Modigliani–Miller theoremFrom Wikipedia, the free encyclopediaJump to: navigation, search

The Modigliani–Miller theorem (of Franco Modigliani, Merton Miller) forms the basis for modern thinking on capital structure. The basic theorem states that, under a certain market price process (the classical random walk), in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market, the value of a firm is unaffected by how that firm is financed.[1] It does not matter if the firm's capital is raised by issuing stock or selling debt. It does not matter what the firm's dividend policy is. Therefore, the Modigliani–Miller theorem is also often called the capital structure irrelevance principle.

Modigliani was awarded the 1985 Nobel Prize in Economics for this and other contributions.

Miller was a professor at the University of Chicago when he was awarded the 1990 Nobel Prize in Economics, along with Harry Markowitz and William Sharpe, for their "work in the theory of financial economics," with Miller specifically cited for "fundamental contributions to the theory of corporate finance."

Contents

 [hide] 

1 Historical background o 1.1 Without taxes o 1.2 With taxes

2 Notes 3 References 4 External links

[edit] Historical background

Miller and Modigliani derived the theorem and wrote their groundbreaking article when they were both professors at the Graduate School of Industrial Administration (GSIA) of Carnegie Mellon University. The story goes that Miller and Modigliani were set to teach corporate finance for business students despite the fact that they had no prior experience in corporate finance. When they read the material that existed they found it inconsistent so they sat down together to try to figure it out. The result of this was the article in the American Economic Review and what has later been known as the M&M theorem.

=

Consider two firms which are identical except for their financial structures. The first (Firm U) is unlevered: that is, it is financed by equity only. The other (Firm L) is levered: it is financed partly by equity, and partly by debt. The Modigliani–Miller theorem states that the value of the two firms is the same.

[edit] Without taxes

Proposition I: where is the value of an unlevered firm = price of buying a firm composed only of equity, and is the value of a levered firm = price of buying a firm that is composed of some mix of debt and equity. Another word for levered is geared, which has the same meaning.[2]

To see why this should be true, suppose an investor is considering buying one of the two firms U or L. Instead of purchasing the shares of the levered firm L, he could purchase the shares of firm U and borrow the same amount of money B that firm L does. The eventual returns to either of these investments would be the same. Therefore the price of L must be the same as the price of U minus the money borrowed B, which is the value of L's debt.

This discussion also clarifies the role of some of the theorem's assumptions. We have implicitly assumed that the investor's cost of borrowing money is the same as that of the firm, which need not be true in the presence of asymmetric information, in the absence of efficient markets, or if the investor has a different risk profile to the firm.

Proposition II:.

Proposition II with risky debt. As leverage (D/E) increases, the WACC (k0) stays constant.

is the required rate of return on equity, or cost of equity. is the company unlevered cost of capital (ie assume no leverage).

is the required rate of return on borrowings, or cost of debt.

is the debt-to-equity ratio.

A higher debt-to-equity ratio leads to a higher required return on equity, because of the higher risk involved for equity-holders in a company with debt. The formula is derived from the theory of weighted average cost of capital (WACC).

These propositions are true assuming the following assumptions:

no transaction costs exist, and individuals and corporations borrow at the same rates.

These results might seem irrelevant (after all, none of the conditions are met in the real world), but the theorem is still taught and studied because it tells something very important. That is, capital structure matters precisely because one or more of these assumptions is violated. It tells where to look for determinants of optimal capital structure and how those factors might affect optimal capital structure.

With taxes

Proposition I:

where

is the value of a levered firm. is the value of an unlevered firm. is the tax rate ( ) x the value of debt (D) the term assumes debt is perpetual

This means that there are advantages for firms to be levered, since corporations can deduct interest payments. Therefore leverage lowers tax payments. Dividend payments are non-deductible.

Proposition II:

where

is the required rate of return on equity, or cost of levered equity = unlevered equity + financing premium.

is the company cost of equity capital with no leverage (unlevered cost of equity, or return on assets with D/E = 0).

is the required rate of return on borrowings, or cost of debt.

is the debt-to-equity ratio. is the tax rate.

