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TIME VALUE OF MONEY
Present value of any
future sum of money =
Compounding
=
the amount of money today that would
be needed at current interest rates to
produce that future sum
interest remains in the bank and ALSO earns
interest
P = present value of dollars
F = Future value of money
r = interest rate in decimals
N = number of years
$F = $P x (1 + r)
$F = $P x (1 + r)N
$P = __$F__
(1 + r)
$P = __$F__
(1 + r)N
Assume the interest rate is 10% in all of the examples below
• If I lend $1 today how much will I be paid one year from now?
$F = $P x (1 + r)
$F = 1 x (1 + .1)
$F = 1 x 1.1
$F = $1.10
Assume the interest rate is 10% in all of the examples below
• How much will I have to lend out today to have $1 a year from?
$P = __$F__
(1 + r)
$P = ___1___
(1 + .1)
$P = _1_
1.1
$P = $.91
Assume the interest rate is 10% in all of the examples below
• If I Deposit $50 in a bank account how much will I have one
year from now?
$F = $P x (1 + r)
$F = 50 x (1 + .1)
$F = 50 x 1.1
$F = 55
Assume the interest rate is 10% in all of the examples below
• How much do I need to deposit in a bank account today to
have $50 one year from now?
$P = __$F__
(1 + r)
$P = _$50_
(1 + .1)
$P = _$50_
1.1
$P = $45.45
Suppose you have to choose one of three projects to undertake. Project A
costs nothing and has an immediate payoff to you of $100. Project B requires
that you pay $10 toady in order to receive $115 a year from now. Project C
gives you an immediate payoff of $119 but requires you pay $20 a year from
now. Assume the interest rate is 10%. Calculate the net present value to
determine which project is most profitable.
Project
A
B
C
Dollars
realized
today
Dollars
realized one
year from
today
Present value of
dollars realized one
year from now
Dollars realized today
+ present value of
dollars realized one
year from now = net
present value
Suppose you have to choose one of three projects to undertake. Project A
costs nothing and has an immediate payoff to you of $100. Project B requires
that you pay $10 toady in order to receive $115 a year from now. Project C
gives you an immediate payoff of $119 but requires you pay $20 a year from
now. Assume the interest rate is 10%. Calculate the net present value to
determine which project is most profitable.
Project
Dollars
realized
today
$100
A
-$10
B
$119
C
Dollars
realized one
year from
today
Present value of
dollars realized one
year from now
Dollars realized today
+ present value of
dollars realized one
year from now = net
present value
Suppose you have to choose one of three projects to undertake. Project A
costs nothing and has an immediate payoff to you of $100. Project B requires
that you pay $10 toady in order to receive $115 a year from now. Project C
gives you an immediate payoff of $119 but requires you pay $20 a year from
now. Assume the interest rate is 10%. Calculate the net present value to
determine which project is most profitable.
Project
Dollars
realized
today
Dollars
realized one
year from
today
$100
0
-$10
$115
$119
-$20
A
B
C
Present value of
dollars realized one
year from now
Dollars realized today
+ present value of
dollars realized one
year from now = net
present value
Suppose you have to choose one of three projects to undertake. Project A costs nothing and has
an immediate payoff to you of $100. Project B requires that you pay $10 toady in order to receive
$115 a year from now. Project C gives you an immediate payoff of $119 but requires you pay $20
a year from now. Assume the interest rate is 10%. Calculate the net present value to determine
which project is most profitable.
Project
Dollars
realized
today
Dollars
realized one
year from
today
$100
0
-$10
$115
$119
-$20
Present value of
dollars realized one
year from now
A
B
C
$P = __$F__
(1 + r)
Dollars realized today
+ present value of
dollars realized one
year from now = net
present value
Suppose you have to choose one of three projects to undertake. Project A costs nothing and has
an immediate payoff to you of $100. Project B requires that you pay $10 toady in order to receive
$115 a year from now. Project C gives you an immediate payoff of $119 but requires you pay $20
a year from now. Assume the interest rate is 10%. Calculate the net present value to determine
which project is most profitable.
Project
Dollars
realized
today
Dollars
realized one
year from
today
Present value of
dollars realized one
year from now
$100
0
_
-$10
$115
$104.55
$119
-$20
$-18.18
A
B
C
$P = __$F__
(1 + r)
Dollars realized today
+ present value of
dollars realized one
year from now = net
present value
Suppose you have to choose one of three projects to undertake. Project A costs nothing and has
an immediate payoff to you of $100. Project B requires that you pay $10 toady in order to receive
$115 a year from now. Project C gives you an immediate payoff of $119 but requires you pay $20
a year from now. Assume the interest rate is 10%. Calculate the net present value to determine
which project is most profitable.
