Merger Math is Everywhere!

Merger & Acquisitions MERGER MATH The Shark Bite The Bear Hug Merger Math is Everywhere! MoneyWatch.com Merger math: if you know where to look, there are lots of tempting targets Merger of Equals - Merger Math? How do you think about accretion / dilution analysis on a merger of equals? For example if Yahoo / MSFT would have merged obviously it would extremely dilutive because you are giving up so much stock. What s the best way to think about shares outstanding and the dilution to the pro forma company? Sometimes Merger Math Just Doesn't Add Up WBA BOLT Summer Leadership Summit 1

Start with the Mechanics of a Stock for Stock Deal We will start our merger discussion with the accounting requirements that the acquirer (shark) and the acquiree (target) might accept. Note: we are not determining in the first part of this exercise if the merger makes investor sense (i.e value enhancing to shareholders in the long run), just accounting sense. It is important not to confuse the two! VS WBA BOLT Summer Leadership Summit 2

What will the shark want? 1. The shark s shareholders will not want EPS dilution. In fact they prefer accretion so a higher EPS x (P/E) = higher stock price! Assumption is P/E will at least remain the same. 2. The shark will want to maintain control, in other words after the merger the shark s stockholders want to have more shares than the target s shareholders have. What will the target want? 3. The target s shareholders will not take less for their stock than it is currently worth (less than current MKT VALUE). Let s Look at 3 Very Important Pieces of Merger Math Information 1. How many shares can the Shark offer the target without diluting the Shark s EPS? 2. What is the maximum price per share the Shark will offer the Target? 3. What is the minimum number of shares the Target will take in exchange for its stock? Remember the currency here is shark stock not cash! WBA BOLT Summer Leadership Summit 3

Variables/Data S S = existing Shark Shares Outstanding S T = existing Target Shares Outstanding = New Shark Shares offered to Target NIAT S = Earnings of the Shark (Net Income after Tax) NIAT T = Earnings of the Target (Net Income after Tax) P S = the Shark s stock price P T = the Target s stock price 1. How many shares the shark can offer the target without diluting earnings? WBA BOLT Summer Leadership Summit 4

Non-dilution of Shark EPS means EPS (SHARK or SHARES S TARGET) EPS SHARK NIAT S NIAT T NEW SHARK SHARES OFFERED TO TARGET NIAT S SHARES S NIAT S (S S + ) S S (NIAT S + NIAT T ) NIAT S NIAT T S S or, solving for SS NIATT NIAT S NIAT NIAT SS T S NIAT EPS S T TARGET' S EARNINGS EPS SHARK Pretty obvious and intuitive result! If target makes $100 and I want EPS = 20, then I can only offer up to 5 shares! WBA BOLT Summer Leadership Summit 5

The picture can't be displayed. June 13, 2017 Example: NIAT T = 100, EPS S = 10 Non-diluting max shares shark can offer target is NIAT T /EPS S = 100/10 = 10 shares Shark NIAT 500 Shares 50 EPS 10 Target NIAT 100 Merged NIAT 600 (500 + 100) Shares 60 (50 + 10) EPS 10 What if shark gave the target 11 shares? Question: what if shark only had to give 5 shares? 600/55 = 10.91 accretion Merged NIAT 600 (500 + 100) Shares 61 (50 + 11) EPS 9.84 dilution! 2. What is the most the shark will pay per share for the target s outstanding shares without diluting Shark EPS? The price per share offered to the Target (P OT ) for its existing shares is P OT Value of Number New Shares Offered of Shares of Target P OT New Shares Offered Number of Price of Shark Shares of Target Shares Which, when we plug in the max the shark can offer without diluting the EPS of the merged bank equals Comments: 1) this better be target s current price/share or NIAT T PS EPS NO DEAL. AMOUNT over P T is the PREMIUM. 2) in some cases S S P S might be substituted for OT (NIAT T /EPS S ) if the control constraint is more Number Shares of Target restrictive than non-dilution Note: if I offer a price more than this then I must be offering (effectively) more than NIAT T /EPS S shares. As we saw before, offering more than this number of shares is dilutive to earnings and violates the conditions of the deal. So, P OT is the MOST I will pay per share for the target s existing shares. The shark would prefer to offer a lower price, i.e. fewer shares if possible +to get EPS accretion. WBA BOLT Summer Leadership Summit 6

