70391 - finance the valuation of common...

70391 - Finance

The Valuation of Common StockWhere do Stock Prices Come From?

Stock Valuation

Future Free Cash Flow (FCF)

Profitability and Efficiency

Profit margins Operating efficiency Capital (asset) efficiency ROIC

Growth Opportunities New customers New products R&D, innovation

Sustainability Barriers to entry Specialized skills, processes Patent protection Brand loyalty

Market Interest Rates

Efficient Markets Market forces will tend to drive market value toward intrinsic value

Cost of Capital (%)

Investors required rate-of-return

Intrinsic Value of Operations (Discounted FCF)

Market Value of the Firm

Total Debt

Market Value of Equity

Share Price

Number of Shares

Non-Operating Assets (Cash)

Discounted by

Capital Markets Capital Structure (firm’s choice

of debt and equity)

Stock Valuation 2

Game Plan

Where do stock prices come from?

:1: “Multiples of comparables”

:2: Dividend discount model

:3: Dividend discount model with growth and earningsreinvestment

:4: PV the firm, subtract the debt:

Price per Share (PPS) =PV(FCF)−Debt

Number of Shares

Stock Valuation 3

Multiples of Comparables

Stock Valuation 4

Multiples of Comparables

:: Compare some accounting ratio of the company of interest tosome appropriate (“comparable”) benchmark (e.g., industryaverage, similar companies)

:: Most common: “price-earnings-ratio,” P/E ratio

:: Also: “market-book ratio,” “price-dividend ratio,”EV/EBITDA, etc.

Stock Valuation 5

“Growth Hunt Lifts Tech Stocks”Source: WSJ, July 20 2015

“Already sky high, valuations risk further as NASDAQ Compositesurges to record”

Stock Valuation 6

Toothless Fangs and BatsSource: Toothless, Financial Times, LEX, June 15, 2016

China has a lot of eyeballs, but its internet companies are valued more cheaply than their US counterparts. Concerns about regulation and trustworthiness of service may be factors, as well as a lack of investor familiarity. The country’s top internet companies are all listed outside mainland China

FT graphic Sources: FT Research, Thomson Reuters Datastream; S&P Capital IQ

Internet stocks: sales, profits and capitalisation

0 10 20 30 40 50 60 70 80 90 110100Revenue ($bn)

Market cap ($bn)

US v China stock performance

Alibaba

Tencent

Facebook Amazon

Netflix

Google Share price performance since start2015 ($bn)

2015 2016

GoogleAmazon

BaiduAlibaba

337.5204.7 325.9

The Financial Times Limited 2016. You may share using our article tools.Please don't cut articles from FT.com and redistribute by email or post to the web.© FT and 'Financial Times' are trademarks of The Financial Times Ltd.

Date: Wednesday June 15, 2016

Page: 14

Region: UK

Edition: 01

Copyright

Stock Valuation 7

From Textbook

Source: Brealey-Myers-Allen, 11th ed., Chapter 4

Stock Valuation 8

Price/Dividend RatioLook at GPS/AEO data online

Stock Valuation 9

Price/Earnings Ratio

P/E ratio: more common multiple.

:: But what is the interpretation? Stockholders get dividends,not earnings.

:: Answer coming soon. First, Comps Spreadsheet

Stock Valuation 10

Recursive Valuation of Dividends(Basis of the “Dividend Discount Model”)

Stock Valuation 11

Conundrum?

(1) “Share prices equal the present value of all future dividends.”

(2) “Investors hope for capital gains, in addition to dividends.”

:: i.e., investors hope to “buy low, sell high”

:: Why doesn’t the share price in (1) depend on capital gains?

Stock Valuation 12

Numerical Examples

:: What is the value of the stock?

:: [risk-free] dividends of

:: $10 per share at year 1,

:: $10 per share at year 2,

:: $10 per share at year 3

:: Zero ($0) per share at year 4, 5, 6 and so on

:: The discount rate, r , is 18%. Constant (simplification).

:: What if you plan to hold the stock for only 1 year?

Stock Valuation 13

Numerical Examples$10 per share at year 1. $10 per share at year 2. $10 per share at year 3. Zero ($0) per share at year 4, 5, 6 and so on. Thediscount rate is 18%.

0 1 2 3 4 ...

0 10 10 10 0 0

Stock Valuation 14

One Year OnlyPrice at date 1 = 15.66 ... price at date 0 = PV of 10 + 15.66

0 1 2 3 4 ...

0 10 10 10 0 0

Stock Valuation 15

Recursive Valuation

General case:

:: Dividends of $dt (riskless)

:: The discount rate is r

:: Does it matter how long you plan on holding the stock?

Stock Valuation 16

Recursive Valuation

Stock Valuation 17

Recursive Valuation: PointDecompose return into capital gain and dividend yield

:: Stock valuations are determined by the value of the cash-flowthat accrues to the owner of the stock.

