1. Stern School of Business
New York University
Stern School of Business
Equity Valuation
Prof. Ian Giddy
New York University

2. Objective: Maximize the Value of the Firm
First Principles
Invest in projects that yield a return greater than the minimum acceptable hurdle rate.
The hurdle rate should be higher for riskier projects and reflect the financing mix used - owners’ funds (equity) or borrowed money (debt)
Returns on projects should be measured based on cash flows generated and the timing of these cash flows; they should also consider both positive and negative side effects of these projects.
Choose a financing mix that minimizes the hurdle rate and matches the assets being financed.
If there are not enough investments that earn the hurdle rate, return the cash to stockholders.
The form of returns - dividends and stock buybacks - will depend upon the stockholders’ characteristics.
Objective: Maximize the Value of the Firm
This returns us to the original objective function, with which we started this discussion, which is the maximization of firm value. In this section, we link the investment, financing and dividend decisions to the value of the firm.

3. Discounted Cashflow Valuation: Basis for Approach
where,
n = Life of the asset
CFt = Cashflow in period t
r = Discount rate reflecting the riskiness of the estimated cashflows
The basics of valuation are no different from the basics of project analysis. The value of any asset is the present value of the expected cash flows over its life.

4. Equity Valuation versus Firm Valuation
value just the equity stake in the business
value the entire firm, which includes, besides equity, the other claimholders in the firm
In equity valuation, we look at the entire analysis from the perspective of equity investors in the firms. (This is analogous to an equity approach in investment analysis)
In firm valuation, we try to value the underlying business, with all the different claims on it (debt, equity and preferred stock)

5. I.Equity Valuation
The value of equity is obtained by discounting expected cashflows to equity, i.e., the residual cashflows after meeting all expenses, tax obligations and interest and principal payments, at the cost of equity, i.e., the rate of return required by equity investors in the firm.
where,
CF to Equityt = Expected Cashflow to Equity in period t
ke = Cost of Equity
The dividend discount model is a specialized case of equity valuation, and the value of a stock is the present value of expected future dividends.
The value of equity is the present value of cash flows to the equity investors discounted back at the rate of return that those equity investors need to make to break even (the cost of equity).
In the strictest sense of the word, the only cash flow stockholders in a publicly traded firm get from their investment is dividends, and the dividend discount model is the simplest and most direct version of an equity valuation model.

6. II. Firm Valuation
The value of the firm is obtained by discounting expected cashflows to the firm, i.e., the residual cashflows after meeting all operating expenses and taxes, but prior to debt payments, at the weighted average cost of capital, which is the cost of the different components of financing used by the firm, weighted by their market value proportions.
where,
CF to Firmt = Expected Cashflow to Firm in period t
WACC = Weighted Average Cost of Capital
One way to think about the value of the firm is in terms of the different claimholders in the firm.
The cash flow to the firm is the cumulated cash flows obtained by all claimholders in the firm (Equity investors get dividends, debt holders get interest and principal payments and preferred stockholders get preferred dividends).
The appropriate discount rate for these cash flows has to be the weighted average of all of their required rates of return, which is the cost of capital.

7. Equity versus Firm Valuation
It is often argued that equity valuation requires more assumptions than firm valuation, because cash flows to equity require explicit assumptions about changes in leverage whereas cash flows to the firm are pre-debt cash flows and do not require assumptions about leverage. Is this true?
Yes No
Both approaches need the same amount of information. In the case of equity valuation, leverage has to be explicitly modeled into the cash flows in the form of interest and principal payments. In the case of firm valuation, leverage has to show up in the discount rate.
Practically speaking, it might be simpler to do the latter than the former when leverage is changing.

8. First Principle of Valuation
Never mix and match cash flows and discount rates.
The key error to avoid is mismatching cashflows and discount rates, since discounting cashflows to equity at the weighted average cost of capital will lead to an upwardly biased estimate of the value of equity, while discounting cashflows to the firm at the cost of equity will yield a downward biased estimate of the value of the firm.
This principle of consistency implies that
Cash flows to equity (firm) be discounted at the cost of equity (capital)
Dollar (DM) cash flows be discounted at dollar (DM) discount rates
Nominal (real) cash flows be discounted at nominal (real) discount rates

9. Valuation: The Key Inputs
A publicly traded firm potentially has an infinite life. The value is therefore the present value of cash flows forever.
Since we cannot estimate cash flows forever, we estimate cash flows for a “growth period” and then estimate a terminal value, to capture the value at the end of the period:
In practical terms, this means that we have to estimate detailed cash flows until we expect the firm to be in stable growth.
The alternative way of applying closure, which is to estimate the terminal value by applying a multiple of earnings to the fifth or tenth year’s earnings ends up being a relative valuation rather than a discounted cash flow valuation. (The value is heavily influenced by the multiple used to get terminal value)

