Equity Valuation

Finding Mispriced Securities• Finding undervalued securities is not easy in efficient markets.

• However, opportunities exist as markets not perfectly efficient.

• Fundamental analysis aims at determining fair market value of a company’s stock based on present and future profitability.

• To identify mispriced securities, fundamental analysis looks at some measure of ‘true value’ derived from observable financial data.

Alternative Measures of Value

• Valuation by Comparables• Book Value• Liquidation Value• Replacement Cost• Tobin’s q• Intrinsic Value

Intrinsic Value

• Intrinsic Value (V0) of a share is the present value of all cash payments to the investor in the stock, including dividends as well as the proceeds from the ultimate sale of the stock, discounted at the appropriate risk-adjusted interest rate, k.

• Whenever the intrinsic value exceeds the market price, the stock is considered undervalued and a good investment.

The Valuation Process• Understand the business through macro-economic and

industry analysis.• Forecast company performance• Select the appropriate valuation model (absolute valuation

models such as DCF models or relative valuation models).• Convert a forecast to a valuation• Make investment recommendation.

Dividend Discount Models• The intrinsic value of common stock is viewed as the present value of its expected

future cash flows.

• The most widely used definitions of cash flows associated with common stock are dividends and free cash flows.

• The dividend discount models define cash flows as dividends.

• A discounted dividend approach is most suitable for dividend paying stocks in which the companies have a discernible dividend policy that has an understandable relationship to the company’s profitability, and the investor has a non-control (minority ownership) perspective.

• These include seasoned profitable companies operating outside the economy’s fastest growing subsectors.

Dividend Discount Models• When you buy stock in a publicly traded firm, the only cash

flow you receive directly from this investment is expected dividends.

• The DDM builds on this simple proposition and argues that the value of a stock has to be the present value of expected dividends over time.

1 20 2 (1)(1 ) (1 ) (1 )

nn

DD DVk k k

Dividend Discount Models• The DDM in the form of equation (1) showing the discounted

value of future dividends is not useful in valuing a stock because it requires dividend forecasts for every year into the indefinite future.

• To make the model practical, it is assumed that dividends trend upward at a stable growth rate g.

• The equation for V0 can be simplified as:

• Equation (2) is called the constant growth DDM or the Gordon Model.

10 (2)DV

k g

Dividend Discount Models• Growth comes from retention and reinvestment of profits. If b

denotes the retention ratio and r denotes the ROE, the growth rate g =b*r

• If the dividends are not expected to grow, then the dividend stream will be a simple perpetuity and the valuation formula will be V0 = D1/k.

• Since D1 for a no growth company is E1 , V0 is also equal to E1/k.

• In case of preferred stock, the constant growth rate of dividend is zero. If a preferred stock pays a fixed dividend of Rs.10 per share and the discount rate is 8%, the price will be Rs.10/0.08 = Rs.125.

Implications of Constant Growth DDM

1. The model implies that a stock’s value will be greater:• the larger the expected dividend per share• the lower the market capitalization rate, k.• the higher the expected growth rate of dividends.

2. The stock price is expected to grow at the same rate as dividends.

Example

Expected dividend (D1) =4.00 k=0.10 g = 0.05

P0 = 4/(0.10-0.05) = 80 D2 = 4.20 P1 = 4.20/(0.10-0.05) =84

The price has increased by 5%, the same rate asgrowth rate of dividends.

Implications of Constant Growth DDM

From

• When P0 =V0 , the market capitalization rate can be calculated using the above relationship.

• The constant growth dividend discount model cannot be used when g >k

• It is best suited for firms with well established dividend payout policies and which are growing at a rate equal to or lower than the growth in the economy

10

DPk g

1

0

(3)Dk gP

Two-Stage DDM• This model allows for two stages of growth-an initial phase

where the growth rate is not a stable growth rate and a subsequent steady phase where the growth rate is stable and is expected to remain so for the long-term.

• The growth rate in the initial phase can be higher or lower than the stable growth rate.

• This model is best suited for firms that are in the high growth and expect to maintain that growth rate for a specific period after which the sources of high growth are expected to disappear (expiry of patents, disappearance of barriers to entry).

Two-Stage DDM

00

1

(1 ) (1 ) 1(1 ) (1 )

tns n ct n

t c

D g D gV

k k g k

Where:D0 = Current Dividendgs = Sub-normal or Super-normal Growth rate of Dividendgc = Constant growth rate of DividendDn =Dividend at the end of the normal growth periodk = required rate of return

Example –Two Stage DDM

• Given D0 = Rs.1.00, gs = 12%, gc =6%, n=3 and k=10%

V0 =

= 1.02+1.04+1.05+27.97

= 31.08

2 3 3

2 3 3

1(1.12) 1(1.12) 1(1.12) 1(1.12) (1.06) 1(1.10) (1.10) (1.10) (0.10 0.06) (1.10)

Two-Stage DDM There are two major problems in applying the two-stage DDM• Defining the length of the extraordinary growth period. There

are three major considerations:– Size of the firm– Existing growth rate– Magnitude of sustainable competitive advantage

• Deciding on the shift from high to stable rate. The two-stage model is suited to firms with moderate growth only where the shift will not be dramatic.

