Interview Question - can't quite crack

A buddy of mine got this interview question for management consulting:

Company A has a higher Debt-to-Equity ratio than Company B. Assuming they both have the same net income, how can you determine their P/E ratio and which one is higher? If you can’t determine it, what factors/determinants would you need in order to do so?

The question has me scratching my head a little. Level of debt doesn’t really have a direct relationship to P/E and even the D/E is a ratio, so you could have a different answer depending on the different size/structure of the companies. How would you answer this? It can’t be as simple as saying please give me the share price and the earnings per share, haha.

If everything else was equal, my first thought would be Company A has a lower P/E than Company B. If you look at the implied P/E formula = P/E = (D1/E) / r-g ,r goes up if there is a higher D/E ratio, as the relevered beta (again, if all else were equal, except the D/E) would be higher, resulting in a higher required rate of return and a lower overall value, which results in a lower P/E.

Then I’d go on to get into the nitty gritty, are these companies even in the same industry? Size? Country? Growth? ect ect…

What factors would you ask the interviewer for that you feel are critical for solving P/E given the information we have… without being so direct as Price and EPS

This is a tricky one the cost of equity of company A would be more because of higher beta. However the growth (g) will also be higher because of higher RoE (same net income lower equity) this would offset the higher cost of equity. g=(Retained earnings/Total Earnings)XRoE

My previous the arguement assumes the capital employed is the same. That has to be clarified.

^ great points that didn’t even cross my mind… good stuff. My case was assuming a long-term perpetual growth rate of an equal number for both companies.

I’ve read also that more financial leverage could lead to a willingness to pay a higher multiple because of extra juice provided by the leverage.

Looks like that was addressed. Okay, thanks.

Still struggling with how to explain this to him! What would be your answer to the interviewer? What questions would you need answered to solve and then given that information how would you solve?

Sounds like one of McKinsey’s wacky questions

this is a really dumb question. there’s no real answer. the interviewer just wants to see how you think about it, and walk through it

the company with the higher Debt/equity would have a lower p.e as it would have a higher cost of capital. also p/e=market capitalisation/net earnings

You would need to know the price and earnings of each company…

Both market cap would do, as you have net income, like meeee20 said.

It doesn’t even state that both companies are similar or even in the same industry.

Maybe not. It would have higher EBITDA (since it has higher interest expense), which might command a higher P/E, since the you would be willing to pay more for $1 worth of earnings.

not sure how you figure this as 1$ of equity funding is almost always more expensive than 1$ of debt funding but it clearly depends on cap structure

Agree with this.

That’s not a dumb question necessarily. I like to ask a couple questions that there is no way the candidate would know the answer for. That’s how you tell if a guy will BS and screw you up when presented with the unknown, or if he has the higher level humility to admit he doesn’t know all yet has the confidence to know that’s not always a problem. I wouldn’t ask this specific question because it is quite bad, but you can learn a lot about a candidate from how they approach these situations.

but as an equity investor u would be more concenred wth PBT/PAT+Doereciation as a measure of cash earnings. and mine was more of a straight forward answer, offcourse the answer would depend on the capital structure, whether the company with more debt has been paying off the debt in the recent years and does more debt here refers to overleveraged capital structure or an optimal capital structure etc etc etc.