# Net Present Value (NPV)

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.

## 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.

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 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

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.

## 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 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