Valuation Principles

Professor Mike Paganomichael.pagano@villanova.edu

The primary goal is shareholder wealth maximization, which translates to maximizing stock price.– Should firms behave ethically? YES!– Do firms have any responsibilities to society at

large? YES! Shareholders are also members of society.

2

Goals of the Corporation

3

Common Stock: Owners, Directors, and Managers

Common Stock represents ownership.

Ownership implies control.

Stockholders elect directors.

Directors hire management.

Since managers are “agents” of shareholders, their goal should be: Maximize stock price (as noted in prior slide!)

• Improved corporate focus on a common goal• More informed decisions • Greater knowledge of key drivers of corporate success• Better communication between departments / business

units• Improved financial disclosures (e.g., SFAS 142)

4

Benefits of Value-based Decision-making

Magnitude of cash flows expected by shareholdersRiskiness of the cash flows Timing of the cash flow stream

5

Key Factors that Affect Stock Price

“M.R.T.”

Sales– Current level– Short-term growth rate in sales– Long-term sustainable growth rate in sales

Operating ExpensesInvestments: Capital expenditures / R&D / Advertising / D

Net Working Capital

Operating Cash Flow (OCF) Net Invest. Oper. Capital

6

Three Key Determinants of Cash Flows

𝑭𝑪𝑭=(𝑺−𝑪 ) ∙ (𝟏−𝑻 )+𝑫𝑬𝑷− 𝑰𝑵𝑽 −∆𝑵𝑾𝑪

Factors that Affect the Level and Risk of Cash Flows

Decisions made internally by financial managers:– Investment decisions (product lines, production

processes, geographic market, use of technology, marketing strategy)

– Financing decisions (choice of debt policy and dividend policy)

The External environment (e.g., credit crisis, government policies)

7

Value = + + ··· +FCF1 FCF2 FCF∞

(1 + WACC)1 (1 + WACC)∞

(1 + WACC)2

Free cash flow(FCF)

Market interest rates

Firm’s business risk

Market risk aversion

Firm’s debt/equity mixCost of debt

Cost of equity

Weighted average

cost of capital(WACC)

Net operatingprofit after taxes

Required investmentsin operating capital

−

=

Determinants of Intrinsic Value:The Weighted Average Cost of Capital

9

Cost of Capital components– Debt– Preferred Stock– Common Equity

WACC = weighted average of these costs

Opportunity costs

Weighted Average Cost of Capital

10

= return on long-term debt = marginal corporate tax rate = return on preferred stock = return on common stock

Weighted Average Cost of Capital

Equity LT Debt Pref. Stock

Capital Components

Capital components are sources of funding that come from investors.

Accounts payable, accruals, and deferred taxes are not sources of funding that come from investors, so they are not included in the calculation of the cost of capital.

We do adjust for these items when calculating the cash flows of a project, but not when calculating the cost of capital.

11

Web resources for WACC: www.thatswacc.com

12

13

Estimating the Cost of Debt

Method 1: Ask an investment banker what the coupon rate would be on new debt.

Method 2: Find the bond rating for the company and use the yield on other bonds with a similar rating.

Method 3: Find the current market yield-to-maturity on the company’s debt, if it has any.

14

A 15-year, 12% semi-annual bond sells for $1,153.72. What’s rd ?

60 60 + 1,00060

0 1 2 30rd = ?

-1,153.72...

30 -1153.72 60 1000

5.0% x 2 = rd = 10% N I/YR PV FVPMT

INPUTS

OUTPUT

15

Component Cost of Debt

Interest is tax deductible, so the after-tax (AT) cost of debt is: rd AT = rd BT x (1 – T)

rd AT = 10% x (1 – 0.40) = 6.00%.

Use nominal rate.

Flotation costs small, so ignore.

16

Cost of Preferred Stock: Pps = $116.95; 10%; Par = $100; F=5%

Use this formula (with flotation cost of 5%):

rps =Dps

Pps (1 – F)=

0.1($100)

$116.95(1 – 0.05)

=$10

$111.10= 0.090 = 9.0%

17

Time Line of Preferred Stock

2.50 2.502.50

0 1 2 ∞rps = ?

-111.10...

$111.10 = DQrPer

= $2.50rPer

rPer =$2.50

$111.10 = 2.25%; rps(Nom) = 2.25%(4) = 9%

18

Notes:

Flotation costs for preferred are significant, so they are reflected. Use net price.

