APPENDIX C
Time Value of Money
BRIEF EXERCISES
BEC–1 Oprah is deciding between investment options. Both investments earn an
interest rate of 7%, but interest on the first investment is compounded annually,
while interest on the second investment is compounded semiannually. Which
investment would you advise Oprah to choose? Why?
Understand simple versus
compound interest (LO1)
BEC–2 Dusty would like to buy a new car in five years. He currently has $10,000
saved. He’s considering buying a car for around $14,000 but would like to add a
Turbo engine to increase the car’s performance. This would increase the price of
the car to $18,000. If Dusty can earn 10% interest, compounded annually, will he
be able to get a car with a Turbo engine in five years?
Calculate the future value
of a single amount (LO2)
BEC–3 Arnold and Maria would like to visit Austria in three years to celebrate
their 25th wedding anniversary. Currently, the couple has saved $22,000, but
they expect the trip to cost $26,000. If they put $22,000 in an account that
earns 6% interest, compounded annually, will they be able to pay for the
trip in three years?
Calculate the future value
of a single amount (LO2)
BEC–4 Calculate the future value of the following single amounts.
Calculate the future value
of a single amount (LO2)
1.
2.
3.
Initial Investment
Annual Rate
Interest Compounded
Period Invested
$7,000
5,000
8,000
9%
10
8
Annually
Semiannually
Quarterly
8 years
5 years
4 years
BEC–5 Maddy works at Burgers R Us. Her boss tells her that if she stays with
the company for four years, she will receive a bonus of $5,000. With an
annual discount rate of 7%, calculate the value today of receiving $5,000
in four years.
Calculate the present
value of a single
amount (LO2)
BEC–6 Ronald has an investment opportunity that promises to pay him $45,000
in five years. He could earn an 8% annual return investing his money elsewhere.
What is the most he would be willing to invest today in this opportunity?
Calculate the present
value of a single
amount (LO2)
BEC–7 Calculate the present value of the following single amounts.
Calculate the present value
of a single amount (LO2)
1.
2.
3.
Future Value
Annual Rate
Interest Compounded
Period Invested
$9,000
6,000
5,000
5%
6
16
Annually
Semiannually
Quarterly
4 years
7 years
3 years
BEC–8 Tom and Katie were recently married and want to take a cruise. To do so, the
couple needs to save $20,000. They plan to invest $3,000 at the end of each year for the
next six years to earn 9% compounded annually. Determine whether Tom and Katie
will reach their goal of $20,000 in six years.
Calculate the future value
of an annuity (LO3)
BEC–9 Matt plans to start his own business once he graduates from college. He plans to
save $2,000 each six months for the next four years. If his savings earn 8% annually (or
4% each six months), determine how much he will save by the end of the fourth year.
Calculate the future value
of an annuity (LO3)
BEC–10 Calculate the future value of the following annuities, assuming each annuity
payment is made at the end of each compounding period.
Calculate the future value
of an annuity (LO3)
Annuity Payment
1.
2.
3.
$3,000
6,000
5,000
Annual Rate
Interest Compounded
Period Invested
7%
8
12
Annually
Semiannually
Quarterly
6 years
9 years
5 years
APPENDIX C
Time Value of Money
Calculate the present
value of an annuity (LO3)
BEC–11 Tatsuo has just been awarded a four-year scholarship to attend the university
of his choice. The scholarship will pay $8,000 each year for the next four years to
reimburse normal school-related expenditures. Each $8,000 payment will be made
at the end of the year, contingent on Tatsuo maintaining good grades in his classes
for that year. Assuming an annual interest rate of 6%, determine the value today of
receiving this scholarship if Tatsuo maintains good grades.
Calculate the present
value of an annuity (LO3)
BEC–12 Monroe Corporation is considering the purchase of new equipment. The
equipment will cost $35,000 today. However, due to its greater operating capacity,
Monroe expects the new equipment to earn additional revenues of $5,000 by the end
of each year for the next 10 years. Assuming a discount rate of 10% compounded
annually, determine whether Monroe should make the purchase.
