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FINANCE ACCOUNTING
===CHAPTER - 2===

Chapter:2 COST OF CAPITAL
A company may raise long term finance from various sources such as : Long term debts, Equity share capital, preference share capital and retained earnings. Capital is a ascarce source, hence raising the funds from various sources. But the cost of capital depends upon the risk incidence born by the provider of finance.

Specific Cost Of Capital
The cost of each component of long term finance is termed as specific or component cost of capital. Cost is denoted as K.

1. Cost of Debt(Kd) 2. Cost of preference shares(Kp) 3. Cost of equity (Ke) 4. Cost of retained Earnings (Kre)

Cost of Debt, cost of preference shares and cost of equity are called external finance or explicit cost. cost of retained earnings is called internal finance or implicit cost.

Explicit Cost
This is the cost associated with raising of external finance. The external finance cash inflows are received by a firm on which it pays cash outflows. The Explicit cost is related to extra cash flows that result from the raising of such external finance.

Implicit Cost
It is the implied cost of the opportunity cost of investors shareholders that they are required to incur or lose on account of the company/firms retaining the earnings and not distributed it as dividends amongst the shareholders

1. Cost of Debt(Kd)
A company may raise debt funds by taking loans or issuing debentures or bonds or accepting public deposits, etc. The providers of debt funds expect to receive/earn interest on the amount loaned by them. This interest is their income and cost for the company pays them. There is a need of computing an effective rate of debt cost to the company on annual basis. The computation of cost of debts depends upon the fact that the debt is the redeemable or irredeemable. The basic principle of computing effective post tax Kd (in case income tax is applicable) is the same. The annual cost to the company is the numerator and the funds to be utilized by the company over its lifetime in denominatior.

A. Cost of Irredemable/perpetual debt = I(1-t)/NP
Q.1) Compute Kd for x ltd if it is issuing 12% debentures of Rs. 100 each 100000 in numbers. ignore Income Tax. Soln: Kd = I/P             I = amount of annual interest            P = price of debt instrument          100000 * 100 = 10000000          (1200000/10000000) * 100 = 12%

Q.2) Presuming in Q.1, the debentures are issued at a discount of 10%.  Soln: 100000 * 90 = 9000000              (1200000/9000000) = 13.33%

Q.3) Premune in Q.1, the debentures are issued at a discount of 5% and floataion cost of issue is 4% of issue price.   Soln: Kd=I/P               = 1200000/(9500000-380000)               = 13.5%

Floatation Cost
It is the cost associated with the floating/making the issue of securities and includes expenses such as :- printing cost of prospectus and application forms, advertisement cost, brokerage, legal fees in regard to making the issue, underwriting commissing, etc.

Notes: In case percentage of floatation cost is given andd it is not mentioned as to this percentage is tobe applied on issue price or face value, then give a note that the percentage of floatation cost is being applied to issue price.

Q.4) Y ltd is issuing debentures of coupon rate(rate of interest) 13.5%. Numbers of debentures being issued is 200000. Face value of debentures is rs. 100. The debentures are being issued at a premium of 5%, the floatation cost is rs. 500000. Compute Kd. Soln: Kd=I/NT            =13.5/105-2.5            = 2700000/(21000000-500000)            = 13.17%

Role of Income Tax computation of Kd
Interst is a tax deductable expense. interest is allowed as an expense and after deducting interest expense, the remaining income will be chargeable to income tax. Hence, it can be said that interest expense saves tax. While computing effective cost of debt, this feature of tax savings on interest will be taken to consideration. The cost of irredeemable/perpetual debt can be said to be post tax annual interest expense in relation to net proceeds on the amount which is to be utilized by the firm/company in perpetuity or forever. Ke = I(1-t)/NP where, I = amount of interest expense. t = corporate income tax rate NP = net proceeds or issue price net of floatation cost

B. cost of Redeemable debt
The equation used for computing cost of redeemable debt is different from the equations used for computing cost of irredeemable debt, the fact that the principle amount is to be repaid at the end of a fixed pre defined maturity affects the annual cost of debts. Kd = [I(1-t)+(RV-NP/n)]/[(NP+RV)/2] where, RV=Redeemable Value NP=Net Proceeds n=number of years

Q.1) P lts is issuing rs. 50000000 worth debentures (500000 debts of rs.100 each) at par. Their debentures are redeemable at the end of 10 years at par. The coupon rate payable is 1250 basis points, the company is in an income tax braket of 40%. Compute post tax Kd.  Soln: Kd = I(1-t)/NP             = 12.5(1-0.4)/100             = 7.5%

