Barrier to Entry - A form of Durable competitive advantage

Low barriers to entry mean that new competitors can easily enter the industry, which makes the industry highly competitive.  Companies in relatively competitive industries typically have little pricing power.

High barriers to entry mean that existing companies are able to enjoy economic profits for a long period of time.  These companies have greater pricing power.

However, the above mentioned characteristics of high and low barrier industries are not always observed.

Further it is important to note that:

• Barriers to entry should not be confused with barriers to success.
• Barriers to entry can change over time.

Relationship between Price and Maturity of Bonds

If the yield remains constant:

• A premium bond's value decreases towards par as it nears maturity.
• A discount bond's value increases towards par as it nears maturity.
• A par bond's value remain unchanged as it nears maturity.

Costs of trading, illiquid markets and costs associated with gathering and analyzing information affect security prices.

Two securities that should trade for the exact same price in an efficient market may trade at different prices for various reasons:

1. If the costs of trading on the mispricing (to make a profit) for the lower cost traders are greater than the potential profit.
2. In such cases, these prices are still "efficient" within the bounds of arbitrage.  The bounds of arbitrage are relatively narrow in highly liquid markets (e.g., U.S. T-bills), but wider in relatively illiquid markets.
3. There are always costs associated with gathering and analyzing information.  Net of information acquisition costs, the return offered on a security should be commensurate with the security's level of risk.  If superior returns can be earned after deducting information-acquisition costs, the market is relatively inefficient.

Factors Contributing to and Impeding a Market's Efficiency

Market participants:   

The greater the number of active market participants (investors and financial analysis) that analyze an asset or security, the greater the degree of efficiency in the market.

Information availability and financial disclosure:

The availability of accurate and timely information regarding trading activities and traded companies contributes to market efficiency.

Limits to trading:

The activities of arbitrageurs, who seek opportunities to trade on mispricings in the market to earn arbitrage (riskless) profits, contribute to market efficiency.

Transactions costs and information acquisition costs:

Investors should consider transaction costs and information-acquisition costs in evaluating the efficiency of a market.

Market Value versus Intrinsic Value

Market Value

The market value or market price of the asset is the price at which the asset can currently be bought or sold.  

It is determined by the interaction of demand and supply for the security in the market.


Intrinsic Value

Intrinsic value or fundamental value is the value of the asset that reflects all its investment characteristics accurately.

Intrinsic values are estimated in light of all the available information regarding the asset; they are not known for certain



Efficient Market

In an efficient market, investors widely believe that the market price reflects a security's intrinsic value.


Inefficient Market

On the other hand, in an inefficient market, investors may try to develop their own estimates of intrinsic value in order to profit from any mispricing (difference between the market price and intrinsic value).

Efficient Market versus Inefficient Market

An information efficient market (an efficient market) is one where security prices adjust rapidly to reflect any new information.

It is a market where asset prices reflect all past and present information.

Investment managers and analysts are interested in market efficiency because it dictates how many profitable trading opportunities may abound in the market.



Efficient market

In an efficient market, it is difficult to find inaccurately priced securities.  

Therefore, superior risk-adjusted returns cannot be attained in an efficient market.

It would be wise to pursue a passive investment strategy which entails lower costs.

In an efficient market, the time frame required for security prices to reflect any new information is very short.   

Further, prices only adjust to new or unexpected information (surprises).



Inefficient market

In an inefficient market, securities may be mispriced.

Trading in these securities can offer positive risk-adjusted returns. 

In such a market, an active investment strategy may outperform a passive strategy on a risk-adjusted basis.

Overview of a Fixed-Income Security (Bonds)

Who are the issuers of fixed-income security or bonds?

• Supranational organizations
• Sovereign (national) governments
• Non-sovereign (local) governments
• Quasi-government entities

Credit worthiness of Bonds

Bond issuers can also be classified based on their credit worthiness as judged by credit rating agencies.

Bonds can broadly be categorized as

• investment-grade bonds or
• non-investment grade (or high yield or speculative) bonds.

Maturity of Bonds

Fixed-income securities which, at the time of issuance, are expected to mature in one year or less are known as money market securities.

Fixed-income securities which, at the time of issuance, are expected to mature in more than one year are referred to as capital market securities.

Fixed-income securities which have no stated maturity are known as perpetual bonds.

