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
0
1
2
3
4
5
I
I
I
I
I
I
$1
FV= $1.61051
 Present Value: fv=$1, n=5, i=10%; Table 2
0
1
2
3
4
5
I
I
I
I
I
I
PV=0.62092
$1
Ordinary Annuity
 Future
Value: R=$1, n=5,i=10%; Table 3
0
1
2
3
4
5
I
I
I
I
I
I
$1 $1
$1 $1 $1 FV-OA=$6.1051
 Present Value: R=$1, n=5, i=10%; Table 4
0
1
2
3
4
5
I
I
I
I
I
I
PV-OA=$3.79079 $1
$1 $1 $1 $1
Annuity Due
 Future
Value:R=$1;n=5;i=10%; No Table
0
1
2
3
4
5
I
I
I
I
I
I
$1 $1 $1 $1 $1 FV-AD=$6.71569
 Present Value: R=$1;n=5;i=10%; Table 5
0
1
2
3
4
5
I
I
I
I
I
I
PV-AD=$4.16986 $1
$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
0 1 2 3 4 5 6 7 8 9 10
I I I I I I I I I I I
$1 $1 $1 $1 $1 $1 $1
Deferred Annuity Due--first rent
occurs y periods from now
Future Value
Present Value
R x (FVF-AD;n,i)
R x [(PVF-AD;n+y,i) - (PVF-AD;y,i)]
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
I I I I I I I I I I I
$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
periods: PV=R x {(PVF-AD;8,10%) - (PVF-AD;4,10%)}
=$500 x {5.86842 -3.48685} = $1,190.79
Bond Valuation
 On
1/1/95, X Co. issued $1,000, 8%, 3-year
bonds with semiannual interest (market rate
is 10%), what is the sale price of the bond?
 Answer:
PV of $1,000= $1,000 x (PVF;6,5%)=$747
PV of interest= $40 x (PVF-OA;6,5%)=$203
PV of bonds= $747 + $203 = $950