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Cost of Capital Minimum rate of return which a company is expected to earn from a proposed project so as to make no reduction in the earning per share to equity shareholders and its market price. In economic terms there are two approaches to define CoC: It is the borrowing rate of the firm, at which it can acquire funds to finance the proposed project It is the lending rate which the firm could have earned if the firm would have invested elsewhere CoC is a combined cost of each type of source by which a firm raises funds.

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CoC Also referred to as cut-off rate, target rate, hurdle rate, minimum required rate of return, standard return, etc. Assumption: that the firm’s business and financial risks are unaffected by the acceptance and financing of projects. Business risk – is the risk to the firm of being unable to cover fixed operating costs. Measured by: (ΔEBIT/EBIT)/ (ΔSales/Sales) Financial risk – is the risk of being unable to cover required financial obligations such as interest, preference dividends. Measured by: (ΔEPS/EPS)/ (ΔEBIT/EBIT)

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**Importance of CoC Capital Budgeting Decisions**

Designing the Corporate Financial Structure Deciding about the method of financing – in lieu with capital market fluctuations Performance of top management Other areas – eg., dividend policy, working capital

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Measuring CoC A realistic measure of CoC should have the following qualities of capital expenditure decisions: It must account for the general uncertainty of expected future returns from investment proposals. It must allow for the various degrees of uncertainty of expected future returns associated with different uses of funds. It must allow for the effects of uncertainty associated with an incremental investment and the uncertainty of returns from the entire asset portfolio of the firm. It must account for a variety of financing means available to a firm. It must allow for the differential effects of financing combination on the amount and quality of residual net benefits accruing to shareholders. It must reflect the changes in the capital market.

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Basic costs of capital Cost of Equity Capital: the cost of obtaining funds through the sale of common stock. Cost of Preference Shares Cost of Debt Cost of Retained Earnings

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Cost of Equity Capital Ke is defined as the minimum rate of return that a firm must earn on the equity-financed portion of an investment project in order to leave unchanged the market price of the shares. It is the rate at which investors discount the expected dividends of the firm to determine its share value. The two approaches to measure ke are i. Dividend valuation approach and ii. Capital asset pricing model.

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Cost of Equity Most difficult and controversial cost to work out. Conceptually, the cost of equity ke may be defined as the minimum rate of return that a firm must earn on the equity financed portion of an investment project in order to leave unchanged the market price of the shares. The cost of equity capital is higher than that of preference and debt because of greater uncertainty of receiving dividends and repayment of principal at the end.

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**2 approaches to measure Ke**

1. Dividend approach – dividend valuation model: assumes that the value of a share equals the present value of all future dividends that it is expected to provide over an indefinite period. Ke accordingly is defined as the discount rate that equates the present value of all expected future dividends per share with the net proceeds of the sale (or the current market price) of a share.

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**Formula =Σ D1(1+g)n-1/(1+ke)n N**

Po(1-f)=Σ D1/(1+ke) + D2/(1+ke)2 +….+ ∞ n=1 =Σ D1(1+g)n-1/(1+ke)n Po(1-f) = D1/(ke–g) or Ke = (D1/Po) + g; where D1 = expected dividend per share Po = net proceeds per share/current market price g = growth in expected dividends

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**Assumptions of the Dividend Approach**

The market value of shares depends upon the expected dividends. Investors can formulate subjective probability distribution of dividends per share expected to be paid in various future periods. The initial dividend is greater than 0. Dividend payout ratio is constant. Investors can accurately measure the riskiness of the firm so as to agree on the rate at which to discount the dividends.

