# Investment Appraisal

November 17, 2021

How to calculate NPV with Formula and Examples

How To Calculate NPV (With Formula and Examples)

Net present value (NPV) is a capital budgeting technique used to estimate the current value of the future cash flows a proposed project or investment will generate. NPV is a favourite of most capital budget planners because it provides results in pound value and is a more accurate predictor of an investment's profitability. To calculate NPV, it is important to know the NPV calculation formula and how to use it to determine future earnings of a project.

What is the NPV calculation formula? The NPV calculation formula is a method of determining the profitability of an investment by discounting the future cash flows of the investment to today's value. Unlike the Internal Rate of Return (IRR), the NPV calculation formula requires a discount rate.

The NPV formula also depends on the intervals and number of future cash flows for the investment. This means that the formula for calculating the NPV for a short-term project with one cash flow differs from that of a multi-year investment with multiple cash flows.

NPV formula for an investment with a single cash flow When calculating the NPV for a short-term project with a single cash flow, the only variables required to get the present value are the cash flow, time period of the cash flow and the discount rate.

Here is the NPV formula for a one-year project with a single cash flow:

NPV = [Cash flow/ (1+i)^t] - initial investment

Where:

i = discount rate t = number of time periods NPV formula for a project with multiple cash flows and longer duration For longer-term investments with multiple cash flows, the formula is almost the same, except that you will discount each cash flow individually and then add them together.

Here is the NPV formula for a longer-term project with multiple cash flows:

NPV = Sum of present value of expected cash flows - initial investment.

What to include in the NPV calculation formula To use the NPV calculation formula, you must include the following variables:

Annual net cash flows You can estimate each year's net cash flows by adding the expected cash inflows from projected revenues to potential savings in labor, materials and other components of the initial project cost. Then, deduct the costs incurred over the new project, i.e., cash outflows during a single period. You will also add the tax savings on the depreciation of project assets to the expected cash inflows.

Cash inflows must be positive, while cash outflows must be negative. If your expected cash inflows exceed outflows, you will have a net cash inflow. However, you will have an expected net cash outflow if the expected cash outflow exceeds expected inflows.

Interest rate The interest rate is also vital to the calculation of the NPV. Most managers use the discount rate to represent the interest rate, but it can also be called the cost of capital, cutoff rate, required rate of return and hurdle rate. The interest rate or discount rate is the cost of capital or return that could be earned in an alternative investment. Interest rate can be derived by comparing the rate of return of alternative investments or projects with similar initial costs.

The NPV of projects with a constant payment size and a fixed interest rate is usually straightforward and easier to calculate.

Time period The time period is the interval at which new cash flows are invested into the new project.

How to use the NPV calculation formula To use the NPV formula to estimate the net present value of a proposed investment, you need to determine the expected net present value of the future cash flows from the investment and deduct the project's initial investment. Accept the project if the NPV result is zero or positive. A negative NPV result means the project won't be profitable and should be rejected. Below are examples of how to use the NPV formula to calculate the net present value of capital projects:

Example one ABC Inc. is planning a project with an initial investment of £5,000. The investment is projected to generate a cash flow of £5,600 in the next year. What is the NPV assuming that the required rate of return is 10% and there is no residual value at the end of the project?

Solution

NPV = [£5,600/ (1+0.1) ^1] - £5,000

NPV = £90.90

This NPV shows that the project will be profitable, so managers can accept it.

Example two Project XYZ requires an initial investment of £45,000 and is expected to generate £30,000 per year for two years. What is the NPV if the discount rate is 8%?

Solution

To estimate the NPV of this project, you will find the individual NPV of both cash flows and add the results. Then you will deduct the initial investment from the sum of the NPVs.

NPV of project R = [£30,000/ (1+0.08) ^1] + [£30,000/ (1+0.08) ^2] - £45,000

NPV = (£27,777.78 + £25,720.17) - £45,000

NPV = £8,497.95

The answer shows the NPV of project R is positive and the investment will turn a profit.

Example three The initial investment for Project YME is £50,000. It is expected to provide revenues of £13,000, £26,000 and £23,000 for the first, second and third years, respectively. What is the NPV for the project if the company's cost of capital is 13%?

Solution

NPV of Project Nathan = [£13,000/ (1+0.13) ^1] + [£26,000/(1+o.13) ^2] + [£23,000/ (1+0.13)] - £50,000

NPV = (£11.504.43 + £18,012.37 + £15,940.15) - £50,000

NPV = £45,456.95 - £50,000

NPV = -£4,543.05

The NPV for Project Nathan shows that the investment will result in a loss. Therefore, planners should reject the project.

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