Confusing Technical Question

"Q: There are two companies with identical growth prospects, margins, business models, etc. The only difference is that one company has 50% debt-to-total capitalization, while the other has 0%. If you were a PE firm and were going to bring the company’s debt-to-total capitalization to 70%, which investment would yield a higher IRR (assuming that the equity purchase price is the same)?

A: We recognize that the two company’s initial debt-to-total capitalization is irrelevant from a returns basis. It does not matter if you are the firm who raised the debt or if the debt was refinanced from before, the IRR and returns will be the same mathematically. At 70% debt-to-total capitalization, the EV of the two companies would be the same, implying that the IRR would be the same as well.

However, this assumes that the purchase EV is the same in both situations. This is not entirely correct because sponsors typically have to pay a premium on equity (control premium), which does not apply to debt. In this case, the company with the higher debt will result in a higher IRR because it will have a lower purchase price."

I'm having trouble wrapping my head around this. If the Equity values are the same, then wouldn't the same control premium be paid in both cases?

 

This question confused the fuck out of me too. I just think it's worded poorly.

I think it means if the equity value is the same in both situations, the company that had the lower amount of equity to begin with will yield a higher IRR. The company with 70% debt, would have 30% equity vs. the other company with 50% equity. And the sponsor is paying a control premium on 30% equity vs. 50% equity.

It's a weird question but I think thats what its asking. If this isn't the way to solve it then I really have no idea.

 

Agreed on the wording.

Would the % equity make a difference in the control premium? The question states that one company has 0% debt, so let's assume it's financed by 100% equity. The other company has 70% debt, so financed by 30% equity. It also explicitly states that equity value is the same - let's give that a value of $100m.

In both scenarios, we are still purchasing $100m of equity. In both scenarios, this $100m of equity represents full control of the equity. Should they not have the same premium?

 

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