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Archive:Business finance

2006-11-22T03:08:55Z

24.196.6.224: Replacing page with 'The Time Value of Money Some Future Value Definitions • Future Value (FV): The amount an investment is worth after one or more periods. • Simple Interest: Interest earne...'

Archive:Business finance

2006-11-22T03:08:25Z

24.196.6.224:

The Time Value of Money

Some Future Value Definitions

• Future Value (FV): The amount an
investment is worth after one or more
periods.
• Simple Interest: Interest earned only on
the original principal amount invested.
More Future Value Definitions
• Compound Interest: Interest earned on
both the initial principal and the interest
reinvested from prior periods.
• Compounding: The process of
accumulating interest on an investment
over time to earn more interest.

Calculating Future Value
• Future Value of $1:
FV =
• Future Value Factor: (1 + r)t
Future Value: Example #1
• You deposit $500 into a savings account.
You plan on withdrawing the money and
closing the account exactly two years from
today. Interest rates are 10%, compounded
annually, and will remain constant over the
two years.
Future Value: Example #1
• How much money will you have when you
close the account (Future Value)?
• How much simple interest did you
accumulate?
• How much compound interest did you
accumulate?

The Effects of Compounding
• The effects/benefits of compounding:
– Increase with time.
– Increase with the frequency of compounding.
(more on the details of this later.)
Future Value: Example #2
• You are scheduled to receive $17,000 in
two years. When you receive it, you will
invest it for six more years at 6 percent per
year. How much will you have in eight
years?
Future Value: Example #3
• You are trying to save to buy a new
$60,000 Jaguar. You have $22,000 today
that can be invested at your bank. The
bank pays 4 percent annual interest on its
accounts. How long will it be before you
have enough to buy the car?
The Time Value of Money

Future Value: Example #4
• Assume you are only willing to wait 15
years in the previous example. What rate
of return would you need to earn?
Some Present Value Definitions
• Present Value (PV): The current value of future
cash flows discounted at the appropriate discount
rate.
• Discount: Calculate the present value of some
future amount.
• Discount Rate: The rate used to calculate the
present value of future cash flows.
Calculating Present Value
• Present Value of $1 (i.e., $1 is the FV):
PV = =
• Present Value Factor:
1
----------------------------------------
(1 + r)t

Present Value: Example #1
• You have five of the six Florida Lottery
numbers. Lottery officials offer you the
choice of the following alternative payouts:
– Alternative 1: $100,000 one year from now.
– Alternative 2: $200,000 five years from now.
Present Value: Still Example #1
• Which alternative would you choose if
interest rates are 12%?
• What rate makes the two alternatives
equally attractive?
Present Value: Example #2
• You have just received notification that
you have won the $1 million first prize in
the Centennial Lottery. However, the prize
will be awarded on your 100th birthday
(assuming you are around to collect), 80
years from now. What is the present value
of your windfall if the appropriate discount
rate is 15%?

Present Value: Example #3
• Suppose you are still committed to owning
a $60,000 Jaguar. If you believe your
mutual fund can achieve a 9 percent annual
rate of return and you want to buy the car
in 10 years, how much must you invest
today?
Tips on Solving Present Value
and Future Value Problems
• Present value factor (PVF) is the reciprocal
of the future value factor (FVF).
• FVt = CF0 × (1 + r)t
• PV = CFt / (1 + r)t
• For multiple cash flows, just add up the
individual present (or future) values.
Tips on Solving Present Value
and Future Value Problems
• As t ↑, PV ↓ and FV ↑
• As r ↑, PV ↓ and FV ↑
• There are (currently) only 4 components:
PV, FV, t, and r
–With ANY 3 components, you can solve
for the 4th
The Time Value of Money
FINC 3610 -- Yost 7
Suggested Problems
• Critical Thinking and Concepts Review
– 1, 2, 3, 4, and 5
• Questions and Problems:
– 1, 6, 9, 13, 14, 15, 16, 18, 20, 22, 23, and 25
Additional Practice
$50,000 9 $25,000
$245,498 15% $15,000
$18,395 9% 13
5% 7 $40,000
Future
Value
Interest
Rate Years Present
Value
Additional Practice
• You are offered an investment that requires
you to put up $13,000 today in exchange
for $40,000 twelve years from now. What
is the average annual rate of return on this
investment?
• Would you accept it if the appropriate
discount rate was 8%?

Additional Practice
• You have the opportunity to make an
investment that costs $900,000. If you
make this investment now, you will receive
$120,000 one year from today, $250,000
and $800,000 two and three years from
today, respectively. The appropriate
discount rate for this investment is 12%.
Additional Practice (continued)
• Should you make the investment? What is
the net present value?
• If the discount rate is 10%, should you
invest?
Calculator Tips
• Make sure you set the number of payments
per year to 1.
• Clear when necessary.
• Either PV or FV must be negative.
• Enter the interest rate as a whole number.