Calculate the present
value of an annuity (LO3)
BEC–13 Calculate the present value of the following annuities, assuming each annuity
payment is made at the end of each compounding period.
Annuity Payment
1.
2.
3.
$4,000
9,000
3,000
Annual Rate
Interest Compounded
Period Invested
7%
8
8
Annually
Semiannually
Quarterly
5 years
3 years
2 years
EXERCISES
Calculate the future value
of a single amount (LO2)
EC–1 The four people below have the following investments.
Invested Amount
Interest Rate
$12,000
15,000
22,000
18,000
12%
8
7
9
Jerry
Elaine
George
Kramer
Compounding
Quarterly
Semiannually
Annually
Annually
Required:
Determine which of the four people will have the greatest investment accumulation in
five years.
Calculate the future value
of a single amount (LO2)
EC–2 You want to save for retirement. Assuming you are now 20 years old and you
want to retire at age 60, you have 40 years to watch your investment grow. You decide
to invest in the stock market, which has earned about 12% per year over the past 80
years and is expected to continue at this rate. You decide to invest $1,000 today.
Required:
How much do you expect to have in 40 years?
Calculate the present
value of a single
amount (LO2)
EC–3 The four actors below have just signed a contract to star in a dramatic movie
about relationships among hospital doctors. Each person signs independent contracts
with the following terms:
Contract Terms
Derek
Isabel
Meredith
George
Contract Amount
Payment Date
$500,000
540,000
450,000
400,000
2 years
3 years
Today
1 year
APPENDIX C
Time Value of Money
Required:
Assuming an annual discount rate of 10%, which of the four actors is actually being
paid the most?
EC–4 Ray and Rachel are considering the purchase of two deluxe kitchen ovens. The
first store offers the two ovens for $2,500 with payment due today. The second store
offers the two ovens for $2,700 due in one year.
Calculate the present
value of a single
amount (LO2)
Required:
Assuming an annual discount rate of 10%, from which store should Ray and Rachel
buy their ovens?
EC–5 Lights, Camera, and More sells filmmaking equipment. The company offers three
purchase options: (1) pay full cash today, (2) pay one-half down and the remaining
one-half plus 10% in one year, or (3) pay nothing down and the full amount plus 15%
in one year. George is considering buying equipment from Lights, Camera, and More
for $100,000 and therefore has the following payment options:
Payment Today
Option 1
Option 2
Option 3
$100,000
50,000
0
Payment in One Year
$
0
55,000
115,000
Calculate the present
value of a single
amount (LO2)
Total Payment
$100,000
105,000
115,000
Required:
Assuming an annual discount rate of 12%, calculate which option has the lowest total
cost in present value terms.
EC–6 GMG Studios plans to invest $50,000 at the end of each year for the next four
years. There are three investment options available.
Annual Rate
Option 1
Option 2
Option 3
6%
8
12
Interest Compounded
Annually
Annually
Annually
Calculate the future value
of an annuity (LO3)
Period Invested
4 years
4 years
4 years
Required:
Determine the accumulated investment amount by the end of the fourth year for each
of the options.
EC–7 You would like to start saving for retirement. Assuming you are now 20 years old
and you want to retire at age 60, you have 40 years to watch your investment grow. You
decide to invest in the stock market, which has earned about 12% per year over the
past 80 years and is expected to continue at this rate. You decide to invest $1,000 at the
end of each year for the next 40 years.
Calculate the future value
of an annuity (LO3)
Required:
Calculate how much your accumulated investment is expected to be in 40 years.
EC–8 Denzel needs a new car. At the dealership, he finds the car that he likes. The
dealership gives him two payment options:
1. Pay $30,000 for the car today.
2. Pay $3,000 at the end of each quarter for three years.
Required:
Assuming Denzel uses a discount rate of 12% (or 3% quarterly), determine which
option gives him the lower cost.
Calculate the present
value of an annuity (LO3)
APPENDIX C
Time Value of Money
PROBLEMS: SET A
Calculate the future value
of a single amount (LO2)
PC–1A Alec, Daniel, William, and Stephen decide today to save for retirement.
