Category Finance

Finding the specific after-tax cost of common stock (rp)

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Our next concern is to find the after-tax cost of common stock, after attending to finding the after-tax cost of long-term debt and after-tax cost of preferred stock.

Common stock

Common stock, which is also called common shares or ordinary shares, refers to the category of ownership of the enterprise. Common shares generally have voting rights and better potential for appreciation of shares compared to preferred stock.

However, holders of common stock generally do not have fixed dividends and cannot receive dividends until dividends are paid out to preferred stock holders. Moreover, in case of liquidation, holders of common stock only have claim on company’s assets if claims of all creditors as well as holders of preferred stock are satisfied. Therefore, common stock is more risky than preferred stock.

Cost of common stock (rp)

To determine the specific after-tax costs of common stock (rp), you can use two techniques: Gordon model or the CAPM (Capital Asset Pricing Model)

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Finding the after-tax cost of preferred stock (rp)

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After discussing the cost of long-term debt, we must now find the cost of preferred stock (after-tax). Preferred stock, which is also called preferred shares or preference shares, refers to the category of ownership that has preferential claim on earnings and assets of the firm, compared to common stock ownership.

The preferential claim is generally manifested in the fact that dividends cannot be distributed to common stockholders until it is distributed to holders of preferred stock first. Further, in case of liquidation, holders of the preferred stock also have preferential claim on assets of the firm, compared to the holders of common stock.

Preferred stock is a hybrid instrument as it has characteristics of both debt and equity. The drawback of preferred shares, compared to the common stock, is lower potential for appreciation of shares as well as absence of voting rights.

Calculating the cost of preferred stock

To calculate the specific after-tax cost-of-preferred-stock all we need to do is to take the preferred stock dividend and divide it by the net proceeds from the sale of the preferred stock (funds received minus flotation cost).

Cost-of-preferred-stock (rp) = Preferred stock dividend/(Funds received – Flotation costs)

Because preferred stock is paid out of the after-tax earnings, the cost-of-preferred-stock is already after-tax.

EXAMPLE:

If Company A issued 9% preferred stock at $100 and the flotation cost is $8, then the calculation will be as follows:

rp = 100*9%/100-8

rp =9/92

rp =9.8%

Test yourself

A corporation is issuing 10% preferred stock that should be sold for $15 each. The business will incur flotation costs of $2 per share.

REQUIRED: What is the cost-of-preferred-stock?

SOLUTION:

10%*15/15-2

1.5/13

The answer is 11.54%

Note: If you struggle with a calculation, read using a financial calculator article for some simple tips on using a financial calculator.

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Cost of long term debt

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The first long term source of finance that we consider is the cost of long term debt, which is usually the cheapest of the long-term sources of finance. The majority of long term debt of large corporations is the result of issuing bonds.

Flotation cost

Companies that issue bonds have to take into account the flotation cost, which is the complete cost the company has to incur to issue and sell a security, such as common stock, preferred stock and bonds. This cost reduces the company’s net proceeds from issuing security.

Flotation cost consists of underwriting and administrative costs. Underwriting costs are payment to investment bankers for their services and administrative costs are costs other than the underwriting costs of issuing bonds.

Finding the before-tax cost of long-term debt (rd)

To find the after-tax cost of long term debt, we first need to find the before-tax cost of long term debt (rd). As mentioned above, the majority of long term debts of large corporations are the result of issuing bonds. By using a financial calculator, we can find the before tax cost of a bond (cost of long-term debt).

THE CALCULATION FOLLOWS:

FV – (future value of the bond which refers to its par value, which is also called the face value, and is usually $1,000)

PV – the value of the bond today at which it is sold (after deducting the flotation cost)

PMT – payment on the bond (for example, at 8% coupon interest rate a bond issuer will have to make annual payments of $80 if the par value is $1,000). Payments can also be made more frequently, such as semi-annually or even monthly, but in such a case we need to adjust the amount of payment and number of periods.

For example, if payment is made semi-annually, we will need to divide $80 by 2 and we will need to multiply number of periods by 2.