Archive:Business finance

2006-11-22T03:07:18Z

24.196.6.224:

The Time Value of Money

The Time Value of Money
Some Future Value Definitions

• Future Value (FV): The amount an
investment is worth after one or more
periods.
• Simple Interest: Interest earned only on
the original principal amount invested.
More Future Value Definitions
• Compound Interest: Interest earned on
both the initial principal and the interest
reinvested from prior periods.
• Compounding: The process of
accumulating interest on an investment
over time to earn more interest.

Calculating Future Value
• Future Value of $1:
FV =
• Future Value Factor: (1 + r)t
Future Value: Example #1
• You deposit $500 into a savings account.
You plan on withdrawing the money and
closing the account exactly two years from
today. Interest rates are 10%, compounded
annually, and will remain constant over the
two years.
Future Value: Example #1
• How much money will you have when you
close the account (Future Value)?
• How much simple interest did you
accumulate?
• How much compound interest did you
accumulate?

The Effects of Compounding
• The effects/benefits of compounding:
– Increase with time.
– Increase with the frequency of compounding.
(more on the details of this later.)
Future Value: Example #2
• You are scheduled to receive $17,000 in
two years. When you receive it, you will
invest it for six more years at 6 percent per
year. How much will you have in eight
years?
Future Value: Example #3
• You are trying to save to buy a new
$60,000 Jaguar. You have $22,000 today
that can be invested at your bank. The
bank pays 4 percent annual interest on its
accounts. How long will it be before you
have enough to buy the car?
The Time Value of Money

Future Value: Example #4
• Assume you are only willing to wait 15
years in the previous example. What rate
of return would you need to earn?
Some Present Value Definitions
• Present Value (PV): The current value of future
cash flows discounted at the appropriate discount
rate.
• Discount: Calculate the present value of some
future amount.
• Discount Rate: The rate used to calculate the
present value of future cash flows.
Calculating Present Value
• Present Value of $1 (i.e., $1 is the FV):
PV = =
• Present Value Factor:
1
----------------------------------------
(1 + r)t

Present Value: Example #1
• You have five of the six Florida Lottery
numbers. Lottery officials offer you the
choice of the following alternative payouts:
– Alternative 1: $100,000 one year from now.
– Alternative 2: $200,000 five years from now.
Present Value: Still Example #1
• Which alternative would you choose if
interest rates are 12%?
• What rate makes the two alternatives
equally attractive?
Present Value: Example #2
• You have just received notification that
you have won the $1 million first prize in
the Centennial Lottery. However, the prize
will be awarded on your 100th birthday
(assuming you are around to collect), 80
years from now. What is the present value
of your windfall if the appropriate discount
rate is 15%?

Present Value: Example #3
• Suppose you are still committed to owning
a $60,000 Jaguar. If you believe your
mutual fund can achieve a 9 percent annual
rate of return and you want to buy the car
in 10 years, how much must you invest
today?
Tips on Solving Present Value
and Future Value Problems
• Present value factor (PVF) is the reciprocal
of the future value factor (FVF).
• FVt = CF0 × (1 + r)t
• PV = CFt / (1 + r)t
• For multiple cash flows, just add up the
individual present (or future) values.
Tips on Solving Present Value
and Future Value Problems
• As t ↑, PV ↓ and FV ↑
• As r ↑, PV ↓ and FV ↑
• There are (currently) only 4 components:
PV, FV, t, and r
–With ANY 3 components, you can solve
for the 4th
The Time Value of Money
FINC 3610 -- Yost 7
Suggested Problems
• Critical Thinking and Concepts Review
– 1, 2, 3, 4, and 5
• Questions and Problems:
– 1, 6, 9, 13, 14, 15, 16, 18, 20, 22, 23, and 25
Additional Practice
$50,000 9 $25,000
$245,498 15% $15,000
$18,395 9% 13
5% 7 $40,000
Future
Value
Interest
Rate Years Present
Value
Additional Practice
• You are offered an investment that requires
you to put up $13,000 today in exchange
for $40,000 twelve years from now. What
is the average annual rate of return on this
investment?
• Would you accept it if the appropriate
discount rate was 8%?

Additional Practice
• You have the opportunity to make an
investment that costs $900,000. If you
make this investment now, you will receive
$120,000 one year from today, $250,000
and $800,000 two and three years from
today, respectively. The appropriate
discount rate for this investment is 12%.
Additional Practice (continued)
• Should you make the investment? What is
the net present value?
• If the discount rate is 10%, should you
invest?
Calculator Tips
• Make sure you set the number of payments
per year to 1.
• Clear when necessary.
• Either PV or FV must be negative.
• Enter the interest rate as a whole number.

