A general approach for obtaining the combined effects of operating and financing cash flows of a project is to make use of the additive property of net present values by calculating an adjusted net present value. The adjusted net present value (APV) is the sum of the net present value (NPV) of the operating cash flow plus the net present value of the financial cash flow due to borrowing or raising capital (FPV). Thus,

(6.25)

where each function is evaluated at i=MARR if both the operating and the financing cash flows have the same degree of risk or if the risks are taken care of in other ways such as by the use of certainty equivalents. Then, project selection involving both design and financing alternatives is accomplished by selecting the combination which has the highest positive adjusted present value. The use of this adjusted net present value method will result in the same selection as an evaluation based on the net present value obtained from the combined cash flow of each alternative combination directly.

To be specific, let A_t be the net operating cash flow, be the net financial cash flow resulting from debt financing, and AA_t be the combined net cash flow, all for year t before tax. Then:

(6.26)

Similarly, let and YY_t be the corresponding cash flows after tax such that:

(6.27)

The tax shields for interest on borrowing (for t = 1, 2, ..., n) are usually given by

(6.28)

where I_t is the interest paid in year t and X_t is the marginal corporate income tax rate in year t. In view of Eqs. (6.13), (6.27) and (6.28), we obtain

(6.29)

When MARR = i is applied to both the operating and the financial cash flows in Eqs. (6.13) and (6.28), respectively, in computing the net present values, the combined effect will be the same as the net present value obtained by applying MARR = i to the combined cash flow in Eq. (6.29).

In many instances, a risk premium related to the specified type of operation is added to the MARR for discounting the operating cash flow. On the other hand, the MARR for discounting the financial cash flow for borrowing is often regarded as relatively risk-free because debtors or holders of corporate bonds must be paid first before stockholders in case financial difficulties are encountered by a corporation. Then, the adjusted net present value is given by

(6.30)

where NPV is discounted at r and FPV is obtained from the r_f rate. Note that the net present value of the financial cash flow includes not only tax shields for interest on loans and other forms of government subsidy, but also on transactions costs such as those for legal and financial services associated with issuing new bonds or stocks.

The evaluation of combined alternatives based on the adjusted net present value method should also be performed in dollar amounts which either consistently include or remove the effects of inflation. The MARR value used would reflect the inclusion or exclusion of inflation accordingly. Furthermore, it is preferable to use after-tax cash flows in the evaluation of projects for private firms since different designs and financing alternatives are likely to have quite different implications for tax liabilities and tax shields.

In theory, the corporate finance process does not necessarily require a different approach than that of the APV method discussed above. Rather than considering single projects in isolation, groups or sets of projects along with financing alternatives can be evaluated. The evaluation process would be to select that group of operating and financing plans which has the highest total APV. Unfortunately, the number of possible combinations to evaluate can become very large even though many combinations can be rapidly eliminated in practice because they are clearly inferior. More commonly, heuristic approaches are developed such as choosing projects with the highest benefit/cost ratio within a particular budget or financial constraint. These heuristic schemes will often involve the separation of the financing and design alternative evaluation. The typical result is design-driven or finance-driven planning in which one or the other process is conducted first.

Example 6-4: Combined Effects of Operating and Financing Plans

A public agency plans to construct a facility and is considering two design alternatives with different capacities. The operating net cash flows for both alternatives over a planning horizon of 5 years are shown in Table 6-4. For each design alternative, the project can be financed either through overdraft on bank credit or by issuing bonds spanning over the 5-year period, and the cash flow for each financing alternative is also shown in Table 6-4. The public agency has specified a MARR of 10% for discounting the operating and financing cash flows for this project. Determine the best combination of design and financing plan if

(a) a design is selected before financing plans are considered, or
(b) the decision is made simultaneously rather than sequentially.

The net present values (NPV) of all cash flows can be computed by Eq.(6.5), and the results are given at the bottom of Table 6-4. The adjusted net present value (APV) combining the operating cash flow of each design and an appropriate financing is obtained according to Eq. (6.25), and the results are also tabulated at the bottom of Table 6-4.

Under condition (a), design alternative 2 will be selected since NPV = $767,000 is the higher value when only operating cash flows are considered. Subsequently, bonds financing will be chosen because APV = $466,000 indicates that it is the best financing plan for design alternative 2.

Under condition (b), however, the choice will be based on the highest value of APV, i.e., APV = $484,000 for design alternative one in combination will overdraft financing. Thus, the simultaneous decision approach will yield the best results.

TABLE 6-4  Illustration of Different Design and Financing Alternatives (in $ thousands)

Year	Design Alternative One			Design Alternative Two
	Operating Cash Flow	Overdraft Financing	Bond Financing	Operating Cash Flow	Overdraft Financing	Bond Financing
0 1 2 3 4 5	-$1,000 -2,500 1,000 1,500 1,500 1,700	$1,000 2,500 -1,000 -1,500 -1,500 -921	$3,653 -418 -418 -418 -418 -4,217	$-2,500 -1,000 1,000 1,500 1,500 1,930	$2,500 1,000 -1,000 -1,500 -1,500 -1,254	$3,805 -435 -435 -435 -435 -4,392
NPV or FPV at 10%	761	-277	-290	767	-347	-301
APV = NPV + FPV	484		471	420		466