N – Number of periods

Calculate I – the cost of the bond (for the bond’s issuer it is the cost to maturity of the cash flows, for the bond’s holders it is the return they earn on buying and holding this bond to maturity). Within the context of our discussion, it is also the before-tax cost of long-term debt.

Note that if the net proceeds from the sale of the bond is the same as the face value of the bond than the before-tax cost of long-term debt will be equal to the coupon interest rate. For example, at 8% coupon interest rate, the par value of $1,000 and net proceeds of $1,000 (no flotation costs), the before-tax cost of long-term debt will equal 8%.

Finding the after-tax cost of long-term debt

After we found the before-tax cost of long term debt, we need to find the after-tax cost of long term debt. To do so all we need to do is to multiply the before-tax cost of long-term debt by (1-T), where T stands for the tax rate.

THEREFORE:

ri = rd * (1-T)

EXAMPLE:

If the before-tax cost of long term debt is 10% and tax rate is 28% then the calculation will be as follows:

Ri =10% * (1-.28)

Ri =10% * .72

Ri = 7.2%

Test yourself

You need to calculate the after-tax cost of a 30-year bond. The coupon interest rate is 10%, the par value is $1,000 and the bond is currently selling at $950.

SOLUTION:

PV: -950

FV: 1,000

PMT: 100

N: 30

I: 10.56%

Note: If you struggle with a calculation, read using a financial calculator article for some simple tips on using a financial calculator.

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Long term sources of finance

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Here we will focus only on the long term sources of finance because only long-term sources provide permanent financing. Long-term sources of finance (also called long-term sources of capital) refer to long-term debt and equity on the balance sheet. They include long-term debt, preferred stock and common stock equity, which in turn include issues of new common stock and retained earnings.

Permanent financing generally refers to financing long-term fixed assets, such as machinery or factory. If the pay-off from the asset is over the long-term period (longer than 1 year), the long-term sources of finance should be used to ensure it is less risky to finance such assets. For example, if long-term debt (one of the long-term sources of finance) rather than short-term debt is used, business can be more certain money will be available to cover obligations as they come due.

While focusing on the long-term sources of finance, we will need to focus on the specific cost of finance. We will need to obtain the specific cost of each of the long-term sources of finance, which refers to the after-tax cost of using each of the sources today.

Read related article: Cost of Long Term Debt 

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The cost of capital

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What is the cost of capital? It is the required rate of return a business must earn on its investments (capital budgeting projects) to maintain the market value of the firm’s shares and to attract funds.

It is a measure used to determine whether or not certain project will decrease or increase the firm’s value in the market place and, consequently, whether or not it should be recommended.

If NPV is more than zero and IRR is greater than the cost of total capital, then a proposed project will increase the market value of the firm and it should be recommended.

If, however, NPV is less than zero and IRR is lower than the cost of all capital, then a proposed project will decrease the market value of the firm and it should not be recommended.

Therefore, if a firm’s risk is assumed to be constant, than any projects with the rate of return higher than the cost of all capital will increase the market value of the firm and any projects with the rate of return below the cost of capital of the enterprise will decrease market value of the firm.

In the discussions that follow we assume that the cost of all capital is measured on the after-tax basis and that a firm’s acceptance of the project does not affect FINANCIAL and BUSINESS RISKS.

FINANCIAL RISK is the chance that a firm will not be able to meet its financial obligations, which can result in bankruptcy. Financial risk is directly affected by a firm’s capital structure (its mix of debt and equity financing). The more debt the firm uses in its capital structure mix, the higher the financial risk.

BUSINESS RISK is the chance that a firm will not be able to cover its operating costs. There are three factors that affect business risk. These are increases in operating leverage, revenue instability and cost instability.

1 – Increase in operating leverage refers to higher use of fixed operating costs.

2 – Increase in revenue instability (or decrease in revenue stability) refers to deterioration of stability of sales of the firm.

3 – Lastly, increase in cost instability (decrease in cost stability) refers to how predictable are costs of the firm, such as labour and raw materials’ costs.

Business risk must be taken as is and the capital structure mix the firm chooses does not influence it.

