One of the questions I see a lot in finance interview prep books is the following:
What happens to a firm's EPS when the firm has a higher P/E ratio than the one it acquires?
The "answer" is that the new firm's EPS increases.
Can someone prove this to me?
Thanks.
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Try an example yourself. It works.
you're probably just confused because E is the numerator in one ratio and the denominator in the other
common sense would help
I'll provide an example where I don't think this applies.
Firm A # of shares = 100 Firm B # of shares = 100 Firm A earnings = 100 Firm B earnings = 100 Price/share of Firm A = 200 Price/share of Firm B = 100 (due to lower growth potential) P/E of firm A = 2 P/E of firm B = 1 EPS of firm A = 1 EPS of firm B = 1
Firm (A + B) # of shares = 200 Firm (A + B) earnings = 200 Firm (A + B)EPS = 1
Again, can someone mathematically prove this to me?
This was touched on by somebody else, but you're thinking of this the wrong way. You don't "sum" the shares of the two companies in a merger. The acquiring company has (at the most basic level) 4 ways to finance the acquisition:
1) Stock-for-stock swap (i.e. exchanging AcquireCo's authorized shares for TargetCo shares on the basis of some pre-arranged exchange ratio. TargetCo's former shareholders would then become owners of AcquireCo shares);
2) Issue new AcquireCo shares for cash (i.e. raise capital in a follow-on equity offering) and buy out TargetCo's shareholders at a pre-arranged offer price (typically for a premium to where TargetCo is currently trading);
3) Do the same as #2 only finance it with debt (i.e. a leveraged buyout);
4) Some combination thereof.
Note: There are more exotic ways of financing an acquisition (across every end of the capital structure) but that's not the point here.
So, thinking about financing option #1: If AcquireCo decides to do a 100% stock-for-stock swap, and assuming that the earnings of both companies are perfectly comparable, AcquireCo (trading at a higher P/E multiple) would be using its expensive currency (i.e. its stock) to purchase TargetCo's earnings on the cheap. The acquisition would therefore be Accretive.
Here's an example:
AcquireCo price: $20.00/sh AcquireCo EPS: $1.00/sh AcquireCo P/E: 20x AcquireCo shrs o/s: 100
TargetCo price: $15.00/sh TargetCo EPS: $1.00/sh TargetCo P/E: 15x TargetCo shrs o/s: 200
The cost to buy TargetCo's equity is 200 x $15.00 = $3,000, so AcquireCo has to issue 150 shares ($3,000 / $20.00) to TargetCo shareholders. Pro forma AcquireCo shrs o/s equals 100 + 150 = 250.
AcquireCo is receiving $200 of TargetCo earnings (200 x $1.00) in the acquisition. Pro forma AcquireCo earnings equal $100 + $200 (i.e. AcquireCo's pre-merger earnings, plus TargetCo's earnings) for a total of $300.
Pro forma AcquireCo EPS equals $300 / 250 = $1.20.
The acquisition is therefore $0.20 Accretive to AcquireCo's EPS.
That's the basic math, which ignores synergies, transaction costs, and the reality that both companies' earnings aren't perfectly comparable. But that's the answer the interviewer is looking for.
um you know that the # of shares in the ACQUIRING firm doesn't rise by the # of shares of the company that has been acquired right?
...
Accretive vs. Dilutive acquisition? The earnings are theoretically better relative to price of the second company so if the first company does the acquiring and acquires their revenue and earnings, adding these extra shares should be a benefactor in terms of EPS, since company 2 was better valued.
For bonus points: it also does not include the dilutive effect of options, warrants and other common stock equivalents, asset write-ups, allocation of excess purchase price to identified intangibles, and a number of other equally important factors.
To the original poster - the math is simply an issue of cost of capital. You can do the same exercise with an all-cash transaction. You're just comparing the after-tax cost of cash/debt with the multiple of the purchase.
It also depends on the consideration mix and premium paid. you're assuming stock for stock merger, but if there is some component of debt then things would change.
Obviously, everyone here wants to show off their supposedly deep knowledge here, but what I would say is ask the interviewer to confirm its 100% stock deal at no premium (or that the lower P/E is the offer P/E) and then go ahead with the previous answer.
Don't go too overboard b/c the interviewer will know a whole lot more than you and if you try to show you know too much, they'll bust you.
Haha, agreed.
Just trying to help though.
Regardless of consideration mix, accretion/dilution is something you should be able to do with as much accuracy as a full model, with nothing more than a calculator, and two minutes.
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