Dividend Formulas

Dividend Formulas

Dividend is an important aspect of equity market (stock market) investment. Therefore dividend is used in couple of important calculation i.e. share price valuation, cost of equity etc. Dividend formulas for various calculations have been given below.

Share Valuation (Zero Dividend Growth) Formula

The following formula is known as dividend discount model. Share value is determined by discounting the future dividend using the cost of equity as discounting factor. This basic concept of dividend discounting has been further classified into two formulas i.e. Dividend without Growth and dividend is growing at constant pace).

Share Price = Do                                 Ke

Do= Dividend

Ke= Cost of equity

Share Valuation Example (Zero Growth of Dividend)

Dividend (Current Year) = .9

Dividend Growth Expectation = No Growth

Cost of equity=13%

Solution

=.9/.13

=6.92 (Share Price)

 Share Valuation (Constant Dividend Growth) Formula

Share Price = Do ( 1+g)                                    Ke-g

Do= Dividend

Ke= Cost of equity

g= Dividend Growth

Share Valuation Example (Constant Growth)

Current year announced dividend = .9

Dividend Growth Expectation   =    5%

Cost of equity=13%

Solution

Share Price = Do ( 1+g)        

                       Ke-g

Do=Current Dividend

Ke =Cost of equity

g= Dividend Growth

Share Price = .9(1+5%)

                     13%-5%

Share Price = .9(1+05)

                       .08

Share Price = 11.8

Cost of Equity – (Zero Growth or Constant Dividend)

The following formula is used to calculate Cost of equity, where there is zero growth of dividend.

Cost of Equity =    Do                                    Po

Do= Dividend

Po= Market Share price

Constant Dividend and Cost of Equity

ABC Company Dividend = .7

Nature of Dividend= Constant

Quoted Price = 12

Solution

Cost of Equity = Constant Dividend          

                        Ex Div Market Price

Cost of Equity = .7

                        12

=5.8%

Cost of Equity (Constant Growth of Dividend)

Dividend discount model can be used to calculated cost of equity of company. The following formula is used to calculate cost of equity for constant dividend growth. This formula cannot be used for negative and random dividend growth.

Cost of Equity =[Do (1+g)] + g                                   Po

g = Dividend growth Rate

Ke = Cost of Equity

Do =Current Dividend

Po= Share price

Cost of Equity Example (Constant Growth of Dividend)

Dividend for the Year = .7

Growth rate of Dividend (Expected)   = 9%

Share price= 20

Solution

Cost of Equity =[Do (1+g)] + g                                   Po

Do=Current Dividend

Ke =Cost of equity

g= Dividend Growth

Share Price = .7(1+9%)   + 9%

                          20

Share Price = .7(1+.09) + 9%

                          20

Share Price = 12.81%

Dividend Payout Ratio Formula

Dividend payout ratio show the proportionate of earning distributed among the equity holder of shareholder. This concept has been explained in detail in my other article. Dividend payout ratio is calculated simply by dividing the dividend by the EPS (Earning per Share).

Dividend Payout Ratio =            Dividend      x100                                                        EPS

Dividend Payout Formula Example

Dividend Announced = 50 cent

Earnings per Share   = 80 Cent

Calculate Payout ratio of the company?

Solution

Dividend Payout Ratio =            Dividend during the year    

                                                     EPS or Earning

Company A = .5  x 100  

                     .8

=62.5%

Dividend Yield Formula

Dividend yield explains the return on the investment in the form of dividend. This is useful tool for many investors.

Dividend Yield =      Dividend During Year                                       Share Market Price

Dividend Yield Formula Example

Dividend Paid =8

Market Price of Share = 30

Dividend Yield?

Solution

Earning Yield = 8

                      30

= 24%

Ex Divided Share Price Formula

Ex dividend share price formula is used to calculate the share price before the payment of dividend. The ex dividend share price concept is used in dividend discount model for calculating the cost of equity. Ex Dividend price is simply calculated by excluding dividend to be paid from the share price.

