Time value 1

ACCT 302
by Professor Hsieh
Chapter
Time Value of Money Concepts

Time Value of Money Concepts 2
Time Value of Money
The dollar amount cash flows difference between
the present value of an amount and its future
value. The difference is also referred to as the
interest.
Example:
The time value of $100 for one year at i = 10%.
Present value=$100
Future value=$100 x (1+10%)=$110
The time value of one year for this $100
=$110-$100=$10

A.Future Value of A Single Amount
FV= I x ( 1 + i)n
Where:FV = Future value of the invested amount;
i = Amount invested at the beginning of the
period;
n = the number of compounding periods.
Example: The future value of $10,000 invested on
1/1/x1, at the end of year 2 (i.e.;12/31/x2)
with i=10%.
$10,000 x (1+i)2
= $12,100

B.Present Value of A Single Amount
FV = I x (1 + i)n
I = FV / (1 + i)n
Where: I = Present value of a single amount.
Example: The present value of $12,100 to be
received two years from now with i =10%
$12,100 / (1+10%)2
= $10,000

C. Annuity
The cash flows of a constant amount to be
received or paid each period.
Case 1: Future value of an ordinary annuity
FVA: Annuity amount x future value annuity factor
Example:The future value of paying $10,000 every year
for the following three years at i= 10%. The first
$10,000 is to be paid one year from today (n=0).
Diagram of these payments
0
End of
Year 1
End of
Year 2
End of
Year 3
First payment
$10,000
2nd payment
$10,000
3rd payment
$10,000

C.Annuity (contd.)
Case 1 (contd.)
The future value of these payments (an ordinary
annuity) is:
Payment FV of $1,
i=10%
Future Value
(at the end of year 3) n
First Payment $10,000 x 1.12a = $12,100 2
Second
Payment
$10,000 x 1.10b
= $11,000
1
Third Payment $10,000 x 1.00 = $10,000 0
Total 3.31 = $33,100
The future value
annuity factor
The future value

C.Annuity (contd.)
Case 1 (contd.)
A short cut:
FVA = $10,000 x 3.31
the future value annuity factor
(Table 6A-3 under 10%, n=3)
a=(1+10%)2
=1.21
b=(1+10%)1
=1.10

C.Annuity (contd.)
Case 2: Future Value of An Annuity Due
Diagram of this annuity
0
End of
Year 1
End of
Year 2
End of
Year 3
2nd payment
$10,000
3rd payment
$10,000
future valueFirst
payment
$10,000
Note:
This annuity is similar to that of Case 1
except that the first payment was made at
the beginning of year 1.

C.Annuity (contd.)
Case 2: (contd.)
Future value of these payments:
Payment FV of $1,
i=10%
Future Value
(at the end of year 3) n
First Payment $10,000 x
(1+10%)3
=1.331
= $13,310
3
Second
Payment
$10,000 x
(1+10%)2
=1.21
= $12,100
2
Third Payment $10,000 x (1+10%) = $11,000 1
Total 3.641 = $36,410
A short cut: $10,000x3.641=36,410
(Table 6A-3, the factor under 10%, 4 period minus one.
or Table 6A-5, under 10%, n=3)

C.Annuity (contd.)
Case 3:Pre. Val. of An Ordinary Annuity
PVA=annuity amount x present value annuity
factor
Example: The present value of paying $10,000
every year for the following three years at
i=10%. The first $10,000 is to be paid
one year from today (n=0).
Diagram of these payments
0
End of
Year 1
End of
Year 2
End of
Year 3
First
payment
$10,000
2nd
payment
$10,000
3rd
payment
$10,000
Present
Value
?

C.Annuity (Contd.)
Case 3: (contd.)
The Present value of these payments (an ordinary
annuity) is: Payment PV of $1,
i=10%
Present Value
(at the end of year) n
First Payment $10,000 x 0.90909a = $9,091 1
Second
Payment
$10,000 x 0.82645b
= $8,264
2
Third Payment $10,000 x 0.75131 = $7,513 3
Total 2.48685 = $24,868
a=1/(1+10%)=0.90909
b=1/(1+10%)2
=0.82645
A short cut: $10,000 x 2.48685=24,868
The present value annuity factor(Table 6A-4,under 10%, n=3)

C.Annuity (contd.)
Case 4: Pre. Value of An Annuity Due
Diagram of this annuity
Note:
This annuity is similar to that of Case 3
except that the first payment was made at
the beginning of year 1.
0
End of
Year 1
End of
Year 2
End of
Year 3
First
payment
$10,000
2nd
payment
$10,000
3rd
payment
$10,000
Present Value ?

C.Annuity (contd.)
Case 4 : (contd.)
The present value of these payments:
Payment PV of $1,
i=10%
Present Value
(at the beg.of year 1) n
First Payment $10,000 x 1.000 = $10,000 0
Second
Payment
$10,000 x
0.90909
= $9,091
1
Third Payment $10,000 x 0.82645 = $8,264 2
Total 2.73554 = $27,355
A short cut: $10,000 x 2.73554=$27,355
(Table 6A-4, the factor under i=10%, n=2 plus one.
Or Table 6A-6, factor under i= 10%, n=3)

Time value 1

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