capital structure

Hand notes on cost of capital and capital

structureDisclaimer:

This hand note shall not in any time be regarded as a substitute for students not to visit library, text books and web for acquiring knowledge on this topic, where you find it is suitable then you can rely.

1st draftComposed by:H. B. Hamad

2010

1 of 53 1st Draft to be improved

Introduction You often hear corporate officers, professional investors, and analysts discuss a company's capital structure. You may not know what a capital structure is or why you should even concern yourself with it, but the concept is extremely important because it can influence not only the return a company earns for its shareholders, but whether or not a firm survives in a recession or depression. Sit back, relax, and prepare to learn everything you ever wanted to know about investments and the capital structure of the companies There are several types of value, of which we are concerned with four:

Book Value – The carrying value on the balance sheet of the firm’s equity (Total Assets less Total Liabilities)

Tangible Book Value – Book value minus intangible assets (goodwill, patents, etc)

Market Value - The price of an asset as determined in a competitive marketplace

Intrinsic Value - The present value of the expected future cash flows discounted at the decision maker’s required rate of return

Capital Structure - What It Is and Why It MattersThe term capital structure refers to the percentage of capital (money) at work in a business by type. Broadly speaking, there are two forms of capital: equity capital and debt capital. Each has its own benefits and drawbacks and a substantial part of wise corporate stewardship and management is attempting to find the perfect capital structure in terms of risk / reward payoff for shareholders. This is true for big companies and for small business owners trying to determine how much of their startup money should come from a bank loan without endangering the business. Let's look at each in detail: Equity Capital: This refers to money put up and owned by the shareholders (owners). Typically, equity capital consists of two types:


1. Contributed capital, which is the money that was originally invested in the business in exchange for shares of stock or ownership and

2. Retained earnings, which represents profits from past years that have been kept by the company and used to strengthen the balance sheet or fund growth, acquisitions, or expansion.

Many consider equity capital to be the most expensive type of capital a company can utilize because it’s "cost" is the return the firm must earn to attract investment. A speculative mining company that is looking for silver in a remote region of Africa may require a much higher return on equity to get investors to purchase the stock than a firm such as Procter & Gamble, which sells everything from toothpaste and shampoo to detergent and beauty products. Debt Capital: The debt capital in a company's capital structure refers to borrowed money that is at work in the business. Bonds are generally considered the safest type (long-term) because the company has years, if not decades, to come up with the principal, while paying interest only in the meantime. Other types of debt capital can include short-term commercial paper utilized by giants companies that amount to billions of shillings in 24-hour loans from the capital markets to meet day-to-day working capital requirements such as payroll and utility bills. The cost of debt capital in the capital structure depends on the health of the company's balance sheet - a triple AAA rated firm is going to be able to borrow at extremely low rates versus a speculative company with tons of debt, which may have to pay 15% or more in exchange for debt capital.

Other Forms of Capital: There are actually other forms of capital, such as vendor financing where a company can sell goods before they have to pay the bill to the vendor, which can considerably increase return on equity but don't cost the company anything. In the case of an insurance company, the policyholder "float" represents money that doesn't belong to the firm but that it gets to


use and earn an investment on until it has to pay it out for accidents or medical bills, in the case of an auto insurer. The cost of other forms of capital in the capital structure varies greatly on a case-by-case basis and often comes down to the talent and discipline of managers.

Seeking the Optimal Capital StructureMany middle class individuals believe that the goal in life is to be debt-free (see should I Pay Off My Debt or Invest?). When you reach the upper echelons of finance, however, that idea is almost anathema. Many of the most successful companies in the world base their capital structure on one simple consideration: the cost of capital. If you can borrow money at 7% for 30 years in a world of 3% inflation and reinvest it in core operations at 15%, you would be wise to consider at least 40% to 50% in debt capital in your overall capital structure. Do you agree with me? I can imagine you are not!!.Of course, how much debt you take on comes down to how secure the revenues your business generates are - if you sell an indispensable product that people simply must have, the debt will be much lower risk than if you operate a theme park in a tourist town at the height of a boom market. Again, this is where managerial talent, experience, and wisdom come into play. The great managers have ability for consistently lowering their weighted average cost of capital by increasing productivity, seeking out higher return products, and more. To truly understand the idea of capital structure, you need to take a few moments to read Return on Equity: The DuPont Model to understand how the capital structure represents one of the three components in determining the rate of return a company will earn on the money its owners have invested in it. Whether you own a doughnut shop or are considering investing in publicly traded stocks, its knowledge you simply must have.Most investors assess a stock's promise by weighing common-sense factors about the prospects of the company: the quality of its products or services, its future demand and the nature and strength of the


competition. But this qualitative analysis often fails to answer the critical question of valuation: Given the company's profit potential, is its stock a good investment at today's market price? Professional stock analysts use models to estimate a company's inherent worth and to determine whether the company's stock is a bargain. These models require many inputs. One of the most important to consider is the company's weighted average cost of capital.Companies are vehicles for the productive investment of capital. A typical clothing manufacturer, for instance, may use its cash to buy cotton, pay workers to sew the cotton into sweaters, and then pay a sales force to sell the sweaters for a profit. In this way, the company's ability to raise capital plays a crucial role in its ability to grow profitably.

Costs of CapitalBusinesses can't make money. One choice is to borrow money, either from a bank or through a bond sale. Another option is to sell a piece of the business through an offering of stock, or equity.Both of these alternatives come at a cost. For debt, the company must make interest payments. For equity, it may make dividend payments, and shareholders will expect capital gains. The average of the costs of these two sources of capital, weighted for the proportion of each that the company uses to fund itself, is called the weighted average cost of capital. It is represented in the following formula:We can measure cost to equity in almost three ways.

1. Dividends valuation (dividend yield) method2. Gordon’s dividend growth model3. risk measured analysis

Dividends valuation methodthe price of stock is equal to the present value of all future dividends the intuition behind this insight is that the cash payoff to owners of the stock is equal to cash dividends plus capital gain or losses .Thus expected return


that an investor expects from an investment in a stock over a set period of time is equal to:

Expected return on stock (r) = divident + Capital gain

investment

(r) = Div1+ P1 − PO

PO

Whereby Div1 and P1 denote the dividend and stock price in year1 when we isolate the current stock price Po in the expected price return formula.

(Po) = Div1 + P1

1 + r

The equation then becomes what determines next years price P1 by changing the subscripts next year’s price is equal to the discounted value of the sum of dividends and expected price in year 2

P1= Div2 +P2

1 +r

Po =Div1

1+r+

Div2

(1+r )2 +Div 3+P2

(1+r )3 +. . .. .Div t+P t

(1+r )t

Whereby: t= horizon. It is clearly assumed that, the value to stock is equal to present value of all dividends out of the investment at time t and stock’s present value at time t. when you move to time horizon (t) the present value of stock should not change and assumed to be zero.

P t

(1+r )t=0 Hence the value of stock should be equal to present value

of all future dividends Po = ∑t=1

∞ Divt

(1+r )t

In valuing the common stock, we have made two assumptions: We know the dividends that will be paid in the future. Div1

We know how much you will be able to sell the stock for in the future.

Both of these assumptions are unrealistic, especially knowledge of the future selling price.


Furthermore, suppose that you intend on holding on to the stock for twenty years, the calculations would be very tedious!

Assume: a share or stock is selling for Shs. 75 a share (Po =75). Investment expect a Shs.. 3 cash dividend over the next year (Div1=3). They also expect the stock to sell for Shs.. 81 a year hence (P1 = 81). Then what is the expected return to stockholders?

Expected rate of return (r) = Div1+ P1 − PO

PO = (3+ 81-75)/75 = 12%So 12% is appropriate discounted rate that investor would be like to take on the investment other things constant. Is just a present value of future cash flow that investment is going to generate to its owner. It is further assumed that, this 12% and shs.. 75 are the right discounted rate and right price of stock respectively in any fair market. So you agree with me? I can imagine your answer in NO, ok buddy just follow me with these two scenarios: One: What happen when Po is above shs.. 75? Say shs.79, expected return would be lower than 12% i.e 6.33% hence investor will run away with these investment rushing to other investment of similar risk in the market, they will start to sell their share hence price will drop of cause to shs.. 75 which is market price.Two: assume the price of stock is little bit lower than shs.. 75 say shs..70, what happen to rate? It definitely will rise above 12% i.e 20%. This will lead to many investors rushing in buying share forcing rise to shs.. 75.