Par Value

The par value (also known as face value, nominal value, redemption value and maturity value ) of a bond refers to the principal amount that the issuer promises to repay bondholders on the maturity date.

Bond prices are usually quoted as a percentage of the par value.

• When a bond's price is above 100% of par, it is said to be trading at a premium
• When a bond's price is at 100% of par, it is said to be trading at par.
• When a bond's price is below 100% of par, it is said to be trading at a discount.

Coupon Rate and Frequency

The coupon rate (also known as the nominal rate) of a bond refers to the annual interest rate that the issuer promises to pay bondholders until the bond matures.

The amount of interest paid each year by the issuer is known as the coupon, and is calculated by multiplying the coupon rate by the bond's par value.

Zero-coupon (or pure discount) bonds are issued at a discount to par value and redeemed at par (the issuer pays the entire par amount to investors at the maturity date).  The difference between the (discounted) purchase price and the par value is effectively the interest on the loan.

Currency Denomination

Dual currency bonds make coupon payments in one currency and the principal payment at maturity in another currency.

Currency option bonds give bondholders a choice regarding which of the two currencies they would like to receive interest and principal payments in.

Yield Measures

The current yield or running yield equals the bond's annual coupon amount divided by its current price (not par value), expressed as a percentage.

The yield to maturity (YTM) is also known as the yield to redemption or the redemption yield.  It is calculated as the discount rate that equates the present value of a bond's expected future cash flows until maturity to its current price.

Given a set of expected future cash flows, the lower  the YTM or discount rate, the higher the bond's current price.

Given a set of expected future cash flows, the higher the YTM or discount rate, the lower the bond's current price.

Important Relationships of Fixed Income Securities (Bonds)

Defining the Elements of a Bond

Coupon rates and bond prices

The higher the coupon rate on a bond, the higher its price.

The lower the coupon rate on a bond, the lower its price.


Interest rates and bond prices

An increase in interest rates or the required yield on a bond, will lead to a decrease in price.

A decrease in interest rates or the required yield on a bond will lead to an increase in price.

That is, bond prices and yields are inversely related.


Bonds risks and bond yields 

The more risky the bond, the higher the yield required by investors to purchase the bond, and the lower the bond's price.

Contingent Convertible Bonds ("CoCos")

CoCos are bonds with contingent write-down provisions.

They differ from traditional convertible bonds in two ways:

• Unlike traditional convertible bonds, which are convertible at the option of the bondholder, CoCos convert automatically upon the occurrence of a pre-specified event.
• Unlike traditional convertible bonds, in which conversion occurs if the issuer's share price increases (i.e. on the upside), contingent write-down provisions are convertible on the downside.

Warrants

A warrant is somewhat similar to a conversion option, but it is not embedded in the bond's structure.

It offers the holder the right to purchase the issuer's stock at a fixed exercise price until the expiration date.

Warrants are attached to bond issues as sweeteners, allowing investors to participate in the upside from an increase in share prices.

Understanding the importance and implications of Leverage

Importance of Leverage

Leverage increases the volatility of a company's earnings and cash flows, thereby increasing the risk borne by investors in the company.

The more significant the use of leverage by the company, the more risk it is and therefore, the higher the discount rate that must be used to value the company.

A company that is highly leveraged, risks significant losses during economic downturns.



Leveraged is affected by a company's cost structure.

Generally companies incur two types of costs:

• Variable costs: vary with the level of production and sales (e.g., raw materials costs and sales commissions).
• Fixed costs:  remain the same irrespective of the level of production and sales (e.g., depreciation and interest expense).

Conclusion:

The higher the proportion of fixed costs (both operating and financial) in a company's cost structure (higher leverage) the greater the company's earnings volatility.

The greater the degree of leverage for a company, the steeper the slope of the line representing net income.

Leverage

Leverage refers to a company's use of fixed costs in conducting business.

Fixed costs include:

• Operating costs (e.g., rent and depreciation)
• Financial costs (e.g., interest expense)

Convertible Bonds

A convertible bond gives the bondholder the right to convert the bond into a pre-specified number of common shares of the issuer.


Why may convertible bonds be attractive to investors?

Convertible bonds are attractive to investors as the conversion (to equity) option allows them to benefit from price appreciation of the issuer's stock.