Project
Dollars
realized
today
Dollars
realized one
year from
today
Present value of
dollars realized one
year from now
$100
0
_
Dollars realized today
+ present value of
dollars realized one
year from now = net
present value
$100
-$10
$115
$104.55
$94.55
$119
-$20
$-18.18
$100.82
A
B
C
Which project should you choose? WHY?
Consider the three project from the previous page. This
time however, suppose that the interest rate is only 2%.
Calculate the net present value to determine which
project is most profitable.
Project
A
B
C
Dollars
realized
today
Dollars
realized one
year from
today
Present value of
Dollars realized today
dollars realized one
+ present value of
year from now
dollars realized one
year from now
Consider the three project from the previous page. This time however,
suppose that the interest rate is only 2%. Calculate the net present value to
determine which project is most profitable.
Project
Dollars
realized
today
Dollars
realized one
year from
today
$100
0
-$10
$115
$119
-$20
Present value of
dollars realized one
year from now
A
B
C
$P = __$F__
(1 + r)
Dollars realized today
+ present value of
dollars realized one
year from now = net
present value
Consider the three project from the previous page. This time however,
suppose that the interest rate is only 2%. Calculate the net present value to
determine which project is most profitable.
Project
Dollars
realized
today
Dollars
realized one
year from
today
Present value of
dollars realized one
year from now
$100
0
0
-$10
$115
$112.75
$119
-$20
$-19.61
A
B
C
$P = __$F__
(1 + r)
Dollars realized today
+ present value of
dollars realized one
year from now = net
present value
Consider the three project from the previous page. This time however,
suppose that the interest rate is only 2%. Calculate the net present value to
determine which project is most profitable.
Project
Dollars
realized
today
Dollars
realized one
year from
today
Present value of
dollars realized one
year from now
$100
0
0
Dollars realized today
+ present value of
dollars realized one
year from now = net
present value
$100
-$10
$115
$112.75
$102.75
$119
-$20
$-19.61
$99.39
A
B
C
Which project should be selected now?
Explain why the preferred choice is different with a 2% interest rate
than it was with a 10% interest rate.
The following Examples all involve time periods of more than 1 year.
What is the present value of $100 realized two years from now if the
interest rate is 10%?
$P = __$F__
(1 + r)N
$P =_$100_
(1 + .1)2
$P = _$100
1.21
$P = $82.64
The following Examples all involve time periods of more than 1 year.
What is the amount you will receive in three years if you loan $1,000
at 5% interest?
$F = $P x (1 + r)N
$F = $1000 x (1 + .05)3
$F = $1000 x (1.16)
$F = $1,160
The following Examples all involve time periods of more than 1 year.
What is the present value of $1,000 received in three years if the
interest rate is 5%
$P = __$F__
(1 + r)N
$P = $1,000
(1 + .05)3
$P = $1,000
1.16
$P = $862.07
Imagine that General Motors is thinking about building a new factory. Suppose that
the factory will cost $100 million today and will yield the company $200 million in 10
years. Should General Motors undertake the project? HINT - To make its decision, the
company will compare the present value of the $200 million return to the $100
million cost.
If the interest rate is 5% what is the present value of the $200 million?
$P = __$F__
(1 + r)N
$P = $200
(1 + .05) 10
$P = $200
1.63
$P = $122.70
Imagine that General Motors is thinking about building a new factory. Suppose that
the factory will cost $100 million today and will yield the company $200 million in 10
years. Should General Motors undertake the project? HINT - To make its decision,
the company will compare the present value of the $200 million return to the $100
million cost.
If the interest rate is 5% what is the present value of the $200 million?
P = $122.70
Should General Motors make this investment?
Imagine that General Motors is thinking about building a new factory. Suppose that
the factory will cost $100 million today and will yield the company $200 million in 10
years. Should General Motors undertake the project? HINT - To make its decision,
the company will compare the present value of the $200 million return to the $100
million cost.
If the interest rate is 8% what is the present value of the $200 million?
$P = __$F__
(1 + r)N
$P = $200
(1 + .08) 10
$P = $200
2.16
$P = $93
Imagine that General Motors is thinking about building a new factory. Suppose that
the factory will cost $100 million today and will yield the company $200 million in 10
years. Should General Motors undertake the project? HINT - To make its decision,
the company will compare the present value of the $200 million return to the $100
million cost.
If the interest rate is 8% what is the present value of the $200 million?
$P = $93
Should General Motors make this investment NOW?