In concluding, this formula is unrealistic ∑t=1

∞ Divt

(1+r )t as it is not easy to predict all future dividend going to be paid, hence we should assume that constant dividend paid in perpetuity then our formula should be amended

to r = Div1

r where Div1 = Div0 +g and g is growth rateGordon’s dividend growth modelThe Gordon Growth Model (or Constant Growth Model) is a financial model used to determine the “intrinsic” value of a stock, based on future dividends, which are assumed to grow at a constant rate. Named after


Myron J. Gordon and originally published in 1959, the model values a business as the present value of all future dividends and leverages a required rate of return that the investor could receive on similar

alternative assets.Po = current stock price, D1 =future dividend= Do (1+g) whereby g is growth rate.Arriving at Present ValueThe Gordon Growth Model is the best known of a class of discounted dividend models and is a variation of the discounted cash flow valuation model. The Gordon approach assumes that the company pays a dividend that grows at a constant rate. It also assumes that the investor’s required rate of return for the stock is held constant and is equal to the cost of equity for that company. The model sums this discounted, infinite series of payments to the shareholder to arrive at the present value.A Stock as PerpetuityNote that if the stock is never sold, then it is essentially perpetuity to the investor and its price would equal the sum of the present value of its dividends. Because the model considers the current price of the stock to be equal to its future cash flows, then it follows that the future sale price of the stock would equal the sum of the cash flows subsequent to the sale discounted by the required rate of return.Under the Gordon Model the investor holds the stock for the sole purpose of receiving income from company operations through dividend payments. Investors who look at stocks as if they were buying a private business may benefit from this valuation approach.

.

Summing the infinite series we get,

，

In practice this P is then adjusted by various factors e.g. the size of the company.


，

K or r denotes expected return = yield + expected growth.It is common to use the next value of D given by: D1 = D0(1 + g), thus the Gordon's model can be stated as

. Note that the model assumes that the earnings growth is constant for perpetuity. In practice a very high growth rate cannot be sustained for a long time. Often it is assumed that the high growth rate can be sustained for only a limited number of years. After that only a sustainable growth rate will be experienced. This corresponds to the terminal case of the discounted cash flow model. Gordon's model is thus applicable to the terminal case.When the growth g is zero, that a company pays out all its earning as dividend and nothing retained for investment, i.e g =0

. Write this as

So the return k is the dividend divided by the price.When g is very close to k, the price is very high, going to infinity when g is equal to k.

Problems with the modela) The model requires one perpetual growth rate greater than

(negative 1) and less than the cost of capital. But for many growth stocks, the current growth rate can vary with the cost of capital significantly year by year. In this case this model should not be used.

b) If the stock does not currently pay a dividend, like many growth stocks, more general versions of the discounted dividend model must be used to value the stock. One common technique is to


assume that the Miller-Modigliani hypothesis of dividend irrelevance is true, and therefore replace the stock’s dividend D with E earnings per share. But this has the effect of double counting the earnings. The model's equation recognizes the trade off between paying dividends and the growth realized by reinvested earnings. It incorporates both factors. By replacing the (lack of) dividend with earnings, and multiplying by the growth from those earnings, you double count.

c) Gordon's model is sensitive if k is close to g. For example, if dividend = shs.1.00 cost of capital = 8% Say the growth rate = 1% - 2% So the price of the stock assuming 1% growth= shs.14.43 = 1.00(1.01/.07) assuming 2% growth= shs.17.00 = 1.00(1.02/.06) The difference determined in valuation is relatively small. Now say the growth rate = 6% - 7% So the price of the stock assuming 6% growth= shs.53 = 1.00(1.06/.02) assuming 7% growth= shs.107 = 1.00(1.07/.01) The difference determined in valuation is large.

Cost of Newly Issued Stock Cost of Newly Issued StockCost of newly issued stock (kc) is the cost of external equity, and it is based on the cost of retained earnings increased for flotation costs (cost of issuing common stock). For a constant-growth company, this can be calculated as follows:

R= D1

Po(1−f )+g

where:f = the percentage flotation cost, or (current stock price - funds going to company) / current stock price

Example: cost of newly issued stockassume the company’s stock is selling for shs. 40, its expected ROE is 10%, next year’s dividend is shs. 2 and the company expects to pay out


30% of its earnings. Additionally, assume the company has a flotation cost of 5%. What is cost of new equity?

Capital asset pricing modelCapital asset pricing model (CAPM): This is an equation expressing the relationship between the degree of risk of an investment and the expected return on the investment.The model brings together aspects of share valuations, the cost of capital and gearing. For our purposes, we can make the assumption that there are two basic functions associated with theCAPM:

Attempting to establish the ‘correct’ equilibrium market value of a company’s shares;

Calculating the cost of a firm’s equity (and thus the weighted average cost of capital), as an alternative approach to the dividend valuation model,

RISKThere is risk associated with investment in any security, the greater the risk, the greater the required return from the investment. However, one type of stock which has a low risk and which is assumed in portfolio theory to be risk-free, is government stock

The only way for an investor to avoid risk altogether is to invest solely in government securities

Risk comprises financial and business risk; investors tend to diversify their portfolios to reduce their risk while maintaining their return.

The risk, which can be diversified away is known as unsystematic risk and is unique to a particular company.

The risk related to the market, however, cannot be diversified and is known as systematic or market risk.

Systematic risk is unavoidable risk. Systematic risk may also vary between projects. Such risk may arise as a result of government legislation, from adverse trends in the economy or from other external factors over which the company has no control.


MEASURING SYSTEMATIC RISKThe CAPM splits the total risk of a security into the unsystematic risk and the remainder. The remainder is the relevant risk for appraising investments.CAPM is concerned with:

How systematic risk is measured; How systematic risk affects required returns and share prices.

To measure systematic risk, we use the beta factorThe CAPM is based on the assumptions those investors:

In shares require a return in excess of the risk-free rate (i.e. a premium) as compensation for taking the systematic risk of the investment;

Should not require a premium for unsystematic risk as this may be diversified and removed from the portfolio (as discussed earlier);

Will expect a greater return from companies with greater systematic risk (as measured by their beta factors).

MARKET RISK AND RETURNThe CAPM was formulated principally to evaluate investments in stocks and shares (‘the market’ meaning the stock market) rather than in companies’ investment projects.Market risk is almost impossible to determine accurately, as it is based on the variability of the total market return. As the components of the market fluctuate constantly, so the systematic risk attached to shares will also change.A measure of the relationship between the returns of the company and those of the market is given by the beta factor (β) for that company. The line of best fit, also known as the characteristic line,Therefore, the cost of equity is basically what it costs the company to maintain a share price that is satisfactory (at least in theory) to investors. The most commonly accepted method for calculating cost of equity comes from the Nobel Memorial Prize-winning capital asset pricing model (CAPM), where:


Cost of Equity (Re) = Rf + Beta (Rm-Rf). The formula is expressed as:(Re - Rf) = β (Rm - Rf)orRe = Rf + β (Rm - Rf)Where: Re = expected return from an individual investmentRf = the risk-free rate of returnRm = the market rate of return (the return on the all share index)β = the beta factor of the investmentLet's explain what the elements of this formula are: Rf - Risk-Free Rate - This is the amount obtained from investing in securities considered free from credit risk, such as government bonds from developed countries. The interest rate of Treasury bills or the long-term bond rate is frequently used as a proxy for the risk-free rate. ß - Beta - This measures how much a company's share price moves against the market as a whole. Where β > 1, the shares are described as aggressive: they outperform the market. This means they give a bigger return than the market when the market return is positive and a bigger loss than the market when the market return is negative.Where β = 1, the shares are described as neutral: their returns are in line with the average return of the Stock Market.Where β < 1, the shares are described as defensive: they are less risky than the market generally.The market as a whole has a beta factor of 1. If a company’s beta factor is 2, its return will vary twice as much as the return on the market as a whole.If the market return (Rm) is 5 per cent above the risk-free rate of return, then the expected return for this company with a beta factor of 2 is 10 per cent above the risk-free rate of return.If the market return is 3 per cent below the risk-free return, the expected return for the company is 6 per cent below the risk-free return. The actual return for the company may differ from the expected return because of


variations due to the company’s unsystematic risk, which is unique to the company.