The same relationship as earlier described stating that the cost of equity rises with leverage, because the risk to equity rises, still holds. The formula however has implications for the difference with the WACC. Their second attempt on capital structure included taxes has identified that as the level of gearing increases by replacing equity with cheap debt the level of the WACC drops and an optimal capital structure does indeed exist at a point where debt is 100%

The following assumptions are made in the propositions with taxes:

corporations are taxed at the rate on earnings after interest, no transaction costs exist, and individuals and corporations borrow at the same rate

Miller and Modigliani published a number of follow-up papers discussing some of these issues.

The theorem was first proposed by F. Modigliani and M. Miller in 1958.

[edit] Notes

1. ̂ MIT Sloan Lecture Notes, Finance Theory II, Dirk Jenter, 20032. ̂ Arnold G. (2007)

[edit] References

Brealey, Richard A.; Myers, Stewart C. (2008) [1981]. Principles of Corporate Finance (9th ed.). Boston: McGraw-Hill/Irwin. ISBN 978-0-07-340510-0.

Stewart, G. Bennett (1991). The Quest for Value: The EVA management guide. New York: HarperBusiness. ISBN 0-88730-418-4.

Modigliani, F.; Miller, M. (1958). "The Cost of Capital, Corporation Finance and the Theory of Investment". American Economic Review 48 (3): 261–297. http://www.jstor.org/stable/1809766.

Modigliani, F.; Miller, M. (1963). "Corporate income taxes and the cost of capital: a correction". American Economic Review 53 (3): 433–443. http://www.jstor.org/stable/1809167.

Miles, J.; Ezzell, J. (1980). "The weighted average cost of capital, perfect capital markets and project life: a clarification". Journal of Financial and Quantitative Analysis 15: 719–730. DOI:10.2307/2330405. http://www.jstor.org/stable/2330405.

Cost of capitalFrom Wikipedia, the free encyclopedia

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The cost of capital is a term used in the field of financial investment to refer to the cost of a company's funds (both debt and equity), or, from an investor's point of view "the shareholder's required return on a portfolio of all the company's existing securities".[1] It is used to evaluate new projects of a company as it is the minimum return that investors expect for providing capital to the company, thus setting a benchmark that a new project has to meet.

Contents

[hide]

1 Summary 2 Cost of debt 3 Cost of equity

o 3.1 Expected return o 3.2 Comments

3.2.1 Cost of retained earnings/cost of internal equity 4 Weighted average cost of capital 5 Capital structure 6 Modigliani-Miller theorem 7 See also 8 References 9 Further reading

[edit] Summary

For an investment to be worthwhile, the expected return on capital must be greater than the cost of capital. The cost of capital is the rate of return that capital could be expected to earn in an alternative investment of equivalent risk. If a project is of similar risk to a company's average business activities it is reasonable to use the company's average cost of capital as a basis for the evaluation. A company's securities typically include both debt and equity. One must therefore calculate both the cost of debt and the cost of equity as well as the cost of preference shares and retained earnings to determine a company's cost of capital. However, a rate of return larger than the cost of capital is usually required.

The cost of debt is relatively simple to calculate, as it is composed of the rate of interest paid. In practice, the interest-rate paid by the company can be modelled as the risk-free rate plus a risk component (risk premium), which itself incorporates a probable rate of default (and amount of

recovery given default). For companies with similar risk or credit ratings, the interest rate is largely exogenous (not linked to the company's activities).

The cost of equity is more challenging to calculate as equity does not pay a set return to its investors. Similar to the cost of debt, the cost of equity is broadly defined as the risk-weighted projected return required by investors, where the return is largely unknown. The cost of equity is therefore inferred by comparing the investment to other investments (comparable) with similar risk profiles to determine the "market" cost of equity. It is commonly equated using the CAPM formula (below), although articles such as Stulz 1995 question the validity of using a local CAPM versus an international CAPM- also considering whether markets are fully integrated or segmented (if fully integrated, there would be no need for a local

Once cost of debt and cost of equity have been determined, their blend, the weighted-average cost of capital (WACC), can be calculated. This WACC can then be used as a discount rate for a project's projected cash flows.