3. What is the necessary condition for the target to accept the deal? The necessary condition to get the target to sell is that the shark must pay the target s stockholders more than their company is currently worth, i.e. Value offered the Target current Market Value of the Target s shares P S P T S T or, solving for the share exchange rate /S T P T /P S Which says that the exchange rate is simply the ratio of the individual stock prices. The # of shark SHARES EXCHANGED for each share of the target s stock DEPENDS ON WHETHER the shark s price is above or below the target s price. The higher the shark s stock price is relative to the target s stock price, the fewer shares the shark must offer per share of target stock. Simple Example Suppose P T = $10, S T = 100 shares so MKTVAL T = $1000 If P S = $20, then has to be at least 50 shares, 50 x $20 - $1,000 in value, to at least equal the current MKTVAL of the target. /S T P T /P S S T P T P S 50 100 $10 $20 50/100 $10/$20 =.5 WBA BOLT Summer Leadership Summit 7

Let s see what happens if we try to make everyone happy simultaneously! In other words, let s put it all together starting with the value offered the target equation at the top of the page 2 slides back (what the target wants) and then impose the nondilution constraint (that the shark wants) and see what we learn. The target wants *P S > S T * P T that is at least its current market cap. The shark does not want to dilute the EPS of the shark, i.e. [NIAT T /EPS S ]. so let s put these both together to keep everyone happy! Value offered > current value This is the famous P/E Rule in mergers. WBA BOLT Summer Leadership Summit 8

The Rule says several things: 1. The ultimate determinant of whether the shark can make an offer the target might accept without diluting the shark s EPS is whether the shark s P/E exceeds the target s P/E. 2. The actual stock prices do not matter except for the calculation in the share exchange equation. 3. The actual earnings do not matter either. 4. What matters is the relative P/E ratios. In other words, the real key in a non-diluting merger deal is not the stock price or earnings but their ratio- the P/E ratio. 5. Intuitively this says if the Target s P/E is higher than the Shark s, then the Target wants too much for its earnings! What about control? WBA BOLT Summer Leadership Summit 9

4. Need one more equation! The Control Constraint Now we can explain why the condition that the shark has the higher P/E is necessary to make a non-dilutive offer but not sufficient if the shark wants to maintain control as well. So, the shark will need (P/E) S > (P/E) T and something else to make the deal work. 4. Now let s add one additional constraint that the shark must maintain control. Shark must maintain control: Shares owned by Shark shareholders > New shares it gives the Target 1. S S and, the Shark must offer target more than it is currently worth, 2. *P S S T *P T Now multiply both sides of (1) by P S to get 3. S S *P S *P S which says current MKTCAP S has to be value of new shares offered Now use the Transitive Property of Inequalities and combine (3) and (2) to get S S *P S *P S S T *P T which says. MKTCAP S MKTCAP T WBA BOLT Summer Leadership Summit 10

So, we need to satisfy two conditions to make a controlling, non-dilutive merger deal that might be acceptable to both the Shark and Target on a pure accounting basis. 1. (P/E) S > (P/E) T, and 2. MKTCAP S > MKTCAP T Necessary condition for making an offer the target might accept (ie offering them more per share than they are currently worth) without diluting the shark s EPS Necessary condition for shark to maintain control (ie shares offered target are less than current outstanding shark shares) So here is really the mathematical system we are dealing with: The condition that shark EPS will not be diluted (NIAT T /EPS S ) The condition that the shark offer more than the target is currently worth. * P S S T *P T The condition that the shark does not lose control < S S (or equivalently MKTCAP S >MKTCAP T) Here are the conditions that must apply for all of this to happen simultaneously (P/E) S > (P/E) T or equivalently P S /P T > EPS S /EPS T MKTCAP S >MKTCAP T And, of course, the number of shares the shark must acquire from the target S T = S* WBA BOLT Summer Leadership Summit 11

