Case Study Cost of Capital

COST OF CAPITAL

CHETAN SUKHDEO RANPISE

DPGD/JA10/0052

SPECIALIZATION: FINANCE

WELINGKAR INSTITUTE OF MANAGEMENT

DEVELOPMENT & RESEARCH

YEAR OF SUBMISSION: -NOVEMBER 2011

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ACKNOWLEDGEMENT

With immense pleasure I would like to present this report on “COST OF CAPITAL”

I would like to thanks Welingkar Institute of Management for providing me opportunity to

Present this project.

My special thanks to Mr. Permeshwar Welekar (project Guide) for his invaluable guidance,

co-operation and for taking time out his busy schedule to help me.

Acknowledgments due to my parents, family members, friends and all those people who have

helped me directly or indirectly in the successful completion of the project.

Chetan Sukhdeo Ranpise

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CERTIFICATE FROM THE GUIDE

This is to certify that the project work titled COST OF CAPITAL is a bonafide work carried out

by CHETAN SUKHDEO RANPISE

(Admission No.) DPGD/JA10/0052

A candidate for the Post Graduate Diploma examination of the Welingkar Institute of

Management under my guidance and direction.

SIGNATURE OF THE GUIDE

NAME: Mr. PERMESHWAR WELEKAR

DESIGNATION: DEPUTY MANAGER (FINANCE)

ADDRESS: INDIAN OIL CORPORATION LTD.

NEAR RAILWAY GOODS SHED,

BHIALI-3, DIST. DURG.

CHHATISGARH.

DATE:

PLACE:

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TABLE OF CONTENTS

TITLE PAGE……………………………………………………………………………........1 ACKNOLEDGMENT…………………………………………………………………..........2 CERTIFICATE FROM GUIDE……………………………………………………………..3

A. INTRODUCTION

Objective……………………………………………………………………………11 Motivation…………………………………………………………………………..12 Cost of Component………………………………………………………………..13 Application of the Cost of Capital………………………………………………...14

B. BACKGROUND

Cost of capital for MNC……………………………………………………………15 Cost of capital across countries…………………………………………………..16 The cost of capital background for a firm………………………….…………….17 Required rate of return on project………………………………………………..18 Effect of debt on required returns………………………………………………..19 Cost of capital issues……………………………………………………………...19 Relationship between implied cost of capital and realized returns……………24 Adjusting forecasts for predictable errors…………………………………….....27

C. METHDOLODGY

Weighted average cost of capital(WACC)………………………………………34 Cost of debts……………………………………………………………………….37 Cost of preferred stock…………………………………………………………….41 Cost of equity……………………………………………………………………….42

D. CONCLUSION………………………………………………………………………………53

E. RECOMMENDATIONS…………………………………………………………………….56

F. LIMITATIONS………………………………………………………………………………..58

BIBLIOGRAPHY…………………………………………………………………………….60

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INTRODUCTION

In the context of financial management, the term “cost of capital” refers to the remuneration

required by the investors or lenders to induce them to provide funding for an ongoing business.

If the firm’s goal is to remain profitable and to increase value to its shareholders, any use of

capital must return at least its cost of capital, and optimally, an amount greater than its cost of

capital. The Weighted Average Cost of Capital (WACC) is often used as benchmarks, or “hurdle

rate” when evaluating new project and business that would require use of the scare resources of

funding.

The cost of capital is the required rate of return that a firm must achieve in order to cover the

cost of generating funds in the marketplace. Based on their evaluations of the riskiness of each

firm, investors will supply new funds to a firm only if it pays them the required rate of return to

compensate them for taking the risk of investing in the firm’s bonds and stocks. If, indeed, the

cost of capital is the required rate of return that the firm must pay to generate funds, becomes a

guidelines for measuring the profitability’s of different investments. When there are differences

in the degree of risk between the firm and its divisions, a risk-adjusted discount-rate approach

should be used to determine their profitability.

Cost of capital plays a central role in valuations, portfolio selections, and capital budgeting.

Therefore, measuring and validating the cost of capital metrics has been the subject of much

research. While cost of debt is usually directly observable, the cost of equity capital is not and

needs to be inferred. Researchers have attempted to validate the inferred measures of cost of

equity capital in two ways: (1) correlations with ex-ante proxies for risk such as beta, earnings

variability, leverage and growth, and (2) correlations with realized returns [see Gebhardt, Lee

and Swaminathan (2001) and Gode and Mohanram (2003) among others]. Prior research has

demonstrated that while implied cost of capital estimates correlate well with ex-ante proxies for

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risk, but correlate poorly with realized returns. Such low correlations can be attributed to four

factors: (1) realized returns are affected by economic surprises regarding future cash flows or

discount rates [Vuolteenaho (2002)], (2) market inefficiencies, e.g., the market consistently

overestimates or underestimates future earnings [e.g. the accrual anomaly documented in sloan

(1996)], (3) researcher’s measurement of market expectations are incorrect, e.g., analyst

earnings forecasts are a poor proxy of market expectations of earnings [see Hughes, Liu and Su

(2008)]. and (4) researches have used an incorrect model of earnings dynamics to estimate

extrapolate earnings beyond the analyst forecast horizon, i.e., researchers have measured

terminal value at the end of analyst forecast horizon incorrectly. In this paper, we focus on the

third aspect and show that errors in analyst earnings forecasts contribute to the low correlation

between implied cost of capital and realized returns. We then use insight from recent research

that demonstrates that the errors in analyst forecasts are predictable. Correcting the forecasts

to better measure market’s expectations of earnings leads to significantly improved correlation

between implied cost of capital and realized returns. Without the corrections, the difference in

mean implied cost of capital estimates between the top and bottom quintile of portfolios formed

on the basis of implied cost of capital is 7.8%, but the difference in mean realized returns is a

statistically insignificant 0.35%. Moreover, the relationship between implied cost of capital and

realized returns is not even monotonic across the quintiles. After correcting earnings forecasts,

the difference in mean implied cost of capital between the top and bottom quintiles is 6% and

the difference in mean realized returns is 6.6% with a strong monotonic progression across

quintiles. We use the abnormal earnings growth model or the OJ model developed in Ohlson

and Juettner-Nauroth (2005) because it is theoretically rigorous yet parsimonious, and provides

a simple closed form solution for the implied cost of capital. 1 Further, prior research has

documented that while the OJ model provides cost of capital estimates that are highly correlated

with ex-ante risk factors [Gode and Mohanram (2003)], they are weakly correlated with realized

returns [Easton and Monahan (2005)]. We also use the PEG model, a restricted and simplified

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version of the OJ model, as prior research has suggested that the simple version may

outperform the full version [Easton (2004), Easton and Monahan (2005)]. The risk premiums

derived from the full OJ and the abbreviated PEG model are denoted as RPOJ and RPPEG

respectively. We begin our analysis by replicating prior results that demonstrate a strong

association between risk premiums and risk factors, but a weak and non-monotonic association

between risk premium and realized returns. Consistent with prior research, we observe a strong

positive monotonic relationship between implied risk premium and risk factors such as beta,

standard deviation of returns and standard deviation of analysts EPS forecasts, and a strong

negative monotonic relationship between risk premium and firm size and analyst following.

further, the relationship between implied risk premium and ex-post realized returns are weak

and nonmonotonic. As mentioned earlier, the spread in returns between firms in the highest and

lowest quintile of RPOJ is merely 0.35% compared to 7.8% spread in risk premium.

We then explore how predictable forecast errors may bias implied cost of capital. We find that

the highest RP quintile also has the highest negative ex-post earnings surprise, which suggests

that the relationship between risk premiums and realized returns may be weak due to errors in

measuring expected earnings. Hughes, Liu and Su (2008) show that while analyst forecast

errors are predictable, one cannot generate excess returns by predicting forecast errors, which

suggests that the market does not use the forecasts at face value, but “corrects” them.

Therefore, one can more reliably estimate implied cost of capital by using adjusted analyst

forecasts, and this more reliable estimate may exhibit a higher correlation with realized returns.

