Net Present Value: What is it and how to calculate it?

Posted on May 17, 2008
Filed Under Money |

Net present value (NPV) is a standard method for the financial appraisal of long-term projects. Used for capital budgeting, and widely throughout economics, it measures the excess or shortfall of cash flows, in present value (PV) terms, once financing charges are met.

Formula

Each cash inflow/outflow is discounted back to its PV. Then they are summed. The formula for computing Net Present Value is given below,

Net Present Value formula

Where,

t - the time of the cash flow
N - the total time of the project
r - the discount rate (the rate of return that could be earned on an investment in the financial markets with similar risk.)
Ct - the net cash flow (the amount of cash) at time t (for educational purposes, C0 is commonly placed to the left of the sum to emphasize its role as the initial investment.).

The Discount Rate

The rate used to discount future cash flows to their present values is a key variable of this process. A firm’s weighted average cost of capital (after tax) is often used, but many people believe that it is appropriate to use higher discount rates to adjust for risk for riskier projects. A variable discount rate with higher rates applied to cash flows occurring further along the time span might be used to reflect the yield curve premium for long-term debt.

Another approach to choosing the discount rate factor is to decide the rate which the capital needed for the project could return if invested in an alternative venture. If, for example, the capital required for Project A can earn five percent elsewhere, use this discount rate in the NPV calculation to allow a direct comparison to be made between Project A and the alternative. Related to this concept is to use the firm’s Reinvestment Rate. Reinvestment rate can be defined as the rate of return for the firm’s investments on average. When analyzing projects in a capital constrained environment, it may be appropriate to use the reinvestment rate rather than the firm’s weighted average cost of capital as the discount factor. It reflects opportunity cost of investment, rather than the possibly lower cost of capital.

NPV value obtained using variable discount rates (if they are known) with the years of the investment duration better reflects the real situation than that calculated from a constant discount rate for the entire investment duration. Refer to the tutorial article written by Samuel Baker for more detailed relationship between the NPV value and the discount rate.

For some professional investors, their investment funds are committed to target a specified rate of return. In such cases, that rate of return should be selected as the discount rate for the NPV calculation. In this way, a direct comparison can be made between the profitability of the project and the desired rate of return.

To some extent, the selection of the discount rate is dependent on the use to which it will be put. If the intent is simply to determine whether a project will add value to the company, using the firm’s weighted average cost of capital may be appropriate. If trying to decide between alternative investments in order to maximize the value of the firm, the corporate reinvestment rate would probably be a better choice.

Using variable rates over time, or discounting “guaranteed” cash flows different from “at risk” cash flows may be a superior methodology, but is seldom used in practice. Using the discount rate to adjust for risk is often difficult to do in practice (especially internationally), and is really difficult to do well. An alternative to using discount factor to adjust for risk is to explicitly correct the cash flows for the risk elements, then discount at the firm’s rate.

What NPV Means

NPV is an indicator of how much value an investment or project adds to the value of the firm. With a particular project, if Ct is a positive value, the project is in the status of discounted cash inflow in the time of t. If Ct is a negative value, the project is in the status of discounted cash outflow in the time of t. Appropriately risked projects with a positive NPV could be accepted. This does not necessarily mean that they should be undertaken since NPV at the cost of capital may not account for opportunity cost, i.e. comparison with other available investments. In financial theory, if there is a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected. The following sums up the NPVs in various situations.

However, NPV = 0 does not mean that a project is only expected to break even, in the sense of undiscounted profit or loss (earnings). It will show net total positive cash flow and earnings over its life.

Common Pitfalls

If some (or all) of the Ct have a negative value, then paradoxical results are possible. For example, if the Ct are generally negative late in the project (eg, an industrial or mining project might have clean-up and restoration costs), then an increase in the discount rate can make the project appear more favourable. Some people see this as a problem with NPV. A way to avoid this problem is to include explicit provision for financing any losses after the initial investment, i.e, explicitly calculate the cost of financing such losses.

Another common pitfall is to adjust for risk by adding a premium to the discount rate. Whilst a bank might charge a higher rate of interest for a risky project, that does not mean that this is a valid approach to adjusting a net present value for risk, although it can be a reasonable approximation in some specific cases. One reason such an approach may not work well can be seen from the foregoing: if some risk is incurred resulting in some losses, then a discount rate in the NPV will reduce the impact of such losses below their true financial cost. A rigorous approach to risk requires identifying and valuing risks explicitly, e.g. by actuarial or Monte Carlo techniques, and explicitly calculating the cost of financing any losses incurred.

Yet another issue can result from the compounding of the risk premium. R is a composite of the risk free rate and the risk premium. As a result, future cash flows are discounted by both the risk free rate as well as the risk premium and this effect is compounded by each subsequent cash flow. This compounding results in a much lower NPV than might be otherwise calculated. The certainty equivalent model can be used to account for the risk premium without compounding its effect on present value.

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