## From Cost of Equity to Cost of Capital

While equity is undoubtedly an important and indispensable ingredient of the financing mix for every business, it is but one ingredient. Most businesses finance some or much of their operations using debt or some security that is a combination of equity and debt. The costs of these sources of financing are generally very different from the cost of equity and the cost of financing for a firm should reflect their costs as well, in proportion to their use in the financing mix. Intuitively, the cost of capital is the weighted average of the costs of the different components of financing -- including debt, equity and hybrid securities -- used by a firm to fund its financial requirements. In this section, we examine the process of estimating the cost of financing other than equity and the weights for computing the cost of capital.

### Calculating the Cost of Debt

The cost of debt measures the current cost to the firm of borrowing funds to finance projects. In general terms, it is determined by the following variables:

(1) The riskless rate: As the riskless increases, the cost of debt for firms will also increase.

(2) The default risk (and associated default spread) of the company: As the default risk of a firm increases, the cost of borrowing money will also increase. In chapter 7, we looked at how the default spread has varied across time and can vary across maturity.

(3) The tax advantage associated with debt: Since interest is tax deductible, the after-tax cost of debt is a function of the tax rate. The tax benefit that accrues from paying interest makes the after-tax cost of debt lower than the pre-tax cost. Furthermore, this benefit increases as the tax rate increases.

After-tax cost of debt = Pre-tax cost of debt (1 - tax rate) In this section, we will focus on how best to estimate the default risk in a firm and to convert that default risk into a default spread that can be used to come up with a cost of debt.

Estimating the Default Risk and Default Spread of a firm

The simplest scenario for estimating the cost of debt occurs when a firm has long term bonds outstanding that are widely traded. The market price of the bond, in conjunction with its coupon and maturity can serve to compute a yield that we use as the cost of debt. For instance, this approach works for a firm like AT&T that has dozens of outstanding bonds that are liquid and trade frequently.

Many firms have bonds outstanding that do not trade on a regular basis. Since these firms are usually rated, we can estimate their costs of debt by using their ratings and associated default spreads. Thus, Boeing with a AA rating can be expected to have a cost of debt approximately 0.50% higher than the treasury bond rate, since this is the spread typically paid by AA rated firms.

Some companies choose not to get rated. Many smaller firms and most private businesses fall into this category. While ratings agencies have sprung up in many emerging markets, there are still a number of markets where companies are not rated on the basis of default risk. When there is no rating available to estimate the cost of debt, there are two alternatives:

1. Recent Borrowing History: Many firms that are not rated still borrow money from banks and other financial institutions. By looking at the most recent borrowings made by a firm, we can get a sense of the types of default spreads being charged the firm and use these spreads to come up with a cost of debt.

2. Estimate a synthetic rating: An alternative is to play the role of a ratings agency and assign a rating to a firm based upon its financial ratios; this rating is called a synthetic rating. To make this assessment, we begin with rated firms and examine the financial characteristics shared by firms within each ratings class. To illustrate, table 8.5 lists the range of interest coverage ratios for small manufacturing firms in each S&P ratings class12.

Table 8.5: Interest Coverage Ratios and Ratings: Low Market Cap Firms

 Interest Coverage Ratio Rating Spread > 12.5 AAA 0.75% 9.5 - 12.5 AA 1.00% 7.5 - 9.5 A+ 1.50% 6 - 7.5 A 1.80% 4.5 - 6 A- 2.00%

12 This table was developed in 1999 and 2000, by listing out all rated firms, with market capitalization lower than \$ 2 billion, and their interest coverage ratios, and then sorting firms based upon their bond ratings. The ranges were adjusted to eliminate outliers and to prevent overlapping ranges.

 3.5 - 4.5 BBB 2.25% 3 - 3.5 BB 3.50% 2.5 - 3 B+ 4.75% 2 - 2.5 B 6.50% 1.5 - 2 B- 8.00% 1.25 -1.5 CCC 10.00% 0.8 - 1.25 CC 11.50% 0.5 - 0.8 C 12.70% < 0.5 D 14.00%

Now consider a small firm that is not rated but has an interest coverage ratio of 6.15. Based on this ratio, we would assess a "synthetic rating" of A for the firm.