Q. G ltd is issuing Rs.100 debentures; 400000 in number at a premium of 4%, the debentures a coupon rate of 1100 basis points. Floatation cost is 2% of issue price. The company is in a tax bracket of 30%. compute Kd. Soln: Kd = I(1-t)/NP = 11(1-0.3)/104-2.08                = 7.7/101.92                 = 7.55%

Q.71) Chap ltd. issues 12% debentures of face value Rs.100 each and realise Rs. 95 per debenture. The debenture are redeemable after 10 years at a premium of 10%. Calculate the cost of capital presuming income tax rate is 50%. Soln: Kd = [I(1-t)+(RV-NP)/n]/[(NP+RV)/2]                  = [12(1-0.5)+(110-95)/10]/[(95+110)/2]                  = (6+1.5)/102.5                  = 7.32%

Optimal Choice of Debt
If a firm can obtain debt funds from more than 1 debt providers, then chose the one having least effective post tax Kd.

2. Cost of preference Shares
Preference shares carry a fix rate of dividends which are not tax deductible. The cost of preference shares(Kp) are computed in the same manner as computation of cost of debt with an exception that interest on debt is a tax deductible expense, whereas preference dividends are not.

A. Cost of irredeemable preference shares
In india issue of irredeemable preference shares is prohibited but internationally, in most of the western countries issue of perpetual preference share is allowed by law. The cost of irredeemable preference share is computed as follows:- Kp=D/NP D = amount of annual preference dividends NP = net proceeds or issue price net of floatation costs.

B. Cost of redeemable preference shares
The cost of redeemable preference shares is also computed in the same manner as computation of cost of debts with an exception that preference shares are payable instead of interest and such dividends are not tax deductable. Kp = [D+(RV+NP)/n]/[(NP+RV)/2]

where, D = Amount of preference dividends RV = Redeemable Value NP = Net Proceeds n = number of years to maturity

3. Cost of Equity(Ke)
Unlile debt and preference share capital, equity shares do not require any fixed payments to be made to equity shareholders. Thus there is no single model acceptable by all analysts as to computation of cost of equtiy. Equity shareholders are the owners of the company and the equity capital is the permanent source of long term funds. The basic objective of financial management is maximisation if wealth of equity sharholders. There are several methods/models of determining the required rate of return of equity shareholders. These are: 1. Dividends Price Model/Dividends Yield Model 2. Earning Price Model/Earnings Yield Model 3. Dividends Growth Model/Dividends Discount Model/Gordon Model 4. Earnings Growth Model 5. Capital Assets Pricing Model 6. Realised Yield Model

1. Dividends Price Model
According to this model, the equity shareholders expect to earn dividends each year (a fixed amount) in relation to the market value of the equity share. This model consider the basic principle of return on investment from the point of view of an equity investor. The market price per share is invested by an investor to earn dividends return. i.e. ke = DPS/MPS

Assumptions
This model assumes that DPS( Dividends Per Share) and MPS(Market price Per Share) will remain constant forever.

Q. Number of equity shares = 1000000 Face value of Equity shares = Rs. 10     MPS = Rs. 25     Total Equity Dividends = Rs. 5000000 Compute Ke using dividends price mode.

Soln: Ke = DPS/MPS = 5/25             = 20%    DPS = 5000000/1000000 = Rs. 5

2. Earnings Price Model
According to this model, an equity shareholder expects the entire earnings available for equity shareholder whether distributed or not. The desired returns of equity shareholders is the rate of EPS in relation to MPS.

Ke = EPS/MPS

Assumption
Thos model assumes that the business risk of a firm remains constant and hence the relationship between EPS and MPS remains constant.

3. Dividends Growth Model/Gordon Model
According to Myron Gordon, the long term equity investors expect to receive dividends every year. These dividends should grow annually as the same rate as the growth rate in earrnings of the company. Further the equity shareholders expect a capital growth or growth in the market value of equity shares. The expectation of equity shareholders or equity capitalisation rate (Ke) is hence the sum of annual dividends yield and capital growth.

