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Chapter. Time Value of Money Concepts. 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 - PowerPoint PPT PresentationTRANSCRIPT
ACCT 302by 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
Time Value of Money Concepts 3
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
Time Value of Money Concepts 4
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
Time Value of Money Concepts 5
C. Annuity The cash flows of a constant amount to be received or
paid each period.
Case 1: Future value of an ordinary annuityFVA: Annuity amount x future value annuity factorExample: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
0End of Year 1
End of Year 2
End of Year 3
First payment$10,000
2nd payment$10,000
3rd payment $10,000
Time Value of Money Concepts 6
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
SecondPayment
$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
Time Value of Money Concepts 7
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=1.21b=(1+10%)1=1.10
Time Value of Money Concepts 8
C.Annuity (contd.) Case 2: Future Value of An Annuity Due Diagram of this annuity
0End 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.
Time Value of Money Concepts 9
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
SecondPayment
$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)
Time Value of Money Concepts 10
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
0End 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
?
Time Value of Money Concepts 11
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
SecondPayment
$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%)=0.90909b=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)
Time Value of Money Concepts 12
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.
0End 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 ?
Time Value of Money Concepts 13
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
SecondPayment
$10,000 x0.90909
= $9,0911
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)