Basic Tax/Interest expense question

Can someone please you basic plain simple english to explain how the tax savings work when you issue debt and how the formulas work?

So for the free cash flow to firm formulas, you add back interest expense * (1-tax rate).

I understand that when you issue debt (interest expense), you get a tax savings. But that formula just seems odd.

For level 1, i just memorized it, but I think I hsould probably fully understand it.

Also, in another FCFF formula, where you use ebit, you need to add back (Depreciation * tax rate)… can someone help in explaining that as well?

Thank you and happy sunday studying everyone.

Example: Let’s assume you have a 40% tax rate EBIT = 100 Interest Expense = 10 Therefore: Net Income = (100-10) * 0.60 = 54

Now, imagine there’s no debt (so no interest expense)

Therefore: Net Income = 100 * 0.60 = 60

The difference in Net Income between debt scenario and no debt scenario is: 60-54 = +6

Which is: 10 * 0.60 = 6 = Interest Expense * (1-tax rate)

so, the idea is your savings to net income with no interest expense is partially offset by the increased taxes you pay.

This is a NI example, but the general concept to free cash flow to the firm is basically the same i believe (just getting to Corp Finance!).

The EBIT formula requires you to add back FULL depreciation amount.

The EBITDA formula is when you add back deprec(tax)