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**Note 1: if the growth rate is not uniform, then, **

Po(1-f)or Po=D1/(1+ke) + D1(1+g1)/(1+ke)2 + D1(1+g1) (1+g2)/(1+ke)3 ….+ ∞ Note 2: if we limit the dividend payment upto N years, then, Po(1-f)or Po=D1/(1+ke) + D1(1+g)/(1+ke)2 +…+ D1(1+g)N-1 /(1+ke)N +….+ PN/(1+ke)N Where, PN is the share value at the end of the Nth year. Example: Expected dividend is Rs.2 in 1st year. Growth rate expected 4% in perpetuity. Floatation cost is 2%. What is the cost of equity? Assume market price of share is Rs. 20. So, 20(1-0.02)=2/ke-0.04 ke=0.04+2/20(1-0.02)=14.20% If there are no floatation costs, then, ke=g+D1/P0=0.04+2/20=14%

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**The Fincon Ltd. is planning an equity issue in Jan 1998**

The Fincon Ltd. is planning an equity issue in Jan it has an EPS of Rs.25 and declared a dividend of Rs.15 per share in the current year. Its present P/E ratio is 8. It wants to price the issue at market price and floatation costs are expected to be 10% of the issue price. Determine required rate of return for equity shares before issue and after the issue. How will dividend tax under the Indian Income Tax Act affect your calculations? Cost of present equity: Ke=[EPS/P0(1-f)]=[D1/Po(1-f)]+g=reciprocal of P/E multiple g=%Retimes[EPS/Po(1-f)] Ke=1/8=.125=12.5% OR Ke=15/200+25/200(1-15/25)=.125=12.5%

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**Cost of equity for new issue:**

Ke=15/200(1-0.10)+[25/200(1-0.10)](1-15/25)=15/180+(25/180)(0.40)=.1388=13.9% Under new tax laws: Po=D1/(Ke-g) OR Ke=D1/P0+g But 10% tax is paid by company out of profits. Thus, retained earnings or g alone is affected. Thus, revised formula for g is: g=EPS/P0[1-DPS(1+dt)/EPS] or g=[EPS-DPS(1+dt)]/P0 where, dt is dividend tax For existing issue, Ke=D1/P0+[EPS-DPS(1+dt)]/P0 Ke=15/200+[25-15(1+0.1)]/200=15/200+[ ]/200=15/ /200=.1175=11.75%

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**For further issue of equity, Ke=D1/P0(1-f)+[EPS-DPS(1+dt)]/P0(1-f)**

The new tax laws would result in: Lower cost of equity Perhaps it would promote investment also.

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**n=6 Example: suppose current dividend (D0)=Rs. 2**

Current share price P0=Rs.100 Company growth rate: upto 5th year – 10% 6-10th year=8% 11th year & beyond=6% Then, P0 5 =Σ 2*1.10(1.1)n-1/(1+ke)n + n=1 10 Σ D6(1.08)n-1/(1+ke)n + n=6 ∞ Σ D6(1.06)n-1/(1+ke)n + n=11

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**2. Capital Asset Pricing Model approach**

The CAPM explains the behavior of security prices and provides a mechanism whereby investors could assess the impact of proposed security investment on their overall portfolio risk and return. In other words, it formally describes the risk-return trade-off for securities. The basic assumption of CAPM are related to A. the efficiency of the market, and B. investor preferences.

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**A. Efficient Market implies**

All investors have common (homogeneous) expectations regarding the expected returns, variances and correlation of returns among all securities; All investors have the same information about securities; There are no restrictions on investments; There are no taxes; There are no transaction costs; and No single investor can affect the market price significantly.

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B. Investors’ preference assumption is that all investors prefer the security that provides the highest return for a given level of risk or the lowest risk for a given level of return. That is, investors are risk averse.

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**Risk to which security investment is exposed to are of 2 types:**

Diversifiable/unsystematic risk: is the portion of the security’s risk that is attributable to firm-specific random causes; can be eliminated through diversification. Eg., management capabilities and decisions, strikes, unique government regulations, availability of raw materials, competition.

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Systematic/Non-diversifiable risk: is the relevant portion of a security’s risk that is attributable to market factors that affect all firms; cannot be eliminated through diversification. Eg., interest rate changes, inflation or purchasing power change, changes in investor expectations about the overall performance of the economy and political changes. Since diversifiable risks can be eliminated through diversification, investors should be concerned with only non-diversifiable risks.

