Black Scholes Option Pricing Model
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After completing this reading, you should be able to:
Capital structure refers to the proportion of equity and debt employed by a company or a firm to finance its operations and assets.
When companies are raising funds, the goal is usually to maximize the shareholders’ wealth. This may be done through financing the purchase of long-lived assets, capital expansion projects, etc. In some cases, capital is raised only to keep the company as a going concern.
The two most popular ways of financing that companies use include equity and debt.
Under equity financing, the company raises capital by selling part or whole of its stock to investors. Unlike debt securities, equity securities do not impose an obligation on the issuer to repay the amount financed. Instead, the investors receive an ownership interest in the company, which allows them to participate in the company’s future earnings and running by selecting the company management.
Equity can be split into two main categories: common/ordinary securities and preference securities.
Common shares give the holders a right to ownership of the company and a claim to the company’s net assets in the event of a liquidation.
In addition to the above, common shares allow the holders to:
Some options also have call or put options attached to them:
Given that common shares do not guarantee dividend income to the shareholder and the fact that they will rank last during liquidation, common shareholders would, in practice, demand higher returns compared to any other stockholders to compensate them for the risk of losing their whole investment.
Preference shares give the holders priority over common shares with respect to the payment of dividends and claim on net assets upon liquidation.
Additionally, preference shares:
In general, investors expect lower risks and returns from preference shares than from common shares because dividends on preference shares are fixed, preference shareholders have priority to dividend payments, and liquidation proceeds claimed by preference shares are known (although not guaranteed).
Preference shareholders usually expect more of their total return to come from dividend income, while common shareholders typically expect more return from capital appreciation.
Callable common or preference shares are riskier than their non-callable counterparts, while putable common or preference shares are less risky than their non-putable counterparts.
Determine which of the following is the most likely reason for an investor to choose a company’s preference shares over common shares?
The correct answer is C.
While the dividend yield on preference shares won’t always exceed the dividend yield on common shares, this is often the case.
Option A is incorrect: Since even participating preference shares offer limited upside potential, common shares should offer investors more exposure to the upside potential.
Option B is incorrect: While preference shareholders hope to receive fixed dividend payments, the dividend payments are not guaranteed by the issuing company.
Option D is incorrect: Preference shares do not have voting rights.
In addition to issuing common or preference shares, companies are also able to issue different classes of these shares to further tailor the securities to the needs of the company and its investors.
What type of preference share is likely to give the investor the most exposure to a company’s upside potential?
The correct answer is C.
There is no limit to the potential upside of convertible preference shares since they are convertible to common shares at a fixed ratio.
Option A is incorrect: Cumulative preference shares may help an investor recover lost income if a company is returning to profitability, but ultimately shareholders capture minimal returns on the upside.
Option B is incorrect: Similarly, participating shares are limited to a fixed bonus dividend on the upside.
Two types of companies exist:
When a company is private, its shares are not be listed on the stock exchange and thus may not able to issue shares directly to the public.
It may, however, raise equity capital through some of the following avenues:
If a private company seeks to issue shares to the public, it would have to obtain a quotation and meet the listing authority conditions to allow its shares to be issued to the public.
Once a private company has obtained a quotation, it can then issues its shares through an initial public offering (IPO).
Initial public offerings describe the issuer’s first sale of a security to the public. An IPO may involve the sale of totally new shares or allow the existing shareholders to sell some of their shares.
The issuing company may either sell the shares directly to the public or hire an investment bank to assist in the sale of the securities by finding investors (book building).
Investment banks take part in two main offerings:
Once the company or the issuing house agree on the approach, the shares are offered to the public through either of the following:
Investment banks hired to assist in the sale of securities generally have a conflict of interest in that the issuer wants to maximize the sale price of their securities. Still, the investment bank can reduce its risk of buying overpriced securities and indirectly helping its other clients by offering lower prices.
