Thursday, February 28, 2008

cost of capital

Cost of CapitalTapen GuptaHIM Kala Amb




Introduction
The project’s cost of capital is the minimum required rate of return on funds committed to the project, which depends on the riskiness of its cash flows.
The firm’s cost of capital will be the overall, or average, required rate of return on the aggregate of investment projects.
Minimum rate of return expected by its investor
Weighted average cost of various sources of finance used by firm
Minimum rate of return expected by investors , maintain the market value of the share at its present level
To achieve the wealth maximization
Definitions
Cost of obtaining funds
"The rate that must be earned on the net proceeds to provide the cost element of the burden at the time they are due" by Hunt , William , Donaldson
" The minimum required rate of earning or the cut off rate of capital expenditure" by Solomon Ezra
"The rate of return the firm requires from investor in order to increase the value of the firm in the market place" by Hampton Jhon
Three basic aspect
Cost of capital is not a cost as such
Minimum rate of return
Comprises of 3 components
The expected normal rate of return at zero risk level (rate of int. allowed by bank)
Premium of business risk
Premium of financial risk

Significance of the Cost of Capital
Evaluating investment decisions
Designing a firm’s debt policy, (capital structure)
Appraising the financial performance of top management
The Concept of the Opportunity Cost of Capital
The opportunity cost is the rate of return foregone on the next best alternative investment opportunity of comparable risk.
General Formula for the Opportunity Cost of Capital
Opportunity cost of capital is given by the following formula:

where Io is the capital supplied by investors in period 0 (it represents a net cash inflow to the firm), Ct are returns expected by investors (they represent cash outflows to the firm) and k is the required rate of return or the cost of capital.
The opportunity cost of retained earnings is the rate of return, which the ordinary shareholders would have earned on these funds if they had been distributed as dividends to them.
Classification of cost
Historical cost & Future cost
Specific cost & Composite cost
Average cost & Marginal cost
Weighted Average Cost of Capital Vs. Specific Costs of Capital
The cost of capital of each source of capital is known as component, or specific, cost of capital.
The overall cost is also called the weighted average cost of capital (WACC).
Relevant cost in the investment decisions is the future cost or the marginal cost.
Marginal cost is the new or the incremental cost that the firm incurs if it were to raise capital now, or in the near future.
The historical cost that was incurred in the past in raising capital is not relevant in financial decision-making.
Computation of cost of capital
Cost of specific source of finance
Weighted average cost of capital
Computation of cost of specific source of finance
Cost of Debt
Rate of interest payable on debt
1) Co issues Rs 100000 10% Deb at par; the before tax cost of this debt will also be
10%
Before tax cost Kdb = I
P
Where Kdb = before tax cost of debt
I = Interest
P = Principal
When debt is raised at premium or discount
Kdb= I
NP Where NP= Net Proceeds
Computation of cost of specific source of finance
Kda = Kdb (1-t)=I (1-t)
NP
Where Kda = After cost of debt
t = Rate of Tax
Cost of Redeemable Debt
Before tax cost of debt
Kdb = I+(P-NP)
n
P+NP
2
I=Interest
N=Number of years in which debt to be redeemed
P= Proceeds at par
NP= Net Proceeds
After tax cost of debt Kda = Kdb (1-t)
Kdb = I+(P-NP)
n
(P+NP)
2
X ltd issues Rs. 50000 8% Deb at par. The tax rate applicable to the company is 50%
Y Ltd. Issues Rs. 50000 8% deb @ 10% premium Tax rate 60%
A Ltd. Issues Rs. 50000 8% deb @ 5% discount Tax Rate 50%
B ltd. Issues 100000 9% deb @ 10% premium cost of floatation 2% Tax Rate 60%
Kda = I(1-t) = 4000 (1-.50)
NP 50000
= 4%
Kda= I(1-t) =4000/55000(1-.60)
NP = 2.91%
Kda = 4000/47500(1-.50) = 4.21%
Kda = 9000/107800(1-.60) = 3.34%
100000+10000-(2/100*110000)=107800
Cost of redeemable at premium
Before tax cost of debt
Kdb = I+(RV-NP)/n
(RV+NP)/2
I=interest
RV = Redeemable value of debt
n=no of years in which debt redeemed
NP=Net Proceeds
After tax cost of debt
Kda= Kdb(1-t)
t = tax rate
Cost of preference capital
1) Co issues Rs 100000 10% preference share at par
Kp = D
P
where Kp = cost of preference capital
D = Annual preference Dividend
P = Principal share capital
When Preference capital is raised at premium or discount
Kp = D
NP Where NP= Net Proceeds
Dividends are not allowed to be deducted in computation
Of tax , no adjustment is required for taxes
Cost of redeemable P.share
Kpr = D+(MV-NP)/n
(MV+NP)/2
D=Dividend
MV = Maturity value
n=no of years in which debt redeemed
NP=Net Proceeds