The Graphics of a Non-dilutive Deal 1. The value of shares offered equation: the shark has to offer new shares at its existing share price that equal or, more realistically, exceed the current market value of the target. *P S S T* P T or (P T /P S )*S T 20 (P T /P S )*S T If we are on this line then the value offered just equals the current MKTCAP of the Target If above the line then the value offered exceeds the current MKTCAP of the Target Example: if P T = $100 and P S = $50 then the Shark has to give up at least 2 shares of its stock for every share of the Target. If the Target has 10 shares, the Shark must offer at least 20 shares, or $1000 of Shark stock for a $1,000 of target stock. 10 S T 2. The Non-dilution of Shark EPS constraint: the shark cannot offer SNEW that dilutes its post merger EPS. NIAT T /EPS S which is a constant given NIAT and EPS. S T Example: if NIAT T = $100 and EPS S = $25 Shark can only offer 4 shares WBA BOLT Summer Leadership Summit 12

3. The shark cannot give up control by offering more shares than it currently has constraint. < S S which is a constant S T 4. The there are S T shares of the target to buy out equation. S T = S* which is a constant S T WBA BOLT Summer Leadership Summit 13

Putting it all together (P T /P S )S T The Value to the Target Equation <S S NIAT T /EPS S Do Not give up Control constraint Non-dilution constraint Game will be played in here: both of these would be non-dilutive and would offer the target value Equal to or above its current mkt value S T =S* (ie target has this many shares) S T Examples and Lessons Bank Price NIAT Shares EPS P/E MKTCAP 1 $20 $50 20 2.5 8 $400 2 $30 $60 30 2.0 15 $900 3 $45 $200 40 5.0 9 $1800 4 $35 $50 20 2.5 14 $700 5 $100 $100 10 10.0 10 $1,000 Case 1: Shark has higher P/E and higher MKTCAP Example: Can Bank 2 buy Bank 1 with stock? WBA BOLT Summer Leadership Summit 14

2 buys 1 Here, offer is 25*$30=$750 or $37.50/share>$20/share, so target might accept. EPS is now ($60+$50)/55=2.0 so no dilution =(20/30)S T <30 $50/$2.0 =25 Do Not give up Control constraint Non-dilution constraint 13.33 Game will be played in here: both of these would be non-dilutive and would offer the target value above its current mkt value S T =20 shares Here, offer is 13.33*$30=$400 or $20/share $20/share, so target might accept. EPS is now ($60+$50)/43.33=2.54 Per share so no dilution! S T Examples and Lessons Bank Price NIAT Shares EPS P/E MKTCAP 1 $20 $50 20 2.5 8 $400 2 $30 $60 30 2.0 15 $900 3 $45 $200 40 5.0 9 $1800 4 $35 $50 20 2.5 14 $700 5 $100 $100 10 10.0 10 $1,000 Case 2: Shark has lower P/E and lower MKTCAP Example: Can Bank 4 buy Bank 2 with stock? NOTE: 4 has the higher stock price! WBA BOLT Summer Leadership Summit 15