[edit] Cost of debt

The cost of debt is computed by taking the rate on a risk free bond whose duration matches the term structure of the corporate debt, then adding a default premium. This default premium will rise as the amount of debt increases (since, all other things being equal, the risk rises as the amount of debt rises). Since in most cases debt expense is a deductible expense, the cost of debt is computed as an after tax cost to make it comparable with the cost of equity (earnings are after-tax as well). Thus, for profitable firms, debt is discounted by the tax rate. The formula can be written as (Rf + credit risk rate)(1-T), where T is the corporate tax rate and Rf is the risk free rate.

The yield to maturity can be used as an approximation of the cost of debt.

[edit] Cost of equity

Cost of equity = Risk free rate of return + Premium expected for riskCost of equity = Risk free rate of return + Beta x (market rate of return- risk free rate of return) where Beta= sensitivity to movements in the relevant market

Where:

Es

The expected return for a security

Rf

The expected risk-free return in that market (government bond yield)

βs

The sensitivity to market risk for the security

RM

The historical return of the stock market/ equity market

(RM-Rf)

The risk premium of market assets over risk free assets.

The risk free rate is taken from the lowest yielding bonds in the particular market, such as government bonds.

An alternative to the estimation of the required return by the CAPM as above, is the use of the Fama–French three-factor model.

[edit] Expected return

The expected return (or required rate of return for investors) can be calculated with the "dividend

capitalization model", which is

[edit] Comments

The models state that investors will expect a return that is the risk-free return plus the security's sensitivity to market risk times the market risk premium.

The risk premium varies over time and place, but in some developed countries during the twentieth century it has averaged around 5%. The equity market real capital gain return has been about the same as annual real GDP growth. The capital gains on the Dow Jones Industrial Average have been 1.6% per year over the period 1910-2005. [2] The dividends have increased the total "real" return on average equity to the double, about 3.2%.

The sensitivity to market risk (β) is unique for each firm and depends on everything from management to its business and capital structure. This value cannot be known "ex ante" (beforehand), but can be estimated from ex post (past) returns and past experience with similar firms.

[edit] Cost of retained earnings/cost of internal equity

Note that retained earnings are a component of equity, and therefore the cost of retained earnings (internal equity) is equal to the cost of equity as explained above. Dividends (earnings that are paid to investors and not retained) are a component of the return on capital to equity holders, and influence the cost of capital through that mechanism.

[edit] Weighted average cost of capital

Main article: Weighted average cost of capital

The Weighted Average Cost of Capital (WACC) is used in finance to measure a firm's cost of capital.

The total capital for a firm is the value of its equity (for a firm without outstanding warrants and options, this is the same as the company's market capitalization) plus the cost of its debt (the cost of debt should be continually updated as the cost of debt changes as a result of interest rate changes). Notice that the "equity" in the debt to equity ratio is the market value of all equity, not the shareholders' equity on the balance sheet.To calculate the firm’s weighted cost of capital, we must first calculate the costs of the individual financing sources: Cost of Debt, Cost of Preference Capital and Cost of Equity Cap..

Calculation of WACC is an iterative procedure which requires estimation of the fair market value of equity capital.[3]

[edit] Capital structure

Main article: Capital structure

Because of tax advantages on debt issuance, it will be cheaper to issue debt rather than new equity (this is only true for profitable firms, tax breaks are available only to profitable firms). At some point, however, the cost of issuing new debt will be greater than the cost of issuing new equity. This is because adding debt increases the default risk - and thus the interest rate that the company must pay in order to borrow money. By utilizing too much debt in its capital structure, this increased default risk can also drive up the costs for other sources (such as retained earnings and preferred stock) as well. Management must identify the "optimal mix" of financing – the capital structure where the cost of capital is minimized so that the firm's value can be maximized.

The Thomson Financial league tables show that global debt issuance exceeds equity issuance with a 90 to 10 margin.weighted average cost of capital

[edit] Modigliani-Miller theorem

Main article: Modigliani-Miller theorem

If there were no tax advantages for issuing debt, and equity could be freely issued, Miller and Modigliani showed that, under certain assumptions, the value of a leveraged firm and the value of an unleveraged firm should be the same.