Firms usually try to maintain an optimal mix of financing (debt and equity) referred to as the target capital structure. Firms have various sources of capital and the cost of capital may be different for each source of financing. When determining the cost of capital, it is helpful to determine an average cost of all sources of capital, which is called the weighted average cost of capital (WACC).

 

Capital Rationing

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Many firms operate under capital rationing. Firms ration capital because more often than not firms do not have unlimited funds to invest. Therefore, not all acceptable projects can be actually accepted. This is, of course, contradictory with goal of maximizing shareholders value.

We can formally define the rationing of capital as follows: It is a situation when firms do not accept all acceptable projects due to a limited amount of funds or due to limits imposed on investments. The goal is to select portfolio of projects with the highest net present value.

Under situations involving scarce capital, businesses will select a portfolio of projects with the highest NPV and which does not exceed the allocated budget. There are two commonly used techniques to select projects in these situations, the net present value NPV approach and the internal rate of return (IRR) approach.

The IRR approach graphs return against the total investment on the investment opportunities schedule (IOS) and by drawing the budget constraint shows the group of projects that are acceptable to be invested in. The NPV approach ranks projects by IRR and than generates a portfolio of projects with the highest overall present value.

When selecting projects, the net present value (NPV) approach is preferred because it maximizes shareholders’ returns whereas an internal rate of return (IRR) approach just generates a portfolio of acceptable projects.

 

Annualized Net Present Value (ANPV)

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The annualized Net Present Value (ANPV) technique is the best method to use when comparing mutually exclusive projects which have unequal duration. ANPV is the most efficient technique to convert Net Present Values (NPVs) of projects with unequal duration into an ANPV for each specific project, which can then be compared.

To find ANPV, the following calculation must be made:

1 – Find NPVs for each project

2 – Divide the NPV of each project by PVIFAr,n (Present Value Interest Factor for Annuity) at the project’s required cost of capital and number of periods. The amount for PVIFAr,n can be found in financial tables.

3 – The project with the higher Annualized Net Present Value (ANPV) is preferred.

Alternatively, ANPV can be found by using a financial calculator, as shown below:

PV = use NPV

N = Number of periods over the duration of the project (e.g. number of years)

I = required cost of capital (e.g. 10%)

Find PMT = this will be the annualized net present value (ANPV)

Test yourself

ABC Corporation has two mutually exclusive projects A and B that it can invest in. Initial investments investments required for project A and B are $150,000 and $200,000 respectively. The duration of project A is 4 years and of project B is 3 years. Expected annual cash inflows from project A are $40,000 and from project B is $70,000. The terminal cash flows from projects A and B are $21,000 and $34,000 respectively. The cost of capital of ABC Corporation is 9% and both projects have an average risk, which means that alteration for risk adjusted discount rate is not required. The 9% for cost of capital should be used for both projects.

What is the ANPV for projects A and B?

SOLUTION:

By using a financial calculator, we can find the solution to this problem. First we need to establish the net present value (NPVs) for projects A and B.

NET PRESENT VALUE (NPV) FOR PROJECT A:

Clear calculator: second function, “C ALL”

CFo: -150,000

CF1: 40,000

CF2: 40,000

CF3: 40,000

CF4: 61,000 (40,000 + 21,000)

I: 9

Second function, NPV: 5,534.28

NET PRESENT VALUE (NPV) FOR PROJECT B:

Clear calculator: second function, “C ALL”

CFo: -200,000

CF1: 70,000

CF2: 70,000

CF3: 104,000 (70,000 + 34,000)

I: 9

Second function, NPV: 3,444.86

However, because the projects have different duration, we need to convert Net Present Values (NPVs) found above into ANPV for each project.

CONVERTING NPV TO ANPV FOR PROJECT A:

Clear calculator: second function, C ALL

PV: – 5,534.28

N: 4

I: 9

Find PMT: $1,708.26

CONVERTING NPV TO ANPV FOR PROJECT B:

Clear calculator: second function, C ALL

PV: – 3,444.86

N: 3

I: 9

Find PMT: $1,360.91

Since the ANPV of project A ($1,708.26) is higher than that of project B ($1,360.91), project A should be selected.