(Rm – Rf) = Equity Market Risk Premium - The equity market risk premium (EMRP) represents the returns investors expect, over and above the risk-free rate, to compensate them for taking extra risk by investing in the stock market. In other words, it is the difference between the risk-free rate and the market rate. It is a highly contentious figure. Many commentators argue that it has gone up due to the notion that holding shares has become riskier. Once the cost of equity is calculated, adjustments can be made to take account of risk factors specific to the company, which may increase or decrease the risk profile of the company. Such factors include the size of the company, pending lawsuits, concentration of customer base and dependence on key employees. Adjustments are entirely a matter of investor judgment and they vary from company to company.Cost of DebtThe cost of debt is simply the cost of borrowing money, or the interest rate that the company would pay on the borrowed amount. When a company is considered risky, it’s cost of borrowing money rises, and when a company is considered stable, its cost of borrowing money falls. For companies that have issued bonds previously, it's possible to estimate the cost of debt by looking at the yield of those bonds.The cost of debt explains the negative reaction that occurs when a company's bonds are downgraded by a ratings agency such as Standard & Poor's. With a lower rating, the company will have to pay higher interest to borrow capital, raising its overall cost of capital.Cost of bank borrowingsBank borrowings do not have a market price with which to relate interest and payments to in order to calculate their cost as is the case with securitized debt. Thus, to approximate the cost of bank borrowings the interest rate paid on the loan should be taken, making the appropriate calculation to allow for the tax deductibility of the interest payment


Cost of preferred stock kP is the minimum required rate of return required on newly issued preference sharesIs given by the equation kP= Dp/Pp

Where:Dp = expected dividend per year and Pp = per share market price of the stockNote: the minimum required rate of return is based on the value of the stock as perpetuityNote: unlike interest expense on debt, preferred stock dividends are viewed as a return to equity, hence there is not tax adjustmentFor instance Zantel preferred stock is selling for shs. 95 per share and pays a dividend of 4% of par value (shs. 100). The cost of preferred stock is kP = 0.4(100)/95 =4.2%

The cost of debt capital which has already been issued is the rate of interest (the internal rate of return) which equates the current market price with the discounted future cash flow from the security.

Irredeemable debtFor redeemable debt the cost is calculated as the interest payable over the market value of debt.

IPo

if tax rate is applied then

I (1− tc )P

0

The tax is included because interest on loan is allowable for tax purposes so if a company use borrowed capital there is always a saving due to tax relief on interest paid.

Cost of redeemable debt

These are debts with a defined period or date of repayment. The cost of these debts will be found by using the internal rate of return.Example:Peet Ltd has 7% debentures in issue. The market price is shs. 95.75 ex


interest. Ignoring taxation, calculate the cost of this capital if the denture is:-Irredeemable.-Redeemable at par after 5 years.Solution(a) The cost of irredeemable debt capital is: 7.3%(b) The cost of debt capital is 7.3% if irredeemable. The capital profit that will be made from now to the date of redemption is shs. 4.25 ( shs. 100 – shs. 95.75). This profit will be made over five years which gives an annualised profit of shs. 0.85.(4.25/5) which is about 0.9% of current market value. The best trial and error figure to try first is, therefore, 7.3% + 0.9% = 8.2% say 8% to the nearest.

Year

cash flow

discount rate (8) PV

discount rate (10) PV

095.75 1

-95.75 1

-95.75

1-5 7 3.993 27.95 3.791 26.545 100 0.681 68.10 0.621 62.1 0.30 -7.11

The approximate cost of debt capital is therefore: 8.1%The cost of debt capital estimated above represents the cost of continuing to use the finance rather than redeeming the debt securities at their current market price. It would also represent the cost of raising additional finance if we assume that the cost of additional capital would be equal to the cost of that already issued. A company with no debt capital can make the calculations using the information of another company which is judged to be similar as regards to risk.

Weighted Average Cost of Capital - WACC

What Does Weighted Average Cost Of Capital - WACC Mean?A calculation of a firm's cost of capital in which each category of capital is proportionately weighted. All capital sources - common stock, preferred stock, bonds and any other long-term debt - are included in a WACC


calculation. All else help equal, the WACC of a firm increases as the beta and rate of return on equity increases, as an increase in WACC notes a decrease in valuation and a higher risk.

The WACC equation is the cost of each capital component multiplied by its proportional weight and then summing:

Where: Re = cost of equity Rd = cost of debt E = market value of the firm's equity D = market value of the firm's debt V = E + D E/V = percentage of financing that is equity D/V = percentage of financing that is debt Tc = corporate tax rate Businesses often discount cash flows at WACC to determine the Net Present Value (NPV) of a project, using the formula: We should consider discount rate that is after tax, remember interest payable in the form of corporate tax is deductible and hence reduce the tax liabilities, but payment of dividends to shareholder is not allowable hence does not reduce the tax liability of company, for this case in the formula of WACC tax has to be included in debt part D/V * rd * (1-tc)ASSUMPTIONS WHEN USING WACC

The cost of capital used in project evaluation is the marginal cost of funds raised to finance the project;

New investments must be financed from new sources of funds, including new share issues, new debentures or loans;

The weighted average cost of capital must reflect the long-term future capital structure of the company.


ARGUMENTS AGAINST USING THE WACC Businesses may have floating rate debt whose cost changes

frequently The business risk of individual projects may be different from that of

the company and will thus require a different premium included in the cost of capital.

The finance used for the project may alter the company’s gearing and thus its financial risk.

ASSESSMENT OF RISK IN THE DEBT VERSE EQUITY DEBT

Fixed interest payment in each period, whether the company makes profit or not If redeemable, then loan amount will have to be paid in the future

In case of default, in interest payment the company may be forced into liquidation

Loans if secured is charged over fixed asset Interest payments are tax deductible, where a company makes

profit Loan will increase the company’s gearing level

EQUITY Ordinary shareholders are the owners of the organization, and are

paid dividends Where organisation does not make profit, dividends may not be paid, without forcing the organisation into liquidation

Dividends paid to shareholders are not tax deductible Equity will reduce the gearing (risk) level

COST OF CAPITAL FOR UNQUOTED COMPANIES


To estimate an approximate cost of capital the firm can use the cost of equity of a similar quoted company and adjust it for difference in financial and business riskCOST OF CAPITAL FOR NOT-FOR-PROFIT ORGANISATIONSGovernment departments do not have a market value, nor do they have business or financial risk, hence they cannot calculate the cost of capital. They therefore use the targeted ‘real rate of return’ set by the treasury as the cost of capitalFactors Influencing Capital StructureBusiness riskRisk associated with the nature of the industry the business operates and if the business risk is higher the optimal capital structure is required.Tax positionDebt capital is regarded as cheaper because interest payable is deductible for tax purposes. Advantage not much for businesses with unrelieved tax losses, depreciation tax shield as they already have an existing lower tax burden.Financial flexibilityDepends on how easy a business can arrange finance on reasonable terms under adverse conditions. Flexibility in raising finance will be influenced by the economic environment (availability of savers and interest rates) and the financial position of the business.Managerial styleHow much to borrow also depend on managers approach to finance risk. Conservative managers will usual try to keep the debt equity ratio low.

Business and Finance RiskBusiness riskThe variability in operating income caused but inherent factors of the business other than debt financing can be influenced by changes in prices, variability of inputs, sales volume, and competition levels.


Finance riskAdditional variability in return that arises because the financial structure contains debt. Finance risk measured through gearing/leverages ratios.Financial gearing

Extent to which debt finances firms total capital structureDebt equity ratio: Total debt/Total assetsTimes interest earnedMeasures the firm’s ability to meet its annual finance interest payments.TIE ratio = Earnings before interest and taxInterest charges Operational gearingMeasures to what extent are fixed costs used in firms operations. Breakeven point analysis will measure the relationship between sales volume, variable cost and the fixed costs. Breakeven point is the level of sales where the firm is neither making profits nor losses i.e. Sales value equals costs.Financial gearing can reach very high levels, with companies preferring to raise additional capital for expansion by means of loans rather than issuing new equity, but there are limits.

Restrictions on further borrowing might be contained in the denture trust deed for a company’s current debenture stocks in issue.

Occasionally, there might be borrowing restriction in the articles of association.

Lenders might want security for extra loan which the would be borrowers cannot provide.

Lenders might simply be unwilling to lend more to a company with high gearing or low interest cover.

Extra borrowing beyond a safe level will cost more interest. Companies might not be willing to borrow at these rates.

Apart from the limitations stated above, there are other side effects associated with high gearing which may include the following:


Financial distress where obligations to the conditions are not met or they are met with difficultiesCosts: -

Loss of key suppliers Uncertain customers Low asset value Loss of staff moral Legal costs Agency costs in trying to negotiate additional loan facilities through

an agent. High interest rates Need to sign loan covenants thereby loosing financial freedom Borrowing cap Limits set by lenders on amount available Financial slack – Highly geared firms fail to seize opportunities as

they arise due to unwillingness of lenders for more fund advancements.

High gearing might send bad signals on company’s liquidity to employees as well as lenders

Loss of decision making on certain areas to lenders due to loan covenants

Despite mentioning all the limitations and cost of high gearing mentioned above company’s still uses debt capital. Apart from being cheaper than share capital the following attributes compels the company to use the debt capital.

