Applying Present Value Models

1.  Where Gordon Growth Model is highly appropriate

The Gordon Growth Model is highly appropriate for valuing dividend-paying stocks that are relatively immune to the business cycle and are relatively mature (e.g., utilities).

It is also useful for valuing companies that have historically been raising their dividends at a stable rate.



2.  Where DDM or Gordon Growth Model is difficult to use

Applying the DDM is relatively difficult if the company is not currently paying out a dividend.  

A company may not pay out a dividend because:

• It has a lot of lucrative investment opportunities available and it wants to retain profits to reinvest them in the business.
• It does not have sufficient excess cash flow to pay out a dividend.

Even though the Gordon Growth Model can be used for valuing such companies, the forecasts used are generally quite uncertain.

Therefore, analysts use one of the other valuation models to value such companies and may use the DDM model as a supplement.

3.  Multi-stage DDM can be employed 

The DDM can be extended to numerous stages.  For example:

A.   A three-stage DDM is used to value fairly young companies that are just entering the growth phase.  Their development falls into three stages - 

• growth (with very high growth rates), 
• transition (with decent growth rates) and 
• maturity (with a lower growth into perpetuity).

B.  A two-stage DDM can be used to value a company 

• currently undergoing moderate growth, but 
• whose growth rate is expected to improve (rise) to its long term growth rate.

Return on Share Investment = Dividend Yield + Growth over Time (Gordon Growth Model)

Rearranging the Dividend Discount Model (DDM) formula:

PV = D1 / (k-g)

k = (D1/PV) + g
   = Dividend yield + growth over time.

This expression for the cost of equity (required rate of return) tells us that the return on an equity investment has two components:

• The dividend yield (D1/PV at year 0)
• Growth over time (g)

Return on share investment = Dividend Yield + Growth over Time:

Dividend Discount Model

Dividend Discount Model

Where:

V = the value

D₁ = the dividend next period

r = the required rate of return

1.  One year holding period

If our holding period is just one year, the value that we will place on the stock today is the present value of the dividends that we will receive over the year plus the present value of the price that we expect to sell the stock for at the end of the holding period.

Present Value of the dividends that we will receive over one year 
= Dividend to be received/(1+r)^1

Present value of the price we expect to sell the stock for at the end of the holding period
= Year-end price / (1+k)^1


Value 
= PV of dividends receive over 1 year + PV of price we expect to sell at end of 1 year
= [Dividend to be received/(1+k)^1]  +  [Year-end price /(1+k)^1]

k = cost of equity or required rate of return



2.  Multiple-Year Holding Period DDM

We apply the same discounting principles for valuing common stock over multiple holding periods.

In order to estimate the intrinsic value of the stock, we first estimate the dividends that will be received every year that the stock is held and the price that the stock will sell for at the end of the holding period.

Then we simply discount these expected cash flows at the cost of equity (required return).

PV of Dividends received in Year 1 = D1/(1+k)^1
PV of Dividends received in Year 2 = D2/(1+k)^2
PV of Dividends received in Year .. =
PV of Dividends received in Year n= Dn/(1+k)^n
Price of stock sold at end of holding period n = Pn / (1+k)^n

Value
= PV of D1 + PV of D2 + PV of D3 +.................. PV of Dn + PV of Holding-Period Price
= [D1/(1+k)^1]  + [D2/(1+k)^2]  + .[D3/(1+k)^3]..........[.Dn/(1+k)^n]  + [Pn / (1+k)^n]




3.  Infinite Period DDM (Gordon Growth Model)

Assumptions of the Infinite Period DDM (Gordon Growth Model):

• The infinite period dividend discount model assumes that a company will continue to pay dividends for an infinite number of periods.
• It also assumes that the dividend stream will grow at a constant rate (g) over the infinite period.

In this case, the intrinsic value of the stock is calculated as:

Value = PV of D1 + PV of D2 + PV of D3 + ...........PV of Dn....... + PV of Dinfinity


PV of Dividends received in Year 1 = D1/(1+k)^1 = D0(1+g)^1/(1+k)^1
PV of Dividends received in Year 2 = D2/(1+k)^2 = D0(1+g)^2/(1+k)^2
PV of Dividends received in Year .. =
PV of Dividends received in Year n= Dn/(1+k)^n = DO(1+g)^infinity / (1+k)^infinity

D0 = Dividends received at year 0

This equation simplifies to:

PV at year 0
= D0(1+g)^1/(k-g)^1
= D1/(k-g)






The critical relationship between k and g in the infinite-period DDM (Gordon Growth Model)

The relation between k and g is critical:

• As (k-g) increases, the intrinsic value of the stock falls.
• As (k-g) narrows, the intrinsic value of the stock rises.
• Small changes in either k or g, can cause large changes in the value of the stock.