Preferred dividends are not deductible, so no tax adjustment. Just rps.

Nominal rps is used.

19

Why is there a cost for reinvested earnings?

Earnings can be reinvested or paid out as dividends.

Investors could buy other securities, earning a return.

Thus, there is an opportunity cost if earnings are reinvested.

20

Three ways to determine the Cost of Equity: rs

1. CAPM: rs = rRF + (rM – rRF) x b = rRF + (RPM) x b

2. DCF: rs = D1/P0 + g

3. Own-Bond-Yield-Plus-Judgmental-Risk Premium: rs = rd + Bond RP

21

CAPM Cost of Equity: rRF = 5.6%, RPM = 6%, b = 1.2

rs = rRF + (RPM )b= 5.6% + (6.0%)1.2 = 12.8%

22

Issues in Using CAPM

Most analysts use the rate on a long-term (10 to 20 years) government bond as an estimate of rRF.

Most analysts use a rate of 3.5% to 6% for the market risk premium (RPM)

Estimates of beta vary, and estimates are “noisy” (they have a wide confidence interval).

(More…)

23

DCF Cost of Equity: D0 = $3.26; P0 = $50; g = 5.8%

rs =

D1

P0+ g =D0(1 + g)

P0+ g

= $3.12(1.058) $50

+ 0.058

= 6.6% + 5.8%= 12.4%

24

Estimating the Growth Rate

Use the historical growth rate if you believe the future will be like the past.

Obtain analysts’ estimates: Value Line, Zacks, Yahoo!Finance.

Use the earnings retention model, illustrated on next slide.

25

Earnings Retention Model

Suppose the company has been earning 15% on equity (ROE = 15%) and has been paying out 62% of its earnings.

If this situation is expected to continue, what’s the expected future g?

26

Earnings Retention Model (Cont.)

Growth from earnings retention model:

g = (Retention rate)(ROE)

g = (1 – Payout rate)(ROE)

g = (1 – 0.62)(15%) = 5.7%

This is close to g = 5.8% given earlier.

27

Could DCF methodology be applied if g is not constant?

YES, nonconstant g stocks are expected to have constant g at some point, generally in 5 to 10 years.

But… calculations get complicated. See the Web 09A worksheet in the file Ch09Tool Kit.xls.

28

The Own-Bond-Yield-Plus-Judgmental-Risk-Premium Method: rd = 10%, RP = 3.2%

rs = rd + Judgmental risk premium rs = 10.0% + 3.2% = 13.2%

This judgmental-risk premium CAPM equity risk premium, RPM.

Produces ballpark estimate of rs. Useful check.

29

What’s a reasonable final estimate of rs?

Method EstimateCAPM 12.8%DCF 12.4%rd + judgment 13.2%Average 12.8%

30

Determining the Weights for the WACC

The weights are the percentages of the firm that will be financed by each component.

If possible, always use the target weights for the percentages of the firm that will be financed with the various types of capital.

31

Estimating Weights for the Capital Structure

If you don’t know the targets, it is better to estimate the weights using current market values than current book values.

If you don’t know the market value of debt, then it is usually reasonable to use the book values of debt, especially if the debt is short-term.

(More…)

32

Estimating Weights

Suppose the stock price is $50, there are 3 million shares of stock, the firm has $25 million of preferred stock, and $75 million of debt.

Vs = $50(3 million) = $150 million.Vps = $25 million.Vd = $75 million.

Total Firm Value = $150 + $25 + $75 = $250 million.

33

Estimating Weights (Continued)

ws = $150/$250 = 0.60wps = $25/$250 = 0.10wd = $75/$250 = 0.30

The target weights for this company are the same as these market value weights, but often market weights temporarily deviate from targets due to changes in stock prices.

34

What’s the WACC using the target weights?

WACC = wdrd(1 – T) + wpsrps + wsrs

WACC = 0.3(10%)(1 − 0.4) + 0.1(9%)+ 0.6(12.8%)

WACC = 10.38% ≈ 10.4%

35

Four Mistakes to Avoid

1. Current vs. historical cost of debt

2. Mixing current and historical measures to estimate the market risk premium

3. Book weights vs. Market Weights

4. Incorrect cost of capital components

(More…)

36

Current vs. Historical Cost of Debt

When estimating the cost of debt, don’t use the coupon rate on existing debt, which represents the cost of past debt.

