The document discusses discounting techniques used to determine the present value of future cash flows. It provides formulas to calculate the present value of a single cash flow, an annuity, and an annuity due. Examples are given of calculating the present value of Rs. 50,000 received in 15 years, an ordinary annuity of Rs. 1,000 for 3 years, and an annuity due of Rs. 1,000 for 3 years. The document also provides an example of choosing between a lump sum payment and annual pension based on present value calculations.

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DISCOUNTING TECHNIQUE
Discounting is the process of determining
present value of a series of future cash flows.
Present value of a future cash flow (inflow or outflow) is
the amount of current cash that is of equivalent value
to the decision-maker.
The interest rate used for discounting cash flows
is also called the discount rate.

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The Discounting technique is used to find out the
PRESENT VALUE of a Future Cash.
It can further be explained with reference to:
• The Present value of a single cash flow (Lump
sum amount)
• The Present value of a series of Cash Flows
(Annuity)

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Present Value of a Single Cash Flow
The following general formula can be employed
to calculate the present value of a lump sum to
be received after some future periods:
PVn = FV/(1+r)n
The term in brackets is the discount factor or
present value factor (PVF), and it is always less
than 1.0 for positive i, indicating that a future
amount has a smaller present value.

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Example
Suppose that an investor wants to find out the
present value of Rs.50,000 to be received after
15 years. The interest rate is 9 per cent.

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Present Value of an Annuity
• The computation of the present value of an annuity
can be written in the following general form:
• The term within brackets is the present value factor of
an annuity of Re 1, which we would call PVFA, and it
is a sum of single-payment present value factors.
PV = A x PVAF
( )
1 1
1
n
P A
i i i
 
= − 
+  

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PRESENT VALUE OF ORDINARY ANNUITY
PVAPVA33 = $1,000/(1.07)1
+
$1,000/(1.07)2
+
$1,000/(1.07)3
= $934.58 + $873.44 + $816.30
= $2,624.32$2,624.32
$1,000 $1,000 $1,000
0 1 2 33 4
$2,624.32 = PVA$2,624.32 = PVA33
7%
$934.58
$873.44
$816.30
Cash flows occur at the end of the period

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Value of an Annuity Due
• Annuity due is a series of fixed receipts or
payments starting at the beginning of each period
for a specified number of periods.
• Present Value of an Annuity Due
= × PVFA × (1 + )n,iP A i

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Example of an Annuity Due -- PVAD
PVADPVADnn = $1,000/(1.07)0
+ $1,000/(1.07)1
+
$1,000/(1.07)2
= $2,808.02$2,808.02
$1,000.00 $1,000 $1,000
0 1 2 33 4
$2,808.02$2,808.02 = PVADPVADnn
7%
$ 934.58
$ 873.44
Cash flows occur at the beginning of the period

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At the time of his retirement, Rachel is given a
choice between two alternatives:
an annual pension of Rs120,000 as long as he
lives, or
a lump sum amount of Rs.1,000,000.
If Rachel expects to live for 20 years and the
interest rate is expected to be 10 percent
throughout , which option appears more
attractive

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The present value of an annual pension of Rs.120,000 for
20 years when r = 10% is:
120,000 x PVAF (10%, 20 years)
= 120,000 x 8.5136 = Rs.1,021,632
The second alternative is to receive a lump sum of Rs
1,000,000
Rachel will be better off with the annual pension amount
of Rs.120,000.