The interest coverage ratios tend to be lower for larger firms, for any given rating. Table 8.6 summarizes these ratios:

Table 8.6: Interest Coverage Ratios and Ratings: High Market Cap Firms

 Interest Coverage Ratio Rating Spread > 8.5 AAA 0.75% 6.5-8.5 AA 1.00% 5.5 -6.5 A+ 1.50% 4.25- 5.5 A 1.80% 3- 4.25 A- 2.00% 2.5-3 BBB 2.25% 2- 2.5 BB 3.50% 1.75-2 B+ 4.75% 1.5-1.75 B 6.50% 1.25-1.5 B- 8.00% 0.8-1.25 CCC 10.00% 0.65-0.8 CC 11.50% 0.2-0.65 C 12.70% <0.2 D 14.00%

This approach can be expanded to allow for multiple ratios and qualitative variables, as well. Once a synthetic rating is assessed, it can be used to estimate a default spread which when added to the riskfree rate yields a pre-tax cost of debt for the firm.

Extending the Synthetic Ratings Approach By basing the rating on the interest coverage ratio alone, we run the risk of missing the information that is available in the other financial ratios used by ratings agencies. The approach described above can be extended to incorporate other ratios. The first step would be to develop a score based upon multiple ratios. For instance, the Altman Z score, which is used as a proxy for default risk, is a function of five financial ratios, which are weighted to generate a Z score. The ratios used and their relative weights are usually based upon empirical evidence on firm defaults. The second step is to relate the level of the score to a bond rating, much as we have done in the table above with interest coverage ratios.

In making this extension, though, note that complexity comes at a cost. While credit or Z scores may, in fact, yield better estimates of synthetic ratings than those based upon interest coverage ratios, changes in ratings arising from these scores are much more difficult to explain than those based upon interest coverage ratios. That is the reason we prefer the flawed but simpler ratings that we get from interest coverage ratios.

### Estimating a Tax Rate

To estimate the after-tax cost of debt, we consider the fact that interest expenses are tax deductible to the firm. While the computation is fairly simple and requires that we multiply the pre-tax cost by (1- tax rate), the question of what tax rate to use can be a difficult one to answer because we have so many choices. For instance, firms often report an effective tax rate, estimated by dividing the taxes due by the taxable income. The effective tax rate, though, is usually very different from the marginal tax rate, which is the rate at which the last or the next dollar of income is taxed. Since interest expenses save taxes at the margin (they are deducted from the last or the next dollar of income), the right tax rate to use is the marginal tax rate.

The other caveat to keep in mind is that interest creates a tax benefit only if a firm has enough income to cover the interest expenses. Firms that have operating losses will not get a tax benefit, at least in the year of the loss, from interest expenses. The after-tax cost of debt will be equal to the pre-tax cost of debt in that year. If you expect the firm to make money in future years, you would need to adjust the after-tax cost of debt for taxes.

We will return to this issue and examine it in more detail in chapter 10, where we will look at the same issue in the context of estimating after-tax cash flows.

Illustration 8.10: Estimating the Cost of Debt: Boeing in June 2000

Boeing is rated AA by S&P. Using the typical default spreads for AA rated firms, we could estimate the pre-tax cost for Boeing by adding the default spread13 of 1.00% to the riskless rate of 5%.

Pre-tax cost of debtActual Rating = 5.00% + 1.00% = 6.00%%

Boeing has an effective tax rate of 27% but we use a marginal tax rate of 35%, which is the federal marginal corporate tax rate to estimate the after-tax cost of debt for Boeing. After-tax cost of debt = 6.00% (1-.35) = 3.90%

We could also compute a synthetic rating for Boeing, based upon its interest coverage ratio from 1999. Based upon its operating income of \$1,720 million in 1999 and interest expense of \$453 million in of that year, we would have estimated an interest coverage ratio:

Interest coverage ratioBoeing = 1720/453 = 3.80

Using Table 8.6, we would have assigned a synthetic rating of A- to Boeing. Based upon default spreads prevailing in June 2000, this would have resulted in a default spread of 2.00% and a pre-tax cost of debt of 7.00% for the firm.

Estimating the Cost of Debt for an Emerging Market firm

In general, there are three problems that we run into when assessing the cost of debt for emerging market firms. The first is that most of these firms are not rated, leaving us with no option but to estimate the synthetic rating (and associated costs). The second is that the synthetic ratings may be skewed by differences in interest rates between the emerging market and the United States. Interest coverage ratios will usually decline as interest rates increase and it may be far more difficult for a company in an emerging market to achieve the interest coverage ratios of companies in developed markets. Finally, the existence of country default risk level hangs over the cost of debt of firms in that market.

The second problem can be fixed fairly simply by either modifying the tables developed using U.S. firms or restating the interest expenses (and interest coverage ratios)

in dollar terms. The question of country risk is a thornier one. Conservative analysts often assume that companies in a country cannot borrow at a rate lower than the country can borrow at. With this reasoning, the cost of debt for an emerging market company will include the country default spread for the country.

Cost of debtEmerging Market company= Riskless Rate + Country Default Spread + Company

The counter to this argument is that companies may be safer than the countries that they operate in and that they bear only a portion or perhaps even none of the country default spread.