In the context of our paper, the analyst forecasts may be overly optimistic for the highest RPOJ

Quintile but the market may well be aware of the overstated forecast and may be using a lower

forecasts. The resulting lower stock price when compared with inflated analyst expectations

Would yield a spuriously high implied cost of capital. Consistent with Hughes,Liu and Su (2008),

We choose the following factors to predict forecast errors: accruals (ACCR),book-to-market ratio

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(BM), earnings-to-price ratio (EP), long-term growth (LTG), sales growth (SGR), changes in

PP&E (CH_PPE) trailing return (RETO) and revision in analyst forecasts (REV), we run annual

regressions to predict surprises in one year-ahead and two-year-ahead EPS. Using the

coefficients from once-lagged (twice-lagged) annual regressions to avoid look-ahead bias, we

estimate the predictable errors in EPS1 (EPS2) forecasts. We then remove the predictable error

component of analyst forecasts of EPS1 and EPS2, recomputed the cost of capital based on the

adjusted forecasts and analyze their relationship with realized returns. The results demonstrate

the central point of our paper-the cost of capital implied by the corrected analyst forecasts

shows a must stronger relationship with realized returns. Quintiles formed on the basis of

implied cost of capital show monotonically increasing realized returns.The difference in adjusted

RPOJ (RPPEG) between the top and bottom quintiles is 7% (7.3%) while the difference in

realized returns is 4.2% (4.7%).Finally, we include the initial estimate of implied cost of capital in

our prediction of forecast errors. Instead of reflecting risk, a very high RP estimate might reflect

that the market’s expectations are much lower than analyst forecasts. Therefore, we use lagged

RPOJ(RPPEG) as an additional explanatory variable in the regression to predict forecast errors.

We then use these adjusted forecasts to infer the new cost of capital. This results in a stronger

association between implied cost of capital and realized returns. The spread between the top

and bottom quintile of adjusted RPOJ (RPPEG) is 6.0 %( 6.6%) while the realized returns differ

by 6.6 %(6.7%). To summarize, our paper makes two contributions to the literature. First, it

shows that correcting analyst forecasts to remove predictable errors leads to implied cost of

capital measures that have much higher association with realized returns than has been

documented before. Second, it shows that, in additions to the well known factors used to predict

forecast errors, one should use the implied cost of capital itself to predict surprises, as a very

high cost of capital estimate suggests that the market’s true earnings expectations are lower

then analysts. Section 2 summarizes the prior research related to implied cost of capital as well

as the predictability of analyst forecasts errors. Section 3 outlines the theory underlying the OJ

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model, our empirical execution of the OJ Model to calculate implied cost of capital estimates.

and the sample selection procedure. Section 4 analyzes the relationship between the cost of

capital estimates and returns and sheds light on the significant role of analysts’ forecasts errors.

Section 5 outlines a procedure to correct the predictable errors in analysts’ forecasts and

demonstrates that doing so strengthens the relationship between implied cost of capital and

realized returns, section 6 concludes the paper.

.

Most firms do not rely on only one type of financing, but seek to maintain an acceptable capital

structure using a mix of various elements. These sources of financing include long term debt.

common stock preferred stock & retained earnings.

What impacts the cost of capital?

The cost of capital becomes a guideline for measuring the profitabilities of different investments.

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RISK IN

ESS OF

EARNINGS

E

THE DEBIT TO EQUITY MIX OF THE FIRM

FINANCIAL

SOUNDNESS

OF THE FIRM

INTEREST RATE LEVELS IN THE US/GLOBAL MARKETPLACE

Another way to think of the cost of capital is as the opportunity cost of funds, since this

represents the opportunity cost for investing in assets with the same risk as the firm. When

investors are shopping for places in which to invest their funds, they have an opportunity cost.

the firm, given its riskiness, must strive to earn the investor’s opportunity cost. If the firm does

not achieve the return investors expect (i.e. the investor’s opportunity cost), investors will not

invest in the firm’s debt and equity. As a result, the firm’s value (both their debt and equity) will

decline.

Let’s Takes an Example

The managers of Rocky Mountain Motors (RMM) are considering the purchase of a new tract of

Land which will be held for one year. The purchase price of the land is $10,000. RMM’s capital

structure is currently made up to 40% debt, 10% preferred stock, and 50% common equity. This

capital structure is considered to be optimal, so any new funds will need to be raised in the

same proportions. Before making the decision, RMM’s managers must determine the

appropriate require rate of return. What minimum rate of return will simultaneously satisfy all of

the firm’s capital providers?

Because the current capital structure is optimal, the firm raises funds as follows

Sources ofFunds

Amount Dollar cost After tax cost

Debt $4000 $280 7%Preferred $1000 $100 10%Common $5000 $600 12%TOTAL $10000 $980 9.8%

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The following table shows three possible scenarios:

Rate of Return 8% 9.8% 11%

Total Funds Available $10800 $10980 $11100Less: Debt Cost $4280 $4280 $4280Less: Preferred Cost $1100 $1100 $1100=Remainder to common

$5420 $5600 $5720

Obviously, the firm must earn at least 9.8%. Any less, and the common shareholders will not be

satisfied.

1. Objective

The objectives of cost of Capital are as follows.

I. Managing the right-hand side of the Balance Sheet:

For making a valuable & strong balance sheet the cost of capital is very important. It reflects the

ability & it surviving life in the industries & create trust in the mind of the shareholders.

II. By now, for valuation analysis, we know:

Criteria for NPV, IRR, Payback.

What the relevant Cost of Financing is

How to compute net cost of Financing

How to introduce forecasts error in Cost of Financing.

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III. Source of Financing:

Debt, equity, retained earnings, preferred stock, warrants, venture

Capital and bank loans, strategic alliances.

Bank loans, venture capital, and warrants not discussed.

To simplify, we concentrate only on debt, equity, and retained earnings.

IV. Cost of financing=Cost of Capital=?

Definition: The rate that must be earned to satisfy the required rate of return of the firm’s

investors.

What is the cost of each source of financing?

What is a project’s cost of capital?

2. Motivation

I. Why cost of capital is important?

The cost of capital is important in its Net Present Value term as follows.

If financing cost is reduced Y NPV increases Y more projects end up with NPV>0 Y more

wealth created to shareholders.

II. Some preliminaries

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Minimum required return / cost of capital=that particular discount rate “k” that makes NPV=0

The return generated by a security is the cost of that security to the company that issued it.

Cost of capital to the firm = reward to investors.

The cost of capital depends primarily on the use of funds i.e. the risk of the CFs not on the

source.

I. Risk of CFs (systematic risk)

II. Company capital structure

3. Cost of Components:

Case 1

Assume firm has no debt & has retained earnings. Remember from the chapter performance

Measures;

Net income = total dividend + retained earnings

If a company cannot find profitable projects, i.e. projects with return at least equal to ks, then

the firm should distribute retained earnings to shareholders as dividends.

Thus, if the company is retaining your money, then the minimum acceptable rewards to you (an

average investor) is the required return on equity = required return on retained earnings = ks/

required return on equity.

But reward to investor = cost of capital to the firm.

Required return on equity = cost of retained earnings.

Case 2

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Now suppose firm needs to issue new equity for an expansion project obviously

Ke>ks (cost of new equity) > (Cost of retained earnings) = (required return on new equity)>

(required return on retained earnings)

Since some transactions (floatation) costs have to be paid to investment banks for assisting firm

In selling the new securities.

Case 3

If a company has a “good” project (NPV>0), should it be financed using equity?

Not necessarily, firm should consider using debt.

4. Application of the Cost of Capital

The cost of capital is a measure of the opportunity cost of capital in an economy. A company’s

cost of capital should equal the marginal return available to investors in the next best investment

opportunity of similar risk available in the capital. The cost of capital should reflect:

The return available to investors in the economy on risk-free instruments.

The return that investors require for taking systematic risk over and above the risk-free

rate

Systematic risk is at which cannot be diversified away.

Traditionally measured as the weighted average of the cost of equity and debt, known as

the weighted Average Cost of capital (WACC).

Basically Cost of capital have four applications system which for the management for careful

decision on investment in cost of capital.

Capital budgeting decisions and value-based management

Company valuation

Mergers & acquisitions

Goodwill write-off

BACKGROUND

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As investors desire to obtain the best/highest return on their investments in securities such as

share (Equity) and loans to companies such as debentures (debt), these returns are costs to

companies paying these dividends (on equity) and interest (on debt)! It all depends on the

perspective from which we close to view the calculation (are we Earning or paying?)

Cost of capital for MNC

A firm’s capital consists of equity (retained earnings and funds obtained by issuing stock) and

debt (borrowed funds). The firm’s cost of retained earnings reflect an opportunity cost what

the existing shareholders could have earned if they had received the earnings as dividends and

invested the funds themselves. The firm’s cost of new common equity (issuing new stock) also

reflects an opportunity cost. What the new shareholders could have earned if they had invested

their funds elsewhere instead of in the stock. This cost exceeds that of retained earnings

because it also includes the expenses associated with selling the new stock (flotation costs).

The firm’s cost of debt is easier to measure because that if firms incurs interest expenses as a

result of borrowing funds. Firms attempt to use a specific capital structure or mix of capital

components that will minimize their cost of capital. The lower a firm’s cost of capital, the lower

is its required rate of return on a given proposed project. Firms estimate their cost of capital

before they conduct capital budgeting because the net present value of any project is partially

dependent on the cost of capital.