4 buys 2 Here, offer is 25.714*$35=$900 or $30/share, so target might accept. EPS is now ($60+$50)/45.714=2.41 so EPS diluted (<2.5)! Shark will not do this! =(30/35)S T Nondilution constraint 25.714 shares $60/$2.5= 24 shares S T Here, offer is 24 shares*$35=$840 or $28/share<$30/share, so target will not accept. EPS is now ($50+$60)/44=2.5 per share so no dilution but can t offer target enough value! S T =30 shares Also, with either offer shark loses control Do Not give up Control constraint <20 Examples and Lessons Bank Price NIAT Shares EPS P/E MKTCAP 1 $20 $50 20 2.5 8 $400 2 $30 $60 30 2.0 15 $900 3 $45 $200 40 5.0 9 $1800 4 $35 $50 20 2.5 14 $700 5 $100 $100 10 10.0 10 $1,000 Case 3: Shark has higher stock price, higher earnings, higher MKTCAP but lower P/E Example: Can Bank 3 buy Bank 2 with stock? WBA BOLT Summer Leadership Summit 16

3 buys 2 <40 20*$45+$900 Or $30/share, so this Is just enough value =($30/$45)S T Control constraint 20 shares But, an offer of 20 shares would dilute EPS. ($200+$60)/60 shares=$4.33 share too low! $60/$5=12 Non-dilution constraint S T =30 S T If shark offered non-diluting 12 shares or 12*$45=$540 That would be $540/30=$16/share which the target Would not take! Oh, c mon. I am the big dog here, I should be able to make this work WBA BOLT Summer Leadership Summit 17

Making it happen: the key to most merger deals. It does not work initially because Bank 2 wants too much ($30) for its lousy $2 of earnings per share. What if I thought that if I bought Bank 2 I could decrease expenses in that bank by $90 by closing branches, laying off redundant workers, etc. In other words, I am thinking I am not really buying $60 of NIAT if I buy this bank but I am really buying $150 of after tax earnings. What does the deal look like to me now? What the deal looks like with synergies Bank Price NIAT Shares EPS P/E MKTCAP 2 $30 $150 30 5.0 6 $900 3 $45 $200 40 5.0 9 $1800 The $30 I give them per share actually buys me $5 of earnings not $2! From where I stand I have control and my P/E is actually bigger than their real P/E once I eliminate some costs so this can work. Case 3 revisited with $90 of cost saving synergies <40 $150/$5=30 WITH $90 OF SYNERGIES! 30 SHARES * $45= $1350 OF VALUE TO TARGET. EPS S = ($200 + $150)/70=$5 So no dilution. =($30/$45)S T Control constraint Non-dilution constraint 20 shares, which will not dilute EPS! 20*$45+$900 Or $30/share, so this Is just enough value S T =30 S T WBA BOLT Summer Leadership Summit 18

Practitioners typically ask the question What is the minimum level of after-tax synergies (cost savings and/or incremental income) the shark would need to achieve in order for the deal to be non-dilutive? NO TAX WORLD (can I offer them the shares they need without diluting my earnings? Start with our maximum non-dilutive shares offered equation (NIAT T )/EPS S Set SNEW to the minimum number of shark shares the target needs Add the extra after tax earnings or cost savings created by synergies (X) and solve for X (NIAT T + X) / EPSs Solve for X, X= (EPSs*) - NIAT t. In this example, the minimum cost savings to make it work are therefore $40. $40 = $5*20 - $60 where 20 is the minimum number of share the target would accept * Adjusting Synergy Calculation for Taxes In other words, with taxes, the minimum synergy equation becomes (NIAT T + X[1-t])/ EPSs where X is before tax synergies. Solving for X you get X (* EPSs NIAT T ) / (1-t) In the merge template of the game you will enter before tax synergies as a percent of the target s current expense (i.e. before tax synergies /target current expense) in cell D30 of the statistics tab. In other words, saving (for example) $5 before tax does not generate $5 of after tax income from the target. You have to cut the target s expenses by roughly $10 to generate an extra $5 of after tax income because roughly 50% of the income generated by expense saving will be taxed in the game by the horrid revenuers! WBA BOLT Summer Leadership Summit 19