Use the current interest rate on new debt.

(More…)

37

Estimating the Market Risk Premium

When estimating the risk premium for the CAPM approach, don’t subtract the current long-term T-bond rate from the historical average return on common stocks.

For example, if the historical rM has been about 12.2% and inflation drives the current rRF up to 10%, the current market risk premium is not 12.2% – 10% = 2.2%!

38

Estimating Weights

Use the target capital structure to determine the weights.

If you don’t know the target weights, then use the current market value of equity.

If you don’t know the market value of debt, then the book value of debt often is a reasonable approximation, especially for short-term debt.

39

Capital components are sources of funding that come from investors

As noted earlier, accounts payable, accruals, and deferred taxes are not sources of funding that come from investors, so they are not included in the calculation of the WACC.

We do adjust for these items when calculating project cash flows, but not when calculating the WACC.

Divisional vs. Corporate Cost of Capital

Rate of Return

(%) WACC

Project H

Division H’s WACC

Risk

Project L Composite WACC for Firm A

13.0

7.0

10.0

11.0

9.0

Division L’s WACC

0 RiskL RiskAverage RiskH

40

Corporate Valuation methodology

Stock Valuation Approaches

41

Fundamentals of Corporate Valuation& Stock Valuation

𝐕𝐚𝐥𝐮𝐞𝐨𝐟𝐎𝐩𝐞𝐫𝐚𝐭𝐢𝐨𝐧𝐬=

FCF 1

(1+WACC )1+

FCF2

(1+WACC )2+⋯+

FCF∞(1+WACC )∞

𝐕𝐚𝐥𝐮𝐞𝐨𝐟𝐒𝐭𝐨𝐜𝐤 =

D1

(1+rs )1+

D2

(1+r s )2+⋯+

D∞

(1+rs )∞

Free cash flow

(FCF)

Weighted average

cost of capital(WACC)

Firm’s debt/equity mix

Cost of debt

Cost of equity: The required return on stock

Dividends (D)

Corporate Valuation vs. Stock Valuation

Corporate Valuation: A company owns two types of assets

Assets-in-place

Financial, or non-operating, assets

43

Assets-in-Place

Assets-in-place can be tangible, such as buildings, machines, inventory.

Usually they are expected to grow (g).

They generate free cash flows (FCF).

The PV of their expected future free cash flows, discounted at the WACC, is the value of operations (Vop).

44

Value of Total Operations

45

Vop = ∑∞

t = 1

FCFt

(1 + WACC)t

0 1 2 3 4

How muchIs the firmworth today?

OCF1

- INV1

- D NWC1

FCF4

+ Terminal Value at t=4

PV of FCF’s FCF1 FCF2 FCF3 FCF4 + TV4

Time Line Example for Discounted Cash Flow Analysis (DCF)

46

OCF2

- INV2

- D NWC2

OCF3

- INV3

- D NWC3

Non-operating Assets

Marketable securities.

Ownership of non-controlling interest in another company.

Value of non-operating assets usually is close to figure that is reported on balance sheet (but not always, e.g., real estate purchased many years ago).

Can be very valuable “hidden assets” that affect total market value.

47

Total Corporate Value

Total corporate value is sum of:– Value of operations– Value of non-operating assets

48

Claims on Corporate Value

Debtholders have first claim.

Preferred stockholders have the next claim.

Any remaining value belongs to stockholders (residual claim).

49

Applying the Corporate Valuation Model

Calculate the projected free cash flows and then discount them at the firm’s WACC.

Very Flexible Approach: Model can be applied to a company that does not pay dividends, a privately held company, or a division of a company, since FCF can be calculated for each of these situations.

50

Data for Valuation

FCF0 = $20 millionWACC = 10%g = 5%Marketable securities = $100 millionDebt = $200 millionPreferred stock = $50 millionBook value of equity = $210 millionTotal common shares outstanding = 10 million shares

51

Value of Operations: Constant FCF Growth at Rate of g

52

Vop = ∑∞

t = 1

FCFt

(1 + WACC)t

= ∑∞

t = 1

FCF0(1+g)t

(1 + WACC)t

Constant Growth Formula

Notice that the term in parentheses is less than one and gets smaller as t gets larger. As t gets very large, term approaches zero.

