Net Present Value (NPV)

Net Present Value (NPV)
Net present value (NPV) of a project is the potential change in an investor’s wealth caused by that
project while time value of money is being accounted for. It equals the present value of net cash
inflows generated by a project 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 flows in the calculation.
Net present value calculations take the following two inputs:
§ Projected net cash flows in successive periods from the project.
§ A target rate of return i.e. the hurdle rate.
Where,
Net cash flow equals total cash inflow during a period, including salvage value if any, less cash
outflows from the project during the period. Hurdle rate is the rate used to discount the net cash
inflows. Weighted average cost of capital (WACC) is the most commonly used hurdle rate.
Calculation Methods and Formulas
The first step involved in the calculation of NPV is the estimation of net cash flows from the project
over its life. The second step is to discount those cash flows at the hurdle rate.
The net cash flows may be even (i.e. equal cash flows 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 formula for present value of annuity. However, if they are uneven, we need to calculate
the present value of each individual net cash inflow separately.
Once we have the total present value of all project cash flows, we subtract the initial investment
on the project from the total present value of inflows to arrive at 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
In the above formula,
R is the net cash inflow expected to be received in 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.
When cash inflows are uneven:
NPV =
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 the second period;
R3 is the net cash inflow during the third period, and so on …
Decision Rule
In case of standalone projects, accept a project only if its NPV is positive, reject it if its NPV is
negative and stay indifferent between accepting or rejecting if NPV is zero.
In case of mutually exclusive projects (i.e. competing projects), accept the project with higher
NPV.
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
Example 2: Uneven Cash Inflows: An initial investment of $8,320 thousand on plant and
machinery 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 net 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 calculation is summarized below:
Year 1 2 3 4

Net Cash Inflow $3,411 $4,070 $5,824 $2,065
Salvage Value 900
Total Cash Inflow
× Present Value Factor
$3,411
0.8475
$4,070
0.7182
$5,824
0.6086
$2,965
0.5158
Present Value of Cash Flows $2,890.68 $2,923.01 $3,544.67 $1,529.31
Total PV of Cash Inflows
– Initial Investment
$10,888
– 8,320

Net Present Value $2,568 thousand
Strengths and Weaknesses of NPV
Strengths
Net present value accounts for time value of money which makes it a sounder approach than other
investment appraisal techniques which do not discount future cash flows such payback period and
accounting rate of return.
Net present value is even better than some other discounted cash flows techniques such as IRR. In
situations where IRR and NPV give conflicting decisions, NPV decision should be preferred.
Weaknesses
NPV is after all an estimation. It is sensitive to changes in estimates for future cash flows, salvage
value and the cost of capital.
Net present value does not take into account the size of the project. For example, say Project A
requires initial investment of $4 million to generate NPV of $1 million while a competing Project B
requires $2 million investment to generate an NPV of $0.8 million. If we base our decision on NPV
alone, we will prefer Project A because it has higher NPV, but Project B has generated more
shareholders’ wealth per dollar of initial investment ($0.8 million/$2 million vs $1 million/$4
million).

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