[edit] See also

Preference share Ordinary share

[edit] References

1. ̂ Brealy &al. "Principles of Corporate Finance", Chapter 102. ̂ Fred's Intelligent Bear Site3. ̂ Business Valuation Glossary - WACC Calculation using an Iterative Procedure

[edit] Further reading

Modigliani, F.; Miller, M. (1958). "The Cost of Capital, Corporation Finance and the Theory of Investment". American Economic Review (American Economic Association) 48 (3): 261–297. JSTOR 1809766.

Definition of 'Cost Of Capital'

The required return necessary to make a capital budgeting project, such as building a new factory, worthwhile. Cost of capital includes the cost of debt and the cost of equity.

Investopedia explains 'Cost Of Capital'

The cost of capital determines how a company can raise money (through a stock issue, borrowing, or a mix of the two). This is the rate of return that a firm would receive if it invested in a different vehicle with similar risk.

cost of capital economic value added

Internal Rate of Return

Definition

The opportunity cost of an investment; that is, the rate of return that a company would otherwise be able to earn at the

same risk level as the investment that has been selected. For example, when an investor purchases stock in a company,

he/she expects to see a return on that investment. Since the individual expects to get back more than his/her initial

investment, the cost of capital is equal to this return that the investor receives, or the money that the company misses

out on by selling its stock.

Read more: http://www.investorwords.com/1153/cost_of_capital.html#ixzz20W53md1X

Cost of Capital

How can a company raise money to build, for example, a new factory?

The Capital Components are:

Common Stock

Preferred Stock

Bonds (debt)

Retained Earnings - (profit the company makes, but does not give to the shareholders in

the form of dividends)

Each of these components has a cost. We can determine the cost of each capital component. This

study reviews the various components and their underlying theory / theories.

Cost of Retained Earnings

This is kind of weird to think about. It takes some time to understand so take it slowly. After a company makes money (earnings), who owns that money? The shareholders, right? But when

you retain earnings you are not giving the money to the shareholders. You are keeping it. In a way, you are investing it for them in your company. Well those shareholders want some return on that money you are keeping.. How much return do they expect? They want the same amount as if they had gotten the retained earning in the form of dividends, and bought more stock in your company with them. THAT is the cost of retained earnings. You as a financial genius, have to ensure that if you are retaining earning, that the shareholders will get at least as good a return on the money as if they had re-invested the money back into the company.

If you don't understand this, re-read it and re-think it until you do get it. There is really no "cost" in the cost of retained earnings. I mean, no money is changing hands. You aren't paying anyone anything. But you are keeping the shareholders money. You can't say it is "free" money. Frankly if you did, it would screw up your capital budgeting. So when you are doing your capital budgeting, to ensure that the shareholders are getting a decent rate of return, you "guess" a cost of retained earnings. How?? One way is CAPM. Another way is the bond yield plus risk premium approach, in which you take the interest rate on the company's own long term debt and then add between 5% and 7%. Again, you are kind of guessing here. A third way is the discounted cash flow method, in which you divide the dividend by the price of stock and add the growth rate. Again, a lot of guessing.

Cost of Issuing Common Stock

Flotation Cost of Common Stock

=Costs of issuing the actual stock (ink, printing, paper, computers, etc.)

+The cost of retained earnings.

Cost of Preferred Stock

Cost of Preferred Stock = What you give. divided by What you get.

Cost of Preferred Stock = Dividend divided by Price - Underwriting Costs

Cost of Bonds (debt)

Cost of Debt = Coupon rate on the bonds minus The Tax Savings

Interest on bonds is tax deductible. So we can reduce our taxable income by the amount of money we pay to the bondholders.

WACC - The Weighted Average Cost of Capital.

Every company has a capital structure - a general understanding of what percentage of debt comes from retained earnings, common stocks, preferred stocks, and bonds. By taking a

weighted average, we can see how much interest the company has to pay for every dollar it borrows. This is the weighted average cost of capital.

Capital Component Cost Times % of capital structure Total

Retained Earnings 10% X 25% 2.50%

Common Stocks 11% X 10% 1.10%

Preferred Stocks 9% X 15% 1.35%

Bonds 6% X 50% 3.00%

TOTAL 7.95%

So the WACC of this company is 7.95%.

