Present value of any the amount of money today that would future sum of money be needed at current interest rates to produce ID: 563592
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Slide1Slide2
Time Value of Money
Present value of
any the amount of money today that would future sum of money = be needed at current interest rates to produce that future sum
Compounding = interest remains in the bank and ALSO earns interestSlide3
P = present value of dollars
F = Future value of moneyr = interest rate in decimalsN = number of years
$F = $P x (1 + r)
$P = __$F__ (1 + r)
$F = $P x (1 + r)
N
$P =
__$F__
(1 + r)N
Formulas
Time value of money one year
Time value of money
Multiple yearsSlide4
Assume the interest rate is 10% in all of the examples
belowIf 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 = $1.10Slide5
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 = $.91Slide6
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 Slide7
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 = _$50_ (1 + .1) $P = _$50_ 1.1
$P = $45.45$P = __$F__ (1 + r)
Slide8
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.
ProjectDollars realized today
Dollars realized one year from todayPresent value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value
A
B
C Slide9
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.
ProjectDollars realized today
Dollars realized one year from todayPresent value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value
A
$100
B
-$10
C $119
Slide10
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.
ProjectDollars realized today
Dollars realized one year from todayPresent value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value
A
$100
0
B -$10 $115
C $119 -$20
Slide11
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.
ProjectDollars realized today
Dollars realized one year from todayPresent value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value
A
$100
0 B
-$10 $115
C $119 -$20
$P =
__$F__
(1 + r)
Slide12
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.
ProjectDollars realized today
Dollars realized one year from todayPresent value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value
A
$100
0 _
B -$10 $115
$104.55 C $119 -$20
$-18.18
$P =
__$F__
(1 + r)
Slide13
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.
ProjectDollars realized today
Dollars realized one year from todayPresent value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value
A
$100
0 _ $100
B -$10 $115
$104.55 $94.55 C $119
-$20
$-18.18
$100.82
Which project should you choose? WHY?Slide14
Project
Dollars realized today
Dollars realized one year from todayPresent value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now
A
B
C
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.Slide15
Project
Dollars realized today
Dollars realized one year from todayPresent value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value A
$100
0
B -$10
$115
C $119 -$20
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.
$P =
__$F__
(1 + r)
Slide16
Project
Dollars realized today
Dollars realized one year from todayPresent value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value
A
$100
0
0 B -$10
$115 $112.75
C $119 -$20 $-19.61
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.
$P =
__$F__
(1 + r)
Slide17
Project
Dollars realized today
Dollars realized one year from todayPresent value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value
A
$100
0
0 $100 B -$10
$115 $112.75 $102.75
C $119 -$20 $-19.61
$99.39
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.
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.Slide18
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
Slide19
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
Slide20
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 = $1,000 $P = $1,000 1.16 $P = $862.07
$P = __$F__ (1 + r)N
(1 + .05)
3Slide21
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 Slide22
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? Slide23
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
Should General Motors make this investment NOW?
Slide24
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?