Costs of capital across Countries

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An understanding of why the cost of capital can vary among countries is relevant for three

reasons. First, it can explain why MNCs based in some countries may have a competitive

advantage over others. Just as technology and resources differ across countries, so does the

cost of capital. MNCs based in some countries will have a larger set of feasible (positive net

present value) projects because their cost of capital is lower, thus these MNCs can more early

increase their world market share. MNCs operating in countries with a high cost of capital will be

forced to decline projects that might be feasible for MNCs operating in countries with a low cost

of capital. Second MNCs may be able to adjust their international operations and sources of

funds to capitalize on differences in the cost of capital among countries. Third, differences in the

costs of each capital component (debt and equity) can help explain why MNCs based in some

countries tend to use a more debt-intensive capital structure than MNCs based elsewhere.

Country differences in the cost of debt are discussed next, followed by country differences in the

cost of equity

A firm capital consists of equity (retained earnings and funds obtained by issuing stock)and debt

(borrowed fund).There is an advantage to using debt rather than equity as capital because the

interest payments on debt are tax deductable. The tradeoff between debt’s advantage and its

disadvantage. It is favorable to increase the use of debt financing until the point at which the

bankruptcy becomes large enough to offset the tax advantage of using debt.

Companies MUST consider the cost of financing they receive in the form of equity or debt if they

are to manage their finances better, cheaper finance cost to the company means higher

profitability and in most cases, superior cash flow. Generally the cost of EQUITY has no tax

effect but the costs of DEBIT finance to companies are technically SUBSUDISED by tax since

INTEREST (cost of debt) can be claimed for tax purposes in so for as it is wholly exclusively

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and necessarily incurred for business purposes.

The Cost of Capital Background for a firm:

Cost of capital is a major standard of comparison used in financial analysis and is vital company

statistic needing careful calculation. The return on capital resources must equal or exceed the

cost of that capital. Although zero or negative returns are acceptable in special cases. The

necessary subsidies may lead to costs in another form.

The realities of commercial life have caused the cost of capital to be very complex subject. Any

comparisons must be made between like numbers. A percentage profit before tax made on a

hotel in Bermuda bears no relationship to the same figure made after tax on a farm in Scotland.

A profit expressed as a percentage of capital employed should not be compared with a

discounted cash flow internal rate of return. Capital investment analysis aims to discover the

financial truth about the plan under investigation. If it does not meet the survival standard of the

organization, that fact should be stated clearly before the discussion as to its desirability begins.

In practice, many apparently unprofitable activities which, of course, should out number them.

Most. companies raises funds from many sources- related earnings, new equity, grants and

many forms of loans. The overall cost of capital to the new firm is the return it must earn on its

assets to meet the requirements of all those providing it with financing. Lenders require interest

payments and shareholders expect to receive dividends and see capital growth. In deciding the

appropriate standards for an organization. The marginal cost of capital is a vital guide. In a

growing company, new capital will be needed and, therefore, the return on a project of normal

risk should be judged against a standard of the weighted average cost of new capital.

Companies making investment decision continuously should use this marginal cost of capital as

the standard for all projects with risks normal to the company’s business. if a project cannot

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pass this test, it will diminish the company’s value.

Required Rate of Return on Projects:

Obviously project involves differing risks. Some such a cost saving investments and lease or

buy decisions, are of low risk. Other such as research projects, involves greater than average

levels of risk. A company should classify its risk categories for projects and set required returns

for each. A large project of risk significantly different from normal can alter the overall character

of a company. Its cost of capital, its accepted gearing and the returns expected by financiers.

The required rate of return for a project can be significantly different from the weighted average

cost of capital for the company. High risk project are characterized by high fixed operating

expenditure and high revenue variability. These should be expected earn high earn rate of

return. The exact return required will be depending upon a judgment about the level of risk in

the project compared with the average risk of the company. In the case above where weighted

average cost of capital in real term is 6%, the real required return on a project twice as risky as

the market should be 12% with 10% expected inflation the money required return should be

22%

By evaluating different project at different required rate of return, the company seeks to protect

its shareholders. Shareholders require higher rate of return for higher level of risk, and receive

compensation for high risk in capital markets. Companies undertaking high risk assets

Investment decision must seek to achieve higher returns than their shareholders can earn for

That level of risk in the capital market.

Effect of debt on required returns:

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Unless there are non-financial incentives, a project is acceptable only if it stands on its own feet,

that is, its cash flow should at least meet the company return criterion for the risk involved. With

the possibility of debt financing is the position changed? A typical case arises when new assets

simply increase the total assets on a proportion of which debt is available. The total operating

risk of the company remains constant as more debt financing is used, so it is unrealistic to

believe that the overall cost of funds can be reduced in this way.

For better understanding we take a view of comparison of company cost VS projected cost.

same has been as follows.

Cost of capital issue

Price Base:

WACC may be measured either in real terms or nominal terms. A nominal WACC is expressed

in current terms, while a real WACC is expressed in real/constant terms. Hence, the real WACC

shows the WACC excluding the impact of inflation. The choice of price base should be

consistent with the regulatory pricing regime. If access and interconnection prices are regulated

In real terms, the cost of capital should be expressed in real terms, whereas it should be

expressed in nominal terms if prices are regulated in nominal terms. In the past, prices have

been regulated in nominal terms in Sweden, and there is no indication that this will charge in the

future. Hence the cost of capital should be estimated in nominal terms. By permitting a nominal

return on assets, investors are compensated for both their opportunity cost of capital and

expected inflation. In the view of AMI, the WACC should be stated in nominal terms.

Taxation:

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The WACC may be estimated post-tax or pre tax. The pre tax WACC is the WACC adjusted to

allow for corporate tax payments. When applied to the capital base. It indicates the (pre-tax)

operating profit required to finance tax and interest payments, while providing shareholders with

their required return. The WACC is usually calculated on a post-tax basis, since most market

information is available on this basis. Then, it is converted to a pre-tax WACC. A formula often

used for converting a post-tax WACC to pre-tax WACC is.

WACCpre-tax = WACCpost-tax / (1-T).

Where T is the effective tax rate.

To estimate a pre-tax WACC, a single effective company tax rate must be estimated. This is

problematic as it is difficult to accurately estimate a single effective tax rate, reflecting a

company’s taxation liabilities, as the taxation liabilities will inevitably vary from year to year.

furthermore, forward-looking costs do not depend on the tax rate for previous years, but on the

corporate tax rate can be expected in a forward looking perspective. Therefore, AMI

suggests the pragmatic solution of using the corporate tax rate as a proxy for the effective tax

rate of an SMP operator. Although we acknowledge that this is not theoretically correct, we note

that this eliminates any uncertainty that would otherwise be introduced by attempting to estimate

an effective rate, and further is in line with generally accepted practice.

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Principle for determining the capital structure:

The relative share of debt and equity in a company’s capital structure is called the debt to equity

ratio. Financial gearing refers to the company’s proportions of debt and equity and is defined as

D/ (E+D), where D is the debt and E the equity capital 10. A highly geared company has a high

ratio of debt to equity. There are a number of ways to determine the debt to equity ratio.

A ratio measured on the basis of book values - using a ratio based on the accounting value of

the company’s debt and equity.

A ratio measured on the basis of current market values - based on the observed market value of

the company’s debt and equity.

An (optimal) target ratio that a company decides to use for long –term financing of its

investments. Calculations of the financial gearing should be based on market values (as

opposed to book Values) as these reflect the true economic value of the type of outstanding

financing. The issue is therefore whether to use an operator’s current gearing level based on

current market value or its target ratio.

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Using Company Cost (K) Vs. Project Cost (K)

K

Project risk < firm’s Project risk > firms

Firm’s K

Risk-free Reject good projects Accept Bad Projects

BETA

THE Cost of Capital of a firm is the minimum rate of return which the firm must earn on its

investments in order to satisfy the expectations of investors who provide funds to the firm. It is

the weighted average of the cost of various sources of finance used by it. The method of

computing the cost of capital is to compute the cost of each type of capital and then find the

weighted average of all types of costs of capital. In other words, two steps are involved in

determination of cost of capital of a firm: (I) computation of cost of different sources of capital,

and (II) determining overall cost of capital of the firm. For example a company’s capital structure

is as follows: 14 per cent debentures of Rs.10, 00, 000, 12 per cent preference share capital Rs.