Motivation – Regarded as cheaper source of income New issue stocks may dilute holding Operational and strategic staff more cautious on utilization of funds Flexibility in arrangement than equity

Capital Structure- part 11The purpose of this note is to examine how the value of the firm is affected (holding investment policy and dividend policy constant) by the


way in which the firm finances its investments. For example, can the value of the firm be increased by financing new investments with debt rather than equity? In order to examine the effect of the firm's financing decisions (the firm's capital structure) on the value of the firm, assume that

the firm's investment decision is given, the firm's dividend policy is given, there are no transaction costs involved in either the purchase or sale

of securities Investors can borrow and lend at the same rate that corporations

can borrow and lend.Value of Tax Shields from the Corporate Deduction for Interest

Expense

The capital investment projects undertaken by the firm are usually financed with some combination of debt and equity. In order to understand the effect of this choice on the value of the firm, consider the case where the firm is currently financed entirely (100 percent) by equity. We will also assume that the firm's production capacity is already in place (i.e., the investment decision by the firm is a given) so that any changes in the firm's financing mix (such as replacing equity with debt financing) will have no impact on the cash flows from operations.

To see how the value of the firm changes if equity financing is replaced with debt financing, suppose that the firm issues a perpetual bond that pays one shillings of interest each year. Assuming that the interest payments for the bond are risk-free and that the opportunity cost for risk-free cash flows (before personal tax) is r, the amount that is raised by

issuing this bond is shs 1

rd

The proceeds from the debt issue will be used to repurchase an equal Shilling amount of the firm's outstanding equity shares. Although firms do


not issue perpetual debt in practice, the consequences of using debt as a more or less permanent component of a firm's financing mix are virtually identical.The implications of the “recapitalization” (change in financing mix) described above is to divert one Shilling of before-tax operating income (profit before financing charges and taxes) from stockholders to bondholders. If no debt had been issued, the firm would have to pay corporate taxes on the Shilling in question at a rate of tc. The remainder would be paid to the shareholders, either in the form of a dividend or through reinvestment in the firm resulting in appreciation in the stock price. Since the dividend to the shareholders would have been taxed at a rate of te, the after-tax value of one Shilling of operating income directed toward the stockholders in the firm is

(1 - te) (1 - tc) shs1 .

The net benefit created by corporate borrowing can be determined by comparing the after-tax cash flows to the stockholders with the after-tax cash flows which bondholders receive if the firm issues enough perpetual debt so that one Shilling is diverted to the payment of interest expense. Since corporations are allowed to deduct interest expense prior to computing their corporate tax liability, the interest income to the bondholders is equal to one Shilling. Since interest income is taxed at a rate of to , the after-tax cash flow received by the bondholders is (1 - to) shs 1

The value (if any) of diverting one Shilling of before-tax operating cash flow from the shareholders to the bondholders can be determined by comparing (subtracting) the after-tax cash flows that would have been received by the stockholders to (from) the after-tax payment received by the new bondholders,

[ ( 1 - to ) - ( 1 - te ) ( 1 - tc ) ] shs1 .If these after-tax cash flows are capitalized in perpetuity (i.e., valued as a perpetuity) using the after-tax return required by the bondholders, ( 1 - to )


rD , then the value which is created by diverting one Shilling of before-tax

operating income from the stockholders to the bondholders isshs1

Rearranging the expression above shows that the value created in a recapitalization that causes the firm to pay an additional one Shilling per year of interest expense (in perpetuity) is

[ 1 - ] .For a firm having outstanding debt in the amount of D with yearly interest expense of rD , the total value created by replacing D Shillings of equity (starting from a point of relying solely on equity financing) with D Shillings of debt is obtained by simply multiplying the firm's yearly interest expense (rD) by the value per Shilling of yearly interest expense given above. Therefore, the incremental value created by financing with debt rather than equity is given by

D [ 1 - ] .

The incremental value of the tax shields generated by debt financing is used as an adjustment to the value of an unlevered firm (i.e., one that is 100 percent equity financed). That is the value of the recapitalized or levered firm (i.e., the value after debt has been added to the firm's financial structure) is equal to the value of the unlevered firm (V) plus the value of the tax shields from debt financing

V= V+ D [1 - ] .To illustrate the application of the formula, consider the following special cases.Example 1 :Suppose that the corporate tax rate (tc) is 50 percent, the tax rate on

interest income (to) is 40 percent and the tax rate on equity income (te) is equal to zero. Then the value of the tax shields from one Shilling of debt (not one Shilling of interest expense) is


shs1 [1 - ] =shs1[1- ]

= shs1 [1 - ]

= shs .17.

Therefore, the value of each Shilling of debt added to the firm's financial structure (up to some level consistent with sustained profitability for the firm) is shs.17 per Shilling of debt (not interest expense).Example 2:Assume that the corporate tax rate (tc) is 50 percent and that the tax rate

on interest income (to) is 40 percent as in Example 1. However, assume

that the tax rate on equity income (tE) reflects the fact that 20 percent of

the income to stockholders is in the form of dividend income taxed at 40 percent while 80 percent is in the form of capital gains having (according to many economists) an effective tax rate of zero. Therefore, the tax rate on equity income is approximately 8 percent (.20x.40 + .80x0). In this case, the value of the tax shields from one Shilling of debt is

shs1 [1 - ] = shs1 [1 - ]

= shs1 [1 - ]

= shs .23.Note that the higher the tax rate on equity income, the greater is the value of the tax shields from replacing equity with debt financing.

Example 3:A particularly important example is the case where the tax rate on interest income (to ) is equal to the tax rate on equity income (tE) . In this case the


value of the tax shields from one Shilling of debt (not one Shilling of interest expense) is

shs1 [1 - ] = shs1 [1 - (1 - tc) ]

= shs1 (tc).

This example shows that when equity income and interest income are taxed at identical rates the value of the tax shields from financial leverage is determined entirely by the corporate tax rate, just as if the marketplace ignored the effects of personal income taxes. In other words, when (te) is equal to (to ) , the value each Shilling of debt is equal to tc so that the value of the levered firm is given by

VL = VU + tc D .

Note that the adjustment that has been used to the value of the unlevered firm (with no debt financing) to reflect the value of the tax shields from debt implicitly assumes that the firm holds the level of debt to a (“moderate”) level that allows the firm to sustain consistent (taxable) profitability. So long as the firm is consistently profitable, the full value of the tax shields may be realized (without resorting to tax loss carry forwards). What is moderate will depend critically on the nature of the industry in question. For example, firm's engaged in highly speculative research and development activities have little assurance of utilizing the tax deductions for the interest expense on debt (in addition to providing poor collateral). Therefore, firm's engaged in heavy research and development activities will tend to rely primarily on equity financing. On the other hand, firms in mature industries (e.g., tobacco or food products) that have relatively stable cash flows can often support relatively high levels of debt.


The Impact of Financial Structure in a World with No TaxesTo illustrate the important impact of taxes on the value of financing decisions, it is useful to examine the impact of a recapitalization (issue debt and buy back equity) on the value of the firm under the (artificial) assumption that all of the tax rates considered previously are equal to zero. Given this assumption, the example shows that even though a change in financial structure has no impact on the total value of the firm, the resulting change in the risk profile of the remaining equity shares (including an increase in the expected dividend) precipitates an increase in the cost of equity capital.

Machinga Example:

Number of Shares = 1000Price per Share = shs 10Firm Value = shs 10,000

State 1 State 2 State 3Net Operating Income shs500 Shs 1.000 Shs 2,000Probability 1/4 1/8 5/8Earnings per Share shs .50 shs1.00 shs2.00Return on Equity (ROE) 5% 10% 20%

Given the three possible values for the Return on Equity, the expected (required) rate of return on Machinga's stock is

rE = .05 + .10 + .20 ,

= .15 (15 percent).

Assume that all earnings will be paid out as a dividend (in perpetuity). Then the expected dividend for the firm will be

E(D)= shs.50 + shs1.00 + shs2.00 ,

= shs1.50.


Given that the required rate of return on equity (the cost of equity capital) is 15 percent, it is easy to verify that the price of one share in the firm should be (as we have already assumed)

P0 = = shs 1 .50.15 = shs 10,

Where rE is the required rate of return on equity.

Suppose now that the firm decides to

a) sell shs5000 of debtb) Retire 500 shares of stock with the proceeds from the debt

issue.

Then the new capital structure will be

Number of Shares = 500Price per Share = shs 10Value of Shares = shs 5000Value of Debt = shs 5000

To see why this must be the case, consider the possible realizations of earnings per share and return on equity for the recapitalized or levered firm.