A public company might want to issue additional shares to finance new projects. Raising equity capital for already listed companies is referred to as seasoned offerings. This may be through the following issues:
Transactions of existing securities (usually not involving the issuer) take place in the secondary markets. The secondary markets support the primary markets by offering liquidity to the initial investors in security. This liquidity helps issuers attract more demand for their security offerings in the primary markets, leading to higher initial sale prices and a lower capital cost.
Determine which of the below is a likely benefit of a corporation issuing new securities in a private placement instead of an initial public offering?
Solution
The correct answer is A.
Since less disclosure is usually required of issuers, private placements tend to have lower offering costs than public offerings.
Option B is incorrect: Because private placement securities are less liquid, investors demand a higher return on their capital resulting in lower security prices and, therefore, a higher cost of capital for the corporation.
Option C is incorrect: Because private placement securities are less liquid, investors demand a higher return on their capital. This results in a higher cost of capital for the issuing firm.
Option D is incorrect: Given that private placements do not make use of a regulated exchange, there is a smaller pool of investors available.
The type of security and its features affect its risk/return profile. As an investor’s risk increases, its expected return should also increase to compensate.
There are two primary sources of total return for equity securities: capital appreciation and dividend income.
$$R_tt=\frac{P_t-\ P_{t-1}+\ D_t}{P_{t-1}}$$
Where
\(R_t\)= Total Return
\(P_t\) = Sale price
\(P_{t-1}\)= Purchase price
\(D_t\) = Dividend income
Historically, the reinvestment of dividend income has been a vital source of compound growth. For non-dividend paying stocks, the total return is entirely based upon capital appreciation.
Direct investments in foreign securities or depository receipts have an additional source of return: foreign exchange gains (or losses) arising from changes in exchange rates.
A US investor makes a direct investment in foreign equity security with a current dividend yield of 2.5%.
If the investor holds the stock for ten years, how many components are likely to make up the investor’s total return?
The correct answer is C.
The investor should earn a total return made up of (1) capital appreciation, (2) dividend income, and (3) foreign exchange (gains or losses).
The cost of equity is the minimum expected return rate that a company must offer its investors to purchase its shares in the primary market and maintain its price in the secondary market.
It represents the opportunity cost of capital and is defined as:
$$\text{Cost of Equity}=\text{Risk Free Rate}+\text{Equity Risk Premium}$$
The risk-free rate of return here is the return from a risk-free investment, such as government-issued bonds.
The equity risk premium is an additional reward for covering the additional risk for risky investments (shares of stock) rather than risk-free investments (government bonds).
A company can increase its common equity by either reinvesting its earnings or issuing new stock. Therefore, the cost of equity will be the rate of return required by its shareholders.
Application of the Capital Asset Pricing Model (CAPM) to compute the cost of equity is based on the following relationship:
$$E{(R)}_i=R_f+\beta_i[E\left(R_m-R_f\right)]$$
Where:
\(E(R_i)\) = the cost of equity or the expected return on a stock;
\(R_f\)_{ }= the risk-free rate of interest;
\(β_i\) = the equity beta or the return sensitivity of stock i to the market returns;
\(E(R_m)\) = the expected market return; and
\(E(R_m )-R_f\) is known as the expected market risk premium or equity risk premium.
The risk-free rate of interest may be estimated by the yield on a default-free government debt instrument.
A company’s equity beta is estimated to be 1.2.
If the market is expected to return 8% and the risk-free rate of return is 4%, what is the company’s cost of equity?
The correct answer is E.
The formula to be used is:
$$E{(R)}_i=R_f+\beta_i[E\left(R_m-R_f\right)]$$
The company’s cost of equity is:
$$ E{(R)}_i = 4\%+\ 1.2(8\%-4\%)\ =4\%+4.8\% =8.8\%\ $$
According to the dividend discount model, the intrinsic value of a stock share is the present value of the share’s expected future dividends. However, based on Gordon’s constant growth model, dividends are expected to grow at a constant rate \(g\). Therefore, assuming that the share price reflects the intrinsic value, the value of a stock is:
$$P_o=\frac{D_1}{r_e-g}$$
Where:
\(P_o\) = the current share price;
\(D_1\) = the dividend to be paid in the next period; and
\(r_e\) = the cost of equity.