For the infinite-period DDM model to work, the following assumptions must hold:

• Dividend grows at a rate, g, which is not expected to change (constant growth).
• k must be greater than g; otherwise the model breaks down because of the denominator being negative.

(k-g) = difference between k and g or difference between cost of equity or required rate of return and growth rate.







Additional notes:

Return on investment = Dividend Yield + Growth over Time:

Rearranging the DDM formula:

PV = D1 / (k-g)

k = (D1/PV) + g
   = Dividend yield + growth over time.

This expression for the cost of equity (required rate of return) tells us that the return on an equity investment has two components:

• The dividend yield (D1/PV at year 0)
• Growth over time (g)

Intrinsic Value of Preferred Stock

1.  When preferred stock is non-callable, non-convertible, has no maturity date and pays dividends at a fixed rate, the value of the preferred stock can be calculated using the perpetuity formula:

V = D/r

V = value
D = dividend
r = required rate of return




2.  For a non-callable, non-convertible preferred stock with maturity at time, n, the value of the stock can be calculated using another formula.

Value
= PV of Dividends received + PV of Final Selling Price of Preferred Stock
= D1/(1+r)^1 + D2/(1+r)^2 + ....... + F/(1+r)^n




http://www.investopedia.com/articles/fundamental-analysis/11/valuation-prefered-stock.asp

Multiples based on Comparables

This method compares relative values estimated using multiples to determine whether an asset is 

• undervalued, 
• overvalued or 
• fairly valued.  

The benchmark multiple can be any of:

• A multiple of a closely matched individual stock.
• The average or median multiple of a peer group or the firm's industry.
• The average multiple derived from trend or time-series analysis.

Analyst should be careful to select only those companies that have similar size, product lines, and growth prospects to the company being valued as comparables.

Price to cash flow ratio 

P/CF = Market price of share / Cash flow per share

Price to sales ratio

P/S = Market price per share / Net sales per share

P/S = Market value of equity / Total net sales

Price to Book Value ratio

P/BV = Current market price of share / Book value per share

P/BV = Market vale of common shareholders' equity / Book value of common shareholders' equity

where:

Book value of common shareholders' equity 

= (Total assets - Total liabilities) - Preferred stock

Multiples based on Fundamentals - the Justified P/E ratio

A price multiple may be related to fundamentals through a dividend discount model such as the Gordon growth model.

The expressions developed in such an exercise are interpreted as the justified (or based on fundamental) values for a multiple.


The justified P/E Ratio:

P/E = D/E/(r-g)

r = required rate of return
g = growth


Gordon Growth Model

r = D/P + g
D/P = r-g
P= D/(r-g)
P/E = D/E(r-g)
P/E = Dividend Payout Ratio / (r-g)



Inference

The P/E ratio is inversely related to the required rate of return.
The P/E ratio is positively related to the growth rate.
The P/E ratio appears to be positively related to the dividend payout ratio.

• However, this relationship may not always hold because a higher dividend payout ratio implies that the company's earnings retention ratio is lower.  
• A lower earnings retention ratio translates into a lower growth rate.  
• This is known as the "dividend displacement" of earnings.

Notes:

Higher the growth rate (g), higher the P/E.
Higher the required rate of return (r), lower the P/E.
Higher the DPO ratio, higher the P/E.
Also, higher the DPO ratio, lower the retained earnings,  leading to lower growth rate (g), thus lower P/E. ("dividend displacement" of earnings)

Price Multiples - Relative Valuation

Price multiples are ratios that compare the price of a stock to some sort of value.

Price multiples allow an analyst to evaluate the relative worth of a company's stock.

Popular multiples used in relative valuation include:

• price-to-earnings,
• price-to-sales,
• price-to-book, and
• price-to-cash flow.

Enterprise Value Multiples

Enterprise value (EV) is calculated as the market value of the company's common stock plus the market value of outstanding preferred stock if any, plus the market value of debt, less cash and short term investment (cash equivalent).

EV
= market value of company's common stock
+ market value of outstanding preferred stock
+ market value of debt
- cash and short term investment (cash equivalent)

It can be thought of as the cost of taking over a company.



EV/EBITDA multiple

The most widely used EV multiple is the EV/EBITDA multiple.

EBITDA measures a company's income before payments to any providers of capital are made.

The EV/EBITDA multiple is often used when comparing two companies with different capital structures.


Loss-making companies usually have a positive EBITDA

Loss-making companies usually have a positive EBITDA, which allow analysts to use the EV/EBITDA multiple to value them.  

The P/E ratio is meaningless (negative) for a loss making company as its earnings are negative.