:: Value of cash flows = present discounted value of sum of thedividends (or “payouts”)

:: Value of cash flows = present discounted value of (tomorrow’sdividend + tomorrow’s price)

Pt =∞∑i=0

E (dt+i )

(1 + r)i

=E (Pt+1 + dt+1)

=⇒ 1 + r = EPt+1

Stock Valuation 18

Recursive Valuation: PointDecompose return into capital gain and dividend yield

:: Stock valuations are determined by the value of the cash-flowthat accrues to the owner of the stock.

:: Value of cash flows = present discounted value of sum of thedividends (or “payouts”)

:: Value of cash flows = present discounted value of (tomorrow’sdividend + tomorrow’s price)

Pt =∞∑i=0

E (dt+i )

(1 + r)i

=E (Pt+1 + dt+1)

=⇒ 1 + r = EPt+1

Stock Valuation 18

Earnings, Growth and Reinvestment(The Link Between Earnings and Dividends)

(Understanding the P/E Ratio)

Stock Valuation 19

Dividends

Stock Valuation 20

Understanding the P/E Ratio

Motivation

:1: Earnings, not dividends?

:2: P/E ratio is most common “valuation ratio.”

Stock Valuation 21

Problem

Stock valuation

Pt =∞∑i=0

Et [d̃t+i ]

(1 + E [r ])i

But wait ... some firms don’t pay dividends?

:: Can we stick in earnings? No. Earnings are not the paymentsto stockholders.

:: Two approaches1. Model how earnings affects dividends2. V = D + E : Value the firm’s FCF, subtract the debt, divide by

shares outstanding.

:: Key thing::: Dividend policy (“payout policy”) is a financial decision.

Stock Valuation 22

Problem

Stock valuation

Pt =∞∑i=0

Et [d̃t+i ]

(1 + E [r ])i

:: Can we stick in earnings?

No. Earnings are not the paymentsto stockholders.

shares outstanding.

Stock Valuation 22

Problem

Stock valuation

Pt =∞∑i=0

Et [d̃t+i ]

(1 + E [r ])i

shares outstanding.

Stock Valuation 22

Problem

Stock valuation

Pt =∞∑i=0

Et [d̃t+i ]

(1 + E [r ])i

shares outstanding.

Stock Valuation 22

Problem

Stock valuation

Pt =∞∑i=0

Et [d̃t+i ]

(1 + E [r ])i

shares outstanding.

Stock Valuation 22

Why?[Source: google.com but lots (lots!) of places have this information.]

Why the differences in P/E?

Stock Valuation 23

Accounting Definitions

Most variables are “per share” in Year t.

:: Pt ex-dividend price per share.

:: EPSt = DIVt + REt

:: BVEt = book-value of equity, at the beginning of Year t.

:: Return on Equity: ROE = EPStBVEt

:: Plowback ratio: PLOW = REtEPSt

:: Payout ratio: PAY = DIVtEPSt

= 1− PLOW

Stock Valuation 24

= 1− PLOW

Stock Valuation 24

= 1− PLOW

Stock Valuation 24

= 1− PLOW

Stock Valuation 24

= 1− PLOW

Stock Valuation 24

= 1− PLOW

Stock Valuation 24

Engine of Growth

Assume ROE is constant over time

:: EPSt = ROE × BVEt

:: Just the definition of ROE, rewritten. “To figure out earnings, justmultiply ROE times BVEt”

:: BVEt = BVEt−1 + EPSt−1 × PLOW

:: BVE grows by plowing back earnings. Same as saying “BVE thisyear equals BVE last year plus retained earnings.”

:: Combine these two equations and arrive at growth rate, g :

BVEt = BVEt−1 + ROE × BVEt−1 × PLOW

= BVEt−1

(1 + ROE × PLOW

)︸︷︷︸growth=g

=⇒ g = ROE × PLOW

:: Makes sense: if each dollar of BVE earns an ROE of 12 cents (or 12%),and then 40% of these cents are PLOWED back in, you will have grownby 0.12× 0.40 = 4.8 cents, per dollar of BVE (or 4.8%).

Stock Valuation 25

Engine of Growth

= BVEt−1

(1 + ROE × PLOW

Stock Valuation 25

Engine of Growth

= BVEt−1

(1 + ROE × PLOW

Stock Valuation 25

Engine of Growth

= BVEt−1

(1 + ROE × PLOW

Stock Valuation 25

Growth

:: Since EPSt is proportional to BVEt ,

EPSt = ROE × BVEt

EPSt must grow at rate g .

:: Same, then, applies for DIVt and REt :

DIVt = PAY × EPSt

REt = PLOW × EPSt

:: Growth:

BVEt+1 = BVE1

(1 + g

)tEPSt+1 = EPS1

(1 + g

)t= BVE1 × ROE

(1 + g

)tDIVt+1 = DIV1

(1 + g

)t= EPS1 × PAY

(1 + g

)t= BVE1 × ROE × PAY

(1 + g

)tStock Valuation 26

Valuation

Recall, “growing perpetuity:”

P0 =DIV1

r − g

=PAY × EPS1

r − g

=PAY × ROE × BVE1

r − ROE × PLOW

where r is the cost of capital.

