Interview Question: Finding an Interest Rate from the Leverage and Coverage Ratio

This tricky restructuring interview question is asked fairly often. It's one of those questions that at first blush seems a bit daunting.

However, once you see the solution you'll realize it's entirely straight forward and you'll be able to answer it easily regardless of how they change the numbers around on you. 

The Interview Question

Let's assume we have a leverage ratio of 5 and a coverage ratio of 5. What's the blended interest rate on the debt? 

Whenever you're asked this kind of question the first thing you should do is just write down what we know. Don't try to answer questions like this in your head. 

So we have a leverage ratio (Debt/EBITDA = 5) and a coverage ratio (EBITDA/interest expense = 5). What we are trying to find is the interest rate (a percent value, of course).

There are two general ways to answer this kind of question.

Answer #1: The Plug and Chug Method

Of course, every interviewer wants to hear an elegant solution to their question.

However, your job is to get answers right.

If you get a question like this where you have some known formulas, some known variables, and you know you need to isolate something don't be afraid to just plug and chug.

For example, we know that interest expense is just the interest rate (what we're trying to find) multiplied by the outstanding debt. So if we know the total debt and the total interest expense, then we can back out the interest rate easily enough.

We can use any numbers we want here (as what we're getting is an interest rate that obviously doesn't fluctuate based on nominal amounts that are fixed by our ratios).  

Let's choose some round numbers. We'll say Debt = 500 and EBITDA = 100. These are dummy numbers. They can be anything so long as the ratio of debt to EBITDA is five (because that's our leverage ratio given in the question).

Now we have (EBITDA / Interest expense) = 5 for our coverage ratio. We've already said that EBITDA is 100 so therefore we can isolate interest expense as being 20. 

So we have 20 in annual interest expense on 500 in debt. So the interest rate is just 4% (interest expense / debt = 20/500). 

That's it. Obviously you could have chosen Debt = 1000 and EBITDA = 200 if you wanted and gone through it that way. All you had to do was stay true to the ratios given in the question and you would have come up with 4% as your answer for the interest rate.

Answer #2: Fancy Isolation

Another way (that is perhaps a bit more theoretical and thus perhaps a bit more impressive) is to recognize that all interest expense is, is (interest rate)*(Debt). 

Given that, we can actually isolate the interest rate without having to use any dummy numbers at all. 

We can express the coverage ratio as being (EBITDA / (r)(Debt)), where r is the interest rate.

We've been told that the coverage ratio is equal to 5, therefore we can re-arrange the formula as: 5*(r)(Debt) = EBITDA.

Now, in order to isolate r, we can divide the left-hand side by "Debt" to get => 5*r = EBITDA / Debt

You should recognize that EBITDA / Debt is just the inverse of the leverage ratio (which is 5), so it is therefore 1/5.

Now we can express the formulas as just being 5*r = 1/5. Now just divide the left hand side again by 5 to isolate r (we could have done this all in one step, but I wanted to break it up to be clear). 

Now we have r = 1/25, which is obviously also 4%. 

Conclusion

There you have it! This restructuring question really hinges on realizing that interest expense is really just an interest rate multiplied by the debt amount and thus the interest rate can be isolated with the information given. 

Of course, everyone knows that interest expense is just the interest rate multiplied by the debt amount. But it's one of those things where in an interview you tend to glaze over that simple fact as you rack your brain trying to figure out how to answer the question.

Remember: there's absolutely nothing wrong with just plugging numbers in and figuring out the answer that way. It doesn't matter what numbers you pick for a question like that, since you're ultimately getting a percent not a nominal dollar value.

If you'd like more restructuring interview questions, be sure to check out the Restructuring Interviews course that has hundreds more Q&A along, a nearly 100-page guide, and much more. 

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