On the other hand, if there is a decline in the issuer's share price (which causes a decline in the value of the embedded equity conversion/call option), the price of the convertible bond cannot fall below the price of an otherwise identical straight bond.


Why do issuers use convertible bonds rather than straight bonds?

Because of these attractive features, convertible bonds offer a lower yield and sell at higher prices than similar bonds without the conversion option.

Note however, that the coupon rate offered on convertible bonds is usually higher than the dividend yield on the underlying equity.



Some useful vocabulary

• The conversion price is the price per share at which the convertible bond can be converted into shares.
• The conversion ratio refers to the number of common shares that each bond can be converted into.  It is calculated as the par value divided by the conversion price.
• The conversion value is calculated as current share price multiplied by the conversion ratio.
• The conversion premium equals the difference between the convertible bond's price and the conversion value.
• Conversion parity occurs if the conversion value equals the convertible bond's price.

Why issuers often embed a call option alongside the conversion option in the convertible bond?

Although it is common for convertible bonds to reach conversion parity before they mature, bondholders rarely exercise the conversion option, choosing to retain their bonds and receive (higher) coupon payments instead of (lower) dividend payments.

As a result, issuers often embed a call option alongside the conversion option in the convertible bond, making them callable convertible bonds.






An example:   Proposed ICUL of Aeon Credit

http://www.bursamalaysia.com/market/listed-companies/company-announcements/5374537

Summary of proposed ICUL (Convertible Bond) of Aeon Credit

1.  Proposed right issue to raise RM432,000,000, represented by the 432,000,000 ICULS to be issued.

2.  The coupon rate for the ICULS will be a minimum of 3.5% per annum, payable on an annual basis (“ICULS Coupon Rate”).

3.  The ICULS holders can convert their ICULS held into new ACSM Shares anytime from and including the date of issuance of the ICULS (“Issue Date”) up to its maturity date, which is the third (3rd) anniversary of the Issue Date (“Maturity Date”). 

4.  Any ICULS which are not converted would be mandatorily converted into new ACSM Shares on the Maturity Date.

5.  The conversion price for the ICULS has not been fixed.

6.  The Board shall determine the ICULS conversion price, taking into consideration the following: 

(i) the theoretical ex-all price (“TEAP”) per ACSM Share taking into account the Proposals, calculated based on the 5-market day volume weighted average market price (“VWAMP”) up to the date immediately preceding the Price Fixing Date;

(ii) the then prevailing market conditions; and

(iii) the final ICULS Coupon Rate and pricing for rights issue exercises. 

7.  In any event, the ICULS conversion price shall be determined at a minimum of 15.0% discount to the TEAP as calculated in (i) above.

[Comments:

Benefits for the issuer:

• Using ICULS, the company, Aeon Credit, would be able to raise fund by paying a lower coupon rate of 3.5% per annum.  
• The issuer also embed a call option along side the conversion option in the ICULS; any ICULS that are not converted before the Maturity Date would be mandatorily converted into new ACSM shares on the Maturity Date.

Benefits for the investors:

• The company has proposed that the ICULS conversion price shall be determined at a minimum of 155 discount to the TEAP (theoretical ex-all price) as calculated in (i) above.  Thus, the investors benefit by buying with a discount to the prevailing mother share price.
• The investors of the ICULS hope to benefit from price appreciation of the issuer's stock.]

MULTIPLE PROPOSALS AEON CREDIT SERVICE (M) BERHAD ("ACSM" OR THE "COMPANY") I) PROPOSED BONUS ISSUE; AND II) PROPOSED RIGHTS ISSUE (COLLECTIVELY REFERRED TO AS THE "PROPOSALS").