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Market Portfolio Systematic risk can be measured in relation to the risk of a diversified portfolio which is commonly referred to as the market portfolio of the market. According to CAPM, the non-diversifiable risk of an investment/security/asset is assessed in terms of the beta coefficient. Beta is the measure of the volatility of a security’s return relative to the returns of a broad-based market portfolio. Beta coefficient of 1 would imply that the risk of the specified security is equal to the market.

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**Formula ke = rf + ß(km – rf); Where, ke = cost of equity capital;**

rf = the rate of return required on a risk free asset/security/investment km = required rate of return on the market portfolio of assets that can be viewed as the average rate of return on all assets ß = the beta coefficient. ß for market portfolios is 1, while it is 0 for risk-free investments.

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ke rm rf 1 ß

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**Difference b/w CAPM and Dividend Valuation method**

Valuation model does not consider the risk as reflected in beta. CAPM model suffers from the problem of collection of data. Beta measures only systematic risk. Example: ß=1.4, rf=8%, km=12% ke=8%+1.4(12%-8%) =8%+1.4*4%=13.6%

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**Note: CAPM approach is theoretically sound but has limitations:**

It does not incorporate floatation costs. Difficult to get ß values. Poorly diversified investors would be concerned with not only systematic but total risk. So, dividend approach is better.

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**Cost of Preference Capital**

They are a hybrid security between debt and equity. The shareholders are paid a dividend yearly. Though, this payment is not tax-deductible but the company is required to make payments; since, if it does not pay, it can’t pay dividends to the equity holders. Also, preference dividend, if unpaid, gets accumulated over years. Preference shares may be redeemable/irredeemable. (now irredeemable preference shares are not allowed. Have to be redeemed in maximum 10 years) Cost of preference share capital is the annual preference share dividend divided by the net proceeds from the sale of preference shares. Perpetual security (irredeemable) Cost of redeemable preference share

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**Cost of Preference Shares**

The preference shareholders carry a prior right to receive dividends over the equity shareholders. Moreover, preference shares are usually cumulative which means that preference dividend will keep getting accumulated unless it is paid. Further, non-payment of preference dividend may entitle their holders to participate in the management of the firm as voting rights are conferred on them in such cases. Above all, the firm may encounter difficulty in raising further equity capital mainly because the non-payment of preference dividend adversely affects the prospects of ordinary shareholders.

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**A. Irredeemable (perpetual) kp=dp/P0(1-f); where,**

dp=constant annual dividend, P0=expected sales price of preference share f= floatation costs Example: a 12% irredeemable preference share of face value of Rs.100, f=5%. What is kp if preference share issued at i. par, ii.10% premium, iii. 10% discount At par, kp=12/100(1-0.05)=12/95=12.63% At 10% premium, kp=12/110(1-0.05)=11.48% At 10% discount, kp=12/90(1-0.05)=14.03%

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**n=1 B. Redeemable preference shares N**

Po(1-f)=Σ dp/(1+kp)n +PN/(1+kp)N ; n=1 Example: 14% preference dividend on face value of Rs.100 to be redeemed after 10 years. Floatation cost is 5%. Kp? 100(1-0.05)=Σ 14/(1+kp)n +100/(1+kp)10 ; By trial and error – kp=15% approximately.

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Cost of Debt Debt is the cheapest form of long-term debt from the company’s point of view as: It’s the safest form of investment from the point of view of creditors because they are the first claimants on the company’s assets at the time of its liquidation. Likewise they are the first to be paid their interest. Another, more important reason for debt having the lowest cost if the tax-deductibility of interest payments.

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Cost of Debt It is the interest rate which equates the present value of the expected future receipts with the cost of the project. The present value of tax-adjusted interest costs plus repayments of the principal is equated with the amount received at the time the loan is consummated.

