How NOPAT is calculated

NOPAT is net operating profit after tax. Write it as EBIT times one minus the tax rate:

$$\text{NOPAT} = EBIT(1-t)$$

On $100,000,000 of EBIT at 25 percent tax, NOPAT is $100{,}000{,}000 \times 0.75 = 75{,}000{,}000$, so $75,000,000. The tax on that operating profit is a quarter of EBIT. Interest has not been deducted. The tax in the formula is the tax that would be paid if the firm had no debt, so the number can be compared across capital structures.

The ROIC calculator on this page is this NOPAT in the numerator of a return on invested capital. How ROIC works owns that ratio. This page owns the $75,000,000.

Return on invested capital is NOPAT over the operating capital tied up in the firm. How free cash flow works starts from the same NOPAT and then takes capex and the change in working capital off. Do not print this $75,000,000 as cash the firm can distribute.

Keep EBIT at $100,000,000 and tax at 25 percent, so NOPAT is still $75,000,000. Raise invested capital to $750,000,000. ROIC falls to 10 percent.

Profit after tax did not fall. The capital used to produce it rose. A year of heavy capex can print a fine NOPAT and a worse ROIC: the new assets are in the denominator now, and the profit they will earn may not be. Surplus cash left in invested capital pads the denominator the other way and understates the return.

NOPAT did not move. The reading of it did. That is why this page keeps the dollar in view rather than only the rate.

EBIT is now $80,000,000, tax still 25 percent, invested capital $400,000,000. NOPAT is $60,000,000. ROIC is 15 percent again.

The rate matched the first sheet. The scale did not. Two firms at 15 percent are not the same business. One has $75,000,000 of NOPAT on $500,000,000 of capital. The other has $60,000,000 on $400,000,000. Compare the rate with WACC, then look at the size of the spread times the capital, which is the economic profit.

Net income is profit after interest and tax. NOPAT is operating profit after tax, before interest. A more borrowed firm can print a smaller net income on the same EBIT, because the coupon has already come out. NOPAT on that firm is unchanged, which is the point of the number.

How ROE works divides net income by book equity. On that teaching sheet, $15,000,000 of net income on $100,000,000 of equity is 15 percent ROE. That $15,000,000 is a different firm, a different claim, and a different year from the $75,000,000 of NOPAT on the ROIC sheet. NOPAT against net income is the pair, on two teaching sheets, not one.

Mixing them is how a recapitalisation looks like an operating improvement: net income can fall or rise with the coupon while NOPAT sits still.

Free cash flow takes depreciation add-backs, capex, and the change in working capital off NOPAT. A firm can print $75,000,000 of NOPAT and still consume cash if it is building plants or filling warehouses. The FCF page is that walk. This page stops at $EBIT(1-t)$.

EBITDA is a different starting point again: it is before depreciation. NOPAT is after depreciation and after a tax on EBIT. Do not line a NOPAT figure up next to an EBITDA multiple and call the gap a finding.

It is not a cash forecast, not a net-income engine, and not a claim that 15 percent ROIC is a good rate. The three sheets are $75,000,000 of NOPAT on $500,000,000 of capital (15 percent), the same $75,000,000 on $750,000,000 (10 percent), and $60,000,000 of NOPAT on $400,000,000 (15 percent). This is educational material, not financial advice.