5, 00,000, Equity share capital Rs. 5, 00,000. It is assumed that equity shareholders of such

companies expect 14 per cent dividend. Total capital Rs. 20, 00,000. Income tax rate 30% CDT

15% Total cost = {(98,000 debenture interest taking tax saving at the rate of 30%) + (69,000

preference dividend and corporate dividend tax) + (80500 equity dividend and corporate

dividend tax)} = 2, 47,500

Cost of capital= 2, 47,500 *100 = 12.375 %

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20, 00,000

This company should earn a minimum rate of return of 12.375 per cent on its investments in

various projects in order to satisfy the expectation of investors who have provided funds to it.

(Surcharge and education cess ignored)

Q. No. 1: In considering the most desirable capital structure for a company, the following

estimates of cost of debt and equity capital (after tax) have made at various levels of debt-equity

mix:

Debt as % of total CapitalEmployed

Cost of Debt (%) Cost of Equity (%)

0 5.0 12.010 5.0 12.020 5.0 12.530 5.5 13.040 6.0 14.050 6.5 16.060 7.0 20.0

You are required to determine the optimal debt equity mix by calculating composite cost of

capital. Ignore corporate dividend tax.

Answer:

Debt as % of Total CE Overall cost of capital (Ko) (%)0 12.00

10 0.10(5.00) + 0.90(12.00) = 11.3020 0.20(5.00) + 0.80(12.50) =11.0030 0.30(5.50) + 0.70(13.00) =10.7540 0.40(6.00) + 0.60(14.00) =10.8050 0.50(6.50) + 0.50(16.00) = 11.2560 0.60(7.00) + 0.40(20.00) = 12.20

RECOMMENDATIONDEBT : 30 %

Relationship between implied Cost of Capital and Realized Returns:

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I. Replicating Prior Results Regarding the Association between implied cost of Capital, Risk, measures, and Realized Returns:

In this section, we replicate prior research to validate our approach. Prior research has

Shown a strong positive relationship between RPOJ and other measures of firm risk such as

systematic risk, return volatility and forecast dispersion, and a strong inverse relationship with

the quality of a firm’s information environment captured by proxies such as firm size and analyst

following. However, prior research has not shown a strong association between RPOJ and

realized returns. Each year, we partition our sample into five quintiles based on the level of risk

premium. We then compare the mean values of risk metrics as well as future realized returns

across these five quintiles. We consider the following risk and information asymmetry measures

systematic risk measured as β calculated using monthly returns over the lagged five years

(ensuring that least 12 months returns are available), idiosyncratic risk calculated as the

standard deviation of the past year’s monthly returns (STDRET), and finally analyst forecast

dispersion calculated as the standard deviation amongst individual analysts of the EPS1

forecast (EPS1STD). The quality of the firm’s information environment is captured by firm size

as measured by market capitalization (MCAP) at the time of the analysts forecast, and the

number of analysts following a firm (NUMEST). Table 3, panel A presents the results for

quintiles based on RPOJ. The results confirm a strong relationship between RPOJ and risk and

information asymmetry measures. Across the five quintiles ranging from lowest RPOJ to highest

RPOJ, β increases from 1 to 1.23, STDRET increases from 9.7% to 12.9%, and forecast

dispersion increases from 7.2% to 15.3%. Firms with the highest RPOJ are also the smallest

and least followed while firms with the lowest RPOJ are the largest and most actively followed

panel B presents the results for quintiles based on REEEG and shows that the differences

across the groups are even greater for most of the variables. Overall, the results confirm prior

finding that OJ based implied risk premium metrics are strongly related with other risk metrics.

24

Table 3, panel A also presents the relationship between the implied risk premium measures and

future returns. To mirror the definition of risk premium, we subtract the risk-free rate from buy

and-hold return realized over the 12 month following the forecast to arrive at our return measure

(RET1). The relationship between RPOJ and RET1 is not monotonic. RET1 increases from

quintiles. 1 through 3 and then declines. The difference in returns between the top and bottom

quintiles of risk premium is positive but insignificant 0.35 % and is a fraction of the 7.8% spread

in RPOJ across the top bottom quintile. Table 3, Panel B shows a similar no monotonic

relationship between RPPEG and RET1. RET1 increases from 5.58% to 8.40% from the first to

the third quintile and then declines to 6.63% for the top quintile. The difference across the top

and bottom quintiles in returns is a little stronger at 1.05%, but it is still insignificant, and is only

a fraction of the 8% spread in RPPEG.Table 3, panel C presents the results of a simple

univariate regression with RET 1 as the dependent variable and either RPOJ or RPPEG as the

independent variable. Regressions are run at the firm level, both pooled across the entire

sample as well annually using the Fama-MacBeth procedure. The results indicate a weak or

even non-existent relationship between realized returns and implied cost of capital. For RPOJ

the coefficient is an insignificant 0.0939 for the pooled regression and -0.0280 for the annual

regression. For RPPEG, the coefficient is significant for the pooled regression at 0.1947, but an

insignificant 0.0286 for the annual regressions. All the coefficients are significantly below the

benchmark of 1, which would indicate a perfect relationship between implied cost of capital and

realized returns. Thus the regressions results confirm the weak relationship between risk and

return seen across quintiles.

II. Why Do High Implied RP Firms Not Earn High Realized Returns?

25

What might explain the reversal in returns from the middle quintiles to the top quintiles of risk

premium? Is there a systematic trend in realized bad news across the groups that causes firms

with high implied risk premium to have substantially lower realized returns? To examine this, we

compare the realized earnings surprise across the five quintiles. We define SURP1 as the

difference between realized EPS1 and expected EPS1 scaled by stock price. Table 3, panels A

and B shows a strong inverse trend between earnings surprise and implied risk premium, i.e.

firms with high implied risk premium are far more likely to have negative earnings surprises.

this could be due to two different sets of reasons with widely different consequences for

empirical analysis. The first possibility is that the market expectations are being measured with

error Suppose, for some firms, market expectations are lower than IBES forecasts. For these

firms, The stock price will appear low relative to IBES earnings forecasts, which will inflate the

implied Cost of capital. These firms will have a negative earnings surprise rather than a higher

realized return. The second possibility is that the market is inefficient and has unreasonably high

growth expectations for firms that are perceived to be high risk. It may then be surprised when

the firms do not meet those expectations, which will cause the realized return to be low. We

focus on the first possibility and examine how errors in measuring market expectations bias

implied cost of capital.

III. The Impact of Forecast Accuracy on the Association between OJ Based

Implied Cost of capital and Realized Returns Prior research has shown that when analyst

forecasts are likely to be more accurate, implied risk premium is stronger related with realized

returns (Easton and Monahan (2005)). We test this in our sample by using the realized absolute

forecast error (absolute value of SURP1) as our metric of forecast accuracy. Each year, we

partition our sample into quintiles based on absolute forecasts error and study the relationship

between risk premium and returns within each quintile. Table 4 presents the results for quintiles

26

based on RPOJ. For the first error quintile (most accurate forecasts) we see a strong monotonic

relationship between risk premium and return, with a return difference of 16.6% when the

difference in RPOJ is 6.86% between high and low RPOJ quintiles. For the next two quintiles,

the monotonic relationship continues with return spreads around 10% as against a difference in

RPOJ of 7% across RPOJ quintiles. For the fourth quintile, the relationship is much weaker with

a return difference of only 3.38% and ceases to be monotonic. Finally, for the fifth quintile with

the greatest ex-post forecast error, the relationship is inverted with firms with the highest risk

premium earning 9.18% less than firms with the lowest risk premium. The results for RPPEG in

the columns to the right are almost identical. A couple of points are noteworthy. First high

absolute error groups have high negative SURP1. In other words, when analysts get it really

wrong. They are more likely to be extremely optimistic than extremely pessimistic. Second, the

high RP firms are far more likely to be in the quintiles with the greatest absolute forecast error.

For instance, almost half of the top quintile of RPOJ observations (4,896 out of 10, 896) lie in

the least accurate quintile with most negative surprise. These results show that forecast errors

weaken the relationship between implied cost of capital and realized returns.

Adjusting Forecasts for Predictable Errors:

Identifying Factors that May Predict Forecast Errors

Forecast errors weaken the association between implied cost of capital and realized returns,

either because of market expectations are biased, i.e., market inefficiency, or due to errors in

measuring market expectations, i.e., predictable errors in analyst forecasts, or both. Hughes, Liu

and Su (2008) shows that predicting forecast errors cannot be used to generate excess returns.

Which suggests that the market is aware of analyst forecast errors and corrects for them. Thus

we focus on adjusting analysts forecasts to arrive at better proxies of market expectations,

which, in turn, improve inference of cost of capital. We draw upon prior research to identify

factors that could help us predict analyst forecast errors. As discussed in the literature review

27

section, systematic trends in forecast bias and accuracy have been the subject of much

research. We synthesize these results to identify the following factors to predict forecast errors

(# represents Compustat Annual Data Item,∆ represents change in).