Archive:Business finance

2006-11-22T03:06:51Z

24.196.6.224:

The Time Value of Money

The Time Value of Money
Some Future Value Definitions
• Future Value (FV): The amount an
investment is worth after one or more
periods.
• Simple Interest: Interest earned only on
the original principal amount invested.
More Future Value Definitions
• Compound Interest: Interest earned on
both the initial principal and the interest
reinvested from prior periods.
• Compounding: The process of
accumulating interest on an investment
over time to earn more interest.

Calculating Future Value
• Future Value of $1:
FV =
• Future Value Factor: (1 + r)t
Future Value: Example #1
• You deposit $500 into a savings account.
You plan on withdrawing the money and
closing the account exactly two years from
today. Interest rates are 10%, compounded
annually, and will remain constant over the
two years.
Future Value: Example #1
• How much money will you have when you
close the account (Future Value)?
• How much simple interest did you
accumulate?
• How much compound interest did you
accumulate?

The Effects of Compounding
• The effects/benefits of compounding:
– Increase with time.
– Increase with the frequency of compounding.
(more on the details of this later.)
Future Value: Example #2
• You are scheduled to receive $17,000 in
two years. When you receive it, you will
invest it for six more years at 6 percent per
year. How much will you have in eight
years?
Future Value: Example #3
• You are trying to save to buy a new
$60,000 Jaguar. You have $22,000 today
that can be invested at your bank. The
bank pays 4 percent annual interest on its
accounts. How long will it be before you
have enough to buy the car?
The Time Value of Money

Future Value: Example #4
• Assume you are only willing to wait 15
years in the previous example. What rate
of return would you need to earn?
Some Present Value Definitions
• Present Value (PV): The current value of future
cash flows discounted at the appropriate discount
rate.
• Discount: Calculate the present value of some
future amount.
• Discount Rate: The rate used to calculate the
present value of future cash flows.
Calculating Present Value
• Present Value of $1 (i.e., $1 is the FV):
PV = =
• Present Value Factor:
1
----------------------------------------
(1 + r)t

Present Value: Example #1
• You have five of the six Florida Lottery
numbers. Lottery officials offer you the
choice of the following alternative payouts:
– Alternative 1: $100,000 one year from now.
– Alternative 2: $200,000 five years from now.
Present Value: Still Example #1
• Which alternative would you choose if
interest rates are 12%?
• What rate makes the two alternatives
equally attractive?
Present Value: Example #2
• You have just received notification that
you have won the $1 million first prize in
the Centennial Lottery. However, the prize
will be awarded on your 100th birthday
(assuming you are around to collect), 80
years from now. What is the present value
of your windfall if the appropriate discount
rate is 15%?

Present Value: Example #3
• Suppose you are still committed to owning
a $60,000 Jaguar. If you believe your
mutual fund can achieve a 9 percent annual
rate of return and you want to buy the car
in 10 years, how much must you invest
today?
Tips on Solving Present Value
and Future Value Problems
• Present value factor (PVF) is the reciprocal
of the future value factor (FVF).
• FVt = CF0 × (1 + r)t
• PV = CFt / (1 + r)t
• For multiple cash flows, just add up the
individual present (or future) values.
Tips on Solving Present Value
and Future Value Problems
• As t ↑, PV ↓ and FV ↑
• As r ↑, PV ↓ and FV ↑
• There are (currently) only 4 components:
PV, FV, t, and r
–With ANY 3 components, you can solve
for the 4th
The Time Value of Money
FINC 3610 -- Yost 7
Suggested Problems
• Critical Thinking and Concepts Review
– 1, 2, 3, 4, and 5
• Questions and Problems:
– 1, 6, 9, 13, 14, 15, 16, 18, 20, 22, 23, and 25
Additional Practice
$50,000 9 $25,000
$245,498 15% $15,000
$18,395 9% 13
5% 7 $40,000
Future
Value
Interest
Rate Years Present
Value
Additional Practice
• You are offered an investment that requires
you to put up $13,000 today in exchange
for $40,000 twelve years from now. What
is the average annual rate of return on this
investment?
• Would you accept it if the appropriate
discount rate was 8%?

Additional Practice
• You have the opportunity to make an
investment that costs $900,000. If you
make this investment now, you will receive
$120,000 one year from today, $250,000
and $800,000 two and three years from
today, respectively. The appropriate
discount rate for this investment is 12%.
Additional Practice (continued)
• Should you make the investment? What is
the net present value?
• If the discount rate is 10%, should you
invest?
Calculator Tips
• Make sure you set the number of payments
per year to 1.
• Clear when necessary.
• Either PV or FV must be negative.
• Enter the interest rate as a whole number.