Ke = (D1/P0) + g

where, D1 = Dividends to be paid at the end of the year/ Next expected dividends/ Dividends payable at the end of the year 1/ Dividends payable at the end of current year/ Dividends payable at the beginning of the next year/ Dividends payable out of current year's expected earnings. P0 = Market price Per Share now or at the beginning of current year or today or at 0 period. g = Growth rate of company/ Growth rate in Earnings of company/ Growth rate in Dividends of a company/ capital Growth rate/ Growth rate of market proice of Equity Share.

D1 = E(1-b) where; E = Expected earnings for current year. b = retention ration or 100 - dividends payout ratio/ proportion of earnings desired to be retained by the company for making new investments.

D1 = D0 (1 + g) where; D0 = dividends at 0 period/ Dividends now/ Dividends Just paid/ Dividends paid at the beginning of current year/ Dividends paid at the end of previous year/ Dividends paid out of previous year's earnings.

Assumptions
1. That the firm has infinite life. 2. That the business risk complexion of the firm remains constant. In other words, the rate of return on investment for equity (r) and equity capitalisation rate (Ke) remains constant even after making fresh investments. 3. That the growth rate of a firm is the product of retention ration (b) and rate of return on Investment for equity (r). g = b * r 4. That there are no external sources of finance available for new investments to be made by the firm and only internally generated funds or retained earnings are available for exploiting the new investment opportunity. 5. That the equity capitalisation rate or Ke is more than the growth rate of the firm or g.    Ke > g

Determination of annual growth rate using data of part earnings/dividends/market price:-
Q.1) Years      2010       2011            EPS           20            22 Soln: g[(22-20)/20] = 10%

Q.2) Years      2005       2007            EPS           10          12.1 Soln: DPS (1+g)^2 = DPS             10(1+g) = 12.1                  g = 10%

Q.3) Years       2001        2004           DPS            26             30 Soln: DPS (1+g) ^3 = DPS             26 (1+g)^3 = 30                 (1 + g)^3 = 1.15 Reference to table C (compound value of Rs.1 table) for year 3 gives us:  Growth Rate                  Compound Value         4%                                1.1257, 0.029         5%                                      1.1587     __________                     _____________________        1%                                         0.033

g = 4% + [1% * (0.029/0.033]                   = 4.878%

4. Earnings Growth Model
According to this model, the expectation of Equity shareholders is the sum of earnings tield and capital growth. The equity shareholders are expecting the entire earnings whether distributed or not. Apart from this, they desire capital growth also. Ke = (EPS/MPS) + g Where; EPS = Expected Earnings Per Share for current Year. MPS = Market Price Per Share at the beginning of the year g = capital growth

Assumptions
1. That the firm has infinite life. 2. That there are no external sources of finance available for making new investments only retained earnings will finance new investments. 3. That the business rise complexion remains constant even after making new investments (r and Ke remain contant). 4. That the growth is the product of rtention ratio (b) and the rate of Return On Equity (r). g = b * r

Capital Asset Pricing Model(CAPM)
CAPM was primarily developed by William Sharpe.However, Jan Morrin and John Linter also made their independent contribution towards the development of CAPM in 1990, William Sharpe, Hardy markowitz and Merton Miller shared the Nobel Prize of Economics for their contribution towards the development of CAPM.

According to CAPM, the risk associated with capital assets/securities can be related in a Linear manner with the required rate of return of the investors. CAPM categories risk into 2 types:

1. SYSTEMATIC RISK
It is the risk associated with the entire stock market and hence is non diversible. Each security listed in the stock market is affected by the changes in factors such as : change in general state of econony (BOOM, recession; normal), changes in political conditions of the country etc. However, the levek of effect on each company may differ some companies may be more sensitive to market changes and some of them may be less sensitive.

2. Unsystematic Risk
It is the company/industry. Specific risk does not affect the entire stock market, unsystematic risk can be reduced through diversification as we add more stocks into our portfolio ( investment), the unsystematic risk gets reduced. Factors which may affect the company/ industry only losing of legal suit in court, fire in factory, strike, ill health of key persons of company, ban on use of some products, ban on issuing of license, etc.

CAPM EQUATION
Required Return of Investors(Ke) Time value of money + Risk Premium on Asset Risk Free      +       ß(expected return of Market Risk free return)

Ke = Rƒ + ß[ER(M) - Rƒ]

Determination of required Rate Of Return or Ke with the help of CAPM
According to CAPM, the required rate of return of equity investors depends upon the level of systematic risk of the underlying capital asset. Higher the systematic risk, higher the rate of Return. CAPM requires the investors desired rate of Return to be consisting of 2 parts.

