Thought Experiment on Capital Structure and P/E

Here’s a thought experiment that’s been confusing me lately:
Schindustries raises $100M equity in an IPO and promptly puts it all into 10% muni bonds. The earned interest of $10M/year represents its earnings. There are 100 shares laying claim to the $10M earnings stream and each is obviously worth $1M. Price/earnings ratio is 10.
Chairman and CEO Evan “EPS” Schindewolf then issues $50M debt, also at 10% interest because the market correctly assesses the beta on Schindustries’ assets. He then buys back 50 shares from the market.
Net net, there are 50 shares left. However, they only lay claim to a $5M earnings stream now (since $5M interest on the bonds must be paid). I’d suggest that the per share price here remains $1M each.

Shouldn’t the price stay at $1M per share each after the share buyback? Implying that P/E ratio remains 10? This outcome confuses me because I’ve read countless times that the price to earnings ratio is supposed to be capital structure sensitive. What am I missing?

I used to think that dividends were included in net income, so if the dividend rate on the 100 shares was roughly equivalent to the interest rate, then the argument that P/E should go down with higher leverage made sense – the pre-buyback scenario would have zero net income (and EPS) and the post-buyback would have $5M net income (sending EPS higher to $100k) , but demand a correspondingly lower P/E to adjust EV to the same total. Obviously, dividends are not in net income so this thinking is flawed.

Update:
Here’s an interesting quote from WikiInvest
For example, if a company with debt were to raise money by issuing shares of stock, and then used the money to pay off the debt, this company’s P/E ratio would shoot up because of the increased number of shares – although nothing about the fundamental value of the business has changed.
I’m pretty sure this isn’t true. Let’s say the post-buyback 50% debt Schindustries issues 50 shares of stock at $1M/share (the current trading price  of their shares) and buys back $50M worth of debt. Market cap of equity will have gone up to $100M, but earnings will have gone up as well to $10M (since there’s no longer the $5M debt service burden).

At the end of the day, I’m starting to think both EV/EBITDA and P/E make sense. P/E is levered in the numerator and denominator, while EV is unlevered in both the numerator and denominator. Either way, both make apples to apples comparisons.

12/1/13 Update: Looking back on this after 7 months at a hedge fund, it’s hilarious how little I knew going into this job. At least I was thinking about it, though. And certainly I had a better Corp Fin background than most non-bankers (and even some bankers).

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