Accruals (ACCR): accruals for prior fiscal year, defined as the change in non-cash current

assets (∆ (#4 - #1)) minus depreciation (#14 and the change in current liabilities excluding the

current portion of long term debt and tax payable (∆(# 5 - #34 - #71)), scaled by prior year total

assets (#6)

Book –to-market ratio (BM): the ratio of book value at prior fiscal year end (#60), scaled by

market capitalization measured at the time of the forecasts.

Earnings-to-price ratio (EP): ratio of EPS1 to PRICE

Long term growth (LTG): from IBES

Sales growth (SGR): annual growth in sales (#12) as of the prior fiscal year end

Changes in gross PP&E (CH_PPE): change in gross PPE (#7), scaled by prior year total assets

(#6)

Trailing return (RET0): contemporaneous raw buy-and-hold return for the 12 months ending at

Six months after prior fiscal year end.

Revision in analyst forecasts (REV): revision in EPS1 forecasts from three months after prior

Fiscal year end to six months after prior fiscal year end, scaled by PRICE

Given that we use both one-year-ahead as well as two -year -ahead EPS estimates, we

28

examine Two measures of errors: SURP1 (SURP2), which is the difference between realized

EPS1 (EPS2) and expected EPS1 (EPS2) scaled by stock price. Table 5, panel A provide the

average of annual correlation between the error variables and the factors used in predicting

errors. Figures above/below diagonal are Pearson/Spearman correlations. For SURP1, the

factors ranked from the highest to lowest absolute correlation are as follows: REV, RETO, BM,

EP, LTG, SGR, ACCR, and CH_PPE. The ranking of factors for SURP2 is virtually identical.

This suggests a strong role for prior revisions, returns, and valuation ratios. To avoid look-ahead

bias, we run annual regression of SURP1 (SURP2) at the end of year n on these factors as of

the end of year n-1 (n-2).

Table 5, Panel B presents the summary of annual regressions. Coefficients are mean

coefficients from annual regressions. T-statistics are calculated from the distribution of annual

coefficients using the Fama and MacBeth (1973) methodology. Overall, the adjusted R2 is fairly

high at around 22% for SURP1 and 17% for SURP2. As expected from the correlation table.

REV, RETO, EP, BM and LTG are significant.

To avoid loss of observations, we run a reduced regression with these fewer variables by

excluding the variables pertaining to accruals, sales growth and book-to-market. The results are

essentially unchanged. Table 5, panels C and D presents the details of annual regressions for

the reduced model for SURP1 and SURP2, respectively. Overall, the predictability of forecast

errors lends strong support to the hypothesis that implied cost of capital estimates are biased by

the errors in measurement of market expectations.

29

Predicting Forecast Errors:

We multiply the coefficients from one- year lagged regressions of SURP1 on EP, LTG, CH_PPE

RET0, and REV with the realized values of these variables to arrive at predicted SURP1

(PREDSURP1). That is, we regress the realized earnings forecasts errors at the end of 1982 on

the observable factors at the end of 1981. We then use these regression coefficients and the

observable factors as of the end of 1982 to predict the forecast error for earnings expected at

the end of 1983, and so on, Similarly, we use twice lagged regressions to predict the forecast

errors PREDSURP2 in EPS2

Table 6, panel A summarizes the correlations between predicted and actual earnings surprises

scaled by price. As shown the pearson correlation is about 30%, while the Spearman rank

correlation is slightly higher. Table 6, panel B shows the summary of pooled and annual

regressions of SURP1 on PREDSURP1. The adjusted r-squared is 14% for pooled data and

15% for year-by-year regressions. The r-squared for PREDSURP2 is about 11% and 12% for

pooled and annual regressions, respectively. These results confirm that one can predict

forecast errors with some degree of accuracy and the market is likely to be using these cleaned

up forecasts.

Using Adjusted forecasts to infer Cost of Capital:

We now re-compute the implied cost of capital after removing predicted errors from EPS1 and

EPS2, Table 7, Panel A shows the results. Corrected mean (median) EPS1 is only 88% (85%)

of uncorrected EPS1,Corrected mean (median) EPS2 is only 77%(72%) of the uncorrected

EPS2 short-term growth is not affected much because both EPS1 and EPS2 are revised

downward. Mean (median) PE ratios rise by about 18% (18%) while the mean (median) PEG

30

ratios rise by About 21% (26%).

This suggests significant changes in forecasts and valuation metrics. The lowered forecasts

naturally lead to lower estimates of risk premium. Mean RPOJ declines from 6.4% to 5.3%,

while mean RPPEG declines from 4.4% to 3.3%.This decline is consistent with lowered

aggregate RP estimated by Easton and Sommers (2007) after adjusting for forecast bias. Table

7, Panel B, shows that the adjusted RP measures have a correlation of only about 70% with the

old RP measures corroborating the fact that the adjustment to earnings forecast significantly

impact the implied cost of capital.

Table 7, panel C highlights the main contributions of our paper. It shows that the adjusted cost

of Capital measures have a much stronger and monotonic association with the realized returns.

Quintiles formed on the basis of adjusted implied cost of capital show monotonically increasing

realized returns. The difference in ARPOJ between the top and bottom quintiles is 7 % while the

difference in realized returns is 4.2%. The PEG model shows slightly better results – the

difference in ARPPEG between the top and bottom quintile is 7.3% while the difference in

realized returns is 4.66%.

The strong relationship between the adjusted RP measures and returns is reinforced by the firm

level regressions in Table7, Panel D. Recall that the coefficients on the RP measures were

mostly insignificant when we compute RP using unadjusted analyst forecasts (Table 3, panel C)

In contrast, the coefficients on the adjusted RP measures are all significant and are in the 0.4 to

0.6 range. To illustrate, the coefficient on ARPOJ is 0.4479 for the pooled regressions and

0.5232 for the annual regressions, while the coefficient for ARPPEG is 0.5030 for the pooled

regression and 0.5918 for the annual regressions.

Table 7, panel E shows that we have been largely successful in eliminating the bias due to

31

predictable errors in analyst earnings forecasts. In sharp contrast to Table 4, when we form

quintiles based on realized errors and examine the relationship between implied cost of capital

and realized return within quintile, we find a monotonic and significant relationship for each

quintile. The difference in particularly striking for the fifth quintile of forecast accuracy, where the

return difference across RP quintiles is now 5.87% for ARPOJ quintiles and 5.73% for ARPPEG

quintiles (compared with -9.18% and -9.69% respectively for the unadjusted RPOJ and RPPEG

quintiles within the fifth accuracy quintile in Table4)

Using Implied Cost of Capital to predict Forecast Errors:

In addition to the factors that we have discussed so far, one can also use the implied cost of

capital itself as a predictor of analyst forecast errors. Consider a firm with high implied cost of

capital. Rather than reflecting risk, this could simply reflect that the market expects lower

earnings. Had one used the lower forecast, the implied cost of capital would have been lower.

Table 8, Panel A confirms our intuition that the implied cost of capital may help predict the

forecast errors. There is a negative correlation of about 30 % between forecasts errors (SURP1

And SURP2) and risk premiums (RPOJ and RPPEG). We therefore us ROPJ (and RPPEG) as

additional explanatory variables in the regression to predict SURP1 and SURP2 Table 8, panel

B repeats the analysis in Table 5, Panel B except that we now add unadjusted RPOJ and

RPPEG as explanatory variables. The adjusted R2 for the SURP1 regression increases from

20.50% in Table 5, panel B to 22.6% in Table 8, Panel B if we add RPOJ as an explanatory

variable. If we use RPPEG instead of RPOJ, then the adjusted R2 is even higher at 23.2%

Results for SURP2 are similar.

Table 8, panel C repeats the analysis in Table 7, Panel C except that we now use RPOJ and

32

RPPEG as additional variables to clean the analyst forecasts for expected errors. In Table 7

Panel C, the difference in adjusted RPOJ between the top and bottom quintile is 7 % while the

realized returns differ by 4.2%. In contrast, in Table 8, panel C, the difference in RPOJ between

the top and bottom quintile is 6% while the difference in realized returns is 6.24%. With RPPEG

the difference in expected returns between the top and bottom quintile is 6.6% while the

difference in realized returns 6.69%, which is also a dramatic improvement over Table 7, Panel

C Thus the addition of implied cost of capital as a predictor of forecast errors significantly

Improves the correlation with realized returns. To confirm the stronger relationship between the

adjusted RP measures and returns, we repeat the firm-level regressions. Recall that the

coefficients on the RP measures were in the 0.4 to 0.6 range when we made the first-stage

adjustments (Table 7, Panel C) when we incorporate the initial estimate of RP in our error

prediction regression, the coefficients improve still further to reach the 0.8 level. The coefficient

on ARPOJ is 0.8002 for the pooled regressions and 0.8411 for the annual regressions, while the

coefficient for ARPPEG is 0.7904 for the pooled regression and 0.9456 for the annual

regressions. The coefficients from the annual regressions are insignificantly different from the

theoretical benchmark of 1, which represents a perfect relationship between expected and

realized returns. Our results show that removing predictable errors in analyst forecasts

increases the accuracy of measuring market expectations and significantly strengthens the

association between implied derived from the OJ model (and the simplified PEG model) and

realized returns. Thus the weak results found in prior research were potentially caused not by a

flaw in the valuation model, but by errors in measuring market’s expectations of earnings.

