Chapter 5 of 5 · 11 min

The multiple bridge

A share price is earnings times a multiple, so a return comes from earnings growth, a change in the multiple, or dividends.

By the end of this chapter you can

Split a stock's return into earnings growth, multiple change and dividends
Annualize a total return over several years
Find the exit multiple a target return needs
Separate what the company controls from the market's mood

The intuition

A market stall is worth its yearly profit times what buyers will pay for each dollar of profit. The owner can grow the profit; what buyers will pay per dollar goes up and down with fashion. Sell the stall in five years for more than you paid, and it is worth asking how much of the gain was your work and how much was fashion.

A share price is EPS × P/E, so a stock's return has the same sources: the earnings grew, the multiple changed, or you were paid dividends while you waited. Separating them shows how much of a pitch is a bet on the market re-rating the stock.

The key idea

Price return = (exit P/E ÷ entry P/E) × (1 + growth)ⁿ − 1. From growth = (1 + growth)ⁿ − 1; from the multiple = the rest of the price return. Total = price return + dividend yield × n. Annualized = (1 + total)^(1/n) − 1.

Why it works

The conventions here: dividends are a flat yield on the entry price, simple and not reinvested. The growth piece is the price return at an unchanged multiple; the multiple piece is the rest of the price return.
Earnings growth is the company's work. It compounds and it can repeat.
A change in the multiple is the market's mood. It can reverse, so a return built on re-rating is a one-off.
Annualize with the n-th root, not by dividing. A 61% total over five years is 10% a year, not 12.2%.
Show the flat-multiple case first. If it clears the hurdle, the pitch stands on the company and re-rating is a bonus.
Run it backwards to find the exit multiple a target return needs. If it is well above today's, the pitch is a market call in disguise.

Bought at $40 on 20x; EPS grows 10% a year for 5 years; 2% dividend yield on cost; sold on 18x

Exit EPS: $2.00 × 1.10⁵	$3.22
Exit price: 3.22 × 18	$57.98
Price return: 57.98 ÷ 40 − 1	44.9%
From growth: 1.10⁵ − 1	61.1%
From the multiple: (18 ÷ 20 − 1) × 1.10⁵	−16.1%
Total with dividends: 44.9% + 2% × 5	54.9%, or 9.2% a year

For 12% a year: 20 × (1.12⁵ − 2% × 5) ÷ 1.10⁵ = 20.6x at exit, a 3.2% re-rating.

The formulas

Price = EPS × P/E

Two things can move it.

Price return = (exit P/E ÷ entry P/E) × (1 + growth)ⁿ − 1

The two moves compound together.

From growth = (1 + growth)ⁿ − 1; from the multiple = the rest of the price return

Flat multiple first, then the multiple.

Total return = price return + dividend yield × n

Dividends simple, on cost.

Annualized = (1 + total)^(1/n) − 1

The n-th root, not an average.

Exit P/E for a target = entry P/E × ((1 + target)ⁿ − yield × n) ÷ (1 + growth)ⁿ

Run it backwards.

Worked example

Grow the EPS, apply the exit multiple and compare with the entry price. Growth at a flat multiple is one piece; the rest of the price move is the multiple.

Drawing the numbers…

See it move

Same stock and the same entry price. Change the entry and exit P/Es, earnings growth, the dividend yield, the holding period and your target return.

Drawing the numbers…

Try this

Raise the exit P/E. The multiple bar and the annual return rise; the growth bar and the exit P/E the target needs do not move.
Set the exit P/E equal to the entry P/E. The multiple bar disappears.
Raise earnings growth. The growth bar rises and the exit P/E the target needs falls.
Raise the dividend yield. The dividend bar rises and less re-rating is needed.
Raise the entry P/E. The multiple bar falls and the target needs a higher exit P/E.

Run it backwards

Same stock, reversed: you need a set annual return. What multiple does the stock have to exit on?

Drawing the numbers…

Turn the annual target into a total over the holding period and take off the dividends: that is the price return needed. Divide by what earnings growth supplies, and multiply by the entry P/E.

Compare the answer with today's multiple. Needing a small re-rating is noise; needing a big one means most of the return is a bet on the market changing its mind.

Traps

Adding growth and multiple change.

They multiply: (exit P/E ÷ entry P/E) × (1 + growth)ⁿ. The multiple piece is what is left after growth.

Annualizing by dividing.

Take the n-th root of one plus the total.

Counting dividends on the exit price.

Here they are a yield on the entry price, simple.

Underwriting re-rating.

Show the flat-multiple return first and treat a higher multiple as upside.

Assuming a cheap stock will re-rate.

A multiple needs a reason to change: faster or safer growth, not just a low number.

Say it in the interview

The interviewer asks

“A stock you own has doubled. How would you work out where the return came from?”

Say yours out loud first, then compare.

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

Price return = (exit ÷ entry P/E) × (1 + growth)ⁿ − 1.
Growth repeats; re-rating is a one-off.
Annualize with the n-th root.
The exit P/E a target needs shows how much is a market call.