Time Value of Money Tutorial
Prepared by
Ronald Moy
Tobin College of Business
St. John’s University
Solving Time Value of Money Problems
• To solve a time value of money problem, you
need to ask yourself a number of questions in
order to determine which formula you will be
using.
Let’s Begin*
* Please view as a slideshow
Type of Cash Flow
• Is the amount one lump sum of money?
Yes
No
Present or Future Value
• Are you trying to determine what something is
worth in the future or what some future amount
is worth today?
Worth Today
Worth in the Future
Previous slide
Beginning of tutorial
Annuity or Multiple Cash Flow
• Will you be paying (or receiving) an equal sum
of money made at equal intervals?
Yes
No
Previous slide
Beginning of tutorial
Ordinary Annuity or Annuity Due?
• Is the first cash flow at the beginning of the
period or at the end of the period?
Beginning
Previous slide
End
Beginning of tutorial
Present or Future Value
• You are finding the value of multiple cash
flows. Are you looking for the value of these
cash flows in the future or the value today?
Value in the Future
Previous slide
Value Today
Beginning of tutorial
Future Value of Multiple Cash Flows
• The future value of multiple cash flows is
FV  C1(1  r)(t 1)  C2 (1  r)(t 2)  C3 (1  r)(t 3)  ...Ct (1  r)(t t )
Previous slide
Beginning of tutorial
Example
Annuity Due
• You are dealing with an annuity due. Are you
looking for the value of the annuity in the
future or what the annuity is worth today?
Worth in the Future
Previous slide
Worth Today
Beginning of tutorial
Present Value of Multiple Cash Flows
• You are finding the present value of multiple cash
flows
C3
Ct
C1
C2
PV 


 ... 
2
3
(1  r ) (1  r ) (1  r )
(1  r ) t
Previous slide
Beginning of tutorial
Example
Ordinary Annuity
• You are dealing with an ordinary annuity. Are
you looking for the value of the annuity in the
future or what the annuity is worth today?
Worth in the Future
Previous slide
Worth Today
Beginning of tutorial
Present Value of Ordinary Annuity
• You are looking for the present value of an
ordinary annuity. The present value of an annuity
formula is,
1

1  (1  r ) t
P V  C
r


Previous slide
Beginning of tutorial





Example
Present Value of Annuity Due
• You are looking for the present value of an
annuity due. The present value of an annuity
formula is,
1 

1  (1  r ) t 
P V  C
 1  r 
r




Previous slide
Beginning of tutorial
Example
Future Value of Ordinary Annuity
• You are looking for the future value of an
ordinary annuity. The formula for the future
value of an annuity is
 (1  r ) t  1
FV  C 

r


Previous slide
Beginning of tutorial
Example
Future Value of Annuity Due
• You are looking for the future value of an annuity
due. The formula for the future value of an
annuity is
 (1  r ) t  1
FV  C
1  r 
r


Previous slide
Beginning of tutorial
Example
Present Value of a Lump Sum
• You are looking for the present value of a lump
sum. The present value for a lump sum is
FV
PV 
t
(1  r )
Previous slide
example
Beginning of tutorial
Present value
Future Value of a Lump Sum
• You are looking for the future value of a lump
sum. The future value of a lump sum is,
FV  PV(1  r)
Previous slide
Beginning of tutorial
t
Future Value example
Future Value a Lump Sum Example
• Find the future value in 10 years of $100 received
today, if the interest rate is 8%.
FV  $100(1.08)  $215.89
10
Previous slide
Beginning of tutorial
FV Calculator
Timeline example
Future Value Time Line
0
1 2 3 4
10
...
$100
• Previous slide
$215.89
Beginning of tutorial
19
Present Value of a Lump Sum Example
• Find the present value of $1,000 received 5 years
from today if the interest rate is 9%.
$1,000
PV 
 $649.93
5
(1.09)
Previous slide
Beginning of tutorial
Calculator example
Timeline example
Present Value Time Line
0
1
2
3
4
5
$1,000
$649.93
Previous slide
Beginning of tutorial
Present Value of an Ordinary Annuity
• You can afford to make monthly car payments of
$500 per month for 48 months. If the interest
rate is 12% (1% per month). How much can you
afford to spend on a car? Assume that the first
car payment will be made in one month.
1 