:: This is a model of how earnings maps into dividends.

:: We can use it to get some important insights

Stock Valuation 27

Suppose that ROE = r

P0 =PAY × r × BVE1

r − r × PLOW= BVE1

NPV = 0

:: Makes sense

:: If ROE > r , NPV > 0

:: If ROE < r , NPV < 0

Stock Valuation 28

NPV = 0

:: Makes sense

:: If ROE > r , NPV > 0

:: If ROE < r , NPV < 0

Stock Valuation 28

NPV = 0

:: Makes sense

:: If ROE > r , NPV > 0

:: If ROE < r , NPV < 0

Stock Valuation 28

Growth

PVGO = “Present Value of Growth Options”

PVGO = P0 −EPS1r

=PAY × ROE × BVE1

r − ROE × PLOW− ROE × BVE1

Special cases:

I No growth (PLOW=0): PVGO = 0. But, if ROE > r , NPV is stillpositive. Just none from growing!

I Growth and investing in loser projects. PLOW > 0 and ROE < r . Here,you can verify that PVGO < 0. The firm is growing, but in doing so it iswasting the money of its owners. Recall that if ROE < r then the firmrepresents a negative NPV project. By growing the firm through plowingback earnings, the managers are taking a dumb idea and exacerbating it.

I PLOW > 0 and ROE > r . Well done!

Stock Valuation 29

Growth

PVGO = P0 −EPS1r

=PAY × ROE × BVE1

Special cases:

Stock Valuation 29

Growth

PVGO = P0 −EPS1r

=PAY × ROE × BVE1

Special cases:

Stock Valuation 29

Growth

PVGO = P0 −EPS1r

=PAY × ROE × BVE1

Special cases:

Stock Valuation 29

Growth

PVGO = P0 −EPS1r

=PAY × ROE × BVE1

Special cases:

Stock Valuation 29

Growth

PVGO = P0 −EPS1r

=PAY × ROE × BVE1

Special cases:

I Growth but no growing value. If PLOW > 0 but ROE = r thenPVGO = 0. Competitive markets make us consider this situationseriously. The firm’s growth represents a series of investments inNPV = 0 projects. Growth, per-se, does not give a high P/E.

Stock Valuation 30

Growth

PVGO = P0 −EPS1r

=PAY × ROE × BVE1

Special cases:

I Why do P/E ratios vary in the cross-section? One last way to express themain point is to write the definition of the PVGO as

A high P/E ratio is indicative of either a high PVGO, a lowcost-of-capital, or a bit of both. The “link between the stock price andearnings per share” is that the price will be high, relative to earnings, ifeither (or both) of these things hold.

Stock Valuation 31

Hidden Assumptions

:: ROE, PAY and PLOW are time invariant

:: Constant growth in all variables (earnings, dividends, BVE,etc.)

:: No capital structure (yet)

:: Constant discount rate

Stock Valuation 32

Summary

Stock Valuation 33

Summary: Where do Stock Prices Come From?

:: Where do stock prices come from? DCF

:: PV of all future dividends

:: PV of tomorrow’s dividend and tomorrows stock price:dividend and capital gain

:: Hardest part is getting the discount rate right

Stock Valuation 34

Valuing a stock is similar to valuing a bond:

:: DCF the cash flows: “dividend discount model”

:: If dividends are risky, DCF the expected dividends, discount byappropriate expected return

But the cash flow to the stockholder depends on the financial policy of the firm... it’s payout policy. So,

:1: If you have a good handle on dividends, directly, then P = d/(r − g) orP = E

∑t dt/(1 + r)t or something similar

:2: If you’d like to go slightly deeper, and model where growth comes from,then P = (PAY × ROE × BVE)/(r − ROE × PLOW ).

:3: Or model the FCF, PV it, subtract the debt and divide by number ofshares. This is next. It makes less stringent assumptions about “constantgrowth,” but requires many alternative assumptions.

Stock Valuation 35

Summary: Link Between Dividends and Earnings

:: Strictly speaking, stock holders get dividends, so stock pricesderive from dividends

:: But dividend policies vary a lot across firms, time. Dividendstake many forms. Earnings, in contrast, are not a financialpolicy. They are the outcome of business operations. Sowhat’s the link?

:: If plowback = 0, then EPS=DPS and the link is trivial

:: If plowback > 0, then DPS<EPS. But we can use ROE andplowback to estimate D-growth

:: If plowback > 0, and if its being plowed into NPV>0 projects,then part of firm value is PVGO: growth firm. E/P ratio issmaller than cost-of-capital: “growth firms” have bigger P/Eratios than non-growth firms with same cost-of-capital.

Stock Valuation 36

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