Each person wants to retire by age 65 and puts $10,000 into an account earning 9%
compounded annually.
Person
Age
Initial Investment
Accumulated Investment
by Retirement (age 65)
Alec
Daniel
William
Stephen
50
40
30
25
$10,000
10,000
10,000
10,000
$_________________
$_________________
$_________________
$_________________
Required:
Calculate how much each person will have accumulated by the age of 65.
Consider present
value (LO2, 3)
PC–2A Bruce is considering the purchase of a restaurant named Hard Rock
Hollywood. The restaurant is listed for sale at $1,100,000. With the help of his
accountant, Bruce projects the net cash flows (cash inflows less cash outflows)
from the restaurant to be the following amounts over the next 10 years:
Years
Amount
1–6
7
8
9
10
$ 90,000 (each year)
100,000
110,000
120,000
130,000
Bruce expects to sell the restaurant after 10 years for an estimated $1,200,000.
Required:
If Bruce wants to make at least 12% annually on his investment, should he purchase
the restaurant? (Assume all cash flows occur at the end of each year.)
Determine present value
alternatives (LO2, 3)
PC–3A Hollywood Tabloid needs a new state-of-the-art camera to produce its monthly
magazine. The company is looking at two cameras that are both capable of doing the
job and has determined the following:
Camera 1 costs $5,000. It should last for eight years and have annual maintenance
cost of $200 per year. After eight years, the magazine can sell the camera for $400.
Camera 2 costs $4,500. It will also last for eight years and have maintenance costs
of $800 in year three, $900 in year five, and $1,000 in year seven. After eight years,
the camera will have no resale value.
Required:
Determine which camera Hollywood Tabloid should purchase. Assume that an interest
rate of 9% properly reflects the discount rate in this situation and that maintenance
costs are paid at the end of each year.
PROBLEMS: SET B
Calculate the future value
of an annuity (LO3)
PC–1B Mary Kate, Ashley, Dakota, and Elle each want to buy a new home. Each needs
to save enough to make a 20% down payment. For example, to buy a $100,000 home,
a person would need to save $20,000. At the end of each year for five years, the women
make the following investments:
APPENDIX C
Person
Mary Kate
Ashley
Dakota
Elle
Time Value of Money
Annuity
Payment
Type of
Account
Expected
Annual
Return
Five-Year
Accumulated
Investment
Maximum Home
Purchase
$3,000
4,000
5,000
5,000
Savings
CDs
Bonds
Stocks
2%
4
6
12
$___________
$___________
$___________
$___________
$______________
$______________
$______________
$______________
Required:
1. Calculate how much each woman is expected to accumulate in the investment
account by the end of the fifth year.
2. What is the maximum amount each woman can spend on a home, assuming she
uses her accumulated investment account to make a 20% down payment?
PC–2B Woody Lightyear is considering the purchase of a toy store from Andy
Enterprises. Woody expects the store will generate net cash flows (cash inflows less
cash outflows) of $50,000 per year for 15 years. At the end of the 15 years, he intends
to sell the store for $500,000. To finance the purchase, Woody will borrow using
a 15-year note that requires 8% interest.
Consider the
present value of
investments (LO2, 3)
Required:
What is the maximum amount Woody should offer Andy for the toy store?
(Assume all cash flows occur at the end of each year.)
PC–3B Star Studios is looking to purchase a new building for its upcoming film
productions. The company finds a suitable location that has a list price of $1,500,000.
The seller gives Star Studios the following purchase options:
1. Pay $1,500,000 immediately.
2. Pay $500,000 immediately and then pay $140,000 each year over the next 10 years,
with the first payment due in one year.
3. Make 10 annual installments of $200,000, with the first payment due in one year.
4. Make a single payment of $2,200,000 at the end of five years.
Required:
Determine the lowest-cost alternative for Star Studios, assuming that the company
can borrow funds to finance the purchase at 7%.
Determine present value
alternatives (LO2, 3)