financial presentation complete

8/2/2019 Financial Presentation Complete

1/15


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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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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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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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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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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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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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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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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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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13/15

Perpetuities

PV of a perpetuity = PMT

I

Example:

PVp = 100 0.8

=$ 1250

Pmt = 100Int= 8%

PV = ?
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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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15/15

Thank You
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