Rearranging the equation:
$$ r_e=\frac{D_1}{P_o}+g$$
Where:
\(\frac{D_1}{P_0}\) is known as the forward annual dividend yield.
\(g\) may also be referred to as the sustainable growth rate and can be estimated by the following relationship:
$$g=\left(1-\frac{D}{EPS}\right)\times ROE$$
Where \(ROE\) is the return on equity, \(EPS\) is earnings per share and \(\frac{D}{EPS}\) is the assumed stable dividend ratio, which makes \(\left(1-\frac{D}{EPS}\right)\) the earnings retention ratio.
A company’s current share price is $11.24, and it has just paid a dividend of $1.31 this year.
Using the dividend discount model and assuming a constant growth rate of 5%, what is the company’s cost of equity?
The correct answer is A.
We first need to find the dividend rate next year, \(D_1\):
$$ D_1 = D_0 × (1+g) $$ = $1.31 × (1+0.05) = $1.3755 $$
Now using the equation:
$$r_e=\frac{D_1}{P_o}+g$$
The cost of equity is thus equal to:
$$r_e =\left(\frac{$1.3755}{$11.24}\right)+0.05= 17.23\%$$
According to the bond yield plus risk premium approach, the cost of equity may be estimated by the following relationship:
$$r_e=r_d+\text{Risk Premium}$$
Where:
\(r_e\) = Cost of equity;
\(r_d\) = Before-tax cost of debt; and
\(\text{Risk Premiun}\) = Compensation required by shareholders for the additional risk of equity compared to debt.
For example, if a company’s before-tax cost of debt is 4.5% and the extra compensation required by shareholders for investing in the company’s stock is 3.2%, then the cost of equity is simply 4.5% + 3.2% = 7.7%.
Return on equity is the primary measure that equity investors use to determine whether a company’s management is effectively and efficiently using the owners’ capital to generate profits. Return on equity is calculated by taking net income and dividing it by the average book value of equity:
$$ROE_t=\frac{NI_t}{\frac{\left(BVE_t+BVE_{t-1}\right)}{2}}$$
Where:
\(NI_t\) = Net income in the year;
\(BVE_t\) = Ending book value in the year; and
\(BVE_{t-1}\) = Beginning book value in the year.
The average book value of equity is used when a company’s book value tends to be volatile from year to year or the industry standard. Otherwise, basing ROE on the beginning book value of equity is appropriate.
Investors’ required rate of return on equity securities is more challenging to pin down. An equity investor’s minimum required return rate is based on the future cash flows they expect to receive, which are uncertain and must be estimated. The minimum required return may differ across investors, resulting in a cost of equity that varies from some investors’ minimum required return.
ABC Corp generated a 15% return on equity during 2015. The 2015 beginning and ending book values of equity were the same. In 2016, ABC Corp reported a 15% increase in net income and a 15% increase in the book value of equity from one year prior.
Using the average book value of equity approach, what was ABC’s 2016 return on equity?
The correct answer is A.
Since the return on equity is based on the average book value of equity, the full 15% increase in the book value of equity is not being accounted for in the denominator. Because the beginning and ending book values are averaged together, the average book value used in the calculation would only be 7.5% higher than the same figure in 2015. Net income, however, increases exactly 15%. The 2015 return on equity was 15%, and 2016 net income increased more than the average book value of equity, so therefore 2016 ROE is greater than 15%.
Debt capital is a form of company financing where a company issues loans to raise capital. In exchange, the company pays the investors stream of interest payments plus the eventual return of the principal.
The timings and amount of the capital and interest payments are usually set out at the time of the issue.
These are the loans secured on part or all the assets of the company. In case the company fails to pay the debt, the income from the secured assets may be intercepted, or the possession of the assets is assumed.
