8/2/2019 Financial Presentation Complete
1/15
8/2/2019 Financial Presentation Complete
2/15
THE TIME VALUE OF MONEY
1.0- DEFINITION OF COMPOUNDING
How much will money put into a saving account today be worth in the future
You put money in an account today (PV) for a promised rate of return(interest)
for a number of periods (usually months or years). The interest received inreinvested at the end of each period (compounds)
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Financial Presentation Complete
3/15
1.1- EXAMPLE- COMPOUNDING
Question:
Assume that you plan to deposit $100 in a bank that pays a guaranteed 5%interest each year. How much would you have at the end of year 3?
The Answer:
First step: List all the important information
1- $100 as our beginning amount (PV)2- 5% interest each year paid by bank to us (I)3- Year 3 is our number of time period (N)4- How much will $100 invested today at 5%
be worth in 3 years? FV ????
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Financial Presentation Complete
4/15
FV Future Value or ending amount
N Number of time periods
PV Present Value, or beginning amount
I Interest rate earned per year
FVN= PV (1+I)N
Second step: Apply the formula approach
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Financial Presentation Complete
5/15
FVN= PV (1+I)N
Third step: Fill up the amount in the equation
FV3 = $100 (1 + 0.05)
FV3 = $100 (1.05)
FV3 =$ 115.7625 $115.76
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Financial Presentation Complete
6/15
Fourth step: Sketch the time line
Time(years)
Amount of
beginningof period
0- PV 1 2 3
$100.00 $105.00 $110.25 $115.76
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Financial Presentation Complete
7/15
2.0- DEFINITION OF DISCOUNTING
How much money do I have to put into a savings account today to have Xamount at a certain time in the future
We know the how much we need on a specific date in the future (FV) , sowe should calculate how much we need to invest today (PV) at an interestrate.
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8/15
2.1- EXAMPLE- DISCOUNTING
Question:
How much would an investor have to set aside today in order to have$20, 000 in 5 years from now if the current rate is 15%?
The Answer:
First step: List all the important information
1- $20, 000 as our ending amount (FV)2- 15% interest each year paid by bank to us (I)3- 5 year is our number of time period (N)4- How much we need to spend today to get $20, 000 in coming 5 years at
15% interest rate. PV ????
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Financial Presentation Complete
9/15
Second step: Apply the formula approach
PV = FVN
(1+I)N
PV Present Value, or beginning amount
N Number of time periods
FV Future Value or ending amount
I Interest rate earned per year
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Financial Presentation Complete
10/15
Third step: Fill up the amount in the equation
PV = $20, 000(1 + 0.15)5
PV = $20, 000(1.15)5
PV= $ 9,943.53
PV = FVN
(1+I)N
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Financial Presentation Complete
11/15
Fourth step: Sketch the time line
Time(years)
Amount ofending
of period
0 1 2 3 4 5-FV
$9,943.53 $ $ $ $ $20,000
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12/15
Perpetuities
What is perpetuities?
Stretch of cash payment thatcontinue forever
An annuity with an extended life
PV = ?
1
100
2
100
100
Pmt = 100
I= 8%
PV = ?
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Financial Presentation Complete
13/15
Perpetuities
PV of a perpetuity = PMT
I
Example:
PVp = 100 0.8
=$ 1250
Pmt = 100Int= 8%
PV = ?
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Financial Presentation Complete
14/15
Exercise
Problem What is the present value of perpetuity
that pays $1500 per year if the interestrate is 4%?
Solution
PV p = PMTI
PV p = 1500
0.04
=
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Financial Presentation Complete
15/15
Thank You
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