Examples and Lessons Bank Price NIAT Shares EPS P/E MKTCAP 1 $20 $50 20 2.5 8 $400 2 $30 $60 30 2.0 15 $900 3 $45 $200 40 5.0 9 $1800 4 $35 $50 20 2.5 14 $700 5 $100 $100 10 10.0 10 $1,000 Here are two other cases to consider. Case 4: 2 tries to buy 3 Shark has higher P/E but lower MKTCAP Shark would lose control Case 5: 2 tries to buy 4 Merger of equals Not much room for negotiation Case 4 : 2 buys 3 Shark has Higher P/E and Lower MKTCAP $200/$2= 100 60 Have to offer 60 shares, Offering 60 shares would offer 60*$30 =$1800 which the target might accept But shark would lose control! Non-dilution constraint =($45/$30)S T A 60 share offer would not Dilute EPS though. ($260/90)=$2.88/share which is not dilutive. <30 Control constraint S T =40 S T Target would take a 100 share non-diluting offer (non-diluting because $260/130 = $2/share which is The sharks s EPS, but then shark would lose control. WBA BOLT Summer Leadership Summit 20

Case 5: 2 buys 4 Shark has higher P/E and Higher MKTCAP and lower stock price works but little wiggle room Here, offer is 25*$30=$750 or $37.50/share>$35/share, so target might accep EPS is now ($60+$50)/55=2.0 so no dilution =(35/30)S T <30 $50/$2.0= 25 23.33 Do Not give up Control constraint No dilution constraint S T =20 shares Here, offer is 23.33*$30=$700 or $35/share so might take it. EPS is now ($60+$50)/53.33=2.06 so no dilution S T $ Cash Deals $ Actually, the most common deal. No issue of control in 100% cash deal as target s stockholders get no shares. Are tax issues to consider in real world that are not present in stock deal (pay tax on cash received for stock). This means in real world the shark will have to pay a higher premium for the target to cover the taxes. WBA BOLT Summer Leadership Summit 21

Issues to Consider if Using Cash 1) What About Dilution? Using cash will not dilute EPS S as long as the cost of borrowing money to purchase a share of target stock is less than the earnings purchased. In other words, there will be no dilution of shark EPS as long a Interest cost (after tax) to borrow enough to buy 1 share of stock Earnings Purchased by buying 1 share r(p T ) < EPS T or [1/r] > (P/E) T 2) If you borrow you have to think about violating your required capital ratios A Real Deal Recently in Madison P S $119 S S 492,981 MKTCAP S $58,664,739 EPS S $7.43 NIAT S $3,662,000 (P/E) S 16.02 P T $32 S T 1,247,075 MKTCAP S $39,906,400 EPS T $2.84 NIAT S $3,554,000 (P/E) S 11.23 Share exchange rate = P T / P S = $32/$119 =.26890756 WBA BOLT Summer Leadership Summit 22

Max value they could offer without dilution is 478,331*$119=$56,921,399 which is about 45.64 a share = $13.64 premium! Share exchange equation = Value the target demands (slope is $32/$119) Snew <S S < 492,981 NIAT T /EPS S < 3,554,000/7.43 =478,331 Do Not give up Control constraint Non-dilution constraint =(P T /P S )S calculation (32/119)*1,247,075 = 335,347.9 shares This would be 335,347.9*119 = 39,906,400 of value which is their current MKTCAP and amounts to $32 a share. S T = 1,247,075 S Shark says I am not giving you 478,331 shares. That would keep my EPS constant, not create T value for me and would also give target almost as many shares as my current shareholders have! Target says I want $55,155,192 for my bank or the equivalent of 463,489 shares. Shark says Holy crap, if I do that the EPS accretion will only create an EPS of $7.54 and my price will only go to 16.02 x $7.54 or $120.79! Shark says How about I give you 202,029 shares (value is 202,029 * 119 = $24,041,451 in stock) and $31,114,521 in cash. That totals the $55,155,192 you want. That amounts to $44.23/share for your stock or a premium of 38%! DEAL! How Much Value Was Created? Depends on two things: First, what did it cost to borrow the $31,114,521 of cash? Suppose it cost 4% or $1,244,581 in interest to borrow that money. Then Merged EPS is ($3,662,000 + $3,554,000 - $1,244,581 + cost savings from synergies merger costs) (492,981+202,029 shares) = $8.59/share ignoring the synergies and merger costs. New stock value is 16.02 * 8.59 = $137.64/ share. This ignores any short run merger costs that would reduce this further in the first few years. Second, does the merger change the P/E? WBA BOLT Summer Leadership Summit 23