AEON CREDIT SERVICE (M) BERHAD

Type	Announcement
Subject	MULTIPLE PROPOSALS
Description	AEON CREDIT SERVICE (M) BERHAD ("ACSM" OR THE "COMPANY") I) PROPOSED BONUS ISSUE; AND II) PROPOSED RIGHTS ISSUE (COLLECTIVELY REFERRED TO AS THE "PROPOSALS").
On behalf of the Board of Directors of ACSM, CIMB Investment Bank Berhad wishes to announce that the Company proposes to undertake the following: (i)  Proposed bonus issue of 72,000,000 new ordinary shares in ACSM (“Bonus Shares”) at an issue price of RM0.50 each on the basis of 1 bonus share for every 2 existing ACSM ordinary shares (“ACSM Shares”) held (“Proposed Bonus Issue”); and (ii)  Proposed renounceable rights issue of 3-year minimum 3.5% irredeemable convertible unsecured loan stocks (“ICULS”) on the basis of 2 ICULS for every 1 existing ACSM Share held to raise RM432,000,000 in cash (“Proposed Rights Issue”). (collectively referred to as the “Proposals”) Please refer to the attachment for the full text on the announcement of the Proposals. This announcement is dated 23 March 2017. AEON CREDIT SERVICE (M) BERHAD (“ACSM” OR “COMPANY”) (I) PROPOSED BONUS ISSUE OF 72,000,000 NEW ORDINARY SHARES IN ACSM (“BONUS SHARES”) AT AN ISSUE PRICE OF RM0.50 EACH TO BE CAPITALISED FROM THE COMPANY’S RETAINED EARNINGS ON THE BASIS OF 1 BONUS SHARE FOR EVERY 2 EXISTING ACSM ORDINARY SHARES (“ACSM SHARES”) HELD (“PROPOSED BONUS ISSUE”); AND (II) PROPOSED RENOUNCEABLE RIGHTS ISSUE OF 3-YEAR MINIMUM 3.5% IRREDEEMABLE CONVERTIBLE UNSECURED LOAN STOCKS (“ICULS”) ON THE BASIS OF 2 ICULS FOR EVERY 1 EXISTING ACSM SHARE HELD TO RAISE RM432,000,000 IN CASH (“PROPOSED RIGHTS ISSUE”) Proposed Rights Issue 2.2.1 Details The Proposed Rights Issue will be undertaken after the completion of the Proposed Bonus Issue. As mentioned in Section 2.1.1 of this announcement, the Proposed Rights Issue is not conditional upon the Proposed Bonus Issue, and in the event that the Proposed Bonus Issue is not completed for whatsoever reason, subject to obtaining all relevant approvals, the Proposed Rights Issue will be implemented. The Proposed Rights Issue, to be undertaken on a renounceable basis, involves the issuance of 432,000,000 ICULS at 100% of its nominal value of RM1.00 each in cash on the basis of 2 ICULS for every 1 existing ACSM Share held by the Company’s shareholders (“Entitled Shareholders”) whose names appear in ACSM’s ROD as at the close of business on an entitlement date to be determined by the Board and announced later (“ICULS Entitlement Date”) after the completion of the Proposed Bonus Issue. In the event that the Proposed Bonus Issue is not completed for whatsoever reason, the Proposed Rights Issue shall be undertaken on the basis of 3 ICULS for every 1 existing ACSM Share held. The Proposed Rights Issue will raise RM432,000,000 for the Company from the issuance of a total of 432,000,000 ICULS under the Proposed Rights Issue. The Proposed Rights Issue is renounceable in full or in part. This means that the Entitled Shareholders can subscribe for or renounce their entitlements to the ICULS in full or in part. Any ICULS not subscribed or not validly subscribed for shall be made available for excess applications by the Entitled Shareholders or their renouncee(s)/transferee(s).The Board intends to allocate such excess ICULS in a fair and equitable manner on a basis to be determined later by the Board. The ICULS will be provisionally allotted to the Entitled Shareholders on the ICULS Entitlement Date. Any fractional entitlements of ICULS under the Proposed Rights Issue will be disregarded and shall be dealt with in the Board’s absolute discretion in such manner as it deem fits and in the best interests of ACSM. The coupon rate for the ICULS will be a minimum of 3.5% per annum, payable on an annual basis (“ICULS Coupon Rate”). The final ICULS Coupon Rate shall be reflected in the circular to the Company’s shareholders seeking their approval for the Proposed Rights Issue at an extraordinary general meeting to be convened (“EGM”). The ICULS will be constituted by a trust deed to be executed between ACSM and an appointed trustee for the benefit of the ICULS holders. The indicative principal terms and conditions of the ICULS are set out in Appendix I of this announcement. 2.2.2 Basis of determining and justification for the ICULS issue price and ICULS conversion price The ICULS will be issued at its nominal value of RM1.00 each. The nominal value was fixed after taking into account the aggregate proceeds of RM432,000,000 to be raised from the Proposed Rights Issue, represented by the 432,000,000 ICULS to be issued. Due to the timeframe to implement the Proposed Rights Issue and the potential share price movement of the ACSM Shares during this period, the conversion price for the ICULS has not been fixed. The ICULS conversion price will be determined on the price-fixing date to be announced at a later date (“Price Fixing Date”) after receipt of all relevant approvals but prior to the ICULS Entitlement Date. The Board shall determine the ICULS conversion price, taking into consideration the following: (i) the theoretical ex-all price (“TEAP”) per ACSM Share taking into account the Proposals, calculated based on the 5-market day volume weighted average market price (“VWAMP”) up to the date immediately preceding the Price Fixing Date; (ii) the then prevailing market conditions; and (iii) the final ICULS Coupon Rate and pricing for rights issue exercises. In any event, the ICULS conversion price shall be determined at a minimum of 15.0% discount to the TEAP as calculated in (i) above. For illustration purposes only and taking into account the 5-market day VWAMP per ACSM Share up to 22 March 2017, being the market day immediately preceding the date of this announcement of RM16.24 resulting in a TEAP of RM10.48 and assuming a discount to TEAP of 15.0%, the illustrative conversion price of the ICULS is RM8.91 per new ACSM Share after taking into account the completion of the Proposed Bonus Issue (“Illustrative ICULS Conversion Price”). Using the Illustrative ICULS Conversion Price and for illustration purposes only, a total of 48,484,848 new ACSM Shares will be issued upon full conversion of the ICULS. This represents 18.3% of the Company’s enlarged share capital after the completion of the Proposals. 2.2.3 Ranking of the new ACSM Shares arising from the conversion of ICULS The new ACSM Shares to be issued arising from the conversion of the ICULS shall, upon allotment and issuance, rank equally in all respects with the existing ACSM Shares, save and except that they will not be entitled to any dividends, rights, allotments and/or any other distributions that may be declared, made or paid where the entitlement date is before the allotment date of the new ACSM Shares. Based on the terms of the ICULS, the ICULS holders can convert their ICULS held into new ACSM Shares anytime from and including the date of issuance of the ICULS (“Issue Date”) up to its maturity date, which is the third (3rd) anniversary of the Issue Date (“Maturity Date”). Any ICULS which are not converted would be mandatorily converted into new ACSM Shares on the Maturity Date. 2.2.4 Status of ICULS The ICULS shall constitute direct, unconditional, unsecured and unsubordinated obligations of ACSM and subject to the provisions contained in the trust deed, at all times rank equally, without discrimination, preference or priority between themselves and all present and future direct, unconditional, unsecured and unsubordinated debts and obligations of ACSM except those which are preferred by law.

