A simple merger analysis and the MVBS method of discount rates

There is little less inspiring than studying foreign exchange finance that has managed to permeate the economics, derivatives, accounting, and equity sections of the CFA 2 exam, so a road map to M&A transactions and firm valuation with excess cash sounds like the perfect distraction.

What's in the title?
What is the difference between a merger, an acquisition, and a consolidation? Simply, a merger is a transaction where an acquirer buys the target and the target dissolves as a legal entity (A + B = A). An Acquisition is a transaction where the acquirer buys a majority stake in the target, but the target remains a legal entity (A + B = Ab). Lastly a consolidation is when two similar firms merge and form a new entity, (A + B = C). 

What's a firm worth?
In mergers the acquirer is buying the whole company, not just its equity. Thus when they make an offer for the firm they must take into account the equity holders and the premium they will require, in addition to buying out or assuming the target’s debt holders. This combination can be summed up with the term Enterprise Value (EV), where EV = Equity + Debt - Excess Cash. This is visually displayed in a market value balance sheet.

 

Liabilities are thought of as economic liabilities, or stakeholders of the company’s assets, not accounting liabilities which are by definition distinctly separate from equity.

There are some interesting identities that result from this economic model. One of the largest outside the M&A frame work is a surprising valuation result. The cost of capital of a firm is thought to be the weighted average of the cost of debt and the cost of equity. This "WACC" is a very well excepted method of discounting a firm’s cash flows to arrive at its total value, aka its enterprise value. This is true, however it is only true given a key assumption; the firm holds an immaterial amount of excess cash. Excess can loosely be determined as the cash balance that is above what would be needed for operations, or cash that is not called on through either the longer of a calendar year or a product cycle (make to sell). Most firms don't have this kind of cash, but some do, think Microsoft and Google. I'll do Google as an example below. 

 

Excess cash was assumed to be the balance in their marketable securities account (they have another $3 billion in their cash account) and equity was their May 15th share price close multiplied by the current shares outstanding. Look at that $24 billion in cash. Now look at what it implies about the firms Beta's. 

 

I grabbed the equity beta off of google finance, (ideally I would have taken the time to personally regress it because google finance is known to normalize it's beta using the 1/3 2/3 rule, but the point will still come across) and I assumed the debt beta to be 0.2 which is roughly what it could be. Note this is not the cost of debt, it’s a view of the value of debt in perspective of its credit rating and its relationship with the market. The beta of the firms liabilities corresponds to the risk that would be captured in a WACC discount rate (I do a clarifying example below). The punch line is this: cash has no beta. The beta of the enterprise (beta of the operation assets net of excess cash) can be backed into by the following identity. Beta of Liabilities = Beta of Total Assets. Beta of operation assets = Beta of Total Assets * Market Value of Assets / Enterprise Value. This is why the enterprise has a high beta; the excess cash is having a huge stabilization effect on the beta of debt and equity. Practitioners who simply use WACC to discount the firm’s cash flows grossly overestimate the firm’s value. The same example using discount rates is below. 

 

Excess Cash will not return 0%, it will return ~ 0.5% with today's rate, but this table doesn't concern itself with return, that is something to be modeled into the cash flows. This table concerns itself with the cost of capital and the appropriate discount rate for Google's projects. Practitioners not imbedding the leverage effect of cash, with incorrectly discount Google's project cash flows by a value 1.88% too low. In the terminal calculation, every dollar terminalized will result in a present value that is roughly $53 to high (1/1.88%).

Back to Mergers

I digress. Back to valuing a merger. Using the market value balance sheet discussed above, the acquirer has a pretty good idea of what they will have to pay. They can use the targets excess cash to help pay off the acquisition, (unlike patents and products, a target can't argue for a premium on its mountains of cash) and after a careful study of the bond covenants they will be able to determine what debt can be assumed, and what debt must be paid off with either its own cash or debt it issues itself.

I recently did a case competition that looked at the merger of Bank of New York, and Bank of Mellon. Here is how their MVBS's lined up. 

 

Again the equity is calculated stock price * shares outstanding. Debt is from the balance sheet, and both firms were assumed to have an immaterial amount of excess cash, so enterprise was the simple sum. When the merger took place BNY bought Mellon with an all stock offer, but the exchange ratio was a bit odd, BNY shares would be exchanged at 0.9434 (a large part of our case was arguing why this was too high and how they could bargain it down) and Mellon shares would convert at a 1:1 basis. Because of this quirk it is easier to think of Mellon buying BNY. 

Let’s assume both firms think synergies will be $7.5 billion present valued. Let's also assume synergies will be split in proportion to equity 'brought to the table.' What does the new firm look like? If the market values the synergies at the same value, what should the efficient share price be?

The easiest way to tackle this is to pretend the merger was an all cash offer. If Mellon bought BNY for all cash, they would need to pay $100 billion for the company plus $4.63 billion for their share of the synergies (7.5*26/(16+26)). This would produce a company looking something like this.

Woohoo $7 share price bump! The enterprise value is now the sum of the two companies plus the $7.5b in synergy and the debt is the debt of Mellon, the debt of BNY and $4.63b in BNY's synergy payout. Equity is simply Assets minus Debt, and then we call solve for share price by dividing by the number of shares outstanding. Obviously the firm is far to levered (7 times debt to equity, yikes!) so we need to look at the all stock merger. This is easy to do because we have not yet impounded the markets expected heavy discount on the stock due to our extreme leverage. Leaving this step out (we would need to do it if the merger was indeed all cash), we simply drop the cash payout from debt, and figure out how many shares need to be issued to solve for the same price per share. This is because, economically, the all stock and all cash deal involve the exact same payoffs, and so if we want to reward BNY with the same split of synergy, we simply just need to issue them enough stock to replicate the split they are getting under the current deal. This is how it looks. 

Now the debt equity ratio is a much more reasonable 2 (for a bank), and we have another 666 million shares outstanding that belong to BNY. It's that simple. From here you can play with any stock cash mix you want, and figure out all sorts of cool things like ownership stake, what stock payout is needed to keep within covenant restraints, and the sensitivity to each party in the event that synergy is less or more than expected. 

Oh and that exchange ratio, it’s 666/751.8=0.8858. BNY was arguing speculation had gotten out that the firms were going to merge and so they wanted to use the 6 month average stock prices. Unfortunately over the last 6 months Mellon had experienced a great rally where BNY had underperformed. The lower the equity value pre merger, the less stake you get in the synergies.

Accretion and Dilution

Will the EPS after the merger be higher or lower than it was before? Wither the merger is accretive or dilutive is a very common question from management, because they are used to thinking in terms of earnings per share, and have an expectation that their stock price will trade at a similar P/E multiple after the merger as it did before. The accretion dilution debate is basically economically irrelevant, but for the sake of the interview questions under the above assumptions plus the assumption that synergies are realized evenly, if the acquiring firms P/E multiple is higher than the (offer price)/E_target, the merger will be accretive. In reality it is not this simple; if there are high merger costs up front the merger will be dilutive at first and then can become accretive when synergies overwhelm integration costs later on. Also the reasoning behind the question is flawed, if a high P/E company buys a low P/E company of similar size, the market will adjust the price to a multiple that sits roughly between the two, unless there is good reason to believe that the high growth firm can make the low growth firms assets achieve high growth.