Ex Dividend Price = Share Price b- Dividend (to be paid)

Ex Div Price Formula Example

Share Price (Market value) = 12

Dividend for Year = 4

Calculate Ex Div Price?

Solution

Ex Div Price = Share Price before Dividend- Dividend (to be paid)

= 12-4

=8 (Ex Div Price)

Gordon Dividend Growth Formula

Gordon dividend growth formula establishes a relationship between retention of profit and future growth of dividend (direct relationship).  Gordon says that in case of high retention of profit would result in high growth of dividend. This relationship has been explained in detail in my other article.

g=br

g= Dividend Growth

b= Profit retention proportion

r= Cost of equity

Gordon Dividend Growth Model Example

Profit Retention propionate= 60%

Cost of equity = 12%

Solution

= 60% x 12 %

=7.2% (Dividend Growth)

Simple Dividend Growth Formula

Simple dividend growth formula is used to calculate the simple growth (not compounded). There are some other growth like Gordon dividend growth and compounded dividend growth, those growth are calculated by other formulas.

Simple Dividend Growth Formula =   Current Dividend     - 1  x 100                                                                Last Dividend

Dividend Free Cash flow Ratio

Dividend free cash flow is important consideration for dividend decision. This formula explains about a link between company cash flow and its dividend.

Dividend free cash Flow Ratio =       Dividend for Year                                                                  Free Cash flow

Example

Company ABS has paid following dividend from 2001 to 2005.

Year              Earnings                      Dividend                Free cash Flow

2001             100                             20 million                40 million

2002             100                             40 million                80 million

2003             100                             30 million                60 million

Solution

Year                    Dividend                 Free cash Flow       Dividend /Free cash Flow

2001                   20 million                40 million                20/40 =50%

2002                   40 million                80 million                40/80 = 50%

2003                   30 million                60 million                30/60 = 50%

Cost of Capital Formulas

Cost of Capital Formulas

Cost of Capital Formulas can be classified into Following Formulas. It is to be noted that all three element collectively make the weighted cost of capital (WACC). The following cost of capital formulas has been explained in details in my other articles with examples.

                     Cost of Equity Formulas

                    Cost of Debt Formula

              Cost of Preference Shares

.   Cost of Equity Formulas

Cost of Equity can be calculated primarily by two methods i.e. CAPM and dividend discount model. Both methods formulas have been given below;

Dividend Valuation Model Formula –No Growth (Constant Dividend)

Cost of equity is calculated by simply dividing the dividend by market price of share.

Cost of Equity =    Do                                    Po

Do= Dividend

Po= Market Share price

Dividend Valuation Model Formula – Constant Growth

Cost of equity for company with constant growth in Dividend may be calculated by following formula,

Cost of Equity =[Do (1+g)] + g                                   Po

g = Dividend growth Rate

Ke = Cost of Equity

Do =Current Dividend

Po= Share price

Capital Asset Pricing Model:

Cost of equity can be calculated by capital asset pricing method .Capital asset pricing model takes into account the relative risk of market.

Cost of Equity= Rf + β (Rm- Rf)

Rf= Risk Free Return

Rm= Market Return

Β =Risk Factor

 2 Cost of Debt

Cost of debt can be calculated by the following formulas.

Cost of irredeemable Debt Formula

Cost of debt which will never be paid back is known as irredeemable debt. Cost of irredeemable debt is calculated by the following formula.

Cost of Irredeemable Debt Formula =    Io (1-t)                                                                            Po

Where,

Io= Interest Rate

T= Tax Rate

Po= Market value of debt (Ex interest Price)

Cost of Redeemable Debt Formula

Cost of Redeemable Debt is calculated by the Internal Rate of return formula.