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EBIT-EPS Capital Structure Approach

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The EBIT-EPS capital structure approach focuses on finding a capital structure with the highest EPS (earnings per share) over the expected range of EBIT (earnings before interest and taxes).

The reason why we are interested in finding a capital structure which will permit maximization of the EPS over the expected range of EBIT is because it partially helps us to achieve the ultimate objective of the enterprise. The ultimate objective of the enterprise is to maximize shareholders’ wealth by maximizing its stock price. Two key variables that affect stock price are return (earnings attributed to owners of the enterprise) and risk (which can be measured by required return (rs)). This approach explicitly considers maximization of returns (EPS). However, it is important to note that this approach ignores risk (does not explicitly consider risk).

Major shortcoming of the EBIT-EPS approach

The fact that this approach fails to explicitly consider risk is the major shortcoming of this method. As firm obtains more debt (its financial leverage increases), the risk also increases and shareholders will require higher returns to compensate for the increased financial risk. Therefore, this approach is not completely appropriate because it does not consider one of the key variables (risk), which is necessary for maximization of shareholders’ wealth.

Considering financial risk

As per above, the approach does not explicitly consider financial risk. However, when utilizing the approach, financial risk can be considered in two ways:

1) The approach measures financial risk by the financial breakeven point. The higher the breakeven point the greater the financial risk.

2) The approach also measures the financial risk by the slope of the capital structure line. The steeper the capital structure line the greater the financial risk.

EBIT-EPS graph

It is a graphical approach. EPS is plotted on the vertical axis (x-axis) and EBIT on the horizontal axis (y-axis). By connecting the coordinates for different capital structures (different variations of equity versus debt), capital structure lines for each capital structure are graphed.

We will need to represent EBIT-EPS coordinates (capital structure lines) for different capital structures to ascertain at which levels of EBIT which capital structure is preferred. This will allow us to find a capital structure with the highest EPS over the expected range of EBIT.

For the purposes of this article it is sufficient to mention that to find EBIT-EPS coordinates we can assume particular EBIT values (and associated earnings available for common stockholders values) and calculate EPS in line with such values for different capital structures.

The formula to calculate EPS is as follows:

EPS = Earnings Available for Common Stockholders/ Number of Shares of Common Stock Outstanding Another easy way to find one of the EBIT-EPS coordinates is to use the financial breakeven point calculation. Financial break-even point occurs at the level of EBIT (earnings before interest and taxes) at which EPS (earnings per share) equals zero. At this level of EBIT all fixed financial costs are covered. The formula for calculation of the financial break-even point is as follows:

Financial break-even point = I + PSD/1-T

Where:

I – interest charges

PSD – preferred stock dividends

T – tax rate

***

This capital structure approach does NOT allow us to determine the point where weighted average cost of capital is at a minimum and where stock price is at a maximum (where wealth of the owners of the firm is maximized). The approach focuses on maximizing earnings rather than on maximizing wealth. Therefore, although it is helpful to use when analyzing alternative capital structures, the major shortcoming of this approach should be taken into account.

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Optimal capital structure

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Theoretically, enterprises should try to maintain a certain optimal capital structure, a perfect mix of financing (debt and equity), which results in the lowest possible weighted average cost of capital. At this combination of debt and equity, the stock price is at the maximum. Therefore, attainment of the optimal structure is in line with the main objective of the business, which is the maximization of wealth of the owners of the business. The optimal structure is also referred to as the target capital structure. However, it is important to note the optimal structure exists only in theory.

Theory does not yet offer a methodology that would allow firms’ financial managers to find the optimal capital structure. However, financial managers can determine the approximate optimal structure range, which is close to what they believe the optimal structure for the firm is.

