Whilst preparing for my CFA Level II examinations, I was really perplexed by the calculation of the free cash flow to firm (“FCFF”) especially with regard to the tax saving from interest expenses. Let me elaborate.

The definition of FCFF as per the CFA curriculum is:

“Free cash flow to the firm is the cash flow available to the company’s suppliers of capital after all operating expenses (including taxes) have been paid and necessary investments in working capital (e.g., inventory) and fixed capital (e.g., equipment) have been made.”

Thus, FCFF is the cash flow that is available to both the equity and debt holders of the firm before any payments (such as dividends and interest) are made to these suppliers of capital. Here is the equation to compute FCFF that is prescribed and used universally:

FCFF = Net Income + Non-cash Charges + Interest * (1 – tax rate) – CapEx – Change in Working Capital

## The problem

The thing that bothered me was that the above equation appeared to ignore a very real cash flow in computing FCFF – **the tax savings from interest expenses.** It will be clear with the help of the following hypothetical scenarios:

As you can see, the only difference in the above scenarios is the interest expense. And because of the interest expense, the taxes in Scenario 1 are lower than Scenario 2. Accordingly, when looking at the firm from the perspective of both debt and equity holders put together, we would expect the free cash flow in Scenario 1 to be higher than Scenario 2 by the amount of taxes that are saved because of the interest expense, i.e. 100 * 30% = 30.

So let’s see if this holds true using the formula for FCFF prescribed above:

The above calculation begs the following questions:

- If FCFF is the cash available to the equity and debt holders of the firm, why do we ignore the tax savings from interest?
- Why do we pretend as if there is no interest expense when calculating FCFF?

## The answer lies in the cost of debt…

No discussion of free cash flows is complete without talking about discounting them at the cost of capital/ equity. First principles in finance tell us that when looking at FCFF, we must discount them at the cost of capital (also known by the popular acronym, WACC). Cost of capital as most finance students know is a mix of the cost of equity and **after-tax cost of debt** weighted by the relative weights of equity and debt in the capital structure.

After tax cost of debt is calculated as:

After-tax cost of debt = Pre-tax cost of debt * (1 – tax rate)

Let’s get back to our scenario 1. Suppose the market value of debt in the capital structure in this scenario is 1000. Assuming the debt is recent, this gives us a pre-tax cost of debt as:

Pre-tax cost of debt = Interest expense / Market value of debt

Pre-tax cost of debt = 100 / 1000 = 10%

Now in our cost of capital calculation, we would use the after-tax cost of debt, i.e. 10% * (1 – 30%) = 7%.

Now do you see? The tax savings from interest expense are incorporated in the cost of debt itself. If we include the tax savings from the interest expense in our cash flow computation as well, we would end up double counting the interest tax savings.

The CFA Institute touches upon this aspect in the curriculum with the following two paragraphs:

“After-tax interest expense must be added back to net income to arrive at FCFF. This step is required because interest expense net of the related tax savings was deducted in arriving at net income and because interest is a cash flow available to one of the company’s capital providers (i.e., the company’s creditors). In the United States and many other countries, interest is tax deductible (reduces taxes) for the company (borrower) and taxable for the recipient (lender).As we explain later, when we discount FCFF, we use an after-tax cost of capital. For consistency, we thus compute FCFF by using the after-tax interest paid.”

“Note that we could compute WACC on a pretax basis and compute FCFF by adding back interest paid with no tax adjustment. Whichever approach is adopted, the analyst must use mutually consistent definitions of FCFF and WACC.”

Thus, we could incorporate the interest tax savings either:

- in the cash flows (in which case, we would have to use the pre-tax cost of debt in our WACC computation); or
- in the cost of capital (in which case we have to pretend as if there are no interest expenses)

In my experience, the first method (where we incorporate the tax saving in the cost of debt) is more in use, practically as well as in academia. As long as we are internally consistent, we would be home free.

OK, but suppose that for example debt = 100%, interest = 10%, tax rate = 30%.

Discounting interest after tax for one period (WACC after-tax cost of debt):

7 / 1.07 = 6.54

Discounting interest before tax (WACC before-tax cost of debt):

10 / 1.1 = 9.09

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