33

METHDOLOGY

The cost of capital allowed by a regulator in setting price limits should reflect the opportunity

cost of the funds invested in assets. It represents the rate of return that an investor would be

likely to require in order to invest in a company, given its risk profile compared with other

potential investments. It can also be thought of as the discount rate which an investor would

use in evaluating the income stream to be expected from investing in the company.

1) WEIGHTED AVERAGE COST OF CAPITAL (WACC)

The weighted average cost of capital (WACC) is computed from (a) the average cost of debt for

the various forms of debt held by the company, and (b) the cost of equity. This is the return that

investors (shareholders and lenders of various types) require in order to invest in the company.

The firm’s WACC is the cost of capital for the firm’s mixture of debt and stock in their capital

structure.

WACC= Wd ( Cost of debt) + Ws (cost of stock/RE) + Wp (cost of pf stock)

So now we need to calculate these to find the WACC!

Wd = Weight of debt (i.e. fraction of debt in the firm’s capital structure)

34

Ws = Weight of stock

Wp = Weight of preferred stock

THE FIRMS Think of the firm’s capital structure

CAPITAL as a pie that you can slice into different

STRUCTURE IS shaped pieces. The firm strives to pick

THE MIX OF the weights of debt and equity (i.e. slice

the pie) to minimize the cost of capital.

Calculating Company WACC

Example

Given:

Optimal proportions are 30% Debt, 10% preferred, 60 % common equity

Retained Earnings = $300,000

T= 40%:

Value of k from above examples is used.

$ Financing needed = $200,000

Solution:

If retained earnings are to be used to finance projects, as in this example,

WACC = Wdkd (1-T) + WpsKps + WeKe

35

Wd

Ws

= 0.3(10%) (0.6)+ 0.1(9%)+0.6(14%) + 0

= 1.8% + 0.9% + 8.4%

= 11.1%

Where do the weights come from?

Possibilities include.

Proportional current book value of each component

Proportional current market value of each component

Target capital structure

Should short-term debt be included in wd?

Limitations of WACC

If we use the existing WACC as the hurdle rate in NPV computations (benchmark), we are

assuming that when new funds are raised to finance new projects, the cost of capital will be

unchanged, i.e.

The proportion of debt and equity remain unchanged.

The operating risk of the firm is unchanged.

The finance is not project specific.

2) COST OF DEBT (Kd)

36

The cost of debt measure the combination of interest rates changed by banks to the company

and the return paid by the company on any corporate bonds or other loan instruments issued. It

is standard practice to conceive of this as being made up of a risk free component and a

company specific risk premium.

We use the after tax cost of debt because interest payments are tax deductible for the firm.

Kd after taxes = Kd (1-tax rate)

EXAMPLE

A company raised a debt of Rs 1, 00,000 on 1.1.2001, issue expressed Rs. 10,000, interest rate

20 per cent, debt repayable in five equal installments with interest issue expenses allowed out

of taxable income of first year, interest allowed as deduction out of taxable income of relevant

year. Tax rate 50 per cent. Cash flows as follows.

01.01.2001 Rs.90, 000 inflow (Received Rs. 1, 00,000 as loan minus issue expenses Rs. 10,000)

31.12.2001 Rs. 25000 outflow (Repayment Rs. 20,000 plus interest Rs. 20,000 minus tax

Saving on issued expenses Rs. 5,000 minus tax saving on interest Rs.10,000

31.12.2002 Rs.28, 000 outflow (Repayment Rs. 20,000 plus interest Rs.16,000 minus tax

Saving on interest Rs.8,000)

1.12.2003 Rs. 26,000 outflow (Repayment plus interest minus tax saving on it)

31.12.2004 Rs.24, 000 outflows –do-

37

31.12.2005 Rs. 22,000 Outflow –do-

Here cost of capital is that discount rate at which present value of all future cash outflows

(Rs.25, 000 of 31.12.2001, Rs. 28,000 of 31.12.2002, Rs. 26,000 of 31.12.2003, Rs. 24,000 of

31.12.2004 and Rs.22, 000 of 31.12.2005) would be equal to Rs. 90,000. Finding of this rate

Involves following steps.

(i) Find fake payback period on the basis of average cash outflows. Average cash flow= (25,000

+28,000+26,000+22,000) divided by 5= Rs 25,000.Fake payback period = 90,000/25000 = 3.60

(ii) Locate the figure of fake payback period in annually table against loan repayment period

which is 5 years in this example. The corresponding rate is 12 per cent.

(iii) Discount future cash flows at the rate locate under (ii) if the present value of future cash

flows is more than net cash inflow at the time of raising the loan (i.e. Rs.90, 000 in this example)

discount future cash flows at higher rate than the rate located under (ii) if the present value of

future cash flows is less than net cash inflow at the time of raising the loan, discount the future

cash flows at a rate lower than the rate located under (ii) above.

Present value of future cash flows at 12 percent.

25,000 * .893

28,000* .797

26,000* .712

24,000* .636

22,000*. 567

90,891

38

As present value of future net cash outflows is more than net cash flow at the time of raising the

loan, we shall go for a higher rate. Late the rate be 17 per cent.

25,000*.855

28,000*.731

26,000*.624

24,000*.534

22,000*.456

80915

(iv) Cost of debt

Lower rate NPV

=Lower rate + * Diff. in rates

Lower rate NPV – Higher rate NPV

-891

= 12 + *5 = 12.45 per cent

-891- 9085

There are three difference situations regarding computations of cost of debt. (1) Irredeemable

debts. (2) Debts redeemable after certain period in lump sum, (3) Debts redeemable in

installments. The above explained method of calculation of cost of debt is quite lengthy and

39

complicated. It is unavoidable in third situation, i.e. debts redeemable in installments. In first two

situations, almost similar results can be obtained by simple formula given below.

Irredeemable debt:

Annual Interest (1 – Tax rate)

Cost of debt = * 100

Net proceeds of debt

Debt redeemable after certain period :

(RV – NP)

Annual int. (I -- T) +

N

Kd = * 100

NP + RV

2

Kd = Cost of debt T = Tax rate

RV = Redeemable value of debt

NP = Net proceeds of debt issue

N = Term of debt, i.e., numbers of years for which debt would be outstanding after issue.

Duration of Cost of Debt

40

Duration

3) COST OF PREFERRED STOCK (Kp)

Preferred Stock has a higher return than bonds, but is less costly than common stock. WHY?

In case of default, preferred stockholders get paid before common stock holders. However, in

the case of bankruptcy, the holders of preferred stock get paid only after short and long – term

debt holder claims are satisfied.

Preferred stock holders receive a fixed dividend and usually cannot vote on the firm’s affairs

Preferred stock dividend

Kp = Market price of preferred stock

<OR if issuing of new preferred stock

Preferred stock dividend

Kp = Market price of preferred stock (1- flotation cost)

Unlike the situation with bonds, no adjustment is made for taxes, because preferred stock

41

1 2 3 4 5 6 7 80

20

40

60

80

100

120

140

160

dividends are paid after a corporation pays income taxes. Consequently, a firm assumes the full

market cost of financing by using preferred stock. In other words, the firm cannot deduct

dividends paid as an expenses, like they can for interest expenses.

Example

If cowboy Energy Service is issuing a preferred stock at $100 per share, with a stated

Dividend of $ 12, and a flotation cost of 3% then:

Preferred stock dividend

Kp = Market price of preferred stock (1- flotation cost)

$ 12

= $100 (1-0.03) =12.4 %

Note:

No tax adjustment is needed since preferred dividends are paid from after-tax income.

4) COST OF EQUITY (i.e. Common Stock & Retained Earnings)

The cost of equity is the rate of return that investors require to make an equity investment in a

firm. Common stock does not generate a tax benefit as debt does because dividends are paid

after taxes.

The cost of common stock is the highest Why?