Two categories of debentures exist:
This is a type of loan where there are no particular assets pledged as security on loan. If a company defaults to pay, the lending entity has no choice but to go the legal way to recover their money. In other words, the court will be asked to take control.
This is a type of loan where the major loan takes priority over the minor one. The superiority of the loan entirely depends on the terms of the issue.
These are largely unsecured loans made by issuing bonds that pay regular interest payments plus over the term of the loan and a final redemption amount at the end of the term.
They are usually issued by large corporations and denominated in different currencies.
These are medium-term bond-type loan instruments with variable coupon rates. The coupon rates are usually linked to some benchmark rates such as LIBOR rates, where LIBOR is the benchmark interest rate at which major global banks lend to one another.
The cost of capital for a company refers to the required rate of return, in which investors demand the average-risk investment of a company. It is usually estimated by computing the marginal cost of each of the company’s various capital sources and then taking a weighted average of these costs. This is referred to as the weighted average cost of capital (WACC). Given that it is the cost that a company incurs to raise additional capital, the WACC may also be referred to as the marginal cost of capital (MCC).
WACC is expressed as:
$$WACC=w_dr_d\left(1-t\right)+w_pr_p+w_er_e$$
Where:
\(w_d\) = the proportion of debt that a company uses whenever ut raises new funds;
\(r_d\) = the before-tax marginal cost of debt;
\(t\) = the compnay’s marginal tax rate;
\(w_p\) = the proportion of preferred stock;
\(r_p\) = the marginal cost of preferred stock;
\( w_e\) = the proportion of equity that the company uses when it raises new funds; and
\(r_e\) = the marginal cost of equity.
Suppose that company XYZ has the following capital structure: 25% equity, 10% preferred stock, and 65% debt. Its marginal cost of equity is 12%, its marginal cost of preferred stock is 9%, and its before-tax cost of debt is 7%.
If the marginal tax rate is 35%, what is company XYZ’s WACC?
The correct answer is A.
We need to use the formula:
$$WACC=w_dr_d\left(1-t\right)+w_pr_p+w_er_e$$
In this example,
\(w_d=65\%,r_d=7\%,t=35\%,w_p=10\%,r_p=9\%,w_e=25\% \text{ and } r_e=12\%\)
Therefore, company XYZ’s WACC is:
$$WACC = (0.65)(0.07)(1-0.35)+ (0.1)(0.09) + (0.25)(0.12)= 0.06858 =6.858\%$$
What is the weighted average cost of capital for a company if it has the following capital structure: 30% equity, 20% preferred stock, and 50% debt. Additionally, its marginal cost of equity is 11%, its marginal cost of preferred stock is 9%, its before-tax cost of debt is 8%, and its marginal tax rate is 40%?
The correct answer is B.
We need to use the formula:
$$WACC=w_dr_d\left(1-t\right)+w_pr_p+w_er_e$$
Therefore,
$$WACC=(0.50)(0.08)(1-0.40)+ (0.2)(0.09) +(0.30)(0.11) =7.5%.$$
The traditional theory proposed that since debt finance is cheaper, then the firm’s WACC decreased as the level of debt (gearing) increased. Modigliani and Miller contradicted this, asserting that gearing is irrelevant, and debt cost is directly proportional to equity cost. That is, each increase in debt financing will be associated with a corresponding increase in the cost of equity.
They put together two propositions to support their argument:
Modigliani and Miller’s model assumes the following:
A leveraged firm is a firm that is financed by debt issues in some way. The MM model states that the WACC remains unchanged as the gearing increases.
The model is based on the risk and returns environment in that if equity issues finance the company, then the company’s shareholders are faced with business risk. On the other hand, if the debt issue finances it, it faces financial risk since its return becomes more volatile. The MM model anticipates that for two business entities with the same amount of risk and returns, then WACC is the same regardless of the capital structure.
