is not responsible or liable, directly or indirectly, for any damage, loss, or liability caused or alleged to be caused by or in connection with any use of or reliance on any
content.
P7 Present Value Concept
Answer each of the following questions.
a.) What single investment made today, earning 12% annual interest, will be worth $6,000 at the end of
6 years?
b.) What is the present value of $6,000 to be received at the end of 6 years if the discount rate is 12%?
c.) What is the most you would pay today for a promise to repay you $6,000 at the end of 6 years if your
opportunity cost is 12%?
P8 Cash Flow Investment Decision
Tom Alexander has an opportunity to purchase any of the investments shown in the following table. The
purchase price, the amount of the single cash inflow, and its year of receipt are given for each investment.
Which purchase recommendations would you make, assuming that Tom can earn 10% on his investments?
Case Price Single cash inflow Year of receipt
A $18,000 $ 30,000 5
B $ 600 $ 3,000 20
C $ 3,500 $ 10,000 10
D $ 1,000 $ 15,000 40
P9 Future Value of an Annuity
For each case in the accompanying table, answer the questions that follow.
Case Amount of annuity Interest rate Deposit period (years)
A $ 2,500 8% 10
B $ 500 12% 6
C $ 30,000 20% 5
D $ 11,500 9% 8
E $ 6,000 14% 30
a.) Calculate the future value of the annuity assuming that it is
(1) An ordinary annuity.
(2) An annuity due.
b.) Compare your findings in parts a(1) and a(2). All else being identical, which type of annuity—
ordinary or annuity due—is preferable? Explain why.
COPYRIGHT AND DISCLAIMER NOTICE:
Copyright, 2012. This document is the sole, Copyrighted property of Dr. Michael R. Williams.
Unauthorized republication, redistribution, storage, and/or transmission, by or on any means, electronic, mechanical, photocopying, recording, and so on, for any
reason, educational or otherwise, of any of Dr. Williams’ material, including this Document, in part or in whole, is strictly prohibited without the prior written consent of
Dr. Williams. Additionally, Dr. Williams makes no guarantee, representation, or warranty regarding the information and/or data provided in this Document. The
information provided and/or opinions expressed within this Document are subject to change without notice or liability to any party. Dr. Williams expressly disclaims
any liability arising from or in reliance upon any part of this Document or any other information provided by Dr. Williams or Governors State University. Dr. Williams
is not responsible or liable, directly or indirectly, for any damage, loss, or liability caused or alleged to be caused by or in connection with any use of or reliance on any
content.
P10 Present Value of an Annuity
Consider the following cases.
Case Amount of annuity Interest rate Period (years)
A $ 12,000 7% 3
B $ 55,000 12% 15
C $ 700 20% 9
D $ 140,000 5% 7
E $ 22,500 10% 5
a.) Calculate the present value of the annuity assuming that it is
(1) An ordinary annuity.
(2) An annuity due.
b.) Compare your findings in parts a(1) and a(2). All else being identical, which type of annuity—
ordinary or annuity due—is preferable? Explain why.
P11 Value of a Mixed Stream
For each of the mixed streams of end-of-year cash flows shown in the following table, determine the present
value if deposits are made into an account paying annual interest of 12%, assuming that no withdrawals are
made during the period:
Year A B C
1 $ 900 $ 30,000 $ 1,200
2 $ 1,000 $ 25,000 $ 1,200
3 $ 1,200 $ 20,000 $ 1,000
4 $ 10,000 $ 1,900
5 $ 5,000
COPYRIGHT AND DISCLAIMER NOTICE:
Copyright, 2012. This document is the sole, Copyrighted property of Dr. Michael R. Williams.
Unauthorized republication, redistribution, storage, and/or transmission, by or on any means, electronic, mechanical, photocopying, recording, and so on, for any
reason, educational or otherwise, of any of Dr. Williams’ material, including this Document, in part or in whole, is strictly prohibited without the prior written consent of
Dr. Williams. Additionally, Dr. Williams makes no guarantee, representation, or warranty regarding the information and/or data provided in this Document. The
information provided and/or opinions expressed within this Document are subject to change without notice or liability to any party. Dr. Williams expressly disclaims
any liability arising from or in reliance upon any part of this Document or any other information provided by Dr. Williams or Governors State University. Dr. Williams
is not responsible or liable, directly or indirectly, for any damage, loss, or liability caused or alleged to be caused by or in connection with any use of or reliance on any
content.