1

 (1.01) 48 
P V  $500
  $18,986.98
.01




Previous slide
Calculator example
Beginning of tutorial
Present Value of an Annuity Due
Example
• You can afford to make monthly car payments of
$500 per month for 48 months. If the interest
rate is 12% (1% per month). How much can you
afford to spend on a car? Assume that the first
car payment will be made today.
1 

1

 (1.01) 48 
P V  $500
 (1.01)  $19,176.85
.01




Previous slide
Beginning of tutorial
Calculator example
Future Value of an Ordinary Annuity
Example
• Suppose you want to start saving next year for
your retirement. You save $1,000 per year for the
next 40 years. If the interest rate is 10%, how
much will you have in your account after you
make the last deposit?
 (1.10) 40  1
FV  $1,000
  $442,592.56
.10


Previous slide
Beginning tutorial
Calculator example
Future Value of an Annuity Due
Example
• Suppose you want to start saving today for your
retirement. You save $1,000 per year for the next
40 years. If the interest rate is 10%, how much
will you have in your account after you make the
last deposit?
 (1.10) 40  1
FV  $1,000
(1.10)  $486,851.82
.10


Previous slide
Beginning of tutorial
Calculator example
Present Value of Multiple Cash Flows
Example
• You are considering an investment that will pay you
$1,000 in one year, $2,000 in two years and $3,000 in
three years. If you want to earn 10% on your money,
how much would you be willing to pay?
$1,000 $2,000 $3,000
PV 


 $4,815.93
2
3
(1.10) (1.10) (1.10)
Previous slide
Beginning of tutorial
Calculator example
Timeline example
PV Time Line – Multiple Cash Flows
0
1
1,000
2
3
2,000
4
3,000
909.09
1,652.89
2,253.94
4,815.92
Previous slide
Beginning of tutorial
27
Future Value of Multiple Cash Flows
Example
• Suppose you invest $500 in a mutual fund today
and $600 in one year. If the fund pays 9%
annually, how much will you have in two years?
FV  $500(1.09)  $600(1.09)  $1,248.05
2
Previous slide
Beginning of tutorial
Timeline example
FV Time Line – Multiple Cash Flows
0
1
$500
$600
2
3
4
5
$654.00
$594.05
$1,248.05
Previous slide
Beginning of tutorial
29
PV Calculator
• Calculator solution
N
I/Y
5
9
CPT PV
649.93
Previous slide
PMT
PV
FV
1000
Beginning of tutorial
FV Calculator
• Calculator solution
N
I/Y
10
8
CPT FV
215.89
Previous slide
PMT
PV
FV
-100
Beginning of tutorial
Calc Ex. PV Ordinary Annuity
• Calculator solution
• Make sure calculator is set for “END”
– Set by 2nd BGN 2nd Enter
N
I/Y
PMT
48
1
500
CPT PV
18,986.98
Previous slide
PV
FV
Beginning of tutorial
Calc Ex PV Annuity Due
• Calculator solution
• Make sure calculator is set for “BEG”
– Set by 2nd BGN 2nd Enter
N
I/Y
PMT
48
1
500
CPT PV
19,176.85
Previous slide
PV
FV
Beginning of tutorial
Calc Ex FV Ordinary Annuity
• Calculator solution
• Make sure calculator is set for “END”
– Set by 2nd BGN 2nd Enter
N
I/Y
PMT
40
10
1000
CPT FV
442,592.56
Previous slide
PV
FV
Beginning of tutorial
FV Annuity Due
• Calculator solution
• Make sure calculator is set for “BEG”
– Set by 2nd BGN 2nd Enter
N
I/Y
PMT
40
10
1000
CPT FV
486,851.82
Previous slide
PV
FV
Beginning of tutorial
PV Multiple Cash Flows
• In this case, you will use the Cash Flow
Worksheet on the calculator.
–
–
–
–
–
–
–
–
–
–
CF
CF0
CF01 1000 Enter
F01
CF02 2000 Enter
F02
CF03 3000 Enter
F03
NPV 10 Enter
CPT 4,815.93
Previous slide
Beginning of tutorial