This document discusses valuation principles and the valuation of corporations and stocks. It provides the following key points: 1. The primary goal of corporations is shareholder wealth maximization, which translates to maximizing stock price. Firms should behave ethically and have responsibilities to society. 2. Common stock represents ownership, with owners electing directors who hire management to maximize stock price. 3. Valuing a corporation involves discounting projected free cash flows at the weighted average cost of capital (WACC) to determine the value of operations, plus the value of non-operating assets. 4. Valuing stock involves discounting projected dividends at the cost of equity. The corporate value is divided among deb

1. Valuation Principles
Professor Mike Pagano
michael.pagano@villanova.edu

2. 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. 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!)

4. • 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

5. Magnitude of cash flows expected by shareholders
Riskiness of the cash flows
Timing of the cash flow stream
5
Key Factors that Affect Stock Price
“M.R.T.”

6. Sales
– Current level
– Short-term growth rate in sales
– Long-term sustainable growth rate in sales
Operating Expenses
Investments: 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

7. 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

8. Value = + + ··· +
FCF1 FCF2 FCF∞
(1 + WACC)1 (1 + WACC)∞(1 + WACC)2
Free cash flow
(FCF)
Market interest rates
Firm’s business riskMarket risk aversion
Firm’s debt/equity mix
Cost of debt
Cost of equity
Weighted average
cost of capital
(WACC)
Net operating
profit after taxes
Required investments
in operating capital
−
=
Determinants of Intrinsic Value:
The Weighted Average Cost of Capital

9. 9
Cost of Capital components
– Debt
– Preferred Stock
– Common Equity
WACC = weighted average of these costs
Opportunity costs
Weighted Average Cost of Capital

10. 10
𝑾𝑨𝑪𝑪 =
𝑘=𝟏
𝑛
𝒘 𝒏 ∙ 𝒓 𝒏
𝑾𝑨𝑪𝑪 = 𝒘 𝒅 ∙ 𝒓 𝒅 ∙ (𝟏 − 𝑻) + 𝒘 𝒑𝒔∙ 𝒓 𝒑𝒔 + 𝒘 𝒔 ∙ 𝒓 𝒔
𝒓 𝒅 = return on long-term debt
𝑻 = marginal corporate tax rate
𝒓 𝒑𝒔 = return on preferred stock
𝒓 𝒔 = return on common stock
Weighted Average Cost of Capital
Equity LT Debt Pref. Stock

11. 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

12. Web resources for WACC: www.thatswacc.com
12

13. 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. 14
A 15-year, 12% semi-annual bond sells for $1,153.72.
What’s rd ?
60 60 + 1,00060
0 1 2 30
rd = ?
-1,153.72
...
30 -1153.72 60 1000
5.0% x 2 = rd = 10%
N I/YR PV FVPMT
INPUTS
OUTPUT

15. 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. 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. 17
Time Line of Preferred Stock
2.50 2.502.50
0 1 2 ∞
rps = ?
-111.10
...
$111.10 =
DQ
rPer
=
$2.50
rPer
rPer =
$2.50
$111.10
= 2.25%; rps(Nom) = 2.25%(4) = 9%

18. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 29
What’s a reasonable final estimate of rs?
Method Estimate
CAPM 12.8%
DCF 12.4%
rd + judgment 13.2%
Average 12.8%

30. 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. 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. 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. 33
Estimating Weights (Continued)
ws = $150/$250 = 0.60
wps = $25/$250 = 0.10
wd = $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. 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. 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. 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. 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. 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. 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.

40. 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

41. Corporate Valuation methodology
Stock Valuation Approaches
41
Fundamentals of Corporate Valuation
& Stock Valuation

42. 𝐕𝐚𝐥𝐮𝐞 𝐨𝐟
𝐎𝐩𝐞𝐫𝐚𝐭𝐢𝐨𝐧𝐬
=
FCF1
1 + WACC 1
+
FCF2
1 + WACC 2
+ ⋯ +
FCF∞
1 + WACC ∞
𝐕𝐚𝐥𝐮𝐞 𝐨𝐟
𝐒𝐭𝐨𝐜𝐤
=
D1
1 + rs
1
+
D2
1 + rs
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

43. Corporate Valuation: A company owns
two types of assets
Assets-in-place
Financial, or non-operating, assets
43

44. 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

45. Value of Total Operations
45
Vop = ∑
∞
t = 1
FCFt
(1 + WACC)t

46. 0 1 2 3 4
How much
Is the firm
worth 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

47. 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

48. Total Corporate Value
Total corporate value is sum of:
– Value of operations
– Value of non-operating assets
48

49. Claims on Corporate Value
Debtholders have first claim.
Preferred stockholders have the next claim.
Any remaining value belongs to stockholders (residual claim).
49

50. 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

51. Data for Valuation
FCF0 = $20 million
WACC = 10%
g = 5%
Marketable securities = $100 million
Debt = $200 million
Preferred stock = $50 million
Book value of equity = $210 million
Total common shares outstanding = 10 million shares
51

52. 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

53. 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

54. Constant Growth Formula cont’d
The summation can be replaced by a single formula:
54
Vop =
FCF1
(WACC - g)
=
FCF0(1+g)
(WACC - g)

55. Find Value of Operations
55
Vop =
FCF0 (1 + g)
(WACC - g)
Vop =
20(1+0.05)
(0.10 – 0.05)
= $420

56. 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

57. Value of Equity
Total corporate value = Vop + Mkt. Sec.
= $420 + $100
= $520 million
Value 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

58. 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

59. 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

60. 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

61. 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 =

62. Value of operations is PV of FCF discounted by WACC
62
Vops at 3
0
-4.545
8.264
15.026
398.197
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

63. 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. 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. 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. 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

67. Constant Dividend Growth:
Cumulative Sum of PV of Dt if g < rs
P0 =
t=1
∞
D0
1 + g
1 + rs
t
What happens to P0 as t gets bigger? Consider this:
This sum converges to 1. Similarly, P0 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 D0
1+g
1+rs
t
converges to:
P0 =
D0 1+g
rs−g
=
D1
rs−g
68

69. 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
P0 =
D0 1+g
rs−g
=
D1
rs−g
P0 =
$2.12
0.13−0.06
= $30.29
70

71. Expected Stock Price in 1 Year
In general: Pt =
Dt+1
rs − g
D2 = D1(1+g)
D1 = $2.12(1.06) = $2.2472
P𝟏 =
D 𝟐
rs − g
P0 =
$2.2472
0.13−0.06
= $32.10
71

72. 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. 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. 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 – g
to:
D1
P0
rs
^
= + 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 3
Dt = 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%
75

76. 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. 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.

78. 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 $21.00
6% $42.40 $35.33 $30.29 $26.50 $23.56
7% $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. 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!)
80

81. 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. 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. 83
Using Market Multiples
The 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. 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. 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?