# Net present value

Firms generally have many investment opportunities available. Some of these investment opportunities are valuable and others are not. The essence of successful financial management is identifying which opportunities will increase shareholder wealth.

**Net present value**

or any similar topic only for you

There are three basic and related concepts that form the very foundation of modern day finance: present value, net present value (NPV) and opportunity cost. Present value gives the value of cash flows generated by an investment and NPV gives the effective net benefit from an investment after subtracting its costs. Opportunity cost represents the rate of return on investments of comparable risk. Application of these concepts enables us to value different kinds of assets, especially those which are not commonly traded in well-functioning markets.

NPV of an asset or investment is the present value of its cash flows less the cost of acquiring the asset. Smart investors will only acquire assets that have positive NPVs and will attempt to maximize the NPV of their investments. The rate of return received from an investment is the profit divided by the cost of the investment. Positive NPV investments will have rates of return higher than the opportunity cost. This gives an alternate investment decision rule. Good investments are those that have rates of return higher than the opportunity cost. This opportunity cost can be inferred from the capital market and is based on its risk characteristics of the investment.

To assess why Net Present Value leads to better investment decisions than other criteria, let us start with a review of the NPV approach to investment decision making and then present four other widely used measures. These are: the payback period, the book rate of return, the internal rate of return (IRR) and profitability index. The measures are inferior to the NPV and should not, with the qualified exception of the IRR, normally be relied upon to provide sound investment decisions. These measures are commonly used in practice.

The NPV represents the value added to the business by the project or the investment. It represents the increase in the market value of the stockholders’ wealth. Thus, accepting a project with a positive NPV will make the stockholders better off by the amount of its NPV. The NPV is the theoretically correct method to use in most situations. Other measures are inferior because they often give decisions different from those given by following the NPV rule. They will not serve the best interests of the stockholders (Brealey, 2002).

To calculate NPV we should firstly forecast the incremental cash flows generated by the project and determine the appropriate discount rate, which should be the opportunity cost of capital. Then calculate the sum of the present values (PV) of all the cash flows generated by the investment. NPV = PV of cash inflows – initial investment. To make decision on investment, we should accept projects with NPV greater than zero and for mutually exclusive projects, accept the project with the highest NPV, if the NPV is positive. The NPV represents the value added to the stockholders’ wealth by the project. The discount rate should reflect the opportunity cost of capital or what the stockholders can expect to earn on other investments of equivalent risk (Brealey, 2002).

The NPV approach correctly accounts for the time value of money and adjusts for the project’s risk by using the opportunity cost of capital as the discount rate. Thus, it clearly measures the increase in market value or wealth created by the project. The NPV of a project is not affected by “packaging” it with another project. In other words, NPV(A+B) = NPV(A) + NPV(B). The NPV is the only measure that provides the theoretically correct measure of a project’s value (Ross, 2002).

Payback Period. The payback period is simply the time taken by the project to return your initial investment. The measure is very popular and is widely used; it is also a flawed and unreliable measure. It is simple to calculate and easy to comprehend. However, payback period has very limited economic meaning because it ignores the time value of money and the cash flows after the payback period. It can be inconsistent and the ranking of projects may be changed by packaging with other projects.

Discounted payback is a modified version of the payback measure and uses the discounted cash flows to compute payback. This is an improvement over the traditional payback in that the time value of money is recognized. A project, which has a measurable discounted payback, will have a positive NPV. However, the other disadvantages of payback still apply. It is also not simple anymore (Investment Criteria).

Book Rate of Return (BRR). This is a rate of return measure based on accounting earnings and is defined as the ratio of book income to book assets. Accounting earnings are reported by firms to the stockholders and the book return measure fits in with the reported earnings and the accounting procedures used by firms.

However, the measure suffers from the serious drawback that it does not measure the cash flows or economic profitability of the project. It does not consider the time value of money and gives too much weight to distant earnings. The measure depends on the choice of depreciation method and on other accounting conventions. BRR can give inconsistent ranking of projects and rankings may be altered by packaging. There is very little relationship between the book return and the IRR. (Brealey, 2002).

Internal Rate of Return (IRR). IRR is defined as the discount rate at which the NPV equals zero. Used properly, the IRR will give the same result as the NPV for independent projects and for projects with normal cash flows. As long as the cost of capital is less than the IRR, the NPV for the project will be positive. IRR can rank projects incorrectly, and the rankings may be changed by the packaging of the projects. For mutually exclusive projects, IRR can give incorrect decisions and should not be used to rank projects. If one must use IRR for mutually exclusive projects, it should be done by calculating the IRR on the differences between their cash flows (Ross, 2002).

Profitability Index. Occasionally, companies face resource constraint or capital rationing. The amount available for investment is limited so that all positive NPV projects cannot be accepted. In such cases, stockholder wealth is maximized by taking up projects with the highest NPV per dollar of initial investment. This approach is facilitated by the profitability index (PI) measure. Profitability index is defined as: NPV/Investment. The decision rule for profitability index is to accept all projects with a PI greater than zero.

This rule is equivalent to the NPV rule. The modified rule applied in the case of capital rationing is to accept projects with the highest profitability index first, followed by the one with next highest, and so on till the investment dollars are exhausted. This rule will maximize the NPV and stockholder wealth. If the resource constraint is on some other resources, the profitability index needs to be modified to measure the NPV per unit of the resource that is rationed. The profitability index cannot cope with mutually exclusive projects or where one project is contingent on another (Brealey, 2002).

Thus, comparing NVP with other criteria we can assert that NPV is superior to other criteria. First, it is the only measure, which considers the time value of money, properly adjusting for the opportunity cost of capital. Second, it gives consistent measures of the project’s value (i.e. not affected by packaging with other projects). Third, it clearly measures the value added to the stockholders’ wealth. The only exception to the superiority of NPV is when the firm is constrained by capital rationing. This implies that the firm cannot finance all positive NPV projects and should therefore choose projects that give the highest NPV for each dollar of investment. The profitability index that is defined as the ratio of NPV to the investment amount is used to achieve this selection.

However, the other criteria for the evaluation of projects are found to be popular in practice. If using them, we should make sure we use them in the best possible way and understand the limitations of them. For example, we should always compare mutually exclusive projects on the basis of the difference between their cash flows, because that it is the cash flows that determine the value of a project. Inadequate forecast of the cash flows can be far more disastrous than using the wrong appraisal technique. Cash flow forecasts are difficult to make and can be expensive. It does not make sense to waste the forecasts by using an inferior method of evaluation.

References:

Brealey, Richard A. & Myers, Stewart C. (2002). Principles of Corporate Finance, 7th ed. Chapters 5 – 6. Irwin/McGraw-Hill Book Co.

Investment Criteria, Chapter 9. Introduction to Finance. COMM 203 Homepage. College of Commerce, University of Saskatchewan, 2004 from http://www.commerce.usask.ca/faculty/loescher/Commerce203/CapitalBudgeting/Investment_Criteria.ppt

Ross, S., Westerfield, R., Jordan, B. & Roberts, G. (2002). Fundamentals of Corporate Finance, 4th Edition. McGraw-Hill Ryerson Limited.