Financial Terms: A B C D E F G H I J K L M N O P Q R S T U V W Y Z

CAPM - The Capital Asset Pricing Model

"Cap-M" looks at risk and rates of return and compares them to the overall stock market. If you use CAPM you have to assume that most investors want to avoid risk, (risk averse), and those who do take risks, expect to be rewarded. It also assumes that investors are "price takers" who can't influence the price of assets or markets. With CAPM you assume that there are no transactional costs or taxation and assets and securities are divisible into small little packets. Had enough with the assumptions yet? One more. CAPM assumes that investors are not limited in their borrowing and lending under the risk free rate of interest. By now you likely have a healthy feeling of skepticism. We'll deal with that below, but first, let's work the CAPM formula.

Beta - Now, you gotta know about Beta. Beta is the overall risk in investing in a large market, like the New York Stock Exchange. Beta, by definition equals 1.0000. 1 exactly. Each company also has a beta. You can find a company's beta at the Yahoo!! Stock quote page. A company's

TeachMeFinance

beta is that company's risk compared to the risk of the overall market. If the company has a beta of 3.0, then it is said to be 3 times more risky than the overall market.

Ks = Krf + B ( Km - Krf)

Ks = The Required Rate of Return, (or just the rate of return). Krf = The Risk Free Rate (the rate of return on a "risk free investment", like U.S. Government

Treasury Bonds - Read our Disclaimer) B = Beta (see above) Km = The expected return on the overall stock market. (You have to guess what rate of return

you think the overall stock market will produce.)

As an example, let's assume that the risk free rate is 5%, and the overall stock market will produce a rate of return of 12.5% next year. You see that XYZ company (Read our Disclaimer) has a beta of 1.7.

What rate of return should you get from this company in order to be rewarded for the risk you are taking? Remember investing in XYZ company (beta =1.7) is more risky than investing in the overall stock market (beta = 1.0). So you want to get more than 12.5%, right?

Ks = Krf + B ( Km - Krf) Ks = 5% + 1.7 ( 12.5% - 5%) Ks = 5% + 1.7 ( 7.5%) Ks = 5% + 12.75% Ks = 17.75%

So, if you invest in XYZ Company, you should get at least 17.75% return from your investment. If you don't think that XYZ Company will produce those kinds of returns for you, then you would probably consider investing in a different stock

Who introduced the CAPM - Capital Asset Pricing Model? Harry Markowitz worked on diversification and modern portfolio theory. Jack Treynor, John Lintner, Jan Mossin and William Sharpe all contributed to the theory of CAPM. William Sharpe, Harry Markowitz and Merton Miller jointly got a Nobel Prize in Economics for contributing to financial economics. See, if you study hard and think up new stuff maybe you can get a Nobel Prize too.

Ah, but CAPM has some flaws. (don't we all)

If you go to a casino, you basically pay for risk. It's possible that the folks on Wall Street sometimes have the same mindset as well. Now remember that CAPM assumes that given "X%" expected return investors will prefer lower risk (in other words lower variance) to higher risk.

And the opposite would be true as well - given a certain level of risk investors would prefer higher returns to lower ones. OK, but maybe the Wall Street people get a kick out of "gambling" their investment. Not saying it's been proven to be the case, just saying it could be. CAPM doesn't allow for investors who will accept lower returns for higher risk.

CAPM assumes that asset returns are jointly normally distributed random variables. But often returns are not normally distributed. So large swings, swings as big as 3 to 6 standard deviations from the mean, occur in the market more frequently than you would expect in a normal distribution.

CAPM assumes that the variance of returns adequately measures risk. This might be true if returns were distributed normally. However other risk measurements are probably better for showing investors' preferences. Coherent risk measures comes to mind.

With CAPM you assume that all investors have equal access to information and they all agree about the risk and expected return of the assets. This idea, by the way is called "homogeneous expectations assumption". Be ready for your professor to ask, "What's the Homogeneous Expectations Assumption and do you believe it's valid". Good luck with that one.

CAPM can't quite explain the variation in stock returns. Back in 1969, Myron Scholes, Michael Jensen and Fisher Black presented a paper suggesting that low beta stocks may offer higher returns than the model would predict.

CAPM kind of skips over taxes and transaction costs. Some of the more complex versions of CAPM try to take this into consideration.

