Time Decision
Time decisions
 The
principle to be discussed in this chapter
involves expenditures that must be made
several years before returns are obtained.
Value of $1,00 Compounded Annually at Specified Interest Rates for
Periods Up to 20 years.
No.of
years
Rate of interest
7
8
9
10
12
14
1
$1,0700
$1,0800
$1,0900
$1,1000
$1,1200
$1,1400
2
1,1449
1,1664
1,1881
1,2100
1,2544
1,2996
3
1,2250
1,2597
1,2950
1,3310
1,4049
1,4815
4
1,3108
1,3605
1,4116
1,4641
1,5735
1,6890
5
1,4026
1,4693
1,5386
1,6105
1,7623
1,9254
6
1,5007
1,5869
1,6771
1,7716
1,9738
2,1950
7
1,6058
1,7138
1,8280
1,9488
2,2107
2,5023
8
1,7182
1,8509
1,9925
2,1437
2,4760
2,8526
9
1,8385
1,9990
2,1718
2,3581
2,7731
3,2520
10
1,9672
2,1589
2,3673
2,5939
3,1059
3,7072
15
2,7590
3,1722
3,6424
4,1783
5,4736
7,1380
20
3,8697
4,6610
5,6043
6,7300
9,6463
13,7435
Present Value of $1,00 To Be Received in the year Specified
No.of
years
Rate of interest
7
8
9
10
12
14
1
$0,9346
$0,9259
$0,9174
$0,9091
$0,8929
$0,8772
2
0,8734
0,8578
0,8417
0,8264
0,7972
0,7695
3
0,8163
0,7938
0,7722
0,7513
0,7118
0,6750
4
0,7629
0,7350
0,7084
0,6830
0,6355
0,5921
5
0,7130
0,6806
0,6499
0,6209
0,5674
0,5194
6
0,6663
0,6302
0,5963
0,5645
0,5066
0,4556
7
0,6227
0,5835
0,5470
0,5131
0,4524
0,3996
8
0,5820
0,5403
0,5019
0,4665
0,4039
0,3506
9
0,5439
0,5002
0,4604
0,4241
0,3606
0,3076
10
0,5083
0,4632
0,4224
0,3855
0,3220
0,2697
15
0,3624
0,3152
0,2745
0,2393
0,1827
0,1401
20
0,2584
0,2145
0,1784
0,1486
0,1037
0,0728
 INTEREST-
a payment made for the use of
money over a period of time.
 INTEREST
RATE - The price of using the
money over a period of time
COMPOUNDING calculating the future value
 FUTURE
VALUE FACTOR - The value by which
a present value must be multiplied to calculate its
future value
FVF=(1+i)n
 COMPOUNDING
- Calculation of the future value
of a present sum accounting for the rate of interest
FV=PV*(1+i)n
AN EXAMPLE FOR
CALCULATING COMPOUNDED VALUE
 What
is the future value of 4,000$ after 8 months,
where the compound interest rate is 2% per month
pv=4,000
i=0.02
n=8
fv=?
 F.V.F=(1+0.02)8=1.1717
FV=4,000*1.1717=4,686.6
DISCOUNTING –
calculating the present value
 Present
Value Factor - The value by which a
future value must be multiplied to calculate its
present value
PVF=
 Discounting - Calculation of
the future sum
1
(1+i)n
the present value of
1
pv  fv *
n
1  i 
8
An Example for
Calculating Present Value (Discounting)
What is the present value of $2000 due in 10 years at
5% ?
fv=2000
i=0.05
n=10
pv=?
pvf=1/ (1+0.05)10 =0.6139
pv=2000*0.6139 =1227.83
9
Present Value Annuity Factor
 Denotes
the present value of a series of
equal sums of $1 each, appearing during n
periods of time at i interest rate
 a - the annual sum
 n - number of periods of time the sum
appears
 i - interest rate
pvaf=
(1+i)n-1
i*(1+i)n
10
PVAF - EXAMPLE
We need to buy a new machine We are offered to
pay 3200$ in cash or 500 a year, for 10 years.
 Which way should we prefer , if the interest rate is
8%?

i=8%
n=10
a=500
pv=?
pvaf=
(1+0.08)10-1
=6.7101
0.08* (1+0.08)10
pv=500* 6.7101 =3355
Future Value Annuity Factor

Denotes the future value of a series of sums of $1
each, appearing during n periods of time at i
interest rate .
FVAF=
(1+i)n-1
i
12
FVAF - EXAMPLE
 We
want to save money to buy a new asset in 8
years.
The asset’s price is 3,000$ interest rate is 5%.
Is 300$ a year enough?
FVAF(5%,8) = 9.5491
300*9.5491=2864.73
 Conclusion - 300$ a year would not be
enough.
13
CAPITAL RECOVERY FACTOR

is used to distribute a single amount invested
today over a uniform series of end year payments
which have a present value equal to the amount
invested today.
n
i*(1+i)
CRF=
(1+i) n - 1
where
a= end year payment
i= interest rate
n= number of years
14
Capital Recovery Payments - Example
A
loan of 90,000$ was taken for 20 years at
an interest rate of 5% a year, what are the
annual payment required to recover the
loan.
 pv=90,000
n=20
i=5%
a=?
CRF(5%,20)=0.0802
90,000*0.0802=7,218
15