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You’ll learn about the most common merger model questions in this tutorial, as well as what type of “progression” to expect and the key principles you must understand in order to answer ANY math questions on this topic.

Table of Contents:

3:26 Question #1: The Basic Rules

5:23 Question #2: With Real Numbers

8:21 Question #3: Equity Value, Enterprise Value, and Valuation Multiples

12:17 Question #4: Ranges for the Multiples

14:26 Question #5: What if the Buyer is Twice as Big?

16:26 Recap, Summary, and Key Principles

Question #1: The Basic Rules

"A company with a P / E multiple of 25x acquires another company for a purchase P / E multiple of 15x. Will the deal be accretive or dilutive?"

ANSWER: You can’t tell unless it’s a 100% Stock deal. If it is, it will be accretive because the Cost of Acquisition is 1 / 25, or 4%, and the Seller’s Yield is 1 / 15, or 6.7%. Since the Seller’s Yield is higher, it will be accretive.

For Cash and Debt deals, or deals with a mix of all three, you’d calculate the Weighted Cost of Acquisition by using Foregone Interest Rate on Cash * (1 – Buyer’s Tax Rate) * % Cash + Interest Rate on Debt * (1 – Buyer’s Tax Rate) * % Debt + 1 / (Buyer’s P / E Multiple) * % Stock and compare that to the Seller’s Yield.

Question #2: With Real Numbers

“Let’s say it is a 100% Stock deal. The Buyer has 10 shares at a share price of $25.00, and its Net Income is $10. It acquires the Seller for a Purchase Equity Value of $150. The Seller has a Net Income of $10 as well. Assume the same tax rates for both companies. How accretive is this deal?”

ANSWER: The buyer’s EPS is $10 / 10 = $1.00. It must issue 6 additional shares to do the deal, so the Combined Share Count is 10 + 6 = 16.

Since both companies have the same tax rate and since no Cash or Debt is used, Combined Net Income = $10 + $10 = $20, and Combined EPS = $20 / 16 = $1.25, so the deal is 25% accretive.

Question #3: Equity Value, Enterprise Value, and Valuation Multiples

“What are the Combined Equity Value and Enterprise Value in this same deal? Assume that Equity Value = Enterprise Value for both the Buyer and Seller.”

ANSWER: Combined Equity Value = Buyer’s Equity Value + Value of Stock Issued in the Deal = $250 + $150 = $400.

Combined Enterprise Value = Buyer’s Enterprise Value + Purchase Enterprise Value of Seller = $250 + $150 = $400.

The Combined EV / EBITDA multiple won’t be affected by the mix of Cash, Stock, and Debt, but the P / E multiple will be. It’s 20x here ($400 / $20), but it will change for non-100%-Stock deals.

Question #4: Ranges for the Multiples

“Without doing any math, what ranges would you expect for the Combined EV / EBITDA and P / E multiples, and why?”

ANSWER: They should be somewhere in between the Buyer’s multiples and the Seller’s purchase multiples. It’s almost never a simple average because of the relative sizes of the Buyer and Seller – and for P / E, the purchase method also plays a role.

Question #5: What if the Buyer is Twice as Big?

"What happens if the Buyer is twice as big, i.e. it has an Equity Value of $500 and Net Income of $20?"

ANSWER: The deal becomes *less* accretive because the company making it accretive, the Seller, now has a lower weighting. The Buyer was previously $250 / $400 of the total, but is now only $500 / $650, which is ~63% vs. ~77%, so we’d expect accretion to fall by 10-15%, which it does.

The Combined Multiples will all be closer to the Buyer’s multiples now as well.

Recap, Summary, and Key Principles

Principle #1: If the Seller’s Yield is above the Weighted Cost of Acquisition, it’s accretive; dilutive if the opposite.

Principle #2: Combined Equity Value = Buyer’s Equity Value + Value of Stock Issued in the Deal.

Principle #3: Combined Enterprise Value = Buyer’s Enterprise Value + Purchase Enterprise Value of Seller.

Principle #4: The Combined P / E Multiple is affected by the Cash / Debt / Stock mix, but the Combined EV / EBITDA Multiple is not.

Principle #5: The Combined Multiples will be in between the Buyer’s multiples and the Seller’s purchase multiples – exact numbers depend on sizes of the Buyer and Seller.

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