CAPM assumes that all assets can be divided infinitely and that those small assets can be held and transacted.

Roll's Critique: Back in 1977, Richard Roll offered the idea that using stock indexes as a proxy for the true market portfolio can lead to CAPM being invalid. The true market portfolio should include stuff like real estate, human capital, works of art and so on, basically anything that anyone holds as an investment. However, the markets for those assets are often non-transparent and unobservable. So often financial people will use a stock index instead. Does it kind of seem like they are fudging a little bit. You might argue they are.

CAPM assumes that individual investors have no preference for markets or assets other than their risk-return profile. But is that really the case? Say a guy loves drinking Coke. Only Coke. He's collects old Coke bottles and stuff. OK, now, is that guy going to buy stock in Pepsi based only on its risk-return profile, or is he going to buy stock in Coke so he can brag to everyone about how many shares he has?

The Security Market Line

The formula for CAPM is Ks = Krf + B ( Km - Krf).

Let's assume that the risk free rate is 5%, and the overall stock market will produce a rate of return of 12.5% next year. You see that XYZ company (Read our disclaimer) has a beta of 1.7

I f you make a graph of this situation, it would look like this:

On the horizontal axis are the betas of all companies in the market On the vertical axis are the required rates of return, as a percentage

The red line is the Security Market Line.

How did we get it? We plugged in a few sample betas into the equationKs = Krf + B ( Km - Krf).

Security Beta (measures risk) Rate of Return

'Risk Free' 0.0 5.00%

Overall Stock Market 1.0 12.50%

XYZ Company 1.7 17.75%

BOND VALUATION

BondWhen a company (or government) borrows money from the public or banks (bondholders) and agrees to pay it back later

Par Value The amount of money that the company borrows. Usually it is $1,000.

Coupon Payments

This is like interest. The company makes regular payments to the bondholders, like every 6 months or every year.

Indenture The legal stuff. A written agreement between the company and the bond holder. They talk about how much the coupon payments will be, and when the money (par value) will

be paid back to the bondholder.

Maturity Date Date when the company pays the par value back to the bondholder.

Market Interest Rate

This changes everyday.

The thing about bonds is that the interest rate (coupon payments) is fixed. It doesn't change. And bonds last a long time. Like 10 years or whatever. So in the meantime, the market interest rate (the interest rates in general) go up and down. OK, well, if the coupon payments are for 10% and then the market interest rates fall from 10% to 8%, then that bond at 10% is valuable, right. It is paying 10% while the overall interest rate is only 8%. Exactly how much is it worth? You mean 'what is the present value of a bond?'

The Present Value of a Bond

=The Present Value of the Coupon Payments (an annuity)

+ The Present Value of the Par Value (time value of money)

Example

Par Value = $ 1,000 Maturity Date is in 5 years Annual Coupon Payments of $100, which is 10% Market Interest rate of 8%

The Present Value of the Coupon Payments (an annuity) = $399.27

The Present Value of the Par Value (time value of money) =$680.58

The Present Value of a Bond = $ 399.27 + $ 680.58 = $1,079.86

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Stock Valuation - see our disclaimer

Preferred Stock

Preferred stock is somewhat like a bond. They pay the same equal dividends forever.

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Common Stock

Common stock represents ownership in the company. Sometimes there are dividends, sometimes not.

What is the value of Preferred Stock?

This is easy. Preferred stock is basically a perpetuity.

What is the value of Common Stock?

This is not easy. This is a mess. Think about it. What is the value of a share of stock in a specific company? In one sense it is the price the stock trades at. Both the buyer and seller agree to exchange the stock at that price.

We assume that they are both rational people and both know something about the company and its future plans and profit potential. So, yes, that is one method: check the price of the stock in the paper or on the internet. But that's pretty darn easy. It's not really finance. It's more like reading. And I don't know if you realize this or not, but they don't give Nobel Prizes for reading. So there are other ways of doing stock valuation too.

The Gordon Growth Formula, also known as The Constant Growth Formula assumes that a company grows at a constant rate forever. This, by the way, is impossible. I mean, it can't grow forever. You know, if a company doubles in size every 5 years, pretty soon every single person in the world is their customer and then they can't grow at that rate anymore. (because the world population isn't doubling ever 5 years).