Taxes can have a significant impact on a company’s weighted average cost of capital (WACC). However, taxes affect the cost of capital from different sources of capital in different ways.
In many tax jurisdictions, interest on debt financing is a deduction made prior to arriving at a company’s taxable income. You may recall that in the equation to compute a company’s WACC, the expected before-tax cost on new debt financing, \(r_d\), is adjusted by a factor \((1-t)\). Multiplying \(r_d\), by the factor \((1-t)\), results in an estimate of its after-tax cost of debt.
To illustrate the effect of tax, consider the following scenarios
Here the return on investments is \(\frac{2,500,000}{2,000,000}-1=25\%\).
The earnings per share will equal to \(0.7\times\frac{2,500,000}{2,000,000}=0.875\).
As before, the return on investment will be 25%.
The earnings before tax will equal to \( 2.500,000-\left(0.1\times$500,000\right)=2,450,000\).
The earnings per share will equal to \(EPS = 0.7\times\frac{2,450,000}{1,500,000}=1.14\).
This shows that shareholders’ value is improved when the company uses debt capital.
The return on investment will equal to \(\frac{2,100,000}{2,000,000}-1=5\%\).
The earnings before tax will equal to \(2,100,000-\left(0.1\times500,000\right)=2,050,000\).
The earnings per share will equal to \(0.6\times\frac{2,050,000}{1,500,000}=0.82\).
This shows that when the investment return is lower than the interest charged on debt capital, then the tax-saving benefits are overridden by the high interest paid on the loan. This results in shareholders earning less as more debt is added to the company’s capital structure.
Therefore, finance managers should weigh the benefits from tax savings in relation to the cost of using debt when deciding on the company’s gearing level.
Company XYZ has borrowed a loan worth $100,000 to finance a huge capital project. The loan is subject to interest payments of 10% at the end of each year and final repayment of the principal amount at the end of the loan term.
In the just-concluded financial year, the company recorded earnings before depreciation interest and tax of $90,000, and we are given that the company pays corporation tax at a rate of 35%
Company ABC on the other hand, is fully financed by equity and recorded before-tax earnings of $90,000 and is also subjected to corporation tax at 35%
Demonstrate the impact of tax on the capital structure of the two companies
The after-tax due for company XYZ will be \(0.35\times\left(90,000-10,000\right)=$28,000\).
The after-tax earnings for company ABC will be \(0.35\times90,000=$31,500\).
We notice that despite Company ABC being unlevered, it pays more taxes than the levered Company XYZ. Company XYZ saves $3,500 from tax payments because of using debt. The before-tax cost of debt for company XYZ is the interest charged on the loan, i.e. 10%. If we assume that these tax savings are used to reduce the amount of interest paid on the loan, then XYZ’s after-tax cost of debt would be \(\frac{10,000-3,500}{100,000}=6.5\%\).
Taxes do not affect the cost of common equity or the cost of preferred stock. This is the case because the payments to the owners of these sources of capital, whether in the form of dividend payments or return on capital, are not tax-deductible for a company. This explains why in the equation for computing a company’s WACC, no tax adjustment is made for these sources of capital.
A company’s target capital structure refers to capital which the company is striving to obtain. In other words, the target capital structure describes the mix of debt, preferred stock, and common equity, which is expected to optimize a company’s stock price. As a company raises new capital, it will focus on maintaining this target or optimal capital structure.
In determining the weights to be used in the WACC computation for a company, ideally, a manager should use the proportion of each source of capital that will be used.
For example, if a company has three sources of capital: debt, common equity, and preferred stock, then the proportion of debt will be equal to:
$$w_d = \frac{\text{Market value of debt}}{\text{Market value of debt+Market value of equity+Market value of preferred stock}}$$
The proportion of equity will equal to:
$$w_e = \frac{\text{Market value of equity}}{\text{Market value of debt+Market value of equity+Market value of preferred stock}}$$
And the proportion of preferred stocks will equal to:
$$w_p = \frac{\text{Market value of preferred stock}}{\text{Market value of debt+Market value of equity+Market value of preferred stock}}$$
If the target capital structure is known, and the company attempts to raise capital consistently with this target, then the target capital structure should be used.