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Cost of Debt Cost of debt is the after-tax cost of long-term funds through borrowing. Net cash proceeds are the funds actually received from the sale of security. Flotation cost is the total cost of issuing and selling securities. Cost of perpetual/irredeemable debt Cost of redeemable debt

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**Cost of Perpetual/Irredeemable debt**

The nominal cost of debt is the periodical interest paid on it. The interest rate/market yield is said to be cost of debt. Suppose a bond is issued to procure perpetual debt. Then, ki=I/SV; where I is annual interest payment (coupon payment); SV is sale proceeds of bond/debenture. kd=I(1-T)/SV; where T is tax rate. Example: A 12% perpetual debt of nominal value of Rs Tax rate is 50%. Cost of debt when issued at i. Par, ii. At discount of 5% and iii. premium of 10%. At par ki=12000/100000=12% kd=12%(1-0.5)=6% ii. At discount of 5%, that is value received is 95,000. ki=12000/95000=12.63% kd=12.63%(1-0.5)=6.32%

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**iii. At a premium of 10%, that is value received is 110,000.**

ki=12000/110,000=10.91% kd=10.91%(1-0.5)=5.45% So here (ii) 6.32% is highest cost followed by (i) 6% or (iii) 5.45%.

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**Cost of Redeemable debt**

To find the cost, initial net proceeds are to be equated with net outflows. ∞ Co=Σ In/(1+kd)n +PN/(1+kd)N ; if principal payment is made n= at the end of Nth year Or, ∞ Co=Σ In+PN /(1+kd)n ; if payment of principal is done in n= installments

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**Example: 15% debentures of Rs**

Example: 15% debentures of Rs.1000 (face value) to be redeemed after 10 years. Net proceeds are after 5% floatation costs and 5% discount. The tax rate is 50%. What is the cost of debt? Year Cashflows %of 1000(floatation)-5%ofdiscount =900 1-10 Rs. 15% of 1000(1-0.5)=Rs.75 10 Rs (repayment) 10 So, 900= =Σ 75/(1+kd)n +1000/(1+kd)10 n=1 By trial and error; kd =9% approx. Note: ki route is preferred over kd route.

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**Example: of redemption on yearly basis (coupon rate=15%)**

Example: of redemption on yearly basis (coupon rate=15%). The par value of debenture is Rs the floatation cost is 10%. Principal to be paid back in 5 equal installments at the year end. Tax rate is 50%. Net proceeds= %=90000 Outflows: Net coupon Principal Total Yr (1-0.5)= Yr *.15(1-0.5)= Yr *.15(1-0.5)= Yr *.15(1-0.5)= Yr *.15(1-0.5)= So, 90000=27500/(1+kd)+26000/(1+kd) /(1+kd) /(1+kd) /(1+kd)5 By trial and error, kd=12% approx

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**Cost of Retained Earnings**

May be defined as the opportunity cost in terms of dividends foregone by/withheld from the equity shareholders. Cost of retained earnings is the same as the cost of an equivalent fully subscribed issue of additional shares, which is measured by the cost of equity capital. Retained earnings are “dividends withheld”, that is, if were in the hands of the investors (shareholders) they could have earned on these by investing somewhere else. The assumption is that the firm is earning “at least equal to ke on these retained earnings. So the cost kr is approximately equal to ke (a little less than ke because of floatation costs are not there, kr<ke)

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**Weighted Average Cost of Capital (WACC)**

This gives us the overall cost of capital. Weight age is given to the cost of each source of funds by assessing the relative proportion of each source of fund to the total, and is ascertained by using the book value or the market value of each type of capital. The cost of capital of the market value is usually higher than it would be if the book value is used.

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**Steps in Calculation of WACC (Ko)**

Assigning weights to specific costs. Multiplying the cost of each sources by the appropriate weights. Dividing the total weighted cost by the total weights.

