# Decision Models for Evaluating Alternatives - Financial Management

Four criteria are commonly used for evaluating and selecting investment projects.

• Net present value (NPV)
• Profitability index (PI)
• Internal rate of return (IRR)
• Payback (PB) period

Net Present Value

Recall from Chapter 1 that the net present value rule is the primary decision -making rule used throughout the practice of financial management. The net present value —that is, the present value of the expected future cash flows minus the initial outlay —of an investment made by a firm represents the contribution of that investment to the value of the firm and, accordingly, to the wealth of the firm’s shareholders. In this chapter, we consider the net present value of capital expenditure projects.

The net present value (NPV) of a capital expenditure project is defined as the present value of the stream of net (operating) cash flows from the project minus the project’s net investment. The net present value method is also sometimes called the discounted cash flow (DCF) technique. The cash flows are discounted at the firm’s required rate of return; that is, its cost of capital. A firm’s cost of capital is defined as its minimum acceptable rate of return for projects of average risk.

The net present value of a project may be expressed as follows:

NPV = PVNCF – NINV

where NPV is the net present value; PVNCF, the present value of net (operating) cash flows; and NINV, the net investment. For a series of uneven net (operating) cash flows, the net present value of a project may be calculated as follows:

where NCFt is the net(operating) cash flow in year t, n is the expected project life (years), k is the cost of capital, and PVIFk,t is the present value interest factor. The net (operating) cash flow in the final year (n) of the project, NCFn, includes any salvage value remaining at the end of the project’s life. The summation sign (Σ) represents the arithmetic sum of the discounted cash flows for each year t over the life of the project (n years); that is, the present value of the net cash flows (PVNCF).

If all the net (operating) cash flows are equal over the life of the project, that is, an annuity NCF = NCF1 = NCF2 = . . . =NCFn, then Equation can be expressed as follows:

NPV = NCF _ PVIFAk,n – NINV

where PVIFAk,n is the present value of annuity interest factor (Table IV). the annual net cash flows for normal projects are usually positive after the initial net investment. Occasionally, however, one or more of the expected net cash flows over the life of a project may be negative.When this occurs, positive numbers are used for years having positive net cash flows (net inflows), and negative numbers are used for years having negative net cash flows (net outflows).

To illustrate net present value calculations, suppose Ace Lumber is considering two projects, A and B, having net investments and net cash flows as shown in Table. The net present value computations for the two projects are presented in Table. These calculations assume a 14 percent cost of capital. The calculations in these tables also assume that cash flows are received at the end of each year, rather than as a flow during the year.

This assumption, although a normal one, tends to slightly understate a project’s net present value or internal rate of return. Project A is shown in Table to have a negative net present value of $–1,387, and Project B has a positive net present value of$7,735. Spreadsheet software may also be used to solve for NPV as illustrated here:

Decision Rule

In general, a project should be accepted if its net present value is greater than or equal to zero and rejected if its net present value is less than zero. This is so because a positive net present value in principle translates directly into increases in stock prices and increases in shareholders’ wealth. In the Ace Lumber example, Project A would be rejected because it has a negative net present value, and Project B would be accepted because it has a positive net present value.

If two or more mutually exclusive investments have positive net present values, the project having the largest net present value is the one selected. Assume, for example, that a firm has three mutually exclusive investment opportunities, G, H, and I, each requiring a net investment of $10,000 and each having a 5-year expected economic life.1 Project G has a net present value of$2,000; H has a net present value of $4,000; and I has a net present value of$3,500.

Of the three, H would be preferred over the other two because it has the highest net present value and therefore is expected to make the largest contribution to the objective of shareholder wealth maximization.
Sources of Positive Net Present Value Projects What causes some projects to have a positive net present value and others to have a negative net present value? When product and factor markets are other than perfectly competitive, it is possible for a firm to earn above -normal profits (economic rents) that result in positive net present value projects. The reasons why these above-normal profits may be available arise from conditions that define each type of product and factor market and distinguish it from a perfectly competitive market. These reasons include the following barriers to entry and other factors:

1. Buyer preferences for established brand names
2. Ownership or control of favored distribution systems (such as exclusive auto dealerships)
3. Patent control of superior product designs or production techniques
4. Exclusive ownership of superior natural resource deposits
5. Inability of new firms to acquire necessary factors of production (management, labor, equipment)
6. Superior access to financial resources at lower costs (economies of scale in attracting capital)
7. Economies of large -scale production and distribution arising from
a. Capital -intensive production processes
b. High initial start -up costs
8. Access to superior labor or managerial talents at costs that are not fully reflective of their value

These factors can permit a firm to identify positive net present value projects for internal investment. If the barriers to entry are sufficiently high (such as a patent on key technology) so as to prevent any new competition or if the start -up period for competitive ventures is sufficiently long, then it is possible that a project may have a positive net present value.However, in assessing the viability of such a project, it is important that the manager or analyst consider the likely period of time when above -normal returns can be earned before new competitors emerge and force cash flows back to a more normal level.