An analyst who is external to a company will often not know the company’s target capital structure and will, therefore, have to estimate it using one of the following methods:
Company ABC’s competitors and their capital structures are:
$$ \begin{array}{c|c|c} \text{Competitor} & \text{Market Value of Debt} & \text{Market Value of Equity} \\ \hline \text{X} & \text{\$20 million} & \text{\$40 million} \\ \hline \text{Y} & \text{\$32 million} & \text{\$55 million} \\ \end{array} $$
Additional information is as follows:
Determine the proportion of debt and equity that Company ABC would use if estimating these proportions using:
i. Company ABC’s current capital structure:
The proportion of company ABC’s debt:
$$w_d=\frac{25 \text{million}}{25 \text{million} +35 \text{million}}=0.41667$$
The proportion of company ABC’s equity:
$$w_e =\frac{35 \text{million}}{25 \text{million} +35 \text{million}}=0.58333$$
ii. The average of company ABC’s competitors’ capital structure.
The arithmetic average of company ABC’s competitors’ debt:
$$w_d = \frac{\left(\frac{20\ million}{20\ million+40\ million}\right)+(\frac{32\ million}{32\ million+55\ million})}{2}=\frac{0.33333+0.36782}{2}=0.35057$$
The arithmetic average of company ABC’s competitors’ equity
$$w_e = \frac{\left(\frac{40\ million}{20\ million+40\ million}\right)+(\frac{55\ million}{32\ million+55\ million})}{2}=\frac{0.66667+0.63218}{2}=0.64943$$
Although in the above example, the arithmetic average is calculated, it is also possible to compute the weighted average, which would give greater weight to larger companies.
The cost of debt is the cost of debt financing whenever a company incurs debt by either issuing a bond or taking out a bank loan. Two methods for estimating the before-tax cost of debt are the yield-to-maturity approach and the debt-rating approach.
The yield to maturity of a bond is the annual return that an investor earns on the bond if the investor purchases the bond and holds it until maturity. The yield equates the present value of the bond’s promised payments to its market price.
Assuming that the bond pays semi-annual interest and that any intermediate cash flows are invested at the same rate :
$$P_0=\ \left(\sum_{t=1}^{n}{\frac{{PMT}_t}{(1+\frac{r}{2})^{2t}}\ }\right)+\frac{FV}{(1+\frac{r}{2})^{2t})}$$
Where:
\(P_0\) = the current market price of the bond;
\(PMT_t\) = the interest or coupon payment in period \(t\);
\(r\) = the yield to maturity;
\(n\) = the number of periods remaining to maturity; and
\(FV\) = the maturity/redemption value of the bond.
Suppose Company A issues new debt by offering a 20-year, $100,000 face value, 10% semi-annual coupon bond. Upon issuance, the bond sells for $105,000.
What are company A’s before-tax cost of debt and the after-tax cost of debt if the marginal tax rate is 40%?
The correct answer is A.
We need to use the following formula:
$$P_0=\ \left(\sum_{t=1}^{n}{\frac{{PMT}_t}{(1+\frac{r}{2})^{2t}}\ }\right)+\frac{FV}{(1+\frac{r}{2})^{2t})}$$
From the information given in the question, we have:
$$=\sum_{t=1}^{20}{\frac{5,000}{\left(1+\frac{r}{2}\right)^{40}}+\left(\frac{100,000}{\left(1+\frac{r}{2}\right)^{40}}\right)}$$
Using a financial calculator we get \(\frac{r}{2}\) (the six-month yield) = 4.72%.
