# A372ch6

```Chapter 6 Time Value of
Money and Accounting
 In
theory, the fair value or market price of
assets and liabilities should equal the
present value (PV) of future cash inflows or
outflows
 Examples:
– the fair value of long-term Notes (or Bond)
Receivables (or Payables) equals the PV of the
principal plus the PV of future interests
Single Sum Problem
 Future
Valuet: PV=\$1, n=5,i=10%; Table 1
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\$1
FV= \$1.61051
 Present Value: fv=\$1, n=5, i=10%; Table 2
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PV=0.62092
\$1
Ordinary Annuity
 Future
Value: R=\$1, n=5,i=10%; Table 3
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\$1 \$1
\$1 \$1 \$1 FV-OA=\$6.1051
 Present Value: R=\$1, n=5, i=10%; Table 4
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PV-OA=\$3.79079 \$1
\$1 \$1 \$1 \$1
Annuity Due
 Future
Value:R=\$1;n=5;i=10%; No Table
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\$1 \$1 \$1 \$1 \$1 FV-AD=\$6.71569
 Present Value: R=\$1;n=5;i=10%; Table 5
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\$1 \$1 \$1 \$1
Deferred Annuity--first rent
occurs (y+1) periods from now
Future Value
R x (FVF-OA;n,i)
Present Value
R x [(PVF-OA;n+y,i) - (PVF-OA;y,i)]
or R x [(PVF-OA;n,i) x (PVF;y,i)]
FV= 9.48717
PV=3.6577
e.g.., y=3; n=7; i=10%; R=\$1
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\$1 \$1 \$1 \$1 \$1 \$1 \$1
Deferred Annuity Due--first rent
occurs y periods from now
Future Value
Present Value
or R x [(PVF-AD;n,i) x (PVF;y,i)]
FV = 10.4359
PV= 4.0235
e.g., y=3; n=7; i=10%; R=\$1
0 1 2 3 4 5 6 7 8 9 10
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\$1 \$1 \$1 \$1 \$1 \$1 \$1
Deferred Annuity Exercise
 What
amount must be deposited at 10% on
Jan.1 1995 to permit annual withdrawals of
\$500 each beginning on Jan. 1, 1999 and
ending on Jan, 1 2002?
 Time Diagram:
95 96 97 98 99 00 01 02
P=?
\$500 \$500 \$500 \$500
Solution to the Deferred
Annuity Problem
 An
ordinary annuity of 4 rents deferred for 3
periods: PV=R x {(PVF-OA;7,10%) - (PVF-OA;3,10%)}
=\$500 x {4.86842 - 2.48685} = \$1,190.79
or PV= R x (PVF-OA; 4,10%) x (PVF; 3,10%)
=\$500 x 3.16986 x 0.75131 = \$1,190.79
 An annuity due of 4 rents deferred for 4