• For firms with high growth rates, the transition should be gradual and multi-stage growth models should be used.

Multistage Growth Models• These models allow dividends per share to grow at several different rates

as the firm matures.

• They assume an initial period of high dividend growth, a final period of sustainable growth and a transition period between the two during which the initial high growth rate tapers off to the ultimate sustainable rate.

• These models are similar to the two-stage models but require a larger number of inputs.

• The three-stage DDM with declining growth in stage 2 has been widely used. It has also been adopted by Bloomberg LP, a financial services company that provides ‘Bloomberg terminals’ to professional investors and analysts.

Limitations of DDM • The models are extremely sensitive to the inputs for the

growth rate.• They can lead to misleading results as the growth rate

converges to the discount rate.• The focus on dividends can lead to skewed estimates of value

for firms that are not paying out what they can afford to in dividends.

• In particular, they will underestimate the value of firms that accumulate cash and pay out too little in dividends.

Free Cash Flows• The second definition of stock returns used in DCF techniques of

stock valuation is free cash flows. • Whereas dividends are the cash flows actually paid to

stockholders, free cash flows are the cash flows available for distribution to shareholders.

• Analysts like to use free cash flow as the return whenever one or more of the following conditions is present:

• (1) The company does not pay dividends. (2) The company pays dividends but does not have a discernible dividend policy that has an understandable relationship to the company’s profitability. (3) Free cash flows align with profits within a reasonable forecast period. (4) The investor has a control perspective.

FCFF and FCFE• There are two notions of free cash flows, free cash flow to the

firm (FCFF) and free cash flow to equity (FCFE).• FCFF is the cash flow available to company’s suppliers of

capital after all operating expenses (including taxes) have been paid and the necessary investments in working capital (e.g., inventory) and fixed capital (e.g., equipment) have been made.

• FCFE is the cash flow available to the company’s holders of common equity after all operating expenses, interest and principal payments have been made and necessary investments in working and fixed capital have been made.

FCFF Approach• The free cash flow to the firm (FCFF) is the sum of the cash

flows to all claim holders in the firm including stockholders, bondholders and preferred shareholders.

• There are two ways of measuring FCFF:

1. FCFF =FCFE+ Interest expense (1-t) + Principal repayments – new debt issues + Preference dividend

2. FCFF = EBIT (1-t) + Depreciation- Capital expenditure – Changes in Working Capital

FCFF Approach• From the firm value, the value of the firm’s debt obligation is

deducted to arrive at the firm’s equity value.• FCFF models can also be constant growth, two stage or three-

stage models.• Under the constant growth FCFE model: 1

0FCFF

FCFFVWACC g

Re Re ( )FCFFg investment Rate turnoninvested capital ROIC

Re(1 )

Capex Depreciation WCinvestment RateEBIT t

(1 )EBIT tROIC

Total Capital

FCFE Approach• FCFE = Net income – (capital expenditure-depreciation)-

(changes in non-cash working capital) + (new debt issued –debt repayments)

• If it is assumed that the net capital expenditure and working capital changes are financed using a fixed proportion ( δ) of debt, FCFE can be represented as:

• FCFE = Net income – (capital expenditure-depreciation)(1- δ) -(changes in non-cash working capital) (1- δ)

FCFE Approach• FCFE models can also be constant growth, two stage or three-

stage models.

• Under the constant growth FCFE model:

Equity Reinvestment Rate =

10

e FCFE

FCFEVk g

FCFEg Equity reinvestment rate ROE

Net capex WC Net debt issueNet Income

Calculating Free Cash Flows• When finding the net increase in working capital for free cash

flow, we exclude cash and cash equivalents as well as notes payable and the current portion of long-term debt.

• Cash and cash equivalents are excluded because a change in cash is what we are trying to explain.

• Notes payable and the current portion of long-term debt are excluded because these are liabilities with explicit interest costs that make them financing items rather than operating items.

Calculating Free Cash Flows• Changes in deferred tax liability should not be added back if

the liability is likely to reverse in the near future. The addition may be done when a company is growing and has the ability to indefinitely defer its tax liability.

• Similarly changes in deferred tax asset should be subtracted only when the company is expected to have this asset on a continual basis.