This really helped me conceptually:

The essence of free cash flow is to determine the cash flow that is available to repay creditors or pay dividends and interest to investors.

"Interest Tax Shield Example:

A company carries a debt balance of $8,000,000 with a 10% cost of debt and a 35% tax rate. This company’s tax savings is equivalent to the interest payment multiplied by the tax rate. As such, the shield is $8,000,000 x 10% x 35% = $280,000. This is equivalent to the $800,000 interest expense multiplied by 35%.

The intuition here is that the company has an $800,000 reduction in taxable income since the interest expense is deductible. This reduces the tax it needs to pay by $280,000.

Adding Back a Tax Shield:

When adding back a tax shield for certain formulas, such as free cash flow, it may not be as simple as adding back the full value of the tax shield. Instead, you should add back the original expense multiplied by one minus the tax rate. This is because the net effect of losing a tax shield is losing the value of the tax shield, but gaining back the original expense as income.

In our interest expense example, the annual value of the shield is $280,000. We now assume, however, that this debt was a convertible bond. To calculate the income effect of this bond’s conversion on diluted EPS, we have to add the after-tax interest expense back to net income. Thus, the value added back is found as follows:

After-Tax Interest Expense = Interest Expense x (1 – Tc)

Our convertible bond pays out a coupon of $800,000 this year. The tax savings, or tax shield, would have been $280,000 had the bond not been converted. If this bond was converted, however, the net value of the lost tax shield is $800,000 (1 – 35%) = $520,000.

The intuition here is that although we lose the $280,000 in tax shield, we gain the interest expense of $800,000 back (since we are not obliged to pay it out anymore). The net effect is -$280,000 + $800,000 = $520,000"