Asset-Based Valuation

Asset-Based Valuation uses market values of a company's assets and liabilities to determine the value of the company as a whole.

Asset based valuation works well for:

• Companies that do not have a significant number of intangible or "off-the-book" assets, and have a higher proportion of current assets and liabilities.
• Private companies, especially if applied together with multiplier models.
• Financial companies, natural resource companies and companies that are been liquidated.

Asset-based valuation may not be appropriate when:

• Market values of assets and liabilities cannot be easily determined.
• The company has a significant amount of intangible assets.
• Asset values are difficult to determine (e.g., in periods of very high inflation).
• Market values of assets and liabilities significantly differ from their carrying values.

Dividend Discount Model

Present Value Models

Dividend Discount Model


1.  If a company pays regular dividends

The dividend discount model (DDM) values a share of common stock as the present value of its expected future cash flows (dividends).

When an investor sells a share of common stock, the value that the purchaser will pay equals the present value of the future stream of cash flows (i.e. the remaining dividend stream).

Therefore, the value of the stock at any point in time is still determined by its expected future dividends.

When this value is discounted to the present, we are back at the original dividend discount model.



2.  If a company pays no dividends currently

If a company pays no dividends currently, it does not mean that its stock will be worthless.

There is an expectation that after a certain period of time the firm will start making dividend payments.

Currently, the company is reinvesting all its earnings in its business with the expectation that its earnings and dividends will be larger and will grow faster in the future.



3.  If the company is making losses

If the company does not make positive earnings going forward, there will still be an expectation of a liquidating dividend.  

The amount of this dividend will be discounted at the required rate of return to compute the stock's current price.




Additional notes:

The required rate of return on equity is usually estimated using the CAPM.

Another approach for calculating the required return on equity simply adds a risk premium to the before-tax cost of debt of the company.

Competitive Strategies

1.  Cost Leadership

Companies pursuing this strategy strive to cut down their costs to become the lowest cost producers in an industry so that they can gain market share by charging lower prices.

Pricing may be

• defensive (to protect market positions when competition is low) or 
• aggressive (to increase market share when competition is intense.)

2.  Product/Service Differentiation

Companies pursuing this strategy strive to differentiate their products from those of competitors in terms of quality, type, or means of distribution.

These companies are then able to charge a premium price for their products.

This strategy is successful only if the price premium is greater than the cost of differentiation and the source of differentiation appeals to customers and is sustainable over time.

Price Competition

1.  Highly competitive industry (commodity products)

• Industries in which price is the most significant consideration in customers' purchase decisions tend to be highly competitive.
• A slight increase in price may cause customers to switch to substitute products if they are widely available.

2.  Franchise industry (franchise products)

• Price is not as important if companies in an industry are able to effectively differentiate their products in terms of quality and performance.  
• Customers may not focus on price as much if product reliability is more important to them.

Factors Affecting Industry Growth, Profitability and Risk

• Macroeconomic influences
• Technological influences
• Demographic influences
• Government influences
• Social influences

Elements that should be Considered in a Company Analysis

A thorough company analysis should:

• Provide an overview of the company.
• Explain relevant industry characteristics.
• Analyze the demand for the company's products and services.
• Analyze the supply of products and services including an analysis of costs.
• Explain the company's pricing environment.
• Present and interpret relevant financial ratios, including comparisons over time and comparisons with competitors.

Industry Life-Cycle Analysis

Stages of Life-Cycle of Business / Industry

• Embryonic
• Growth
• Shakeout
• Mature
• Decline

Embryonic

Industries in this stage are just beginning to develop.

They are characterised by:

• Slow growth as customers are still unfamiliar with the product.
• High prices as volumes are too low to achieve significant economies of scale.
• Significant initial investment.
• High risk of failure.

Companies focus on raising product awareness and developing distribution channels during this stage.

Growth

Once the new product starts gaining acceptance in the market, the industry experiences rapid growth.

The growth stage is characterised by:

• New customers entering the market, which increases demand.
• Improved profitability as sales grow rapidly.
• Lower prices as econmies of scale are achieved.
• Relatively low competition among companies in the industry as the overall market size is growing rapidly.  Firms do no need to wrestle market share away from competitors to grow.
• High threat of new competitors entering the market due to low barriers to entry.

During this stage, companies focus on building customer loyalty and reinvest heavily in the business.

Shakeout

The period of rapid growth is followed by a period of slower growth.

The shakeout stage is characterised by:

• Slower demand growth as fewer new customers are left to enter the industry.
• Intense competition as growth becomes dependent on market share growth.
• Excess industry capacity, which leads to price reductions and declining profitability.

During this stage, companies focus on reducing their costs and building brand loyalty.

Some firms may fail or merge with others.

Mature

Eventually demand stops growing and the industry matures.