53

Vop = ∑∞

t = 1

FCF0 1 + WACC( 1+ g )

t

Constant Growth Formula cont’d

The summation can be replaced by a single formula:

54

Vop = FCF1

(WACC - g)

= FCF0(1+g)(WACC - g)

Find Value of Operations

55

Vop = FCF0 (1 + g)(WACC - g)

Vop = 20(1+0.05)(0.10 – 0.05)

= $420

Deriving the Value of Equity

Sources of Corporate Value– Value of operations = $420– Value of non-operating assets = $100

Claims on Corporate Value– Value of Debt = $200– Value of Preferred Stock = $50– Value of Equity = ?– Stock Price per Share = ?

56

Value of Equity

Total corporate value = Vop + Mkt. Sec.

= $420 + $100 = $520 millionValue of equity = Total Value – Debt – Preferred Stock = $520 - $200 - $50

= $270 million

To get Stock Price per Share, divide by Shares Outstanding:Stock Price = $270 million / 10 million Sh. = $27.00 / share

57

Another Example: Non-constant Growth

Finance planned plant expansion by borrowing $40 million and halting dividends. Firm has no non-operating assets.

Key Assumptions:– Year 1 FCF = -$5 million.– Year 2 FCF = $10 million.– Year 3 FCF = $20 million– FCF grows at constant rate of 6% after year 3.– The WACC, is 10%.– The company has 10 million shares of stock.

58

Horizon (or Terminal) Value

Free cash flows are forecast for three years in this example, so the forecast horizon is three years.

Growth in free cash flows is not constant during the forecast, so we can’t use the constant growth formula to find the value of operations at time 0.

59

Horizon / Terminal Value cont’d.

Growth (g) is constant after the horizon (3 years), so we can modify the constant growth formula to find the value of all free cash flows beyond the horizon, discounted back to the horizon.

Must make sure that long-term constant growth is less than or equal to the economy’s nominal GDP growth rate. Why?

60

Horizon / Terminal Value Formula

Horizon value is also called Terminal Value, or continuing value.

61

Vops at time t = FCFt(1+g)(WACC - g)

TV =

Value of operations is PV of FCF discounted by WACC

62

Vops at 3

0

-4.5458.264

15.026398.197

1 2 3 4rc=10%

416.942 = Vop

g = 6%FCF= -5.00 10.00 20.00 21.2

$21.2. .06

$530.10 0

0

Find the price per share of common stock

Value of equity = Value of operations - Value of debt = $416.94 - $40

= $376.94 million

Stock Price per share = $376.94 /10 mil.= $37.69

63

64

Other Approaches for Valuing Common Stock

Alternatives to the Free Cash Flow model are:

Dividend growth model (Dividend Discount Model):– Constant growth stocks– Nonconstant growth stocks

Using the Market Multiples of comparable firms

65

Stock value = PV of dividends discounted at required return on equity

Conceptually correct, but how do you find the present value of an infinite stream?

P0 =^

(1 + rs)1 (1 + rs)2 (1 + rs)3 (1 + rs)∞

D1 D2 D3 D∞+ + + … +

66

Constant Dividend Growth: PV of Dt if g < rs

$

Years (t)

Dt = D0(1 + g)t

PV of Dt =D0(1 + g)t

(1 + r)t

g < r, D∞ → 0PV of D1

D1

1 2

D0

D2

PV of D2

Constant Dividend Growth:Cumulative Sum of PV of Dt if g < rs

What happens to as t gets bigger? Consider this:

This sum converges to 1. Similarly, converges. See next slide.

67

t 1 2 3 4 5(1/2)t 1/2 1/4 1/8 1/16 1/32

Σ(1/2)t 1/2 3/4 7/8 15/16 Boring!!

68

Constant Dividend Growth Model (g < rs)

If g is constant and less than rs, then converges to:

=

69

Required rate of return: b = 1.2, rRF = 7%, & RPM = 5%

rs = rRF + (RPM)bFirm

= 7% + (5%)(1.2)

= 13%

Use the Security Market Line to calculate rs:

70

Estimated Intrinsic Stock Value: D0 = $2.00, rs = 13%, g = 6%

D1 = D0(1+g)D1 = $2.00(1.06) = $2.12

=

= $30.29

71

Expected Stock Price in 1 Year

D2 = D1(1+g)D1 = $2.12(1.06) = $2.2472

= $32.10

72

Expected Dividend Yield and Capital Gains Yield (Year 1)

Dividend yield = = = 7.0%.$2.12$30.29

D1

P0

CG Yield = =P1 – P0^ P0 $32.10 – $30.29

$30.29

= 6.0%.

