© 2012 Dr. Chula King
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 Definition of Time Value of Money
 Components of Time Value of Money
 How to Answer the Question
 Present Value versus Future Value
 Compounding
 Discounting
 Time Line
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!  Refers to the fact that $1 in hand today is worth
more than $1 promised at some time in the
future
!  The reason for the differential is that $1 today
can be invested to earn a return, called interest.
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3
1
!  I invest $100 in a savings account that pays 10%
interest compounded annually.
!  ……0
1
2
3
|-------------|-------------|-------------|
100.00  100.00
+ 10.00
110.00  110.00
+ 11.00
121.00  121.00
+12.10
= 133.10
© 2012 Dr. Chula King
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!  I invest $100 in a savings account that pays 10%
interest compounded annually.
!  … 0
1
2
3
|-------------|-------------|-------------|
100.00
x1.10
= 110.00
x1.10
= 121.00
x1.10 = 133.10
© 2012 Dr. Chula King
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!  Every Time Value of Money problem involves the
following four items, three of which must be
given:
•  Present and/or Future value amount(s)
  Single Sum
  Annuity – equal periodic payments or deposits
•  A discount or compound rate of interest
•  Number of periods
!  Given three of the items, what is the value of the
fourth item?
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2
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!
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 Financial calculator
 Mathematical formula
 Excel/Numbers
 Time Value of Money Tables
•  Future value of $1 (Future value of a single sum)
•  Present value of $1 (Present value of a single sum)
•  Future value of an ordinary annuity of $1
•  Present value of an ordinary annuity of $1
•  Present value of an annuity due of $1
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© 2012 Dr. Chula King
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!  A present amount is just that. It is the amount of
money that I have or need to have at the present
time
!  A future amount is the amount of money that I
will have in the future
•  A single sum – A dollar amount at one specified time in
the future
•  An annuity – Equal, periodic deposits or payments
occurring in the future.
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© 2012 Dr. Chula King
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Present Value
Future Value
0------------1------------2------------n
|
|
|
|
Present Value 100
100+interest
# Periods 
Future Value
© 2012 Dr. Chula King
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100-interest
100
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!  The interest rate that causes the differential
between present value and future value
!  Unless otherwise noted, always given as an annual
rate, e.g., 10% per year.
© 2012 Dr. Chula King
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10
!  The accumulation of interest on principal/interest
over time from the present to the future
!  100 x 1.10 = 110.00 x 1.10 = 121.00
!  The number of times during the year that
compounding takes place
•  10% compounded annually – 10% once per year
•  10% compounded semi-annually – 5% every six months
•  10% compounded quarterly – 2.5% every three months.
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!  The opposite of compounding
!  The removal of interest on principal/interest over
time from the future to the present
!  121.00 ÷ 1.10 = 110.00 ÷ 1.10 = 100
!  The number of times during the year that
discounting takes place
•  10% compounded annually – 10% once per year
•  10% compounded semi-annually – 5% every six months
•  10% compounded quarterly – 2.5% every three months.
© 2012 Dr. Chula King
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4
!  A graphical representation showing the timing of
cash flows.
!  0
1
2
3
n
|-----------|-------------|-------------|-------------|
!  The present time is denoted by “0”.
!  Time “1” is one period from the present time, time
“2” is two periods from the present time, etc.
!  Periods can be a year, six months, etc.
•  10% compounded annually – one period per year
•  10% compounded semi-annually – two periods per year
•  10% compounded quarterly – four periods per year.
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!  Generally classified into one of two categories
Known Present
Value
Unknown
Future Value
0----------1----------2----------3----------4----------5----------6
Unknown
Present Value
Known Future
Value
0----------1----------2----------3----------4----------5----------6
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!  Equal periodic payment or deposit
•  The amount of the payment or is the same each period
•  The time between payments or deposits is the same
!  Ordinary annuity – payments or deposits occur at
the end of the period
!  Annuity due – payments or deposits occur at the
beginning of the period
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!  Generally classified into one of two categories
Known
Deposits
Unknown
Future Value
0----------1----------2----------3----------4----------5----------6
Unknown
Present Value
Known
Payments
0----------1----------2----------3----------4----------5----------6
© 2012 Dr. Chula King
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 Part 2 – More on How to Solve the Problem
 Part 3 – Future Value of $1 (Single Sum)
 Part 4 – Present Value of $1 (Single Sum)*
 Part 5 - Future Value of an Annuity of $1
 Part 6 – Present Value of an Annuity of $1*
•  Ordinary Annuity
•  Annuity Due
!  Part 7 – Putting It All Together.
© 2012 Dr. Chula King
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