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**Weighting can be using marginal or historical weights**

Why marginal weights? Because it is the new capital being raised for new investment that is important so the weighted cost of new capital is of relevance. Else, projects with costs higher than managerial costs may be accepted, giving negative results and vice-versa. But the problem is that if we go by marginal weighting, we may resort to too much borrowing and accept many projects because of lower cost at the moment. But, at a later date, company may have the problem of raising more finance. Marginal weights ignore long term view. Thus, the fact that today’s financing affects tomorrow’s costs, is not considered in using marginal weights.

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Historical weights take a long term view and try to raise financing also in the proportion of existing capital structure – considered superior. Historical weights can be divided into book value weights and market value weights. Calculations based on the book value weights are more easy operationally while those based on market values are more sound theoretically since the sale price of securities is going to be more close to the market value. But the problem is how to choose the market value because they fluctuate widely sometimes and almost everyday their values are different.

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**=2.4%+3.9%+5.6%=11.9% Example: capital structure (book value based)**

Debt 30% (Rs.6000) cost kd=8% Preference shares 30% (Rs.6000) cost kp=13% Equity 40% (Rs.8000) cost k=14% Ko=WACC= Σwiki=30%*8%+30%*13%+40%*14% =2.4%+3.9%+5.6%=11.9% Note: ko calculated on the basis of market value is likely to be greater than the one calculated on the basis of book value since market values of equity and preference shares is usually higher than book value and hence their weight is more with respect to debt. For example, in the above example, market values are:

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Debt 25% (Rs.60000) cost kd=8% Preference shares 29.17% (Rs.70000) cost kp=13% Equity 45.83% (Rs ) cost k=14% Total=240000 Ko=WACC= Σwiki=0.25* * *0.14= = =12.21%

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**Market Value vs. Book Value Weights**

MV sometimes preferred to BV for the MV represents the true expectations of the investors. However, it suffers from the following limitations: MV undergoes frequent fluctuations and have to be normalized; The use of MV tends to cause a shift towards larger amounts of equity funds, particularly when additional financing is undertaken.

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**MV more appealing than BV as:**

Market values of securities closely approximate the actual amount to be received from their sale Costs of specific sources of finance which constitute the capital structure of the firm are calculated using prevalent market prices.

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**Advantages of BV weights**

The capital structure targets are usually fixed in terms of book value. It is easy to know the book value. Investors are interested in knowing the debt-equity ratio on the basis of book values. It is easier to evaluate the performance of a management in procuring funds by comparing on the basis of book values.

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**Relevant costs closely related to CoC**

1. Marginal cost of capital: average cost of new or incremental funds raised by the firm. MC tens to increase proportionately as the amount of debt increases. 2. Explicit cost and implicit cost: a. Explicit cost: of any source of finance is the discount rate that equates the present value of the cash inflows that are incremental to the taking of the financial opportunity with the present value of the incremental cash outflows. The explicit cost of a debt would be 0 if it is interest free. The explicit cost of a gift would be –100%.

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**b. Implicit cost: is the opportunity cost**

b. Implicit cost: is the opportunity cost. It is the “rate of return” associated with the best investment opportunity for the firm and its shareholders that will be foregone if the project presently under consideration by the firm were accepted. It is not concerned with any particular source of finance. The explicit cost include only the CoC to be paid and ignores the other factors such as risk involved, flexibility and leverage characteristics which are adversely affected with an increase in debt contents in its capital structure and these changes imply additional but hidden costs.

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**3. Future cost and Historical cost**

We always consider the projects’ expected internal rate of return and compare it with the expected (future) cost of capital while making capital expenditure decision. Historical costs (past costs) help in predicting the future costs and provide an evaluation of the past performance

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**4. Specific cost and Inclusive/Combined/Composite CoC**

a. Specific CoC is associated with a specific component of capital structure. b. Inclusive CoC is an aggregate of the CoC from all sources. In other words, it is WACC.

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**5. Spot costs and Normalized costs**

a. Spot costs represent those costs prevailing in the market at a certain time. b. Normalized cost indicate an estimate of cost by some averaging process from which cyclical element is removed.

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