State 1 State 2 State 3Operating Income shs500 Shs 1,000 Shs 2,000Interest Expense Shs 500 Shs 500 Shs 500Net Income shs 0 Shs 500 shs 1500Earnings Per Share (EPS) 0 Shs 1.00 Shs 3.00Return on Equity (ROE) 0 10% 30%


It can be shown that the recapitalization of the firm has increased the expected dividend for the remaining shareholders of Machinga to shs 2.00 per share. (You should be able to compute the expected dividend for the recapitalized firm in the same way that we computed the expected dividend for the unlevered version of Machinga). However, since the required rate of return increases to 20 percent (you can show that the expected Return on Equity is 20 percent), the stock price remains unchanged at shs 10 per share. Therefore, the recapitalization has no effect on the total value of the firm.

The increase in the expected rate of return demanded by shareholders can be motivated by examining the respective payoff patterns for the unlevered (the original debt-free firm) and levered (recapitalized to include debt financing) firm. Consider our projections for ROE and EPS for each of the possible outcomes for net operating income. Although the recapitalization has increased the expected dividend per share, the increase in financial leverage has also increased the range (variability) for both dividends per share (from shs.50-shs2.00 to 0-shs3.00) and Return on Equity (from 5%-20% to 0%-30%). In other words, financial leverage increases the risk associated with the expected returns promised to shareholders. Since we have assumed that there are no tax benefits associated with debt financing (these will be discussed later), the value of the firm's equity shares will not change (this “can be shown”).

To see why the recapitalization has no impact on the total value of the firm, consider the position of an investor who initially owned two shares of stock. Prior to the recapitalization, the investor's income from these two shares would have had the following distribution across states of the world

State 1 State 2 State 3Earnings per Share shs .50 Shs 1.00 Shs 2.00Income from 2 Shares of Stock Shs 1.00 Shs 2.00 Shs 4.00


Given our assumption that the firm is recapitalized by issuing debt to buy back one half of the firm's outstanding stock, an investor with two shares prior to the recapitalization would now have one share of stock and shs 10 (from the sales of one of the shares of stock), which could be invested at 10 percent interest by purchasing shs 10 of the bonds of the recapitalized firm. The total income to the investor from one share of stock (with a market price of shs 10) and one bond (also worth shs 10) paying interest at a rate of 10 percent would be

State 1 State 2 State 3Income from 1 Levered Share 0 shs1.00 shs3.00Income from shs10 in Bonds Shs 1.00 1.00 1.00Total Investment Income Shs 1.00 Shs 2.00 Shs 4.00

The Table above shows that the total investment income for an investor with shs2 0 invested in a portfolio consisting of one share of stock in the recapitalized firm and shs 10 in bonds is identical to the pattern of returns obtained from owning 2 shares in the all equity (unlevered) firm. Therefore, the investor can undo the impact of the recapitalization by simply using the proceeds from selling stock back to the firm to purchase the newly issued bond.Similarly, so long as an investor can borrow at the same interest rate (roughly) as corporations, shareholders can replicate (match) the pattern of payoffs from the levered firm by financing one-half of an investment in 2 shares of stock in an all equity firm by borrowing shs 10 at an interest rate of 10 percent. The distribution of payoffs from this portfolio is shown belo


State 1 State 2 State 3Income from 2 Levered Share 0 Shs 2.00 Shs 4.00Interest on Personal Debt of shs 10 Shs 1.00 1.00 1.00Total Investment Income Shs 0.00 Shs 1.00 Shs 3.00

Which is identical to the dividends from an investment of shs 10 in the shares of the recapitalized firm? In other words, the firm cannot create value for investors by recapitalizing an all equity firm since the shareholders are able to do this for themselves if they wish.

The implications of the analysis above, for which Merton Miller and Franco Modigliani received the Nobel Prize in Economics, is that the financing mix used by the firm (the capital structure) does not matter as long as investors are able to costlessly duplicate (or reverse) the financial implications of any financing decision which the firm might make. These implications can be summarized as

1. The total market value of the debt and equity of a levered firm (using debt financing in addition to equity financing) must be equal to the market value of an unlevered (all equity) firm having the same degree of operating risk. In other words,

VU = VL.

2. Since VL is equal to VU, the two firms must have the same blended cost of funds or weighted average cost of capital, which requires that the cost of equity capital for the levered firm be greater than the cost of equity capital for the unlevered firm (since the cost of debt will always be less than the cost of risky equity capital).

Weighted Average Cost of Capital


The weighted average cost of capital (WACC) is the firm's hurdle rate or opportunity cost of capital. The WACC is used in capital budgeting to compute the net present value for projects which have the same risk and debt capacity as the firm as a whole. In general, the weighted average cost of capital may be thought of as the required return on the portfolio of securities that has been issued to finance the firm's operations. In general, the firm's WACC may be computed using the formula

WACC = rD + rE

Where D is the value of the firm's debt, S is the value of the firm's equity, VL is the total value of the firm, td is the before-tax cost of debt, re is the cost of equity and td is the corporate tax rate.

In the previous example, we assumed that the corporate tax rate (tc) was equal to zero. After the firm was recapitalized to include debt financing, the outstanding value of the firm's debt was shs 5,000, the value of the equity was shs 5,000 and the total value of the firm was shs 10,000. Since the before-tax cost of debt is 10 percent and the required rate of return on the equity in the recapitalized firm is 20 percent, the weighted average cost of capital is

WACC = rD + rE

= shs .5 , 000shs 10 ,000 .10 +

shs .5 , 000shs 10 ,000 .20

= .15 (15 percent).

Note that prior to the recapitalization (using debt financing), the firm relied solely on equity financing with a cost of 15 percent. In other words, there is only one security in the financing portfolio of the all equity firm.


Therefore, the weighted average cost of capital for an all equity firm must be equal to the cost of equity (which is also the required return on the firm's assets for an all equity firm), which in this case was 15 percent. The computations above show that when there is no tax deduction for corporate interest expense, a firm cannot change it's weighted average cost of capital by altering the financing mix used to finance its operations.

Valuation

There are three general approaches to valuation,1. Adjusted Present Value 2. Adjusted Discount Rate 3. Equity Capitalization

For the relatively straightforward examples illustrated here, the three approaches give identical values for the firm and its component securities. However, in some instances, one or more of the valuation approaches suggested above may be difficult to implement. Therefore, it is usually convenient to have more than one valuation technique at your disposal.Adjusted Present ValueThe adjusted present value approach to valuation is a two-step approach requiring that we

value the firm as if the project were to be financed entirely by equity,

Then add on the present value of any special benefits associated with the financing of the project.

Examples of special financing benefits whose value should be accounted for include

the value of the tax shields from debt financing, the value of subsidized financing which may be tied to

undertaking the project (e.g., industrial development bonds or below market loans from foreign governments),


the flotation costs of issuing securities.

To simplify the discussion of the Adjusted Present Value (APV) approach to valuation, consider the case where a firm generates perpetual before-tax operating cash flows denoted by EBIT. As noted above, the first step in the APV approach is to value the firm (or project) as if the financing were all equity. Note that if the financing for a project is 100 percent equity then the cost of equity capital re is equal to the required return on assets, ra. In other words, if there were no debt financing, then after paying corporate taxes at a rate of tc, 100 percent of EBIT can be used to pay dividends to the shareholders. Therefore, the value of the all equity/unlevered firm (Vu) is equal to after-tax EBIT capitalized in perpetuity at the required return on assets

Vu = .

The second step of the APV approach requires that we determine the value of any financing effects associated with a firm or project separately and then add the value of these benefits to the unlevered value of the project. For example, if the firm issues D Shillings of debt then the value of the “recapitalized” firm will be

VL = VU + tc D .

To illustrate the application of the Adjusted Present Value approach, consider a firm which has perpetual EBIT of shs 1,000,000 per year. Assume that the corporate tax (tc) rate is 46 percent and that the required return on assets (rA) is 20 percent. If the firm issues shs 3,000,000 of perpetual debt at an interest rate of 15 percent, then the pre- and post-recapitalization cash flows to the stockholders and bondholders will be

Pre-Recapitalization(All Equity)

Post-Recapitalization(shs3,000,000 of Debt)

EBIT shs1,000,000 shs1,000,000


Less: Interest 0 450,000Net Income shs1,000,000 shs550,000Less: Tax@ .30 300,000 165,000Equity Income Shs700,000 Shs385,000Interest (to Bondholders) 0 450,000Total After-Tax Payout Shs700,000 Shs 835,000

Note that when the firm is financed entirely by equity, the firm pays no interest and the total after-tax payout from the firm is equal to

(1 - tc) EBIT = (1 - .30) shs 1,000,000,

= shs 700,000.If the firm issues shs 3,000,000 in debt at 15 percent, then the cash flow to the stockholders is(1 - tc) [EBIT - rD D] = (1 - .3) [shs 1,000,000 - .15 x shs 3,000,000],

= shs 385,000.The interest to the bondholders is equal to rD D or shs 450,000. Therefore, the sum of the after-tax cash flow to the stockholders and bondholders is

(1 - tc) [EBIT - rD D] + rD D= ( 1 - tc ) EBIT + tc rD D .

