1. Net
Prese
nt
Value
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http://accountingexplained.com/managerial/capital-budgeting/npv

2. Net Present
Value
To discount you go to
the left from FV and
calculate the PV, this
is called discounting.
• Net Present Value is the present
value of net cash inflows
generated by a project including
salvage value, if any, less the
initial investment on the project.
It is one of the most reliable
measures used in capital
budgeting because it accounts
for time value of money by using
discounted cash inflows.
• Before calculating NPV, a target
rate of return is set which is
used to discount the net cash
inflows from a project. Net cash
inflow equals total cash inflow
during a period less the
expenses directly incurred on
generating the cash inflow.

3. Net Present
Value
Calculation Methods
and Formulas
• Calculation Methods and Formulas
• The first step involved in the
calculation of NPV is the determination
of the present value of net cash inflows
from a project or asset.
• The net cash flows may be even (i.e.
equal cash inflows in different periods)
or uneven (i.e. different cash flows in
different periods).
• When they are even, present value can
be easily calculated by using the
present value formula of annuity.
• However, if they are uneven, we need
to calculate the present value of each
individual net cash inflow separately.
• In the second step we subtract the
initial investment on the project from
the total present value of inflows to
arrive at net present value.

4. Net Present
Value
Thus we have the
following two formulas
for the calculation of NPV:
• When cash inflows are even:
• NPV = R × 1 − (1 + i) -n − Initial
Investment i
Investment
• In the above formula,
• R is the net cash inflow expected
to be received each period;
• i is the required rate of return
per period;
• n are the number of periods
during which the project is
expected to operate and
generate cash inflows.

5. Net Present
Value
NPV =
R1 +
R2 +
R3 +
(1 + i) 1 (1 + i) 2 (1 + i)3
• When cash inflows are uneven:
R1 + R2 + R3 + ... −Initial Investment
(1 + i) 1 (1 + i) 2 (1 + i)3
• Where,
• i is the target rate of return per
period;
• R1 is the net cash inflow during
the first period;
• R2 is the net cash inflow during
... − Initial Investment the second period;
• R3 is the net cash inflow during
the third period, and so on ...
NPV =

6. Net Present
Value
NPV =
R1 +
R2 +
R3 + ... − Initial Investment
(1 + i) 1 (1 + i) 2 (1 + i)3
• Decision Rule
• Accept the project only if its
NPV is positive or zero.
• Reject the project having
negative NPV.
• While comparing two or more
exclusive projects having
positive NPVs, accept the one
with highest NPV.

7. Value
• Examples
• Example 1: Even Cash Inflows: Calculate the net present value of a project which
requires an initial investment of $243,000 and it is expected to generate a cash
inflow of $50,000 each month for 12 months. Assume that the salvage value of the
project is zero. The target rate of return is 12% per annum.
• Solution
• We have,
Initial Investment = $243,000
Net Cash Inflow per Period = $50,000
Number of Periods = 12
Discount Rate per Period = 12% ÷ 12 = 1%
• Net Present Value
= $50,000 × (1 − (1 + 1%)^-12) ÷ 1% − $243,000
= $50,000 × (1 − 1.01^-12) ÷ 0.01 − $243,000
≈ $50,000 × (1 − 0.887449) ÷ 0.01 − $243,000
≈ $50,000 × 0.112551 ÷ 0.01 − $243,000
≈ $50,000 × 11.2551 − $243,000
≈ $562,754 − $243,000
≈ $319,754

8. • Example 2: Uneven Cash Inflows: An initial investment on plant and machinery of $8,320 thousand is
expected to generate cash inflows of $3,411 thousand, $4,070 thousand, $5,824 thousand and $2,065
thousand at the end of first, second, third and fourth year respectively. At the end of the fourth year, the
machinery will be sold for $900 thousand. Calculate the present value of the investment if the discount
rate is 18%. Round your answer to nearest thousand dollars.
• Solution
• PV Factors:
• Year 1 = 1 ÷ (1 + 18%)^1 ≈ 0.8475
• Year 2 = 1 ÷ (1 + 18%)^2 ≈ 0.7182
• Year 3 = 1 ÷ (1 + 18%)^3 ≈ 0.6086
• Year 4 = 1 ÷ (1 + 18%)^4 ≈ 0.5158
• The rest of the problem can be solved more efficiently in table format as show below:
• Year 1 2 3 4
• Net Cash Inflow $3,411 $4,070 $5,824 $2,065
• Salvage Value 900
• Total Cash Inflow $3,411 $4,070 $5,824 $2,965
• × Present Value Factor 0.8475 0.7182 0.6086 0.5158
• Present Value of Cash Flows $2,890.68 $2,923.01 $3,544.67 $1,529.31
• Total PV of Cash Inflows $10,888
• − Initial Investment − 8,320
• Net Present Value $2,568 thousand
Net Present
Value

9. • Advantage and Disadvantage of
NPV
• Advantage: Net present value
accounts for time value of money.
Thus it is more reliable than other
investment appraisal techniques
which do not discount future cash
flows such payback period and
accounting rate of return.
• Disadvantage: It is based on
estimated future cash flows of the
project and estimates may be far
from actual results.
• Written by Irfanullah Jan
Present
Value