42

Retained earnings are considered to have the same cost of capital as new common stock. Their

cost is calculated in the same way, EXCEPT that no adjustment is made for flotation costs.

The capital asset pricing model (CAPM) is used to determine the cost of equity, rE, applying the

following equation.

Flotation costs (F) are not part of capital budgeting CFS. Thus, if existing shareholders finance

Project using new equity, they require a higher return to cover this cost Ke >Ks

If PO = $ 50 and F = 15 % of issue price , then additional cost per share = (50) (15%) = $7.5 %

Example: Calculating Component Cost of New Equity

Given:

F = 15% of issue price, Dividend = 4.19, g = 5%, PO = $50%

Ke =?

Solution:

Using equation (4), Chapter 7, and including F, we have:

Accounting vs. Financial / Economic Valuation

Ke = Dividend1 + g

Net Value of new equity per share

= Dividend 1 + g

43

Issue price - floatation cost

= Dividend 1 + g

P0 - (P0) (F)

= Dividend0 * (1 + g) +g

P0 (1 - F)

= $4.19 * (1.05) + .05 = 15.4%

$50 (1- .15)

3 Ways to Calculate

1. Use CAPM

2. (GORDON MODEL) The constant dividend growth model – same as DCF method

3. Bond yield – plus – risk premium

1. Ks using CAPM (capital asset pricing model)

The CAPM is one of the most commonly used ways to determine the cost of common stock

The “cost” is the discount rate for valuing common stock, and provides an estimate of the cost

of issuing common stock.

Ks = Krf +β (Km−Krf )

44

Where:

Krf is the risk free rate

β is the firm’s beta

Km is the return on the market

EXAMPLE

Cowboy Energy Services has a B = 1.6. The risk free rate on

T-bills are currently 4% and the market return has averaged 15%

Ks = Krf + β (Km- Krf)

= 4 + 1.6 (15 -4) = 21.6%

Thus in the standard CAPM there are three determinants of the expected return on any asset

the return on a riskless asset; the market premium over that riskless rate that is earned by

investors as a whole. reflecting systematic risk; and the particular company’s exposure to

systematic risk. As discussed further below, company specific risk do not enter the cost of

capital, as they can, by definition, be diversified away by investors.

2. DCF Approach:

45

Given: dividend 0 = & 4.19, g= 5%, p0 = $ 50

Ks=?

Solution:

From equation (4) chapter 7, we have:

Ks = Dividend1 + g

P0

= Dividend0 * (1 + g) + g

P0

= 4.19 * (1.05) + .05

$50

= 0.088 + 0.05 = 13.8 %

You can use the average of these two approaches = 14%.

WACC: PUTTING IT ALL TOGETHER

RECALL:

WACC = Wd (Cost of debt after tax) + Ws (Cost of stock / RE) + Wp (Cost of PS)

EXAMPLE

46

Cowboy Energy Services maintains a mix of 40% debt, 10% preferred stock, and 50% common

Stock in its capital structure. The WACC is:

WACC = 0.4(6%) + 0.1 (12.4) + 0.5(21.6)

= 2.4 + 1.24 + 10.8

= 14.4 %

Reminder: Read the article “Best practices ‘In Estimating the cost of capital: Survey and

synthesis. It provides excellent information on how some of the most financially sophisticated

companies and financial advisers estimate capital costs.

The Gordon growth model

If a large proportion of earnings is retained and reinvested now rather than being paid out as

dividend then the company will grow. Thus by forgoing dividends now the shareholders will

receive higher dividends in future.

Estimating growth from the Gordon model

If given profit and loss and balance sheet information growth can be estimated as follows.

First we calculate the retention or plough back rate from the profit and loss account. (If 100%

profit is retained = 100 % retention rate)

Retention rate = retained profit * 100

Profit after tax

Secondly we calculate the return on capital employed (ROCE) from the profit and loss account

and balance sheet (as normally done in Ratio analysis or interpretation of Accounts)

ROCE = Profit after tax * 100%

47

Opening net assets

Finally, multiply the two ratio together to estimate dividend growth, g = retention rate * ROCE

Limitation of this method

The accounting ratios calculated are assumed to remain constant over time (which is illogical in

reality)

The model uses accounting data (which can be manipulated to suit management objectives)

The model only works correctly if the company is all equity finances (assumes the company has

no debt, this is not practical in most cases)

Determine the weights to be used

My example above gives you the weights to use in calculating the WACC. How do you calculate

the weights yourself?

The firm’s balance sheet shows the book values of the common stock, preferred stock, and

long-term bonds. You can use the balance sheet figures to calculate book value weights.

though it is more practicable to work with market weights. Basically, market value weights

represents current conditions and take into account the effects of changing market condition

and the current prices of each security. Book value weights, however , are based on accounting

procedure that employ the par values of the securities to calculate balance sheet values and

represents past conditions. The table on the next page illustrates the difference between book

value and market value weights and demonstrate how they are calculated.

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Value Dollar Amount Weights or % of total value

Assumed cost of capital (%)

Book value

Debt

2,000 bonds at par, or $ 1000

2,000,000

40.4 10

Preferred stock

4,500 shares at $ 100 par value

450,000 9.1 12

Common equity

500,000 shares outstanding at $ 5.00 per value

2,500,000

50.5 13.5

Total book value of capital 4,950,00

0

100 11.24 is the WACC

Market value

Debt

2,000 bonds at $ 900 currentMarket price

1,800,000

30.2 10

Preferred stock

4,500 shares at $90 current market price

405,000 6.8 12

Common equity5,00,000 shares outstanding at $ 75 current market

3,75,000 63.0 13.5

Total market value of capital 5,955,000

100 What is the WACC?

Note that the book value that appear on the balance sheet are usually different from the market

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values. Also, the price of common stock is normally substantially higher than its book value

This increases the weight of this capital component over other capital structure components

(Such as preferred stock and long –term debt). The desirable practice is to employ market

weights to compute the firm’s cost of capital. This rationale rests on the fact that the cost of

capital measures the cost of issuing securities – stocks as well as bonds – to finance projects

and that these securities are issued at market value, not at book value.

Target weights can also be used. These weights indicate the distribution of external financing

that the firm believes will produce optimal results. Some corporate managers establish these

weights subjectively, others will use that best companies in their industry as guidelines and still

others will look at the financing mix of companies with characteristics comparable to those of

their own firms. Generally speaking, target weights will approximate market weights. If they

don’t, the firm will attempt to finance in such a way as to make the market weights move closer

to target weights.

Hurdle rates:

Hurdle rates are the required rate of return used in capital budgeting. Simply put, hurdle rates

are based on the firm’s WACC. To understand the concept of hurdle rates, I like to think of it this

way. A runner in track jumps over a hurdle. A project the firm is considering must “Jump the

hurdle” – or in other words – exceed the firm’s borrowing costs (i.e. WACC). If the project does

not clear the hurdle, the firm will lose money on the project if they invest in it – and decrease the

value of the firm. The hurdle rate is used by firms in capital budgeting analysis (one of the next

topics we will be studying). Large companies, with divisions that have different levels of risk,

may choose to have divisional hurdle rates.

Divisional hurdle rates are sometimes used because firms are not internally homogeneous in

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terms of risk. Finance theory and practice tells us that us that investors require higher returns

as risk increase. For example, do the following investment projects have the same level of

risks?

Engineering projects such as highway construction, market-expansion projects into foreign

market, new product introductions, E-commerce startups, etc.

Breakpoints (BP) in the WACC:

Breakpoints are defined as the total financing that can be done before the firm is forced to sell

new debt or equity capital. Once the firm reaches this breakpoint, if they choose to raise

additional capital their WACC increases.

For example, the formula for the retained earnings breakpoint below demonstrates how to

calculate the point at which the firm’s cost of equity financing will increase because they must

sell new common stock. (Note: The formula for the BP for debt or preferred stock is basically

the same, by replacing retained earnings for debt and using the weight of debt.)

BPre = Retained earnings

Weight of equity

Example:

Cowboy Energy Services expects to have total earnings of $840,000 for the year, and it has a

policy of paying out half of its earnings as dividends. Thus the addition to retained earnings will

be $420,000 during the year. We now want to know how much total new capital –debt

preferred and retained earnings –can be raised before the $420,000 of retained earnings is

exhausted and the company is forced to sell new common stock. We are seeking the amount of

capital which represents the total financing that can be done before Cowboy Energy Services is

forced to sell new common stock to maintain their target weights in their WACC, Let’s assume

that cowboy Energy services maintains a capital structure of 60% equity, 40% debt. Using the

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formula above.