= (1 - .30) shs 1,000,000 + .30 x .15 x shs 3,000,000,

= shs 700,000 + shs 135,000.The example shows that adding debt to the financial structure of the firm increases the total after-tax cash flow paid out by shs 135,000, the tax savings attributable to the corporate deduction for interest expense. If this amount is capitalized in perpetuity using the cost of debt (note that we are ignoring personal taxes here), the additional cash flow increases the value of the firm by shs 900,000 (shs 135,000/.15).Applying the formula for the value of the unlevered firm shows that

Vu = ,

= (1−. 30 )shs 1, 000 , 000

0.20 ,= shs 3,500,000.


So that the total value of the levered firm isVL = Vu + tc D

= shs 3, 500,000 + .30 x shs 3, 000,000 = shs 4,400,000.

The example above raises an important fundamental question concerning the application of the formula for the value of the levered firm. The assumption that the firm can issue shs 3,000,000 of debt to repurchase equity is questionable given that the initial value of the all equity firm is only shs 3,500,000. If the primary security for the loan is the collateral (i.e., the value of the underlying assets), then it is unlikely that the required debt financing can be obtained. Note however that the operating cash flow for the firm is more than twice as large as the required interest payments on the debt. While this level of interest coverage would likely place the rating on the firm's debt in the BB- to B+ range, the initial willingness of fixed income investors to purchase the debt of the firm is in doubt given the fact firms in the BBB ratings category have great difficulty issuing debt in tight credit markets. Nevertheless, if the cash flow of the firm is stable, then bondholders may be willing to purchase the debt of the firm based on the adequacy of the cash flows generated by the firm's assets.Adjusted Discount RateThe most important alternative to the Adjusted Present Value method of valuation is the Adjusted Discount Rate approach. Under the Adjusted Discount Rate approach, the present value of the “after-tax operating cash flows” (i.e., the after-tax profits if the project were financed entirely with equity) is determined using an “adjusted discount rate” which takes into account any benefits from the utilization of debt in the financing of the project. That is, the value of the firm or project may also be determined by capitalizing the “after-tax operating cash flows” for the unlevered firm using a discount rate that is adjusted to reflect the tax shields associated with debt financing. This approach can be represented using the following formula for the value of the levered firm

VL = ,


where WACC (sometimes referred to as the weighted average cost of capital) represents the adjusted discount rate.

The adjusted discount rate is most easily defined by noting that the adjusted present value approach and the adjusted discount rate approach should suggest the same value for a firm with perpetual operating cash flow of EBIT and debt financing in the amount of D. In other words, an adjusted discount rate or weighted average cost of capital is defined by the identity,

+ tc D = .

Note that when the corporate tax rate is equal to zero,

= ,

which implies that the value of the tax shields from debt are equal to zero, which in turn implies that the weighted average cost of capital (the adjusted discount rate) is equal to the required rate of return on assets. In other words, when the tax shields from debt have no value, the cost of financing the firm does not depend on the amount of debt in the firm's financial structure.It is fairly easy to show that the weighted average cost of capital defined above is simply the average cost of the portfolio of securities used to finance the firm's operations. For example, if the firm uses only debt and equity to finance its operations, then the WACC is a weighted average of the after-tax cost of debt (to account for the corporate deduction for interest expense) and the cost of equity. The formula for the weighted average cost of capital is

WACC = rD + rE

where the weights of debt and equity in the capital structure are respectively D/VL and S/VL .


To use the formula above to value the firm, we need to know both the cost of equity and the after-tax cost of debt. In the previous example, the cost of debt was 15 percent. Although we know that the required return on assets is 20 percent, which is the cost of equity for a firm with no debt in its financial structure, we don't know the cost of equity for the levered (or recapitalized) firm. We have already shown that financial leverage increases the risk of the cash flows to the shareholders. Further, we know that the increase in risk increases the rate of return required by the shareholders. It turns out that the cost of equity capital is related to the required return on assets (rA ) and the amount of debt in the firm's financial structure by the following formula

rE = rA + .

To show how this formula works, consider the previous example. We saw that after the firm issued shs 3,000,000 of debt (D), the total value of the firm was shs 4,400,000, which implies that the value of the firm's equity is shs 1,400,000. Given a required return on assets of 20 percent, a before-tax cost of debt of 15 percent, and a corporate tax rate of 46 percent, the cost of equity capital is

rE = .20 +

shs 3 ,000shs .1 , 400

(1−.3 )( . 2−. 15)

= 27.5 percent) .

Given the cost of equity capital, we can now determine the weighted average cost of capital,

WACC = rD + rE

= 3 , 0004 ,400

(1−30).15 +

1 , 4004 , 400 .27.5,


= 0.275 (approximately 27.5 percent) .

Once we know the weighted average cost of capital we can determine the value of the firm by discounting the after-tax operating cash flow of the firm using the weighted average cost of capital or adjusted discount rate,

VL = ,

= (1−. 30 )1 ,000 ,000

0 .275

= shs 4,400,000.The calculations above show that under ideal conditions, the Adjusted

Discount Rate approach to valuation and the Adjusted Present Value approach give the same value for the firm. Wonderful you say. So what? Since we needed the value of the firm and the value of the equity (obtained using the APV approach) to determine the weights of debt and equity required to determine the WACC, isn't the logic above circular and therefore useless?The answer to the question above is clearly no, the Adjusted Discount Rate approach (WACC) to valuation is very useful. In fact, we have been using an Adjusted Discount Rate approach to valuation all semester. Recall that our estimates of the cash flows from capital investment projects have never included a charge for any financing costs associated with the project. In other words, the approach that we have followed has always been to estimate the after-tax cash flow from operations, without considering the costs associated with the financing of the project. Implicitly, the costs of financing the project were always taken care of by making the appropriate adjustment to the discount rate used to compute the present value of the project.

With regard to the question of how we determine the relative weights of debt and equity in the capital structure, the Adjusted Discount Rate approach is typically used to value projects that will be financed with the


same mix of securities as the firm's existing assets. Firms usually have a reasonable estimate of the relative importance of debt and equity in both the mix of securities used to finance existing operations and the mix of securities that will be required to finance projects currently in the planning stage. Since the corporation usually has a reasonable estimate of the weights of the various components of the financing mix, computing the weighted average cost of capital is not usually a problem in practice. Therefore, the choice between the Adjusted Discount Rate approach and the Adjusted Present Value approach hinges on whether the financing benefits associated with a project take the form of the tax savings from issuing debt that will provide long-term financing for the project (use APV) or whether the financing benefits include short-term financing benefits such as subsidized financing or loan guarantees.

Equity Capitalization Approach

The equity capitalization approach to valuation calls for valuing the equity of the firm separately using the cost of equity capital. In other words, we value the stock by computing the present value of the after-tax cash flows (after paying interest to the bondholders) available for distribution to the shareholders using the cost of equity capital. The total value of the firm is then determined by adding the value of the firm's outstanding debt to the value of the equity.

The equity capitalization approach is most often used to value1. Real Estate Investments

These projects are usually heavily leveraged. The fact that the debt financing is often specific to the project makes the weighted average cost of capital difficult to determine in some cases.

2. Joint VenturesSince the debt associated with a joint venture is usually a liability of the venture itself rather than of the individual partners, each partner is concerned primarily with the value of their respective


equity shares, rather than with the value of the venture as a whole.

3. Foreign InvestmentsDebt financing is often obtained in one or more foreign countries in order to hedge political and exchange rate risk. Other financing aspects as loan guarantees and subsidized interest rates make the computation of an adjusted discount rate or weighted average cost of capital difficult in such cases.

To illustrate the equity capitalization approach, we continue the preceding example. Since we have already determined that the cost of equity capital for the recapitalized firm is .275 (27.5 percent), all that remains is to determine the after-tax cash flows available for distribution to the shareholders,(1 - tc) [EBIT - rD D]= (1 - .30) [ shs 1,000,000- .15 x shs 3,000,000 ]

= shs 385,000.If we discount the after-tax cash flows to the shareholders at the cost of equity capital, the value for the firm's outstanding equity shares is

S = ,

= (1−. 3 )[1 ,000 ,000−. 15∗3 ,000 , 000 ]. 275 ,

= shs 1,400,000.Adding the value of the firm's outstanding debt, which is shs 3,000,000; we find that the value of the firm is shs 4,400,000 as before.

