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Chapter 2 of 5 · 12 min

The P/E shortcut: cash versus stock

Tell whether a deal is accretive in your head, by comparing the yield you buy with the yield you pay.

By the end of this chapter you can
  • Turn a P/E and an interest rate into yields you can compare
  • Say whether an all-stock or all-debt deal is accretive without building the model
  • Work out the highest premium before a deal turns dilutive
  • Explain which currency is cheaper, and why high-P/E companies pay in stock
1

The intuition

A company trading at 20 times earnings is priced so that each $20 of market value carries $1 of profit: an earnings yield of 5%. Hand a seller $20 of your shares and you hand over $1 of your earnings with them. Issuing stock costs you 5% a year.

Buy a business at 15 times earnings and each $15 you pay brings in $1 of profit: a 6.7% yield. You pay 5% and receive 6.7%, so your EPS rises. Borrowing works the same way, except the cost is the after-tax interest rate.

The key idea

A deal is accretive when the earnings yield you buy is higher than the yield your payment costs. Stock costs 1 ÷ your P/E. Cash or debt costs the interest rate × (1 − t). Always use the P/E you actually pay, premium included.

2

Why it works

  • The yield you buy is 1 ÷ purchase P/E, and purchase P/E = the target's P/E × (1 + premium).
  • Paying in stock costs the acquirer's own earnings yield, 1 ÷ acquirer P/E. So an all-stock deal is accretive exactly when the acquirer's P/E is above the purchase P/E.
  • Paying with debt costs the after-tax interest rate. So an all-debt deal is accretive when the purchase P/E is below 1 ÷ (rate × (1 − t)): the cash breakeven P/E.
  • The highest premium is where the purchase P/E reaches that breakeven: breakeven P/E ÷ target P/E − 1.
  • The cheaper currency is whichever costs the lower yield. For most companies that is debt, which is why high-P/E acquirers, whose stock yield is low, are the ones that pay in shares.
Acquirer at 20x; target at 12x, bought at a 25% premium; debt at 6%, tax 25%
Purchase P/E: 12x × 1.2515.0x
Yield bought: 1 ÷ 156.67%
Cost of stock: 1 ÷ 205.00%, accretive
Cost of debt: 6% × (1 − 25%)4.50%, accretive
Cash breakeven P/E: 1 ÷ 4.5%22.2x
Highest premium in stock: 20 ÷ 12 − 166.7%
Highest premium in debt: 22.2 ÷ 12 − 185.2%
3

The formulas

Purchase P/E = target P/E × (1 + premium)

The multiple you actually pay.

Stock deal accretive ⇔ acquirer P/E > purchase P/E

Your shares are priced higher than the earnings you buy with them.

Cost of stock = 1 ÷ acquirer P/E

The earnings each new share carries away.

Cost of cash or debt = r × (1 − t)

Interest, after the tax it saves.

Breakeven P/E, cash = 1 ÷ (r × (1 − t))

Pay any P/E below this with debt and EPS rises.

Max premium = breakeven P/E ÷ target P/E − 1

How far above the market price you can go.

4

Worked example

An all-debt deal. Turn the interest rate and the purchase P/E into two yields, then compare them.

Drawing the numbers…
5

See it move

Same companies. Change both P/Es, the premium, the interest rate and the tax rate.

Drawing the numbers…
Try this
  • Raise the premium. The purchase P/E climbs and the yield bought falls, so both tests get harder to pass.
  • Raise the acquirer's P/E. The cost of stock falls and the stock breakeven line rises; the debt test does not change.
  • Raise the interest rate, or lower the tax rate. The after-tax cost of debt rises and its breakeven P/E falls.
  • Push the acquirer's P/E up. If its earnings yield drops below the after-tax cost of debt, stock becomes the cheaper way to pay.
6

Run it backwards

Same companies, reversed: in an all-stock deal, how much premium can the acquirer pay before it turns dilutive?

Drawing the numbers…

An all-stock deal breaks even when the purchase P/E equals the acquirer's P/E. The purchase P/E is the target's P/E × (1 + premium), so the highest premium is acquirer P/E ÷ target P/E − 1.

If the acquirer's P/E is below the target's, the answer is negative: the deal is dilutive even at no premium. That is why low-multiple companies rarely buy high-multiple ones with stock.

7

Traps

Comparing the acquirer's P/E with the target's market P/E.
Use the purchase P/E, premium included. That is the price you actually pay for the earnings.
Using the pre-tax interest rate.
Interest is deductible, so the cost that hits net income is r × (1 − t).
Saying stock is free because no cash leaves the company.
Each new share takes a slice of all future earnings. Its cost is the acquirer's earnings yield.
Applying the rule to a deal with synergies or a mix of payment.
The shortcut assumes one currency and no synergies. With either, build the full model from chapter 1.
Saying debt is always cheaper than stock.
Only when r × (1 − t) is below 1 ÷ P/E. A richly valued acquirer can find its stock the cheaper currency.
8

Say it in the interview

The interviewer asks

“Without a model, how can you tell if an all-stock deal is accretive?”

Say yours out loud first, then compare.
9

Check yourself

4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.

Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.

0 of 4
Drawing your questions…
Remember
  • Accretive when the yield bought beats the yield paid.
  • Stock: acquirer P/E above the purchase P/E.
  • Debt: purchase P/E below 1 ÷ (r × (1 − t)).
  • Always include the premium in the purchase P/E.