As per above, an optimal structure maximizes the value of the firm. To find the value of the firm, we can use the following formula:

V=EBIT*(1-T)/ra

Which simplifies into:

V=NOPAT/ra

Where:

V = is the value of the firm

EBIT = is earnings before interest and taxes (see the income statement for how it is calculated)

NOPAT = is the net operating profit after taxes (calculated by formula EBIT*(1-T)/ra)

ra = is the weighted average cost of capital (WACC)

If we assume that NOPAT is consistent, then the value of the firm is affected by WACC (ra, weighted average cost of capital). WACC is affected by both, the cost of debt and equity.

The cost of equity

The cost of equity is higher than the cost of debt and increases as financial leverage increases. This is because equity suppliers will demand higher return for increasing financial risk due to increasing financial leverage.

The cost of debt

The cost of debt initially is relatively low. The major reason for this is due to the fact that interest on debt is tax deductible. This tax deductibility of interest paid on debt is also commonly called the tax shield. However, as debt increases, at certain debt ratio lenders will begin to require higher and higher interest payments from the borrower. This is undertaken in order to compensate for increasing risk due to increasing financial leverage.

There are two other costs of debt that the firm needs to consider:

(1) Debt increases the probability of bankruptcy. This is because lenders can force the firm into bankruptcy if the firm cannot meet its financial obligations to the lender.

(2) Another aspect to consider is the agency cost. This refers to the fact that lenders usually protect themselves from increases in risk of the borrower by imposing different loan provisions, which place constraints on actions and choices of the firm. Such provisions commonly include, but are not limited to, minimum levels of liquidity to be maintained, limits on compensation of the executives and limitations on asset acquisitions.

***

As debt increases from a zero point onwards, WACC initially decreases to the theoretical optimal capital structure point. Thereafter, the increasing equity cost and increasing cost of debt causes WACC to start increasing again. Therefore the theoretical optimal capital structure is obtained at the point where the WACC is the lowest.

In other words, the theoretical optimal capital structure occurs at the point where the benefits from using debts are in equilibrium (in balance) with the costs of using debt. The optimal capital structure can also be seen as the balance between risk and return where the firm’s stock price is maximized.

 

Capital structure decisions analysis with debt ratios

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When analyzing capital structure decisions, external stakeholders can obtain an approximate idea of the capital structure of the particular firm by using information in the firm’s financial statements to calculate various debt ratios.

When analyzing capital structure decisions of firms as outsiders, we need to consider two types of debt measures:

The first type of debt ratio measures the degree of indebtedness. This refers to how much debt the firm has relative to other balance sheet’s amounts. The debt ratio will measure the degree of indebtedness.

The second type of debt ratio measures the ability to service debts. This type of debt ratios measures the ability of the business to meet its obligations associated with debt, as they come due. Times Interest Earned Ratio and Fixed Payment Coverage Ratio will be considered to measure the ability to service debts.

Both techniques are very simple to use and effective at analysing capital structure decisions.

Measuring the degree of indebtedness

THE DEBT RATIO

A direct measure of debt is a debt ratio. Debt ratios provide direct information on the financial leverage of an enterprise. Debt ratios measure how many of the firm’s assets are financed by debt. The higher the debt ratio, the higher the degree of financial leverage (amount of debt) and the higher the risk. The formula for the debt ratio is as follows:

Debt ratio=Total liabilities/Total assets

Example:

For example, assume that ABC’s total liabilities are $1,700,000 and total assets are $4,000,000.

The debt ratio of ABC is as follows: $1,700,000/$4,000,000=42.5%

This means that ABC’s capital structure is 42.5% of debt and 57.5% of equity.

Measuring the ability to service debts

TIME INTEREST EARNED RATIO (INTEREST COVERAGE RATIO)

The Times Interest Earned Ratio (TIER or Interest Coverage Ratio) measures the ability of the enterprise to meet its financial obligations (interest payments on debt that come due).

When analyzing capital structure decisions, we can use the Times Interest Earned Ratio as an indirect measure of the level of debt in the firm’s capital structure. Commonly, the lower the Times Interest Earned Ratio the higher the degree of financial leverage (amount of debt) and the higher the risk.

The formula for the Times Interest Earned Ratio is as follows:

Times Interest Earned Ratio =EBIT/interest charges

EBIT refers to the earnings before interest and taxes, which is also called operating profit (refer to the Income Statement format to see how it is calculated).