1. Risk free Rate of Return(Rƒ)
This is the rate of interest on RBI/central bank's treasury bills. The investors desire to be compensated for parting with their money spent to purchase the share at the beginning of any year. The risk free rate of interest represents the compensation to investors on account of time value of money.

2. Risk Premium on account of systematic risk incidence on the portfolio of their assets/Portfolio or capital Assets Risk Premium::: ß[ER(M) - Rƒ]
Beta is a measure of systematic risk. It is computed in times. ß = 2 implies that the risk or sensitivity or movement or deviation of an asset is twice of the risk or sensitivity or movement or deviation in relation to the market movement. ß = 0.5 implies that the movement of the capital asset is half in relation to the market movement. ß = 1 implies that the movement of the asset is equal in relation to the market movement ß of a risk free asset is 0. An investor desores risk premium on his capital asset (in addition to risk free return), in accordance with the level of systematic risk (ß) of his underlying asset. The risk premium on his asset is the product of Beta coefficient of his asset and the market risk premium.

Ke = Rƒ + ß[ER(M) - Rƒ]

where; Rƒ = Risk Free rate of Return / Risk of interest on Treasury Bills. ß = Beta coefficient or Risk Index or systematic risk or sensitivity of asset in relation to sensitivity of market. ER(M) = Expected return of Market or Mean Return on Market.

[ER(M) - Rƒ] = Market Risk Premium

Security Market Line(SML)
The graphical representation of CAPM equation is termed as SML. Beta coefficient (ß) is plotted on the horizontal (x- axis) and rate of return (Ke) is plotted on the vertical (y-axis). Higher the ß, higer the Ke. Ke is a linear function of Beta and this straigt line showing relationship between ß and Ke is SML. The starting point of SML is risk free rate of Return.

Determination of Rƒ, ER(M) and ß
Rƒ = It is the mean risk free return. It is usually computed by averaging past annual risk free rate of return for a number of years.

ER(M) = It is the mean of market rate of return. It is usually computed by averaging past annual market rate of return for a number of years.

ß(asset) = [(σ(asset) * γ(asset*market)]/σ(market)

σ(asset*market) = coefficient of correlation between asset and market.

Computation of Return on Investment in a Share
R(i) = [(P1 - P0) + D1] / P0

Computation of Mean Returns from Expost data
_                                                         Χ = [(X1 + X2 + X3 + .......... + Xn)/n]

Computation of Standard Deviation and Variance with the help of expost data
_            _               _                         _  Variance of X = [(x1-x)² + (x2-x)² + ..... + (xn-x)²] ÷ n

σx = (Variance)½

Computation of Covariance of X and Y
Covariance of xy = [(x1-x)(y1-ӯ) +....+ (xn-x)(yn-ӯ)]/n

Computation of correlation between x and y
γx  =  [Covariance of xy /  σx * σy]

Computation of Beta of a company as a whole where the company carries out more that one type of business having its own beta
Beta of company as a whole is the weighted average where weights are determined on the basis of amount of equity investments in each business.

Weighted Avegare Cost of Capital(WACC) / Overall cost of Capital (Ko)
A company raises funds from various sources, such as: debt, preference capital and equity capital. The specific/component cost of capital of each source is computed separately and is dependent upon risk incidence of each source. The combined/Overall/average cost of capital of Overall/Total funds is WACC.

If any instrument are to be made, the investment will be made out of the pool of funds. The weights to be taken for computing WACC are the proportion of funds of each source of finance in the total/overall capital employed.

Steps for Computing WACC
1. Compute specific cost of capital of each source of finance (i.e., compute Kd, Kp, Ke, Kre). 2. Determine the weight/proportion of funds raised from each source of finance. 3. Compute the overall cost of capital as follows:-

Source-of-Finance    Amount     weight     Cost-of-Capital              WACC Equity                        50 L             0.5              16%                            8% Preference Capital         30 L             0.3              12.5%                       3.75% Debt. 20 L            0.2                 9%                          1.80%

OR

Ko = (Ke*WE)+(Kp*WP)+(Kd*WD) = (16% * 50/100) + (12.5 * 30/100) + (9% * 20/100)        = 13.55%

Use of Ke for computing Ko
Usually Dividends Growth Model and CAPM are preferred to be used for computation of Ke. In case information of any one of these models is given, then use this model for determining Ke and finally computation of Ko. However, if information of both models (ie. CAPM and Dividends growth model) is given and no single model is preffered in the question specifically, then use average Ke, computed with the help of both these models for computation of Ko.

