• # Net Present Value (NPV)

Net present value (NPV) is the most widely used quantitative method in capital budgeting process. It denotes the sum of present values of all the expected future incremental cash inflows (deducting the cash outflows) if the project is undertaken by the management. The discount rate used to calculate the present value of the future cash flows is same as the cost of capital of the company.

This method considers

• All the cash outflows at the beginning of the project including the initial capital investment and the additional working capital investment etc.
• All the cash outflows in future as well including any future additional working capital investment, additional maintenance cost or any other capital investment required in future.
• All the cash inflows generated by the project in the future.
• Any release of working capital in future as a cash inflow.
• The tax paid for the income generated from the project. As it always considers the incremental cash inflow, it always deducts the applicable tax amount to get the actual cash inflow at present and in future as well.

NPV Formula

The basic calculation formula for NPV is given below.

NPV = CF0 + CF1 /((1+K)^1) + CF2 /((1+K)^2) + ….. + CFn/((1+K)^n)

Where:

CFo = after tax Cash inflow at the beginning of the project (For cash inflow the sign will be positive and for cash outflow or initial capital investment it will negative)

CFn = after tax cash inflow at the end of n-th year (here year is considered as the period interval of receiving cash inflow, it can be months, weeks as well).

K = required rate of return or the average cost of capital for that particular project

Use of NPV in capital budgeting decision making

• If NPV > 0; the project will generate positive cash inflow for the company and it will increase shareholders’ value. In this case project should be accepted.
• If NPV < 0; the project will generate cash outflow for the company (or company will lose money) and it will decrease shareholders’ value. In this case project should be rejected.
• If NPV = 0; the project won’t generate any cash inflow or outflow for the company and there will not be any change in the shareholders’ value. In this case, other evaluation methods should be used and project can be accepted or rejected based on any other reason other than monetary like strategic positioning, gaining more market share, giving tough competition to the competitor etc.

Example of NPV

Let us consider two example projects X and Y to calculate the NPV for the same with the below information

• For project X, the initial investment or cash outflow is 1000 USD, for project Y it is 1000 USD.
• Both the projects are for 5 years and will generate cash inflow for next 5 years. The cash inflows for project X are 400 USD, 350 USD, 300 USD, 250 USD and 200 USD respectively. Total Cash inflow will be 1500 USD over the next 5 years.
• The cash inflows for project Y are 200 USD, 250 USD, 300 USD, 350 USD and 400 USD respectively. Total Cash inflow will be 1500 USD over the next 5 years, same as project X.
• The required rate of return is 10%.
• So the net present value of the project X will be

NPVx = – 1000 + (400/(1+ 0.10)^1) +  (350/(1+ 0.10)^2) + (300/(1+ 0.10)^3) + (250/(1+ 0.10)^4) + (200/(1+ 0.10)^5) = -1000 + 363.64 + 289.26 + 225.39 + 170.75 +124.18 = 173.22 USD

• And the So the net present value of the project Y will be

NPVy = – 1000 + (200/(1+ 0.10)^1) +  (250/(1+ 0.10)^2) + (300/(1+ 0.10)^3) + (350/(1+ 0.10)^4) + (400/(1+ 0.10)^5) = -1000 + 181.82 + 206.61 + 225.39 + 239.05 + 248.37 = 101.25 USD

Both the projects require same capital investment and generate the same total cash inflow over the next 5 years. The difference is mainly because of the discount factor as project X will generate more cash inflow in the beginning years while project Y will generate more cash flows in the later years.