EXAMPLE:

Assume ABC Company has an operating profit of $550,000 and interest charges of $100,000.

The TIER of ABC is as follows:

$550,000/$100,000=5.5

It is generally advisable that the Times Interest Earned Ratio should be between 3 and 5.

ABC’s Times Interest Earned Ratio could be too high. It may be possible that the firm is unnecessarily careful in using debt as a source of capital. This means the risk taken may be lower than average, but so is the return.

When using the Times Interest Earned Ratio, it is important to remember that interest is paid with cash and not with income (since some income may still be in the form of accounts receivable). Therefore, the real ability of the firm to make interest payments may be worse than indicated by the Times Interest Earned Ratio. It is also important to remember that debt obligations include repayment of principal debt as well as payment of interest. The calculation above excludes the principal amount borrowed.

Generally, the higher the Times Interest Earned Ratio the lower the risk an enterprise will not be able to meet its contractual interest obligations on time. Therefore, generally, a higher Times Interest Earned Ratio is the better.

However, cognizance needs to be taken of the fact that the higher the Times Interest Earned Ratio, the lower the risk and lower the return. Therefore, at some point, the Times Interest Earned Ratio may be too high. This will occur if the business is unnecessarily careful with taking up debt as a source of financing, which results in very low risk but also a lower return. This is not aligned with the overall goal of the enterprise which is the maximization of the wealth of its shareholders.

FIXED PAYMENT COVERAGE RATIO

Fixed Payment Coverage Ratio measures the ability of the enterprise to meet all of its fixed-payment obligations on time. When analyzing capital structure decisions, we can use the Fixed Payment Coverage Ratio as an indirect measure of the level of debt in the firm’s capital structure. Commonly, the lower the Fixed Payment Coverage Ratio the higher the degree of financial leverage (amount of debt) and the higher the risk.

The formula for the Fixed Payment Coverage Ratio is as follows:

Fixed Payment Coverage Ratio = EBIT+LP/I+LP +((PP +PSD)*(1/1-T))

Where:

EBIT – earnings before interest and tax (operating profit)

LP – lease payments

I – interest charges

PP – principal payments

PSD – preferred stock dividends

T – tax rate

EXAMPLE:

Assume ABC Company has an operating profit of $550,000 and interest charges of $100,000. The lease payments are fixed at $20,000, principal payments are at $60,000 and preferred stock dividends are at $15,000. The corporate tax rate of ABC is 40%.

The Fixed Payment Coverage Ratio of ABC is calculated as follows:

= 550,000+20,000/100,000+20,000+((60,000+15,000)*(1/1-T))

= 570,000/120,000+((75,000)*1.67)

= 570,000/120,000+125,250

= 570,000/245,250

= 2.3

The Fixed Payment Coverage Ratio of ABC is 2.3. Since EBIT is more than two times larger than fixed-payment obligations, it appears that ABC is in a strong position to live up to its fixed-payment obligations as they come due. However, as with all financial ratios, Fixed Payment Coverage Ratio should be compared to industry average before any conclusions are drawn. Generally, the higher the Fixed Payment Coverage Ratio the lower the risk that enterprise will not be able to meet its fixed-payment obligations on time. Therefore, a higher Fixed Payment Coverage Ratio is the better.

However, as with Times Interest Earned ratio, cognizance needs to be taken of the fact that the higher the Fixed Payment coverage ratio the lower the risk and lower the return. Therefore, at some point, the Fixed Payment Coverage Ratio may be too high. This will occur if the business is unnecessarily careful with taking up more debt which results in a very low risk but also a lower return. This is not aligned with the overall goal of the enterprise which is the maximization of the wealth of its shareholders.

***

When analyzing capital structure decisions with the help of debt ratios, one should compare debt ratios of individual firms to industry averages. There is a large variability of debt ratios’ industry averages between industries. This is because different industries have different operations requirements. There is no one perfect ratio. Appropriate ratios to use should determined by the company in question, taking into account company’s ‘s strategy, operating environment, competitive environment and finances.

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