Illustration 8.11: Estimating the Cost of Debt: Embraer in December 2000

To estimate Embraer's cost of debt, we first estimate a synthetic rating for the firm. Based upon its operating income of \$810 million and interest expenses of \$28 million in 2000, we arrived at an interest coverage ratio of 28.93 and an AAA rating. While the default spread for AAA rated bonds was only 0.75%, there is the added consideration that Embraer is a Brazilian firm. Since the Brazilian government bond traded at a spread of 5.37% at the time of the analysis, you could argue that every Brazilian company should pay this premium, in addition to its own default spread. With this reasoning, the pre-tax cost of debt for Embraer in U.S. dollars (assuming a treasury bond rate is 5%) can be calculated:

Cost of Debt = Riskfree rate + Default spread for country + Default Spread for firm

= 5% + 5.37% + 0.75% = 11.12% Using a marginal tax rate of 33%, we can estimate an after-tax cost of debt for Embraer: After-tax cost of debt = 11.12% (1- .33) = 7.45%

With this approach, the cost of debt for a firm can never be lower than the cost of debt for the country in which it operates. Note, though, that Embraer gets a significant portion of its revenues in dollars from contracts with non-Brazilian airlines. Consequently, it could reasonably argue that it is less exposed to risk than the Brazilian government and should therefore command a lower cost of debt.

13 We used the default spread of 1.00% from table 7.6.

ratings.xls: This spreadsheet allows you to estimate the synthetic rating and cost of debt for any firm.

### Calculating the Cost of Hybrid Securities

While debt and equity represent the fundamental financing choices available for firms, there are some types of financing that share characteristics with both debt and equity. These are called hybrid securities. In this section, we consider how best to estimate the costs of such securities.

### Cost of Preferred Stock

Preferred stock shares some of the characteristics of debt - the preferred dividend is pre-specified at the time of the issue and is paid out before common dividend - and some of the characteristics of equity - the payments of preferred dividend are not tax deductible. If preferred stock is viewed as perpetual, the cost of preferred stock can be written as follows:

k = Preferred Dividend per share ps Market Price per preferred share

This approach assumes the dividend is constant in dollar terms forever and that the preferred stock has no special features (convertibility, callability, etc.). If such special features exist, they will have to be valued separately to estimate the cost of preferred stock. In terms of risk, preferred stock is safer than common equity, because preferred dividends are paid before dividends on common equity. It is, however, riskier than debt since interest payments on debt are made prior to preferred dividend payments.

Consequently, on a pre-tax basis, it should command a higher cost than debt and a lower cost than equity.

Illustration 8.12: Calculating the Cost Of Preferred Stock: General Motors Co.

In March 1995, General Motors had preferred stock that paid a dividend of \$2.28 annually and traded at \$26.38 per share. The cost of preferred stock can be estimated as follows:

Preferred Dividend per share 2.28

Preferred Stock Price 26.38

At the same time, GM's cost of equity, using the CAPM, was 13%, its pre-tax cost of debt was 8.25% and its after-tax cost of debt was 5.28%. Not surprisingly, its preferred stock was less expensive than equity but much more expensive than debt.

### Calculating the Cost of Other Hybrid Securities

A convertible bond is a bond that can be converted into equity, at the option of the bondholder. A convertible bond can be viewed as a combination of a straight bond (debt) and a conversion option (equity). Instead of trying to calculate the cost of these hybrid securities individually, we can break down hybrid securities into their debt and equity components and treat the components separately.

Illustration 8.13: Breaking down a convertible bond into debt and equity components: Amazon Inc

In 1999, Amazon Inc, the online retailer, issued convertible bonds with a coupon rate of 4.75% and a ten-year maturity. Since the firm was losing money, it was rated CCC+ by S&P and would have had to pay 11% if it had issued straight bonds at the same time. The bonds were issued at a price that was 98% of par and the total par value of the convertible bond issue was \$1.25 billion. The convertible bond can be broken down into straight bond and conversion option components.

Straight Bond component = Value of a straight 4.75% coupon bond due in 10 years with an 11% interest rate = \$636 (assuming semi-annual coupons) Conversion Option = \$980 - \$636 = \$344

The straight bond component of \$636 is treated as debt and has the same cost as the rest of debt. The conversion option of \$344 is treated as equity and has the same cost of equity as other equity issued by the firm. For the entire bond issue of \$1.25 billion, the value of debt is \$811 million, and the value of equity is \$439 million.