10. Stable Growth and Terminal Value
When a firm’s cash flows grow at a “constant” rate forever, the present value of those cash flows can be written as:
Value = Expected Cash Flow Next Period / (r - g)
where,
r = Discount rate (Cost of Equity or Cost of Capital)
g = Expected growth rate
This “constant” growth rate is called a stable growth rate and cannot be higher than the growth rate of the economy in which the firm operates.
While companies can maintain high growth rates for extended periods, they will all approach “stable growth” at some point in time.
When they do approach stable growth, the valuation formula above can be used to estimate the “terminal value” of all cash flows beyond.
To apply the terminal value approach, the firm has to be in a growth rate that is sustainable forever. Since no firm can grow faster than the economy in which it operates forever, this puts the logical bound of the economy’s growth rate on this number.
If this is done in real terms, it will be the economy’s real growth rate
To the extent that a firm (like Coca Cola) services the world economy the real growth rate of the world economy can be used.
The nominal growth rate that can be used will depend upon the currency in which the cash flows are estimated. The expected inflation rate in that currency can be added to the real growth rate to arrive at the nominal growth rate.
As a simple rule of thumb, this nominal growth rate should not be much higher than the long term government bond rate.

11. Growth Patterns
A key assumption in all discounted cash flow models is the period of high growth, and the pattern of growth during that period. In general, we can make one of three assumptions:
there is no high growth, in which case the firm is already in stable growth
there will be high growth for a period, at the end of which the growth rate will drop to the stable growth rate (2-stage)
there will be high growth for a period, at the end of which the growth rate will decline gradually to a stable growth rate(3-stage)
The assumption of how long high growth will continue will depend upon several factors including:
the size of the firm (larger firm -> shorter high growth periods)
current growth rate (if high -> longer high growth period)
barriers to entry and differential advantages (if high -> longer growth period)
There is a strong subjective element to this process, since we are looking at estimates for the future. Everything you know about the firm, the sector in which it operates and the overall economy will go into making this judgment.
Microsoft, for instance, is a very large firm, but the barriers to entry it has created may allow it to maintain high growth for a long period.

12. Length of High Growth Period
Assume that you are analyzing two firms, both of which are enjoying high growth. The first firm is Earthlink Network, an internet service provider, which operates in an environment with few barriers to entry and extraordinary competition. The second firm is Biogen, a bio-technology firm which is enjoying growth from two drugs to which it owns patents for the next decade. Assuming that both firms are well managed, which of the two firms would you expect to have a longer high growth period?
Earthlink Network
Biogen
Both are well managed and should have the same high growth period
Biogen, because it has greater barriers to entry can be expected to have a logner growth period. Earthlink might be well managed, but the excess returns will draw competitors into the business, which, in turn, will reduce the potential for high growth in the future.

13. Choosing a Growth Pattern: Examples
Company Valuation in Growth Period Stable Growth
Disney Nominal U.S. $ 10 years 5%(long term Firm (3-stage) nominal growth rate in the U.S. economy
Aracruz Real BR 5 years 5%: based upon Equity: FCFE (2-stage) expected long term real growth rate for Brazilian economy
Deutsche Bank Nominal DM 0 years 5%: set equal to Equity: Dividends nominal growth rate in the world economy
I would not be inclined to use growth periods longer than 10 years. While there are firms like IBM, Microsoft and Coca Cola which have been able to sustain growth for much longer periods, they are more the exception than the rule. Most firms are able to maintain high growth for shorter periods.
I am going to use firm valuation for Disney, because I expect leverage to change, and firm valuation is simpler when that occurs
For Aracruz, I will use FCFE, since I do not expect leverage to change, and do the analysis in real terms, to avoid having to deal with expected inflation in BR
For Deutsche Bank, where it is difficult to estimate free cash flows, I will use dividends and make the assumptions that dividends over time will be equal to FCFE.

14. The Building Blocks of Valuation
Valuation models represent some combination of these three choices - a cash flow, a discount rate and a growth pattern.

15. Value is Not Price What is Intrinsic Value? Self assigned Value
Variety of models are used for estimation
Market Price
What stock can be sold for or bought at
Trading Signal
IV > MP Buy
IV < MP Sell or Short Sell
IV = MP Hold or Fairly Priced
More, less, or same as market portfolio?

16. Value is Not Price When are a company’s shares undervalued?
What is Intrinsic Value?
Self assigned Value
Variety of models are used for estimation
Market Price
What stock can be sold for or bought at
Trading Signal
IV > MP Buy
IV < MP Sell or Short Sell
IV = MP Hold or Fairly Priced
When are a company’s shares undervalued?
More, less, or same as market portfolio?