73

Total Year 1 Return

Total return = Dividend yield + Capital gains yield

Total return = 7% + 6% = 13%

Total return = 13% = rs.

For constant growth stock CG Yield = g:– Capital gains yield = 6% = g.

74

Re-arrange model to rate of return form:

Then, rs = $2.12/$30.29 + 0.06= 0.07 + 0.06 = 13%

^

P0 = ^ D1

rs – gto:

D1

P0rs^ = + g.

75

Suppose the stock price is $32.09. Is this price based mostly on short-term or long-term cash flows?

Year (t) 0 1 2 3Dt = D0 (1+g)t $2.1200 $2.2472 $2.3820

PV(Dt) = Dt/(1+rs)t $1.8761 $1.7599 $1.6509

Sum of PV(Divs.) $5.29

P0 $30.29

% of P0 due to 3 PV(Divs.) 17%% of P0 due

to long-term divs. 83%

76

Intrinsic Stock Value vs. Quarterly Earnings

If most of a stock’s value is due to long-term cash flows, why do so many managers focus on quarterly earnings?

– Changes in quarterly earnings can signal changes future in cash flows. This would affect the current stock price.

– Managers often have bonuses tied to quarterly earnings, so they have incentive to manage earnings.

77

Why are stock prices volatile?

P0 = ^ D1

rs – g

rs could change: rs = rRF + (RPM)bi

– Interest rates (rRF) could change

– Risk aversion (RPM) could change

– Company risk (bi) could change

g could change.

Stock Price Sensitivity: Changes in rs and g

Growth Rate: g Required Return: rs

11.0% 12.0% 13.0% 14.0% 15.0%5% $35.00 $30.00 $26.25 $23.33 $21.006% $42.40 $35.33 $30.29 $26.50 $23.567% $53.50 $42.80 $35.67 $30.57 $26.75

Small changes in g or rs can cause large changes in the estimated price.

78

79

Are volatile stock prices consistent with rational pricing? (Yes!!)

Small changes in expected g and rs cause large changes in stock prices.

As new information arrives, investors continually update their estimates of g and rs.

If stock prices aren’t volatile, then this means there isn’t a good flow of information.

80

Comparing the FCF Model & Dividend Growth Model

Can apply FCF model in more situations (more flexible):– Privately held companies– Divisions of companies– Companies that pay zero (or very low) dividends

FCF model requires forecasted financial statements to estimate FCF (but… needs more inputs and more work!)

81

Relative Valuation Methods:

Shortcut approach based on financial relativism. Many ratios available: P/E, P/CF, M/B, P/S, Dividend Yields.

Using Comparables to determine Appropriate Multiples: – Analyst must choose companies that are as

comparable as possible.– Select the relevant ratio and compare it for the

chosen companies.– It does not determine the absolute value of the

stocks (just identifies ranking).– Can use regression analysis to improve

comparability

82

Using Stock Price Multiples to Estimate Stock Price

Analysts often use the P/E multiple (the stock price per share divided by the earnings per share).

Example:– Estimate the average P/E ratio of comparable

firms (SP / EPS). This is the P/E multiple.

– Multiply this average P/E ratio by the expected earnings of the company to estimate its stock price.

83

Using Market MultiplesThe entity or “enterprise” value (V) is:

– the market value of equity (# shares of stock multiplied by the price per share)

– plus the value of debt.

Pick a measure, such as EBITDA, Sales, Customers, Eyeballs, Click-throughs, etc.

Calculate the average entity ratio for a sample of comparable firms. For example,– V/EBITDA– V/Customers

84

Using Entity Multiples (cont.)Find the entity value of the firm in question. For

example,– Multiply the firm’s sales by the V/Sales multiple.– Multiply the firm’s # of customers by the V/Customers ratio

The result is the firm’s total value.

Subtract the firm’s debt to get the total value of its equity.

Divide by the number of shares to calculate the price per share.

85

Problems with Market Multiple Methods

It is often hard to find comparable firms.

The average ratio for the sample of comparable firms often has a wide range.– For example, the average P/E ratio might be 20,

but the range could be from 10 to 50. How do you know whether your firm should be compared to the low, average, or high performers?