Calculating Intrinsic Value

Free Cash Flow of Firm

FCFF = CFO - Capex
Enterprise Value = FCFF / WACC
Enterprise Value = Equity Value + Net Debt
Equity Value = Enterprise Value - Net Debt


Free Cash Flow of Equity

FCFE = CFO - Capex + Net Debt
Equity Value = FCFE / Required rate of return on equity


Equity Value = Intrinsic Value


Investors compare this Equity Value to the Market Value in their investing.

Market Value > Equity Value = Overvalued
Market Value = Equity Value = Fair Value
Market Value < Equity Value = Undervalued



Additional Notes:

Assuming there is no preferred stock outstanding:

Interest*(1–t) is the firm's after-tax interest expense

If company has zero debt, its FCFF = FCFE

Using Free Cash Flow to Equity to derive the Equity or Intrinsic Value of a Stock

Free cash flow to equity

From Wikipedia, the free encyclopedia

In corporate finance, free cash flow to equity (FCFE) is a metric of how much cash can be distributed to the equity shareholders of the company as dividends or stock buybacks—after all expenses, reinvestments, and debt repayments are taken care of. Whereas dividends are the cash flows actually paid to shareholders, the FCFE is the cash flow simply available to shareholders.^[1][2] The FCFE is usually calculated as a part of DCF or LBO modelling and valuation. The FCFE is also called the levered free cash flow.