17. Fundamental Stock Analysis: Models of Equity Valuation
Basic Types of Models
Balance Sheet Models
Dividend Discount Models
Price/Earning Ratios
Estimating Growth Rates and Opportunities

18. Equity Valuation: From the Balance Sheet
Value of Assets
Book
Liquidation
Replacement
Value of Liabilities
Book
Market
Value of Equity

19. Equity Valuation: From the Balance Sheet
Value of Assets
Book
Liquidation
Replacement
Value of Liabilities
Book
Market
Value of Equity
Book Value
Liquidation Value
Replacement Value
Tobin’s Q: Market/Replacement tends to 1?

20. Dividend Discount Models: General Model
V0 = Value of Stock
Dt = Dividend
k = required return

21. Specified Holding Period Model
PN = the expected sales price for the stock at time N
N = the specified number of years the stock is expected to be held

22. No Growth Model
Stocks that have earnings and dividends that are expected to remain constant
Preferred Stock

23. No Growth Model: Example
E1 = D1 = $5.00
k = .15
V0 = $5.00 / .15 = $33.33

24. g = constant perpetual growth rate
Constant Growth Model
g = constant perpetual growth rate

25. Constant Growth Model: Example
E1 = $5.00 b = 40% k = 15%
(1-b) = 60% D1 = $3.00 g = 8%
V0 = 3.00 / ( ) = $42.86

26. Estimating Dividend Growth Rates
g = growth rate in dividends
ROE = Return on Equity for the firm
b = plowback or retention percentage rate
i.e.(1- dividend payout percentage rate)

27. Shifting Growth Rate Model
g1 = first growth rate
g2 = second growth rate
T = number of periods of growth at g1

28. Shifting Growth Rate Model: Example
D0 = $ g1 = 20% g2 = 5%
k = 15% T = 3 D1 = 2.40
D2 = D3 = D4 = 3.63
V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 +
D4 / ( ) ( (1.15)3
V0 = = $30.40

29. Partitioning Value: Growth and No Growth Components
PVGO = Present Value of Growth Opportunities
E1 = Earnings Per Share for period 1

30. Partitioning Value: Example
ROE = 20% d = 60% b = 40%
E1 = $5.00 D1 = $3.00 k = 15%
g = .20 x .40 = .08 or 8%

31. Partitioning Value: Example
Vo = value with growth
NGVo = no growth component value
PVGO = Present Value of Growth Opportunities

32. P/E Ratios are a function of two factors
Price Earnings Ratios
P/E Ratios are a function of two factors
Required Rates of Return (k)
Expected growth in Dividends
Uses
Relative valuation
Extensive Use in industry

33. P/E Ratio: No expected growth
E1 - expected earnings for next year
E1 is equal to D1 under no growth
k - required rate of return

34. P/E Ratio with Constant Growth
Where
b = retention ratio
ROE = Return on Equity

35. Numerical Example: No Growth
E0 = $ g = 0 k = 12.5%
P0 = D/k = $2.50/.125 = $20.00
PE = 1/k = 1/.125 = 8

36. Numerical Example with Growth
b = 60% ROE = 15% (1-b) = 40%
E1 = $2.50 (1 + (.6)(.15)) = $2.73
D1 = $2.73 (1-.6) = $1.09
k = 12.5% g = 9%
P0 = 1.09/( ) = $31.14
PE = 31.14/2.73 = 11.4
PE = ( ) / ( ) = 11.4

37. Valuation and M&A
Rationale: Firm A should merge with Firm B if
[Value of AB > Value of A + Value of B + Cost of transaction]
Synergy
Gain market power
Discipline
Taxes
Financing

38. Goals of Acquisitions Rationale: Firm A should merge with Firm B if
[Value of AB > Value of A + Value of B + Cost of transaction]
Synergy
Eg Martell takeover by Seagrams to match name and inventory with marketing capabilities
Gain market power
Eg Atlas merger with Varity. (Less important with open borders)
Discipline
Eg Telmex takeover by France Telecom & Southwestern Bell (Privatization)
Eg RJR/Nabisco takeover by KKR (Hostile LBO)
Taxes
Eg income smoothing, use accumulated tax losses, amortize goodwill
Financing
Eg Korean groups acquire firms to give them better access to within-group financing than they might get in Korea's undeveloped capital market

39. Value Changes In An Acquisition10
Taxes on sale of assets 10
Financial structure
improvements
Profit on sale
of assets
Synergies and/
or operating
Value of
acquired
company as
a separate
entity
acquiring
company
without
acquisition 30 30
Takeover premium & costs 50
Gain in
shareholder
value 50 75
250
175
Initial value
plus gains
Final value of
combined company

43. www.giddy.org Ian Giddy NYU Stern School of Business
Tel ; Fax