SO WHAT DOES ALL THIS MERGER TALK HAVE TO DO WITH INCREASING VALUE? Accountant s/investment Banker s View Smart Investor View We are asking whether the merger makes accounting sense in preserving the value of the shark by preserving or enhancing EPS. Based on past information and assumes the past represents the future Smart Investor will say who cares about EPS (E) or the past? Merger makes sense only if it creates more value in the future! It s about the product of (P/E) and E not just about E! Past information can be either misleading or even irrelevant. Both are correct! Accountant s view will determine if the merger will be considered in the first place. Investor view is the real question that needs to be asked. We will return to this to show how these differ! WBA BOLT Summer Leadership Summit 24

Valuation Stock Price = ( P/E ) x EPS But if this falls the Stock price will go down! This can be constant Or even rise (accretion) Relationship Between Stock Price, P/E ratios and EPS in a Simple World For a Single Firm Price per share = P = D 0 (1 + g) where D 0 = initial dividend per share (r - g) g = growth of dividends per share r = stockholder s discount rate for future cash flows P= [D 0 (1 + g)]/(r g) = [ D 0 /EPS ]*[(1 + g)/(r g)] = dividend payout rate*(1+g) E EPS (r-g) NOTE: P/E does not depend solely on EPS. EPS accretion does not necessarily increase P/E if that is your goal. It depends on payout rate and these growth terms. Why was target s P/E less than shark s P/E? Because Dividend payout was lower Discount rate r was higher Growth of dividends g was lower So, to raise P/E if that is your goal, must either 1. raise dividend rate (but this can be limited by your required K/A ratio) 2. lower r which is cost of capital (not easy!) 3. raise g which is growth of earnings WBA BOLT Summer Leadership Summit 25

Why the focus is often on Growth Mkt Value Book Value = Actual ROE Growth Rate Required ROE Growth Rate Growth ROE 1% 4% 7% 10% 13% Market to Book Ratio 23% 1.7 1.9 2.3 3.3 10 20% 1.5 1.6 1.9 2.5 7 17% 1.2 1.3 1.4 1.8 4 14% * 1 1 1 1 1 *Required rate of return 14% Says that if our RROE is 14% and our actual is 17% and we can grow 4% our Mkt/Book might be 1.3. but if we can grow 10% it might go up to 1.8! So value discussions focus on post merger growth! P o = DPS 1 /(k g) where 1 is next period, o last period, k is RROE, g is dividend growth Since DPS 1 = EPS 1 (1- ρ) where ρ is retention rate so (1- ρ) is payout rate P o = [EPS 1 (1- ρ)]/(k g) If we define ROE 1 = EPS 1 /BV 0 where BV is book value P o = [ROE 1 *BV o (1- ρ)]/(k-g) So, P o /Bv o = [ROE 1 (1- ρ)]/(k-g) But to keep K/A constant ρ =g A /ROE 1, where g A is asset growth so P o /BV o = [ROE 1 (1- (g A /ROE 1 )]/(k-g) Or Mkt P o ROE 1 g A Book = BV 0 = k g WBA BOLT Summer Leadership Summit 26

Shark prefers cash to stock if cost of using cash < cost of issuing new stock Cost of cash is after tax cost of borrowing money or after tax opportunity cost of cash. This is r = (1-t)i where i = nominal borrowing rate. Cost of stock is the rate of return you have to provide your stockholders. This is EPS S /P S So cash is cheaper if r < EPS S /P S or if [1/r] > (P/E) S WBA BOLT Summer Leadership Summit 27