Modigliani-Miller theorem


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, and asymmetric information, and in an efficient market, the value of a firm is unaffected by how that firm is financed. 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.The theorem was originally proven under the assumption of no taxes. It is made up of two propositions which can also be extended to a situation with taxes.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.

Without taxes, Proposition I:


where VU is the value of an unlevered firm = price of buying a firm composed only of equity, and VL is the value of a levered firm = price of buying a firm that is composed of some mix of debt and equity.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 or in the absence of efficient markets.

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

ke is the required rate of return on equity, or cost

of equity. k0 is the cost of capital for an all equity firm. kd is the required rate of return on borrowings, or cost of debt. D / E 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).


http://en.wikipedia.org/wiki/File:MM2.png

These propositions are true assuming the following assumptions: no taxes exist, no transaction costs exist, and Individuals and corporations borrow at the same rates.

These results might seem irrelevant (after all, none of the conditions is 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 taxesProposition I:

where VL is the value of a levered firm. VU is the value of an unlevered firm. TCD is the tax rate (TC) x the value of debt (D) the term TCD 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 rE is the required rate of return on equity, or cost of equity. r0 is the cost of capital for an all equity firm. rD is the required rate of return on borrowings, or cost of debt. D / E is the debt-to-equity ratio. Tc 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 TC 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.While it is difficult to determine the exact extent to which the Modigliani-Miller theorem has impacted the capital markets, the argument can be made that it has been used to promote and expand the use of leverage.When misinterpreted in practice, the theorem can be used to justify near limitless financial leverage while not properly accounting for the increased risk, especially bankruptcy risk, that excessive leverage ratios bring. Since the value of the theorem primarily lies in understanding the violation of the assumptions in practice, rather than the result itself, its application should be focused on understanding the implications that the relaxation of those assumptions bring.It can also be misinterpreted to justify excessive leverage in order to extend margins for trading operations, even though this action should not be directly comparable to the capital structure of a financial entity.

Review questionsQuestion no. 1A consultant has collected the following information regarding Young Publishing:


(m/=)Total assets 3,000 Tax rate 40%Operating income (EBIT) 800 Debt/ ratio 0%Interest expense 0 WAC 10%Net income 480 M/B ratio 1.00×Share price (not in millions) 3.00EPS = DPS (not in millions) 3.20

The company has no growth opportunities (g = 0), so the company pays out all of its earnings as dividends (EPS = DPS). The consultant believes that if the company moves to a capital structure financed with 20 percent debt and 80 percent equity (based on market values) that the cost of equity will increase to 11 percent and that the pre-tax cost of debt will be 10 percent. If the company makes this change, what would be the total market value of the firm? (The answers are in millions.)

Question no. 2.ZU Electronics currently has no debt. Its operating income is shs. 20 million and its tax rate is 40 percent. It pays out all of its net income as dividends and has a zero growth rate. The current stock price is shs. 40 per share and it have 2.5 million shares of stock outstanding. If it moves to a capital structure that has 40 percent debt and 60 percent equity (based on market values), its investment bankers believe its weighted average cost of capital would be 10 percent. What would its stock price be if it changes to the new capital structure?

Question no. 3.ZU Software Co. is trying to estimate its optimal capital structure. Right now, ZU has a capital structure that consists of 20 percent debt and 80 percent equity, based on market values. (Its D/S ratio is 0.25.) The risk-free rate is 6 percent and the market risk premium, rM – rRF, is 5 percent. Currently the company’s cost of equity, which is based on the CAPM, is 12 percent and its tax rate is 40 percent. What would be ZU’s estimated cost of equity if it were to change its capital structure to 50 percent debt and 50 percent equity?

Question no. 4.JAK Enterprises Co. Ltd is trying to determine its optimal capital structure. The company’s capital structure consists of debt and common stock. In order to estimate the cost of debt, the company has produced the following table:

% financed

With debt (wd)

% financed

With equity

(wc)

Debt-to-equity ratio (D/S)

Bond Before-tax

rating (%)

Cost of

debt

0.10 0.90 0.10/0.90 = 0.11 AA 70.20 0.80 0.20/0.80 = 0.25 A 7.20.30 0.70 0.30/0.70 = 0.43 A 8.0


0.40 0.60 0.40/0.60 = 0.67 BB 8.80.50 0.50 0.50/0.50 = 1.00 B 9.6

The company’s tax rate, T, is 40 percent.The company uses the CAPM to estimate its cost of common equity, rs. The risk-free rate is 5 percent and the market risk premium is 6 percent. Aaron estimates that if it had no debt its beta would be 1.0. (Its “unlevered beta,” bU, equals 1.0.) On the basis of this information, what is the company’s optimal capital structure, and what is the firm’s cost of capital at this optimal capital structure?

Question no. 5.The A. J. Croft Company (AJC) currently has shs. 200,000 market value (and book value) of perpetual debt outstanding carrying a coupon rate of 6 percent. Its earnings before interest and taxes (EBIT) are shs. 100,000 and it is a zero-growth company. AJC's current cost of equity is 8.8 percent, and its tax rate is 40 percent. The firm has 10,000 shares of common stock outstanding selling at a price per share of shs. 60.00.

a) What is AJC's current total market value and weighted average cost of capital?

b) Now assume that AJC is considering changing from its original capital structure to a new capital structure with 50 percent debt and 50 percent equity. If it makes this change, its resulting market value would be shs. 820,000. What would be its new stock price per share?

c) Now assume that AJC is considering changing from its original capital structure to a new capital structure that results in a stock price of shs. 64 per share. The resulting capital structure would have a shs. 336,000 total market value of equity and shs. 504,000 market value of debt. How many shares would AJC repurchase in the recapitization?

Question no. 6Your company has decided that its capital budget during the coming year will be shs. 20 million. Its optimal capital structure is 60 percent equity and 40 percent debt. Its earnings before interest and taxes (EBIT) are projected to be shs. 34.667 million for the year. The company has shs. 200 million of assets; its average interest rate on outstanding debt is 10 percent; and its tax rate is 40 percent. If the company follows the residual dividend policy and maintains the same capital structure, what will its dividend payout ratio be?

Question no. 7.Chwaka Ltd. expects EBIT of shs. 2,000,000 for the current year. The firm’s capital structure consists of 40 percent debt and 60 percent equity, and its marginal tax rate is 40 percent. The cost of equity is 14 percent, and the company pays a 10 percent rate on its shs. 5,000,000 of long-term debt. One million shares of common stock are outstanding. For the next year, the firm expects to fund one large positive NPV project costing shs. 1,200,000, and it will fund this project in accordance with its target capital


structure. If the firm follows a residual dividend policy and has no other projects, what is its expected dividend payout ratio?

Question no. 8.The following facts apply to your company:

Target capital structure 50% debt; 50% equityEBIT: shs. 200 million.Assets shs. 500 million.Tax rate 40%Cost of new and old debt: 8%.

Based on the residual dividend policy, the payout ratio is 60 percent. How large (in millions of Shillings) will the capital budget be?

Question no. 9.S. S Bakhres & Company is planning a zero coupon bond issue. The bond has a par value of shs. 1,000, matures in 2 years, and will be sold at a price of shs. 826.45. The firm's marginal tax rate is 40 percent. What is the annual after-tax cost of debt to the company on this issue?Question no. 10A 15-year zero coupon bond has a yield to maturity of 8 percent and a maturity value of shs. 1,000. What is the amount of tax that an investor in the 30 percent tax bracket would pay during the first year of owning the bond?

Question no. 11.Machinga Corporation is financing an ongoing construction project. The firm needs shs. 8 million of new capital during each of the next three years. The firm has a choice of issuing new debt and equity each year as the funds are needed, or issuing the debt now and the equity later. The firm's capital structure is 40 percent debt and 60 percent equity. Flotation costs for a single debt issue would be 1.6 percent of the gross debt proceeds. Yearly flotation costs for three separate issues of debt would be 3.0 percent of the gross amount. Ignoring time value effects due to timing of the cash flows, what is the absolute difference in Shillings saved by raising the needed debt all at once in a single issue rather than in three separate issues?

Question no. 12TTCL, a subsidiary of the Postal Service, must decide whether to issue zero coupon bonds or quarterly payment bonds to fund construction of new facilities. The 1,000 par value quarterly payment bonds would sell at shs. 795.54, have a 10 percent annual coupon rate, and mature in ten years. At what price would the zero coupon bonds with a maturity of 10 years have to sell to earn the same effective annual rate as the quarterly payment bonds?