BPre = Retained earnings

Weight of equity

= $420,000/0.60 = $700,000

Thus, Cowboy Energy Services can raise a total of $700,000 in new financing, consisting of

0.6 ($700,000) = $ 420,000 of retained earnings and 0.40($700,000) = $280,000 of debt,

Without altering its capital structure. The BPre = $700,000 is defined as the retained earnings

break point or the amount of total capital at which a break, or jump, occurs in the marginal cost

of Capital.

Can there be other breaks? Yes, there can – depending on if there is some point at which the

firm must raise additional capital at a higher cost.

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CONCLUSION The careful approximation of a firm’s specific financing and WACC is essential to good

financial management. When the WACC is applied to specific investment decisions, it can make

the difference between accretion and erosion of shareholder value. This chapter develops an

alternative approach to discounted cash flow valuation. The cash flow to the firm are discounted

at weighted average cost of capital to obtain the value of the firm, which when reduced by the

market value of outstanding debt, yields the value of equity. Since the cash flow to the firm is a

cash flow prior to debt payments, this approach is more straightforward to use when there is

significant leverage or when leverage changes over time, though the weighted average cost of

capital, used to discount free cash flow to the firm, has to be adjusted for changes in leverage.

Finally, the cost of capital can be estimated at different debt ratios and used to estimate the

optimal debt ratio for the firm. The alternative approach to the firm valuation is the APV

approach, where we add the effect on value of debt (tax benefits – bankruptcy costs) to the

unlevered firm value. This approach can be used to estimate the optimal debt ratio for the firm.

Traditionally, researchers in finance and accounting have used measures of risk, such as β,

Which use realized returns to infer risk? Inferring cost of capital from realized returns has been

Problematic because the correlation between expected returns and realized returns is weak

(Elton, 1996). This has led to attempts to infer the implied cost of capital using an ex-ante

approach that essentially solves for the discount rate that equates current stock price to present

value of expected future dividends. While implied cost of capital metrics have been shown to

have a strong correlation with other risk factors, they display weak correlations with realized

returns This weak correlation has been the subject of much research [see Easton and Monahan

(2005) amongst others]. The general conclusion has been to attribute the lack of association.

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Either to the fact that realized returns are affected by future events that are not predictable, or to

Inadequacies of the valuation models used to calculate the implied cost of capital. Our paper is

focused on identifying another source of such low correlation, notably the error in measuring

market expectations. Prior research has shown that analysts systematically make prediction

errors and the market recognizes this [see Hughes, Liu and Su (2008)]. Hence analysts

forecasts are often poor proxies for the market’s expectations. To the extent these forecasts are

biased or error-prone, so will be the implied cost of capital. We focus on the implied cost of

capital estimates derived from the abnormal earnings growth model or OJ model developed in

ohison and Juettner-Nauroth(2005). The OJ model provides an elegant closed form solution for

the implied cost of capital that is strongly correlated in the expected direction with other risk

factors, but shows the weakest correlation with realized returns. We test to see whether

adjusting analysts forecasts for predictable errors improves the association between implied

cost of capital and realized returns. The main contribution of the this paper is to show that

adjusting the analyst forecasts by removing predictable errors leads to a dramatically improved

association between implied cost of capital and realized returns. While there will always be a

large unpredictable component to realized returns due to economic surprises. It is reassuring to

know that the theoretical relationship between ex-ante risk and realized returns holds up when

one takes careful measures to remove predictable errors in analyst forecast to get a better

estimate of market expectations. Our paper shows that if a stock looks too cheap relative to

analyst earnings forecasts, then the explanation may not be high perceived risk but high

perceived errors in analyst earnings forecasts. One can then use the factors identified in prior

research to adjust the analyst forecast to get a better handle on market perceptions. We also

identify another way of assessing if the analyst forecasts are biased. An abnormally high cost of

capital can itself be an indicator of overly optimistic analyst forecasts. When we use the implied

cost of capital as an additional variable to de-bias the analyst forecasts, the resulting adjusted

implied cost of capital shows an even higher association with realized returns. At the portfolio

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level, we obtain almost identical spreads across quintiles of expected returns and realized

returns. One implication of our results is that is unlikely that the weak relationship between risk

and return shown in prior research is driven by inadequacies in the OJ valuation model. Future

research can improve these estimates even further through more exhaustive or sophisticated

methods of removing known biases from analyst earnings forecasts. Further research can also

test whether similar dramatic improvements can be observed for implied cost of capital

estimates from other valuation models.

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RECOMMENDATION

The cost of capital should be estimated as the Weighted Average cost of Capital (WACC) using

the CAPM to estimate the cost of equity.

Estimation will separate for cost of capital rates for fixed and mobile system.

The calculations should be undertake any company in conjunction with the more thorough

reviews of the cost of capital pricing methodology.

The WACC should be stated in nominal terms.

The WACC should be calculated on a pre-tax basis (converted from a post-tax basis), using the

corporate tax rate.

Calculations should be based on a partially divisionalised approach, where the business of

Providing fixed service and temporarily services are treated separately.

Calculation of the cost of debt as the sum of the risk free rate and a debt premium.

The debt premium should be consistent with the adopted capital structure and credit rating.

Use a benchmarking approach to estimate the debt premium, ensuring consistency with the

maturity period of the government bond used to estimate the risk free rate if any.

Cost of equity should be estimated as the expected return required by a well-diversified

swedish investor.

use historic returns as a starting point for the market risk premium. The historic estimates

should be combined with estimates used by market analyst in Sweden to ensure that current

market expectations are factored in. The historical mean return should be estimated to be in the

range between the arithmetic and geometric mean.

The risk premium should be calculated for a time period of at least 50 years. Ideally, a

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judgment should be made on the basis of different time periods to ensure that the estimate is

not too sensitive to the to the selected period. Beta should be estimated on the basis of daily

observations using a time period of 1-3 years. One could begin by estimating beta over 1, 2 and

3 years. If the beta estimates are fairly stable, one should use 3 years. If they are not stable,

One should use the shorter periods of either 1 or 2 years. If there are signs of serial correlation,

use weekly observations instead of daily observations. Beta estimates should be compared with

beta estimates for comparable operators.

LIMITATIONS

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If you’re going to value something based on its discounted cash flows, you’re going to need a

weighted average cost of capital (or an equity cost of capital) to apply to those cash flows. Duff

and Phelps recently released a paper discussing the difficulty of determining the cost of capital

in today’s environment. Some of the problems they address.

Treasury yields (the risk free rate in CAPM) are temporarily low due to liquidity concern and a

fight to quality, understanding risk. It is difficult to decompose treasury yields into components of

real return, inflation expectations, and reinvestment risk.

The expected equity risk premium (ERP) has increased greatly (as evidenced by the massive

decline in stock prices). However, they claim the equity risk premium ranges from 3.5% to 6.0%

throughout the business cycle, which seems extremely low to me. We are not in a normal

business cycle here. So I think the forward-looking ERP must be higher than 6%.

Declines in financial stock and companies with high leveraged have outpaced the broader

market, leading to a misleading beta calculation that implies risk has actually declined. Beta

measures the covariance of a stock’s returns with the market’s returns. The market had

become overweighed with financial stocks that dragged the index down as they declined. So if

you compare a non-financial company’s stock covariance to the pre-cash market versus its post

crash covariance. It will appear to have decreased, leading to a lower beta. They recommend

using a sum beta calculation to correct for this.

Highly levered companies will probably be unable to sustain their debt loads going forward. The

cost of capital needs to reflect likely changes to the capital structure over time. Alternative, you

could use an approach like adjusted present value(APV) which separates out the value of the

tax shields.

Companies operating with substantial losses may not be able to take advantage of the tax

shield. On interest in the period when it is paid. So the after-tax cost of debt capital may be

inappropriate.

Their final recommendation is that any cost of capital calculation must also pass the

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inappropriate.

The final recommendation is that any cost of capital calculation must also pass the

reasonableness test. Most of these issues stem from the fact hat finance theory attempts to use

past data to predict future performance. That becomes increasingly hard to justify during times

of discontinuous change. Such as the one we’re experiencing now. For more information, the

authors of this paper have published a practitioner’s guide to the cost of capital, available at

amazon.

BIBLIOGRAPHY

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BOOKS:

Cost of Capital - Bodie, alex Kane 3rd edition book 2008

Cost of Capital Teaching Note - Dr. Betty simkins

(Case studies manual in corporate finance)

Working Capital Management Module - ICAI Institute

Cost of Capital Note - Dr. J.B.GUPTA

Cost of Capital Applications & Examples - Shannon P. Pratt and Roger J. Grabowski(Fourth Edition book in Oct 2010)

WWBSITE:

WWW.ICAI.ORG

WWW.ICWAI.ORG

GOOGLE BOOK GALLERIES.

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