BUT, if we go ahead and assume that a company has a constant growth rate, we can use the following formula to get its value.

Constant Growth Formula Po = D 1 / ( Ks - G )

Po = Price D1 = The next dividend. D1 = D0 (1 + G) Ks = Rate of Return G = Growth Rate

What is all this D1 and D0 stuff ?

D1 is the next dividend D0 is the last dividend

Well we are assuming that the company has constant growth, right. So we take the last divided, multiply it by the growth rate and we can get the next dividend.

Example

Last years dividend = $ 1.00 Growth Rate = 5% Rate of Return = 10%

First figure out D1.

D1 = D0 (1 + G) D1 = $1.00 ( 1 + .05) D1 = $1.00 (1.05) D1 = $1.05

Next us the formula.

Po = D 1 / ( Ks - G ) Po = $1.05 / (10% - 5%) Po = $1.05 / 5% Po = $21.00

So, if we want to get a 10% rate of return on our money, and we assume that the company will grow forever at 5% per year, then we would be willing to pay $21.00 for this stock. That is the theory anyways. And again, here is our disclaimer.

Copyright © 1997 - 2009 by Mark McCracken , All Rights Reserved

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Cost of Capital

How can a company raise money to build, for example, a new factory?

What are the Capital Components?

Common Stock Preferred Stock Bonds (debt) Retained Earnings - (profit the company makes, but does not

give to the shareholders in the form of dividends)

Each of these components has a cost. We can determine the cost of each capital component.

Cost of Retained Earnings

This is kind of weird to think about. It takes some time to understand so take it slowly. After a company makes money (earnings), who owns that money? The shareholders, right? But when you retain earnings you are not giving the money to the shareholders. You are keeping it. In a way, you are investing it for them in your company. Well those shareholders want some return on that money you are keeping.. How much return do they expect? They want the same amount as if they had gotten the retained earning in the form of dividends, and bought more stock in your company with them. THAT is the cost of retained earnings. You as a financial genius, have to ensure that if you are retaining earning, that the shareholders will get at least as good a return on the money as if they had re-invested the money back into the company.

If you don't understand this, re-read it and re-think it until you do get it. There is really no "cost" in the cost of retained earnings. I mean, no money is changing hands. You aren't paying anyone anything. But you are keeping the shareholders money. You can't say it is "free" money. Frankly if you did, it would screw up your capital budgeting. So when you are doing your capital budgeting, to ensure that the shareholders are getting a decent rate of return, you "guess" a cost of retained

earnings. How?? One way is CAPM. Another way is the bond yield plus risk premium approach, in which you take the interest rate on the company's own long term debt and then add between 5% and 7%. Again, you are kind of guessing here. A third way is the discounted cash flow method, in which you divide the dividend by the price of stock and add the growth rate. Again, a lot of guessing.

Cost of Issuing Common Stock

Flotation Cost of Common Stock

=Costs of issuing the actual stock (ink, printing, paper, computers, etc.)

+The cost of retained earnings.

Cost of Preferred Stock

Cost of Preferred Stock

=What you give.

divided by What you get.

Cost of Preferred Stock

= Dividend divided by Price - Underwriting Costs

Cost of Bonds (debt)

Cost of Debt = Coupon rate on the bonds minus The Tax Savings

Interest on bonds is tax deductible. So we can reduce our taxable income by the amount of money we pay to the bondholders.

WACC - The Weighted Average Cost of Capital.

Every company has a capital structure - a general understanding of what percentage of debt comes from retained earnings, common stocks, preferred stocks, and bonds. By taking a weighted average, we can see how much interest the company has to pay for every dollar it borrows. This is the weighted average cost of capital.

Capital Component Cost Times % of capital structure Total

Retained Earnings 10% X 25% 2.50%

Common Stocks 11% X 10% 1.10%

Preferred Stocks 9% X 15% 1.35%

Bonds 6% X 50% 3.00%

TOTAL 7.95%

So the WACC of this company is 7.95%.

Financial Terms: A B C D E F G H I J K L M N O P Q R S T U V W Y Z

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