Thus,
$$\text{After-tax cost of debt} =r(1 – t) = 9.44\% (1 – 0.40) = 5.66\% $$
The debt-rating approach is a method for estimating the before-tax cost of debt for a company whenever reliable, current market price data for its debt is unavailable. In this method, the before-tax cost of debt is estimated by using the yield on comparably rated bonds for maturities, which are closely aligned with the maturities of the company’s existing debt.
Suppose Company B has a senior, unsecured debt with an average maturity of 5 years, and the company’s marginal tax rate is 35%. The company’s debt rating is BBB and the yield on similar senior, unsecured debt with the same debt rating and maturity is 9%,
Calculate the company’s after-tax cost of debt.
The correct answer is E.
Here, we simply multiply the comparable company’s yield by \(1 – \text{tax rate}\).
$$ 9\% (1 – 0.35) = 5.85\%$$
When estimating the cost of equity using the Capital Asset Pricing Model (CAPM), a reliable beta estimate must be used.
Beta for a company that is not publicly traded may be estimated using the pure-play method. In the pure-play method, the starting point is the beta for a comparable publicly-traded company, i.e., one with similar business risk or risk relating to revenue uncertainty. This beta is then adjusted for financial leverage differences to derive an estimate of beta for the company. Adjusting for financial leverage differences requires a process of “unlevering” and “levering” the beta.
Step 1: A comparable company is selected.
Step 2: The equity beta of the comparable company, is estimated.
Step 3: The comparable company’s beta is then unlevered by removing the effects of its financial leverage and leaving its business risk. The unlevered beta, Is known as the asset beta.
The equation to represent this is:
$$\beta_{U,comparable}=\frac{\beta_{L,comparable}}{[1+\left(1-t_{comparable}\right)\left(\frac{D_{comparable}}{E_{comparable}}\right)}$$
Where:
\(BU_{\ comparable}\) = asset beta for the comparable company;
\(BL_{\ comparable}\) = equity beta for the comparable company;
\(t_{comparable}\) = marginal tax rate;
\(D_{comparable}\) = debt of the comparable company; and
\(E_{comparable}\) = equity of the comparable company.
Step 4: The comparable company’s asset beta is then adjusted or levered to arrive at an estimate of the equity beta for the company, \(\beta_{L,\ company}\).
The equation to represent this is:
$$\beta_{L,company}=\beta_{U,comparable}\ \left[1+\left(1-t_{company}\right)\left(\frac{D_{company}}{E_{company}}\right)\right]$$
Company PQR is in the telemarketing business. The asset beta for a comparable company in the same industry is 1.3. Company PQR’s debt-to-equity ratio is 1.2, and the corporate tax rate is 35%.
Calculate Company PQR’s equity beta?
The correct answer is B.
The comparable company’s asset beta \(\beta_{U,comprable}\) is given as 1.3. You are also provided with information which indicates that \(t_{comparable}= 35\%\) and
$$\frac{D_{\text{company PQR}}}{E_{\text{company PQR}}}=1.2$$
Solving for \(\beta_{L,company}\)
$$= 1.3\times\left[1 +\left(\left(1-0.35\right)\times 1.2\right)\right]=1.3\times(1+0.78)=2.314 $$
Typically, the shareholders of a company (the principals) hire management as their agents to run the company on their behalf. As such, there might be conflicts of interest – often referred to as principal-agent problems – which lead to agency cost. These agency costs may be incurred as a result of:
Shareholders appoint directors who, in turn, select the management team to run the company. Information asymmetry arises from the fact that managers may know more information about the company than the shareholders. For instance, managers may withhold information about the company’s subpar performance in a given year.
Given that many company decisions are based on sensitive information, this asymmetry may create an agency conflict. The conflicts that arise can be easily solved if the principals and the agents share information regarding the company’s operation. This is the reason why public companies have to disclose a lot of information in their quarterly and interim financial statements.
The Pecking Order Theory, developed by Myers and Majluf (1984), postulates that a company will follow a specific order of preferences when making financing decisions. According to this theory:
This is explained by easy access to internal funds and lesser transaction costs when raising internal funds before opting for debt financing.