Cost of Redeemable Debt=RL+ [      NPVL           ] x (RH-RL)                                                        NPVL-NPVH

R_L= Lower rate of Return

R_H= Higher Rate of Return

NPV_L= NPV with Lower rate of Return

NPV_H= NPV at higher rate of return

Cost of Preference Share

Cost of preference share can be calculated by the following formula. This formula is more like Cost of irredeemable debt, but off course with no tax shield.

Kp =     Do                  Po

Do= Dividend on preference shares

Po= Market Price of preference shares

Cost of Redeemable Debt Formula

Cost of Redeemable Debt Formula

Cost of redeemable debt formula has been given below. Cost of redeemable debt has been explained with an example.

Cost of Redeemable Debt Formula = L +(NPVL/NPVH-NPVL)x (H-L)

Where

R_L= Lower rate of Return

R_H= Higher Rate of Return

NPV_L= NPV with Lower rate of Return

NPV_H= NPV at higher rate of return

Cost of irredeemable debt process has been explained by example;

Cost of Redeemable Debt Formula Example

XYZ Quoted Rate	102
Coupon Rate	12%
Tax rate on companies	40%
Maturity	5 years

Solution

Particulars	Value	Dis. 5%	PV @ 5%	Dis. 10%	PV @ 10
Market Value	108	1	108	1	108
Interest	(7.2)	4.329	(31.172)	3.791	(27.29)
Redemption Value	(100)	.784	(78.40)	.621	(62.1)
			(1.57)		18.61

 Formula = L +(Nl/Nh-Nl)x (H-L)

 = 5% + (1.57/18.61)(7%)

 =.05+.323(.05)

 =5.59%

It is to be noted that interest rate is discounted by annuity factor, because it is a regular payment, while redemption value is discounted at straight discounting factor (at once), because it is onetime payment in five year.

Cost of irredeemable Debt

Cost of irredeemable Debt

Cost of irredeemable debt formula has been given below. Cost of irredeemable debt formula has been explained with an easy example;

Cost of irredeemable Debt Formula = Io ( 1-T)/Po

Where,

Io= Interest rate

T= Tax Rate

Po= Market value of debt (Ex interest Price)

 Cost of irredeemable Debt Formula Example

Interest Rate = 12%

Debt Value= 150

Prevailing Tax Rate =40%

Solution

Io ( 1-T)/Po

= [ 12(1-40%)]/150

=7.2/150

=4.8% (cost of Debt)

CAPM Formula

CAPM Formula

CAPM or capital asset pricing model Formula has been given below. CAPM formula has been explained with an easy example

CAPM = Rf + βe (Rm-Rf)

Rf= Risk Free Rate

Rm= Market Rate

βe = Equity Beta

Risk Free Rate

Risk Free rate is rate offered by the government on bonds. Bank offer rate in the country is also regarded as risk free rate. Risk free rate is lower than market rate due to lower risk.

Market Rate

Expected rate of return from the investment in the stock market is known as market rate or market rate of return. Market rate is expected to be higher than risk free return rate.

Application of CAPM

CAPM is used to calculate cost of equity, other important method of calculating the cost of equity is dividend valuation model. Cost of equity calculation has been explained below.

CAPM Formula Example

Stock Exchange Return Rate= 12%

Bank Risk Free Rate= 10%

Equity Beta= 1.6

Calculate Cost of equity?

Solution

= 10% + 1.6 ( 12%-10%)

=12%+1.6(2)%

=15.32%

 CAPM Formula Learning Example

Market Rate of Return= 13%

Risk Free Return (Rate)= 8%

Equity Beta= 1.3

Calculate Cost of equity?

Solution

= 8% + 1.3 ( 13%-8%)

=8%+1.3(5)%

=8% + 6.5%

=14.5%

Advantage of Using CAPM

CAPM takes into account two important concept of investment i.e. time value of money and risk. Time value of money is represented by risk free rate, while risk is represented by risk premium (premium for risk). Thus CAPM is a preferred method for cost of equity calculation.

Risk Premium = ( Rm-Rf)