It is generally unrealistic to expect to be able to earn above-normal returns over the entire life of an investment project. Thus, it may be possible for a firm to identify investment projects with positive net present values. However, if capital markets are efficient, the securities of the firm making these investments will reflect the value of these projects. Recall that the net present value of a project can be thought of as the contribution to the value of a firm resulting from undertaking that particular project. Therefore, even though a firm may be able to identify projects having expected positive net present values, efficient capital markets will quickly reflect these positive net present value projects in the market value of the firm’s securities.

Suppose Project B in the preceding example was a new baby care product from Johnson & Johnson. Its positive net present vaue could be the result of buyer preferences due to Johnson & Johnson’s established baby care business. Suppose Project A, on the other hand, involved a new soap product to compete with Procter & Gamble’s Tide. Consumers’ brand preferences for Tide, as well as Procter & Gamble’s economies of scale for production and distribution, could easily cause Project A to have a negative net present value.

The net present value of a project is the expected number of dollars by which the present value of the firm is increased as a result of adopting the project. Therefore, as we have pointed out, the net present value method is consistent with the goal of shareholder wealth maximization. The net present value approach considers both the magnitude and the timing of cash flows over a project’s entire expected life.

A firm can be thought of as a series of projects, and the firm’s total value is the sum of the net present values of all the independent projects that make it up. Therefore, when the firm undertakes a new project, the firm’s value is increased by the net present value of the new project. The additivity of net present values of independent projects is referred to in finance as the value additivity principle.

The net present value approach also indicates whether a proposed project will yield the rate of return required by the firm’s investors. The cost of capital represents this rate of return; when a project’s net present value is greater than or equal to zero, the firm’s investors can expect to earn at least their required rate of return.

The net present value criterion has a weakness in that many people find it difficult to work with a present value dollar return rather than a percentage return. As a result, many firms use another present value –based method that is interpreted more easily: the internal rate of return method. It is discussed later in the chapter. Also, the traditional NPV approach does not consider the value of real options that are part of a proposed project. Real options are discussed later in the chapter.

Profitability Index

The profitability index (PI), or benefit–cost ratio, is the ratio of the present value of expected net cash flows over the life of a project (PVNCF) to the net investment NINV. It is expressed as follows:

Assuming a 14 percent cost of capital, k, and using the Ace Lumber data from Table the profitability index for Projects A and B can be calculated as follows:

The profitability index is interpreted as the present value return for each dollar of initial investment. In comparison, the net present value approach measures the total present value dollar return.

Decision Rule

A project whose profitability index is greater than or equal to 1 is considered acceptable, whereas a project having a profitability index less than 1 is considered unacceptable. In the case of Ace Lumber, Project B is acceptable, whereas Project A is not.When two or more independent projects with normal cash flows are considered, the profitability index, net present value, and internal rate of return approaches all will yield identical accept –reject signals; this is true, for example, with Projects A and B.

When dealing with mutually exclusive investments, conflicts may arise between the net present value and the profitability index criteria. This is most likely to occur if the alternative projects require significantly different net investments.

Consider, for example, the following information on Projects J and K. According to the net present value criterion, Project J would be preferred because of its larger net present value. According to the profitability index criterion, Project K would be preferred.

When a conflict arises, the final decision must be made on the basis of other factors. For example, if a firm has no constraint on the funds available to it for capital investment —that is, no capital rationing —the net present value approach is preferred because it will select the projects that are expected to generate the largest total dollar increase in the firm’s wealth and, by extension, maximize shareholder wealth.

If, however, the firm is in a capital rationing situation and capital budgeting is being done for only one period, the profitability index approach may be preferred because it will indicate which projects will maximize the returns per dollar of investment—an appropriate objective when a funds constraint exists.

Internal Rate of Return

The internal rate of return is defined as the discount rate that equates the present value of the net cash flows from a project with the present value of the net investment,that is:

Subtracting NINV from both sides of Equation yields PVNCF – NINV = 0, or NPV = 0, which shows that the internal rate of return is the discount rate that causes a project’s net present value to equal zero. The internal rate of return for a capital expenditure project is identical to the yield to maturity for a bond investment.

PVNCF = NINV

A project’s internal rate of return can be determined by means of the following equation:

where NCFt /(1 + r)t is the present value of net (operating) cash flows in period t discounted at the rate r , NINV is the net investment in the project, r is the internal rate of return, and PVIFr,t is the present value interest factor .
Subtracting the net investment, NINV, from both sides of Equation yields the following:

This is essentially the same equation as that used in the net present value method. The only difference is that in the net present value approach a discount rate, k, is specified and the net present value is computed, whereas in the internal rate of return method the discount rate, r, which causes the project net present value to equal zero, is the unknown. If all the net (operating) cash flows are equal over the life of the project, that is, an annuity NCF = NCF1 = NCF2 = . . . = NCFn, can be expressed as follows:

NCF PVIFAr,n = NINV

where PVIFAr,n is the present value of an annuity factor (Table ).

The internal rate of return for Ace Lumber’s Projects A and B can now be calculated. Because Project A is an annuity, its internal rate of return may be computed directly with the aid of a PVIFA table, such as Table. Substituting NCF = $12,500, NINV =$50,000, n = 6 into Equation yields

\$12,500