X ltd issues Rs. 50000 8% P.share capital at par. cost of floatation 2%
Y Ltd. Issues Rs. 50000 8% P.share capital @ 10% premium cost of floatation 2%
A Ltd. Issues Rs. 50000 8% P.share capital @ 5% discount cost of floatation 2%
B ltd. Issues 100000 9% P.share capital @ 10% premium cost of floatation 2%
Kp = D = 4000 * 100
NP 50000-1000
= 8.16%
Kp = D =4000/55000-1100*100
NP = 7.42%
Kp = 4000/47500--950 = 8.59%
Kda = 9000/107800 = 8.35%
100000+10000-(2/100*110000)=107800
Cost of equity share capital
Dividend yield method or dividend / price ratio method
Ke = D or D
NP MP
Ke = cost of equity capital
D = Expected dividend per share
NP = Net Proceeds
MP = Market price per share
1000 share @ 100 per share
Premium 10 %
Dividend 20 % for past 5 years
Cost of capital
Will it changes if MP 160
Ke= 20/110*100=18.18%
Ke= 20/160*100=12.5%
Dividend yield plus growth in dividend method
Ke = D +G or D +G
NP MP
Ke = cost of equity capital
D = Expected dividend per share at end of year
NP = Net Proceeds
MP = Market price per share
G = Growth rate
1000 share @ 100 per share at par
Floatation cost 5 %
Dividend 10 % for initial year
Growth in dividend 5 %
Cost of capital
Will it changes if MP 150
Ke = (10 /100-5)+5%=15.53%
Ke = (10/150)+5%=11.67%
Earning yield method
Ke = earning per share/net proceeds
Ke = EPS/NP or EPS/MP
Cases
When earning per share remain constant
Retention ratio is zero
MP is influenced by only EPS
No of equity share 10 lakhs
MV of exisiting share 60
Net earning 90 lakhs
New share price 52
Cost of issue new share 2 per share
EPS= 9000000/1000000=9
Ke=9/60*100=15%
Cost of new equity= {9/(52-2)}*100=18%
Realised yield method
Not easy to estimate future earning
Actual rate realised in past
Assumptions
Firm will remain in same risk
Shareholder expectation depend on past earnings
MP doesn’t change significantly
Cost of retained earnings
Kr=(D/NP)+G
To make the tax adjustment & cost of purchasing of new security
Kr= {(D/NP)+G}*(1-t)*(1-b)
T= tax rate
B=cost of purchasing of new sec.
Kr=Ke*(1-t)*(1-b)
Weighted average cost of capital
Kw=Sum of XW / Sum of W
X cost of specific source of finance
W weight , proportion of specific source of finance
Tax rate 50%
Source amount proportion B.tax A.tax Wcost
E.share 20 Lac 50% 15.09 15.09 7.55
10% P S 8 lac 20% 10.00 10.00 2.00
12% Deb 12lac 30% 12.00 6.00 1.80
11.35
Book Value Versus Market Value Weights
Managers prefer the book value weights for calculating WACC:
Firms in practice set their target capital structure in terms of book values.
The book value information can be easily derived from the published sources.
The book value debt—equity ratios are analysed by investors to evaluate the risk of the firms in practice.
Book Value Versus Market Value Weights
The use of the book-value weights can be seriously questioned on theoretical grounds:
First, the component costs are opportunity rates and are determined in the capital markets. The weights should also be market-determined.
Second, the book-value weights are based on arbitrary accounting policies that are used to calculate retained earnings and value of assets. Thus, they do not reflect economic values.
Book Value Versus Market Value Weights
Market-value weights are theoretically superior to book-value weights:
They reflect economic values and are not influenced by accounting policies.
They are also consistent with the market-determined component costs.
The difficulty in using market-value weights:
The market prices of securities fluctuate widely and frequently.
A market value based target capital structure means that the amounts of debt and equity are continuously adjusted as the value of the firm changes.
The Capital Asset Pricing Model (CAPM)
As per the CAPM, the required rate of return on equity is given by the following relationship:
Equation requires the following three parameters to estimate a firm’s cost of equity:
The risk-free rate (Rf)
The market risk premium (Rm – Rf)
The beta of the firm’s share (b )
Cost of Equity: CAPM Vs. Dividend—Growth Model
The dividend-growth approach has limited application in practice
It assumes that the dividend per share will grow at a constant rate, g, forever.
The expected dividend growth rate, g, should be less than the cost of equity, ke, to arrive at the simple growth formula.
The dividend–growth approach also fails to deal with risk directly.
Cost of Equity: CAPM Vs. Dividend—Growth Model
CAPM has a wider application although it is based on restrictive assumptions:
The only condition for its use is that the company’s share is quoted on the stock exchange.
All variables in the CAPM are market determined and except the company specific share price data, they are common to all companies.
The value of beta is determined in an objective manner by using sound statistical methods. One practical problem with the use of beta, however, is that it does not probably remain stable over time.

business firm objective

Objective of business firmTapen GuptaHIM Kala Amb




Objective of firm
Profit maximization
Sales or revenue maximization
Maximization of satisfaction
Security of profit
Growth maximization
Managerial utility maximization
Customer satisfaction
Wealth maximization
Profit maximization
TR-TC
TR = Total revenue
TC = Total cost
Essential for the survival of business
Greater predictive ability
Strongest motive
Common goal
Sales or revenue maximization
Financial institution (index of performance)
Profit fig. annually
Salaries & slack earning of the top mgr. are linked with sales
Routine personal problems are more easily handed
Sales growing (growing mkt. share & greater competitive strength
Maximization of satisfaction
Society
Customers
Employees
Security of profit
Higher the risk higher the profit
Steady flow of porfit
Growth maximzation
Maximization of promoting rate
Expansion of the firm
Managerial utility maximization
Mgr. seeks to maximise their own utility
Minimum level of profit
Satisfy shareholder keep mrg. Unchanged
Expansion of staff


Customer satisfaction
King of the mkt.
Wealth maximaization