Contents

  [hide] 

• 1Basic formulae
• 2FCFF vs. FCFE
• 3Negative FCFE
• 4Use
• 5References
• 6External links

Basic formulae[edit]

Assuming there is no preferred stock outstanding:

${\displaystyle FCFE=FCFF+Net\ Borrowing-Interest*(1-t)}$

where:

• FCFF is the free cash flow to firm;
• Net Borrowing is the difference between debt principals paid and raised;
• Interest*(1–t) is the firm's after-tax interest expense.^[3]

or

${\displaystyle FCFE=NI+D\&A-Capex-\Delta WC+Net\ Borrowing}$

where:

• NI is the firm's net income;
• D&A is the depreciation and amortisation;
• Capex is the capital expenditure;
• ΔWC is the change in working capital;
• Net Borrowing is the difference between debt principals paid and raised;
• In this case, it is important not to include interest expense, as this is already figured into net income.^[4]

FCFF vs. FCFE[edit]

• Free cash flow to firm (FCFF) is the cash flow available to all the firm’s providers of capital once the firm pays all operating expenses (including taxes) and expenditures needed to support the firm’s productive capacity. The providers of capital include common stockholders, bondholders, preferred stockholders, and other claimholders.
• Free cash flow to equity (FCFE) is the cash flow available to the firm’s common stockholders only.
• If the firm is all-equity financed, its FCFF is equal to FCFE.

Negative FCFE[edit]

Like FCFF, the free cash flow to equity can be negative. If FCFE is negative, it is a sign that the firm will need to raise or earn new equity, not necessarily immediately. Some examples include:

• Large negative net income may result in the negative FCFE;
• Reinvestment needs, such as large capex, may overwhelm net income, which is often the case for growth companies, especially early in the life cycle.
• Large debt repayments coming due that have to be funded with equity cash flows can cause negative FCFE; highly levered firms that are trying to bring their debt ratios down can go through years of negative FCFE.
• The waves of the reinvestment process, when firms invest large amounts of cash in some years and nothing in others, can cause the FCFE to be negative in the big reinvestment years and positive in others;^[5]
• FCFF is a preferred metric for valuation when FCFE is negative or when the firm's capital structure is unstable.

Use[edit]

There are two ways to estimate the equity value using free cash flows:

• Discounting free cash flows to firm (FCFF) at the weighted average cost of capital (WACC) yields the enterprise value. The firm’s net debt and the value of other claims are then subtracted from EV to calculate the equity value.

Enterprise Value EV = FCFF/WACC

Enterprise Value EV = Equity Value + net Debt

Equity Value = Enterprise Value EV - net Debt

• If only the free cash flows to equity (FCFE) are discounted, then the relevant discount rate should be the required return on equity. This provides a more direct way of estimating equity value.

Equity Value = FCFE/required return on equity

• In theory, both approaches should yield the same equity value if the inputs are consistent.

Notes:

Equity Value = Intrinsic Value of the Company

FCFF / WACC = Enterprise Value
Enterprise Value = Equity Value + Net Debts
Equity Value = Intrinsic Value of the stock = Enterprise Value - Net Debts

FCFE = CFO - Capex + Net Debts
Equity Value = Intrinsic Value of the stock = FCFE/required rate of return on equity
Equity Value < Market Value = Overvalued

Equity Value = Market Value = Fair Value
Equity Value > Market Value = Undervalued

https://en.wikipedia.org/wiki/Free_cash_flow_to_equity

The Free-Cash-Flow to-Equity (FCFE) Model

Many analysts assert that a company's dividend-paying capacity should be reflected in its cash flow estimates instead of estimated future dividends.

FCFE is a measure of dividend paying capacity.

It can also be used to value companies that currently do not make any dividend payments.

FCF can be calculated as:

FCFE = CFO - FC Inv + Net borrowing


Analysts may calculate the intrinsic value of the company's stock by discounting their projections of future FCFE at the required rate of return on equity.




Reference:

https://en.wikipedia.org/wiki/Free_cash_flow_to_equity

Valuation of Common Stock with Temporary Supernormal Growth

The correct valuation model to value such "supernormal growth" companies is the multi-stage dividend discount model that combines

• the multi-period and 
• infinite-period dividend discount models (Gordon Growth Model).

Value
= Multi-period DDM + Infinite Period (constant growth) DDM
= D1/(1+k)^1 + D2/(1+k)^2 + ..... + Dn/(1+k)^n + Pn/(1+k)^n


Dn = Last dividend of the supernormal growth period
Dn+1 = First dividend of the constant growth period.
Pn = Dn+1 / (k-g) = PV at time n+1 of Dn at a Constant rate of Growth.

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