Characteristics of this stage are:

• Little or no growth in demand as the market is completely saturated.
• Companies move towards consolidation.  They recognize that they are interdependent so they stay away from price wars  However, price wars may occur during downturns.
• High barriers to entry in the form of brand loyalty and relatively efficient cost structures.

During this stage, companies are likely to be pursuing replacement demand rather than new buyers and should focus on extending successful product lines rather than introducing revolutionary new products.

Companies have limited opportunities to reinvest and often have strong cash flows.  

As a result, they are more likely to pay dividends.

Decline

Technological substitution, social changes or global competition may eventually cause an industry to decline.

The decline stage is characterised by:

• Negative growth
• Excess capacity due to diminishing demand.
• Price competition due to excess capacity.
• Weaker firms leaving the industry.

Limitations of Industry Life-Cycle Analysis

The following factors may

• change the shape of the industry life cycle, 
• cause some stages to be longer or shorter than expected, or 
• even result in certain stages being skipped altogether.

These factors are:

• Technological changes
• Regulatory changes
• Social changes
• Demographics

Industry life-cycles analysis is most useful in analyzing industries during periods of relative stability.

It is not as useful in analyzing industries experiencing rapid change.

Not all companies in an industry display similar performance.

Cost of Equity and Investors' Required Rates of Return

You should think about the cost of equity as the minimum expected rate of return that a company must offer investors to purchase its shares in the primary market and to maintain its share price in the secondary market.

If the required rate of return is not maintained, the price of the security in the secondary market will adjust to reflect the minimum rate of return required by investors.

If investors require a higher return than the company's cost of equity, they will sell the company's shares and invest elsewhere, which would bring down the company's stock price.

This decline in the stock price will lead to an increase in the expected return on equity and bring it in line with the (higher) required rate of return.

Investors' Minimum Required Rates of Return, Cost of Debt and Cost of Equity

A company may raise capital by issuing

• debt or 
• equity, 

Both of which have associated costs.



Investors' Minimum Required Rates of Return

Investors' minimum required rates of return refer to the return they require for providing funds to the company.



Cost of Debts

A company's cost of debt is easy to estimate as it is reflected in the interest payments that the company is contractually obligated to make to debt holders.

For investors who provide debt capital to the company, their minimum required rate of return is the periodic interest rate they charge the company for using their funds.

All providers of debt capital receive the same interest rate.

Therefore, the company's cost of debt and investor's minimum required rate of return on debt are the same.



Cost of Equity

Estimating cost of equity is difficult because the company is not contractually obligated to make any payments to common shareholders.

For investors who provide equity capital tot he company, the future cash flows that they expect to receive are uncertain (in both timing and amount), so their minimum required rate of return must be estimated.

Further, each investor may have different expectations regarding future cash flows.

Therefore, the company's cost of equity may be different from investors' minimum required rate of return on equity.





Additional notes:

The company's cost of equity can be estimated using the dividend discount model (DDM) and capital asset pricing model (CAPM).

The costs of debt and equity are used to estimate a company's weighted average cost of capital (WACC), which represents the minimum required rate of return that the company must earn on its investments.

Importance of Equities in Global Financial Markets

In 2008, on a global level, the equity market capitalization to GDP ratio was close to 100% (more than twice the long run average of 50%)

During 1900 - 2008, government bonds and bills earned annualized real returns of 1% to 2% on average, which is in line with the inflation rate.   Equity markets earned real returns in excess of 4% per year in most markets.

In most developed countries, equity ownership as a percentage of the population was between 20% and 50%.

Equity Securities and Company Value (Intrinsic Value of a company)

Book values and ROE do help analysts evaluate companies, but they cannot be used as the primary means to determine a company's intrinsic value.

Intrinsic value refers to the present value of the company's expected future cash flows.

Intrinsic value can only be estimated as it is impossible to accurately predict the amount and timing of a company's future cash flows.

Astute investors aim to profit from differences between market prices and intrinsic values.

Accounting Return on Equity

Return on Equity (ROE) measures the rate of return earned by a company on its equity capital.

It indicates how efficient a firm is in generating profits from every dollar of net assets.


The ROE is computed as net income available to ordinary shareholders (after preference dividends have been paid) divided by the average total book value of equity.

ROE
= Net Income / Average Book Value of Equity
= Net Income /[ (Book Value of Equity FY1 + Book Value of Equity FY2)/2]


An increase in ROE might not always be a positive sign for the company.

• The increase in ROE may be the result of net income decreasing at a slower rate than shareholders' equity.  A declining net income is a source of concern for investors.
• The increase in ROE may be the result of debt issuance proceeds being used to repurchase shares.  This would increase the company's financial leverage (risk).