Simplistic DCF Calculations

To perform a DCF and then compare the resultant value to the current enterprise value, the cash flows used in the calculation should be free cash flow to the firm (FCFF), which measures the true returns-generating capability of the firm (see previous post on Enterprise Value for the reason). This FCFF is also known as unlevered free cash flow.

[Quick recap on FCFF: Using Net Income as a starting point, depreciation and amortization are added back as they are non-cash expenses. Increases in working capital and capital expenditures – which consume cash but are not incorporated as expenses in the net income figure – are subtracted. The cash flow is then unlevered by adding back any interest expense on a tax-adjusted basis. To tax-adjust the interest expense, one must subtract the tax shield provided by the tax-deductible interest payments.]

Should NOPAT be used instead of FCF? How does NOPAT compare with FCF?

Below are some sample calculations for the most simple case:

NOPAT = EBIT*(1-tau) = Operating Profit * (1-tax rate)

= net income + depreciation & amortization – capex – increase in net working capital + interest expense – tax shield provided by tax deductible interest payments
= NI + dep&amort – capex – increase in NWC + int – int*tau
= (EBIT – int)*(1-tau) + dep&amort – capex – increase in NWC + int*(1-tau)
= NOPAT – int*(1-tau) + dep&amort – capex – increase in NWC + int*(1-tau)
= NOPAT + dep&amort – capex – increase in NWC

Another way to writing FCFF in terms of NOPAT is:

FCFF = NOPAT – Change in Net Investment

Net Investment
= Invested Capital
= Working Capital + Fixed Capital (i.e. PP&E) + Other Operating Assets – Non-Interest Bearing Current Liabilities
= Short-Term and Long-Term Debt + Shareholders’ Equity

To obtain a NOPAT based on operating results, remember to do the following adjustments:

  1. Add back Bad Debt Expense to NOPAT because it is non-cash. Similarly, add Bad Debt Reserve back to Accounts Receivable when calculating invested capital.
  2. Add back Goodwill Impairment Charge to NOPAT because it non-cash. Similarly, add back cumulative Goodwill impairment charges when calculating invested capital.
  3. Portion of income tax provision on the income statement that is deferred, should be added back to NOPAT because it is not a current outflow of cash. Total amount of deferred tax liability is considered invested capital because the cash still lies invested within the company.
  4. Deferred tax assets are actual cash taxes paid but not yet showing up as part of the income tax provision on the income statement. Hence NOPAT should be reduced by the deferred tax assets amount because they have already been paid out. Invested capital should not include deferred tax assets because they are already paid out.
  5. Unusual gains and losses should be adjusted as though they did not happen. Hence after-tax losses should be added back to NOPAT, and after-tax gains should be subtracted from NOPAT. For invested capital, we add back cumulative after-tax losses, and substract cumulative after-tax gains.
  6. Depreciation is already subtracted when deriving NOPAT because it is an economic cost. It is not reversed even though it is non-cash because it is an economic outflow. For invested capital, accumulated depreciation should remain, so fixed assets should be considered on a ‘net of depreciation’ basis.
  7. Add back the portion of R&D considered as investment, to NOPAT. That portion of R&D considered as investment should be included as part of invested capital (i.e. capitalized).
  8. Add the change in Deferred Revenue to NOPAT as additional revenue because the cash inflow has already happened, just that it has not yet been recognised in accrual accounting. It should also be considered part of invested capital and not a liability because the cash is in the company.
  9. The adjustments to NOPAT above are the same adjustments to Invested Capital, so FCFF (i.e. NOPAT – Change in Net Investment) is not affected by the adjustments. Note that Return on Investment = NOPAT / Invested Capital.

EBITDA – dep&amort = EBIT

Operating Cash Flow
= EBIT + depreciation & amortization – interest – taxes
= EBIT + dep&amort – int – tau*(EBITDA – (dep&amort + int))
= EBITDA – int – tau*(EBITDA – (dep&amort + int))
= EBITDA*(1-tau) – int + tau*(dep&amort + int)

= (EBITDA – dep&amort – int)*(1-tau)
= EBITDA*(1-tau) – (1-tau)(dep&amort + int)
= EBITDA*(1-tau) + tau*(dep&amort + int) – (dep&amort + int)

Hence Operating Cash Flow
= NI + dep&amort

In the most simplest of cases, using FCF would be equivalent to using (NOPAT + dep&amort – capex – increase in NWC). An alternative definition of FCF (to the firm) that gives the same result is as follows:

= Cash outflow + Change in Cash & Cash Equivalents position
= Cash outflow to debt holders + Cash outflow to equity holders + Change in Cash & Cash Equivalents
= (Debt repayment + after-tax interest expense) + (Share repurchase + dividends) + Change in Cash & Cash Equivalents

In a more realistic scenario, it may be useful to compare the cashflows from using FCF and from using the NOPAT version and understand where the discrepencies arise. For example, to calculate FCFF in some scenarios, you will need to subtract necessary expenditures such as Preferred Stock Dividend Payments, Required Redemption of Preferred Stock, Required Redemption of Debt, etc.

[Note: You don’t have to adjust for “tax shield provided by dep&amort” because it is really given/incurred, it is not a non-cash item that needs to be adjusted.]



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