Optimal Capital Structure
The basic objective of financial management is maximisation of wealth of equity shareholders. A capital structure is said to be optimal if it helps in fulfillment of this objective. An optimal capital structure is one which minimises the overall cost of capital or Ko and maximises the market value of equity shares.

Cost of Debt
If the term cost of debt is given in the problem, then assume it to be pretax cost or interest rate. If post tax or effective cost of debt is given, then the computation of tax saving on debt is not required to be made.

Computation of Cost of Equity when Net Proceeds(NP) are known
The expectation of equity shareholder is in accordance with the market price payable by him/her, but the cost to the company is in accordance with Net Proceeds receivable by it.

Net Proceeds = Issue Price or sale price net of floatation cost today/now.

Cost of Retained Earnings(Kre)
Usually the companies retain a part of their earnings and reinvent them for future expansion of business, diversification and growth. Often, people believe that retained earnings being internally generated funds or being the profits retained have no cost. However, this being a misconception. When a company retains earnings, these earnings basically belongs to the equity shareholders who expects to reinvest this money themselves if it were not retained and were distributed amongst the shareholders. Also, the company shall be required to raise funds from outside if these earnings were not retained. Thus there is an implicit cost or implied cost of earnings retained by the company which is equal to the opportunity cost or required rate of return of equity shareholders.

NOTE : Always remember that Kre will be either to Ke or less than Ke as it does not involve any incurrence of floatation costs.

The Kre is computed with the help of same model as are used for computation of Ke.

Earnings Price/Yield Model
Kre = EPS/MPS

Dividends Price/yield model
Kre = DPS/MPS

Dividends growth/discount Model
Kre = D1/P0 + g

Earnings Growth Model
Kre = EPS/MPS + g

CAPM
Kre = Rƒ +β[ER(M) - Rƒ]

Impacts of Dividends Distribution Tax(DDT) / Corporate Dividend Tax(CDT) on consumption of Kp, Ke and Kre
As per section 115 - 0 of Income Tax Act,1961, a company shall be required to pay DDT on the amount of dividends to be distributed by it among its shareholders (both equity dividends and preference dividends) at the rate prescribed in the said act.

Impact on Cost of Irredeemable Preference Shares
Kp = [D(1 + CDT rate)] ÷ NP/MPS

Impact on cost of Redeemable Preference Shares
Kp = [D(1+CDT rate) + (RV-NP)/n] ÷ [(NP + RV)/2]

Dividends Yield Model
Ke = [DPS(1 + CDT rate)] ÷ (NP/MPS)

Dividends Growth Model
Ke = [D1 (1 + CDT rate) g] ÷ (NP/Po)

Dividend Yield Model
Kre = [DPS (1 + DDT rate)] ÷ MPS

Dividends Growth Model
Kre = [D1(1 + DDT rate) ÷ Po] + g

Market Price to be taken into consideration while computing Kp, Kd, Ke (when NP is not known) and Kre
The appropriate market price to be taken into consideration is Ex-Interest/Ex-Dividends Market Price. in case the problem under consideration takes into account (i.e gives the cum Interet/cum Dividend Market Price, then reduce the Interest) dividends amount therefrom in order to determine ex-Interest/ex-dividends Market Price.

Choice of weigts to be used for computation of overall cost of capital
Usually, after computation of specific cost of capital of each source of finance(i.e, Kd, Kp, Ke, Kre), the next step is to determine the proportion or weight of each source of finance in relation to the overall/total finance. There are two methods of determining the weights to be taken into consideration:-

Book value weights/Accounting Value Weights/Balance Sheet value weights
This method takes into consideration the information from balancesheet of the company. Book value are easily computed with reference to latest drawn BalanceSheet. However, the use of Book Value weights should be made only when the market value data all sources of finance is under unavailable or unrealisable or ineffective.

Market Value Weigts
The book Values are not related to the present economic value of each component/source of finance. The market value are consistent with the concept of the wealth (i.e, market value of the company). The market values are the present economic values of various source of finance which can be arranged from the stock exchange where the security of the company are listed. Market values show the present expectation of investors. However, such weigts cannot be calculated in case of private limited company and unlisted public ltd company. Also market value is used should be avoided if the market value of all sources of finance is not given in the problems(unless it is specifically mentioned in the problem to use market value weights).