P12 Compounding Frequency, Time Value, and Effective Annual Rates
For each of the cases in the following table:
a.) Calculate the future value at the end of the specified deposit period.
b.) Determine the effective annual rate, EAR.
c.) Compare the nominal annual rate, r, to the effective annual rate, EAR. What relationship exists
between compounding frequency and the nominal and effective annual rates?
Compounding Deposit
Amount of Nominal frequency, m period
Case initial deposit annual rate, r (times/year) (years)
A $ 2,500 6% 2 5
B $ 50,000 12% 6 3
C $ 1,000 5% 1 10
D $ 20,000 16% 4 6
P13 Annuities and Compounding
Janet Boyle intends to deposit $300 per year in a credit union for the next 10 years, and the credit union pays an
annual interest rate of 8%.
a.) Determine the future value that Janet will have at the end of 10 years, given that end-of-period
deposits are made and no interest is withdrawn, if:
(1) $300 is deposited annually and the credit union pays interest annually.
(2) $150 is deposited semiannually and the credit union pays interest semiannually.
(3) $75 is deposited quarterly and the credit union pays interest quarterly.
b.) Use your finding in part a to discuss the effect of more frequent deposits and compounding of
interest on the future value of an annuity.
P14 Loan Payment
Determine the equal, annual, end-of-year payment required each year over the life of the loans shown in the
following table.
Loan Car Value DownPay% Interest rate Term of loan (years)
A $ 12,000 40% 8% 3
B $ 60,000 10% 12% 10
C $ 75,000 15% 30% 7
D $ 4,000 21% 14% 5
COPYRIGHT AND DISCLAIMER NOTICE:
Copyright, 2012. This document is the sole, Copyrighted property of Dr. Michael R. Williams.
Unauthorized republication, redistribution, storage, and/or transmission, by or on any means, electronic, mechanical, photocopying, recording, and so on, for any
reason, educational or otherwise, of any of Dr. Williams’ material, including this Document, in part or in whole, is strictly prohibited without the prior written consent of
Dr. Williams. Additionally, Dr. Williams makes no guarantee, representation, or warranty regarding the information and/or data provided in this Document. The
information provided and/or opinions expressed within this Document are subject to change without notice or liability to any party. Dr. Williams expressly disclaims
any liability arising from or in reliance upon any part of this Document or any other information provided by Dr. Williams or Governors State University. Dr. Williams
is not responsible or liable, directly or indirectly, for any damage, loss, or liability caused or alleged to be caused by or in connection with any use of or reliance on any
content.
P15 Monthly Loan Payments
Tim Smith is shopping for a used car. He has found one priced at $74,500. The dealer has told Tim that if he
can come up with a down payment of $15,000, the dealer will finance the balance of the price at a 12% annual
rate over 10 years.
a.) Assuming that Tim accepts the dealer’s offer, what will his monthly (end-of-month) payment amount
be?
b.) Use a financial calculator or spreadsheet to help you figure out what Tim’s monthly payment would
be if the dealer were willing to finance the balance of the car price at a 9% annual rate.
P16 Grandma Problem
Suppose that Bob B. Brown wants to go to beautiful New Jersey for a vacation in 10 years and needs $15,000
for said vacation. He will put $2,500 in an account earning 10% annual interest and will put intermediate
payments into the same account (in annual installments) over the whole 10 years.
a.) How much should his payments be?
b.) If Bob cannot afford the proper payments, and can only put $500 annually in the account, how much
is his shortfall at year 10?
c.) If Bob’s rich grandma could make up the difference by putting a lump sum into an account making
7% interest per year, how much would that lump sum be (at year zero)?
d.) Repeat sub-question c but find the equal installments (with no lump sum)
e.) Repeat sub-question c but find the equal installments assuming she puts in a $500 initial lump sum in
the 7% account in year zero
f.) Repeat sub-questions a-f if Bob chooses to go in 5 years, as opposed to 10 years
P17 Valuation Problem
Suppose that you have the option to purchase a manufacturing plant as an investment. This investment will
produce a $100,000 cash flow in year 1, $25,000 cashflows in years 2 through 4, and then will pay a steady
stream of $12,050 cash flows into the foreseeable future (i.e. forever). Also, your firm has a weighted average
cost of capital of 10%. What is the most you would be willing to pay for this investment opportunity?
Chapter 5 Homework Solutions
P1 Using a Time Line
P2 Future Value Calculation
a.) 1.2544
P3 Future Value
6.11; 11.89
P4 Future Values
a.) 530.66
P5 Time Value
a-i.) 15,457.13
b.) 1,576.01
c.) 16,384.32
P6 Time Value
a.) 8.0186