Question no. 13.Lady and Bros. has 12 percent semiannual bonds outstanding which mature in 10 years. Each bond is now eligible to be called at a call price of


shs. 1,060. If the bonds are called, the company must replace the bonds with new 10-year bonds. The flotation cost of issuing new bonds is estimated to be shs. 45 per bond. How low would the yield to maturity on the new bonds have to be, in order for it to be profitable to call the bonds today? (That is, what is the "breakeven rate"?)

Question no. 14. For the Cook County Company, the average age of accounts receivable is 60 days, the average age of accounts payable is 45 days, and the average age of inventory is 72 days. Assuming a 365-day year, what is the length of the firm’s cash conversion cycle?

Question no. 15 A firm with no debt has 200,000 shares outstanding valued at shs. 20 each. Its cost of equity is 12%. The firm is considering adding shs. 1,000,000 in debt to its capital structure. The coupon rate would be 8% and the firm’s tax rate is 34%. What would the firm be worth after adding the debt?

a) Suppose a firm issues perpetual debt with a face value of shs. 5,000 and a coupon rate of 12%. If the firm is subject to a 40% tax rate and the appropriate discount rate is 10%, what is the present value of the interest tax shield?

b) A firm has 10,000 bonds outstanding, each with a face value of shs. 1,000 and a coupon payment of shs. 55 every six months. If the corporate tax rate is 34%, what is the interest tax shield each year?

c) A firm has a WACC of 16%, a cost of debt of 10% and a cost of equity of 22%. What is the firm’s debt-to-equity ratio? Ignore taxes.

Question no. 16BDJ Ltd Inc. has 31,000 shares of stock outstanding with a market price of shs. 15 per share. If net income for the year is shs. 155,000 and the retention ratio is 80%, what is the dividend per share on BDJ Inc.’s stock?Question no. seventeenLucky Mike’s, Inc. has a target debt/equity ratio of .75. After-tax earnings for 1996 were shs. 850,000 and the firm needs shs. 1,150,000 for new investments. If the company follows a residual dividend policy, what dividend will be paid?

Question no. 17Consider the firm, Alex, Inc. which is financed with 100% equity. The firm has 100,000 shares of stock outstanding, with a market price of shs. 5 per share. Total earnings for the most recent year are shs. 50,000. The firm has cash of shs. 25,000 in excess of what is necessary to fund its positive NPV projects. The firm is considering using the cash to pay an extra dividend of shs. 25,000 or to repurchase stock in the amount of shs. 25,000. The firm has other assets worth shs. 475,000(market value). For each of the following 6 questions, assume that there are no transaction costs, taxes or other market imperfections.

a) Assume the firm pays the shs. 25,000 excess cash out in the form of


a cash dividend. What will the firm’s earnings per share be after the dividend?

b) Assume the firm pays the shs. 25,000 excess cash out in the form of a cash dividend. What will the market price of a share of Alex’s stock be after the dividend?

c) Assume the firm pays the shs. 25,000 excess cash out in the form of a cash dividend. Also assume you owned 1,000 shares before the dividend was paid and that this was your total wealth. Immediately after the dividend is paid, what is your total wealth?

d) Assume the firm uses the shs. 25,000 excess cash to buy back stock at shs. 5 per share. What will the firm’s earnings per share be after the repurchase?

e) Assume the firm uses the shs. 25,000 excess cash to buy back stock at shs. 5 per share. What will the firm’s P/E ratio be after the share repurchase?

f) Assume the firm uses the shs. 25,000 excess cash to buy back stock at shs. 5 per share. What will the market price of a share of Alex’s stock be after the share repurchase?

Question 18a) It is commonly accepted that a crucial factor in the financial decisions

of a company, including the evaluation of capital investment proposals is the cost o capital: required: explain in simple terms what is meant by the cost of equity capital for a particular company

b) Calculate the cost of equity capital for X ltd from the data give below using two alternative methods A dividend growth model The capital asset pricing modelData for X Ltd Current price per share on the stock exchange shs. 1.20 Current annual gross dividend per share shs. 0.10 Expected average annual growth rate of dividends 7% Beta coefficient for X Ltd shares 0.5 Expected rate of return on risk free securities 8% Expected return on the market portfolio 12%

Question no. 19

a) Using: I. The weighted average cost of capitalII. The capital asset pricing model

Calculate the cost of capital for the following company

Company AShs shs

Fixed assets 200,000 200,000 O/ shares at 1/= @ 200,000Current assets 150,000 Retained profit 50,000

Creditors 50,00012% Debentures 50,000

Total 350,000 Total 350,000


Further information:The debentures are repayable in 1995, and have a current market value of shs. 48,490.65. the shares are currently selling a shs. 2.02. The dividend for the current year was shs. 19.5 and its is expected that company will grow at a rate of 5%. The risk free rate is currently 8.5% with the return on the market being 15%. The company’s beta is 1.3

b) Discuss the usefulness and the limitation of the capital asserts pricing model (CAPM) for capital investment decisions

Question no 20Assume that you have graduated as a CPA holder and have just reports to work for a company as financial officer. Your fist assignment is to study the capital structure of the company in order to advise the company’s management about the cost of capital that the company should use. Your boss has developed the following questions which you must answer to explain a number of issues.Required: to explain briefly what you understand by:

a) Capital structure, optimal capital structure, targeted capital structure.

b) Why do public utility companies usually have capital structures that are different form those of retail firms?

c) How might increasingly volatile inflation rates and interest rates affect optimal capital structure for corporation?

Question no.21.On January 1st, the total market value of BBA Company was shs. 60 million. During the year, the company plans to raise and invest shs. 30 million in new projects. The firm’s present value capital structure, shown below is considered to be optimal. Assume that there is not short term debt.

ShsDebt 30,000,000Common stock equity 30,000,000Total 60,000,000

New bonds will have an 8% coupon rate and they will be sold at par. Common stock currently selling at shs. 30/= a share can be sold to net the company shs. 27/= a share. Stockholders’ required rate of return is estimated to be 12% consisting of a dividend yield of 4% and an expected constant growth rate of 8% (the next dividend is shs. 1.2 so shs. 1.2/30 =4%) retained profit for the year are estimated to be shs. 3 million ( the marginal corporate tax rate is 40%)Required:

a) To maintain the present capital structure, how much of the new investment must be financed by common equity?

b) How much of the needed new investment funds must be generated internally? Externally?

c) Calculate the firm’s weighted average cost of capital

Question no.22


A firm needs shs.100 to start and expects: Sales shs.200 Expenses shs.185 Tax rate 33% of earnings

a) What are earnings if the owners put up the shs.100?b) If the firm borrows shs.40 of the initial at 10%, what are the profits

received by the owner?c) What is the return on the owners' investment in each case? Why do

the returns differ?d) If expenses rise to shs.194, what will be the returns in each case? e) In which case did the returns decline more?f) What generalization can you draw form the above?

Question no.23Given the following schedules:

Debt/Assets Cost of Debt Cost of Equity0% 7% 14%10 7 1420 7 1430 8 1440 8 1650 10 1860 10 20

a) What is firm's cost of capital at the various combinations of debt and equity?

b) What is the firm's optimal capital structure? Construct a balance sheet showing that combination of debt and equity financing.

Question no. 24A firm has three investment opportunities. Each costs shs.1,000, and the firm's cost of capital is 10 percent. The cash inflow of each investment is as follows:

Cash Inflow

A B C

Year1 300 500 1002 300 400 2003 300 200 4004 300 100 500

a) If the net present value method is used, which investment(s) should the firm make?

b) What is the internal rate of return of investment A? The internal rate of return of investment B is 10.22% and 6.15% for investment C. Which investment(s) should the firm make?


c) What is the payback period for each investment?

Question no.25Firm A had shs. 10,000 in assets entirely financed with equity. Firm B also has shs.10, 000, but these assets are financed by shs.5,000 in debt (with a 10 percent rate of interest) and shs.5,000 in equity. Both firms sell 10,000 units of output at shs.2.50 per unit. The variable costs of production are shs.1, and fixed production costs are shs.12, 000. (To ease the calculation, assume no income tax.)

a) What is the operating income (EBIT) for both firms?b) What are the earnings after interest?c) If sales increase by 10 percent to 11,000 units, by what percentage

will each firm’s earnings after interest income? To answer the question, determine the earnings after taxed and compute the percentage increase in these earnings from the answers you derived in part b.

d) Why are the percentage changes different?


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