**Monday, December 21, 1998**

**FOOL ON THE HILL**

**An Investment Opinionby
Alex Schay**

**Return on Invested Capital -- Appendix A**

In Dale Wettlaufer's (TMF Ralegh) concise five-part series on the topic of return on invested capital (ROIC), the fundamental equivalence of the operating rate of return and the financing rate of return were outlined. Many investors who haven't had the benefit of perusing the work of Bennett Stewart III in The Quest for Value have forwarded us additonal queries on this topic, that is, questions concerning the seemingly "multiple methods" of calculating a rate of return on total capital.

When asked, "What is the equation for determining ROIC?" The quick answer is invariably, "After tax operating earnings, over -- total assets minus excess cash, minus non-interest bearing current liabilities." So the investor then heads for that operating earnings line, slaps on a deduction for the silent business partner in Washington DC, and then does the necessary balance sheet work in order to calculate the figure in the denominator. While this is correct, it's really a "Cliff Notes" method of getting to ROIC, or more appropriate to the times, a PinkMonkey.com method of getting to ROIC. That's why Dale addressed the adjustments that need to be made to assets -- the addition of equity equivalent reserves to capital -- in order to get the same amount of capital that is found when calculating ROIC from the financing perspective.

The equation for ROIC outlined above is the rate of return on total capital taken from an "operating" perspective. This is in contrast to the rate of return on total capital taken from a financing perspective. Although the calculations seem different, they yield exactly the same results, thanks to the accounting equation, or what Bennett Stewart III describes as "the great duality in the universe (to say nothing of the miracle of double entry bookkeeping)." In true "Appendix" fashion, today's column will serve as a small supplement to Dale's ROIC series. More to the point though, it will provide some additional material on the two rate-of-return perspectives that would have only bogged down the original series.

Understanding the equivalence of the operating and financing approach can lead to the profound realization that competition for capital is really what ultimately drives stock prices. As Bennett Stewart notes:

"There is a sequence of events that ties together the operating and financing approaches. First a company raises a mix of debt and equity [capital defined from the financing perspective (1)] and then invests those funds in its business [in net working capital and net fixed assets comprising capital viewed from an operating perspective (2)]. Next, the business begins to generate sales and incurs genuine operating expenses and taxes [resulting in NOPAT from the operating side (3)], which, in turn, constitutes a pool of cash that is available for distribution to *all* financiers (4)." (Italics mine)

Starting at the beginning, capital is defined as the sum of all the cash that has been invested in a firm's net assets over its life (the issue of "financing form" is addressed when calculating the weighted average cost of capital). Net operating profits after tax, or NOPAT, is the profit derived from the firm's operations after taxes, but before financing costs and non cash items. In calculating the rate of return from an operating perspective then:

NOPAT

r = -----------

capital

where NOPAT Capital

= Sales = Net working capital

- Operating expenses + Net fixed assets

- Taxes

Since net working capital is defined by Stewart as current assets minus non interest bearing current liabilities (NIBCLS), it can be seen that our "quick definition" of capital provided at the beginning of the story (total assets minus excess cash minus NIBCLS) is algebraically equivalent to net working capital plus net fixed assets. Again, the "net" in net fixed assets reflects adjustments made to incorporate certain equity equivalents (like the deferred tax reserve, LIFO reserve, cumulative goodwill amortization, unrecorded goodwill, and net capitalized intangibles -- for a really comprehensive look, you gotta' get the book).

The NOPAT portion of the operating perspective equation reflects, literally, a top-down approach to the income statement, where: recurring operating expenses (including depreciation) are subtracted from sales and then "cash operating taxes" are deducted as well. These cash taxes are derived by taking the accounting provision for taxes and subtracting any increase in deferred taxes, and then any tax savings gained from the interest tax shield are added back to the total. OK, drumroll please, here is the equation for the rate of return from the financing perspective:

NOPAT

r = -----------

capital

where NOPAT Capital

= Income available to = Common equity

common + Equity equivalents

+ Increase in equity

equivalents

----------------------------------------------

Adjusted net income Adjusted common equity

+ Preferred dividend + Preferred stock

+ Minority interest + Minority interest

provision

+ Interest expense + All debt

after tax

Here we have two different ways of ending up with the same result. For the capital portion of the equation the equivalence is easy to see, simply because the accounting equation of assets minus liabilities equals owners' equity can also be stated as assets equals liabilities plus owners' equity -- a figure for capital can then be arrived at by mostly playing with the asset side, or the liabilities and owners' equity side, of the balance sheet.

The NOPAT portion of the financing perspective equation starts at the bottom of the income statement and works its way back up by adding back the necessary items (recall that operating NOPAT essentially does the opposite). They both seem to meet somewhere in the middle though, which despite what Jakob Dylan says, is a good thing for us.

**Related Articles:**

ROIC series -- Part 1 I Part 2 I Part 3 I Part 4 I Part 5 I Compromise ROIC

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