Archive:Business finance

2006-11-22T03:04:53Z

24.196.6.224:

The Time Value of Money

The Time Value of Money
Some Future Value Definitions
• Future Value (FV): The amount an
investment is worth after one or more
periods.
• Simple Interest: Interest earned only on
the original principal amount invested.
More Future Value Definitions
• Compound Interest: Interest earned on
both the initial principal and the interest
reinvested from prior periods.
• Compounding: The process of
accumulating interest on an investment
over time to earn more interest.

Calculating Future Value
• Future Value of $1:
FV =
• Future Value Factor: (1 + r)t
Future Value: Example #1
• You deposit $500 into a savings account.
You plan on withdrawing the money and
closing the account exactly two years from
today. Interest rates are 10%, compounded
annually, and will remain constant over the
two years.
Future Value: Example #1
• How much money will you have when you
close the account (Future Value)?
• How much simple interest did you
accumulate?
• How much compound interest did you
accumulate?
The Time Value of Money
FINC 3610 -- Yost 3
The Effects of Compounding
• The effects/benefits of compounding:
– Increase with time.
– Increase with the frequency of compounding.
(more on the details of this later.)
Future Value: Example #2
• You are scheduled to receive $17,000 in
two years. When you receive it, you will
invest it for six more years at 6 percent per
year. How much will you have in eight
years?
Future Value: Example #3
• You are trying to save to buy a new
$60,000 Jaguar. You have $22,000 today
that can be invested at your bank. The
bank pays 4 percent annual interest on its
accounts. How long will it be before you
have enough to buy the car?
The Time Value of Money

Future Value: Example #4
• Assume you are only willing to wait 15
years in the previous example. What rate
of return would you need to earn?
Some Present Value Definitions
• Present Value (PV): The current value of future
cash flows discounted at the appropriate discount
rate.
• Discount: Calculate the present value of some
future amount.
• Discount Rate: The rate used to calculate the
present value of future cash flows.
Calculating Present Value
• Present Value of $1 (i.e., $1 is the FV):
PV = =
• Present Value Factor:
1
----------------------------------------
(1 + r)t
The Time Value of Money
FINC 3610 -- Yost 5
Present Value: Example #1
• You have five of the six Florida Lottery
numbers. Lottery officials offer you the
choice of the following alternative payouts:
– Alternative 1: $100,000 one year from now.
– Alternative 2: $200,000 five years from now.
Present Value: Still Example #1
• Which alternative would you choose if
interest rates are 12%?
• What rate makes the two alternatives
equally attractive?
Present Value: Example #2
• You have just received notification that
you have won the $1 million first prize in
the Centennial Lottery. However, the prize
will be awarded on your 100th birthday
(assuming you are around to collect), 80
years from now. What is the present value
of your windfall if the appropriate discount
rate is 15%?
The Time Value of Money
FINC 3610 -- Yost 6
Present Value: Example #3
• Suppose you are still committed to owning
a $60,000 Jaguar. If you believe your
mutual fund can achieve a 9 percent annual
rate of return and you want to buy the car
in 10 years, how much must you invest
today?
Tips on Solving Present Value
and Future Value Problems
• Present value factor (PVF) is the reciprocal
of the future value factor (FVF).
• FVt = CF0 × (1 + r)t
• PV = CFt / (1 + r)t
• For multiple cash flows, just add up the
individual present (or future) values.
Tips on Solving Present Value
and Future Value Problems
• As t ↑, PV ↓ and FV ↑
• As r ↑, PV ↓ and FV ↑
• There are (currently) only 4 components:
PV, FV, t, and r
–With ANY 3 components, you can solve
for the 4th
The Time Value of Money
FINC 3610 -- Yost 7
Suggested Problems
• Critical Thinking and Concepts Review
– 1, 2, 3, 4, and 5
• Questions and Problems:
– 1, 6, 9, 13, 14, 15, 16, 18, 20, 22, 23, and 25
Additional Practice
$50,000 9 $25,000
$245,498 15% $15,000
$18,395 9% 13
5% 7 $40,000
Future
Value
Interest
Rate Years Present
Value
Additional Practice
• You are offered an investment that requires
you to put up $13,000 today in exchange
for $40,000 twelve years from now. What
is the average annual rate of return on this
investment?
• Would you accept it if the appropriate
discount rate was 8%?
The Time Value of Money
FINC 3610 -- Yost 8
Additional Practice
• You have the opportunity to make an
investment that costs $900,000. If you
make this investment now, you will receive
$120,000 one year from today, $250,000
and $800,000 two and three years from
today, respectively. The appropriate
discount rate for this investment is 12%.
Additional Practice (continued)
• Should you make the investment? What is
the net present value?
• If the discount rate is 10%, should you
invest?
Calculator Tips
• Make sure you set the number of payments
per year to 1.
• Clear when necessary.
• Either PV or FV must be negative.
• Enter the interest rate as a whole number.