Calculating the Weights of Debt and Equity Components

Now that we have the costs of debt, equity and hybrid securities, we have to estimate the weights that should be attached to each. Before we discuss how best to estimate weights, we define what we include in debt. We then make the argument that weights used should be based upon market value and not book value. This is so because the cost of capital measures the cost of issuing securities - stocks as well as bonds - to finance projects and these securities are issued at market value, not at book value.

What is debt?

The answer to this question may seem obvious since the balance sheet for a firm shows the outstanding liabilities of a firm. There are, however, limitations with using these liabilities as debt in the cost of capital computation. The first is that some of the liabilities on a firm's balance sheet, such as accounts payable and supplier credit, are not interest bearing. Consequently, applying an after-tax cost of debt to these items can provide a misleading view of the true cost of capital for a firm. The second is that there are items off the balance sheet that create fixed commitments for the firm and provide the same tax deductions that interest payments on debt do. The most prominent of these offbalance sheet items are operating leases. In chapter 3, we contrasted operating and capital leases and noted that operating leases are treated as operating expenses rather than financing expenses. Consider, though, what an operating lease involves. A retail firms leases a store space for 12 years and enters into a lease agreement with the owner of the space agreeing to pay a fixed amount each year for that period. We do not see much difference between this commitment and borrowing money from a bank and agreeing to pay off the bank loan over 12 years in equal annual installments.

There are therefore two adjustments we will make when we estimate how much debt a firm has outstanding.

• We will consider only interest bearing debt rather than all liabilities. We will include both short term and long term borrowings in debt.

• We will also capitalize operating leases and treat these expenditures as financing expenses.

### Capitalizing Operating Leases

Converting operating lease expenses into a debt equivalent is straightforward. The operating lease commitments in future years, which are revealed in the footnotes to the financial statements for US firms, should be discounted back at a rate that reflects their status as unsecured and fairly risky debt. As an approximation, using the firm's current pre-tax cost of borrowing as the discount rate yields a good estimate of the value of operating leases.

Outside the United States, firms do not have to reveal their operating lease commitments in future periods. When this is the case, you can get a reasonably close estimate of the estimated debt value of operating leases by assuming that an annuity equal to the current year's operating lease payment for a period that reflects a typical lease period (8 to 10 years).

There is one final issue relating to capitalization. Earlier in this chapter, we argued that the interest coverage ratio could be used to estimate a synthetic rating for a firm that is not rated. For firms with little in terms of conventional debt and substantial operating leases, the interest coverage ratio used to estimate a synthetic rating has to be adapted to include operating lease expenses.

Modified Interest Coverage Ratio = (EBIT + Current year's Operating Lease

Expense)/(Interest Expenses + Current year's Operating Lease Expense)

This ratio can then be used in conjunction with Tables 8.5 and 8.6 to estimate a synthetic rating.

Illustration 8.14: The Debt Value of Operating Leases: Boeing in June 2000

Boeing has both conventional debt and operating lease commitments. In this illustration, we will estimate the "debt value" of Boeing's operating leases by taking the present value of operating lease expenses over time. To compute the present value of operating leases in Table 8.7, we use the pre-tax cost of borrowing for the firm which we estimated to be 6.0% in Illustration 8.10.

 Year Operating Lease Expense Present Value at 6.0% 1 \$ 205 \$ 193.40 2 \$ 167 \$ 146.83 3 \$ 120 \$ 100.75 4 \$ 86 \$ 68.12
 5 \$ 61 \$ 45.58 Yr 6 -15 \$ - \$ - PV of Operating Lease Expenses \$ 556.48

Thus, Boeing has \$556 million more in debt than is reported in the ba

Thus, Boeing has \$556 million more in debt than is reported in the ba ance sheet.

Oplease.xls: This spreadsheet allows you to convert operating lease expenses into debt.

### Book Value versus Market Value Debt ratios

There are three standard arguments against using market value and none of them are convincing. First, there are some financial managers who argue that book value is more reliable than market value because it is not as volatile. While it is true that book value does not change as much as market value, this is more a reflection of book value's weakness rather than its strength since the true value of the firm changes over time as both firm-specific and market information is revealed. We would argue that market value, with its volatility, is a much better reflection of true value than book value.14

Second, the defenders of book value also suggest that using book value rather than market value is a more conservative approach to estimating debt ratios. This assumes that market value debt ratios are always lower than book value debt ratios, an assumption not based on fact. Furthermore, even if the market value debt ratios are lower than the book value ratios, the cost of capital calculated using book value ratios will be lower than those calculated using market value ratios, making them less conservative estimates, not more. To illustrate this point, assume that the market value debt ratio is 10%, while the book value debt ratio is 30%, for a firm with a cost of equity of 15% and an after-tax cost of debt of 5%. The cost of capital can be calculated as follows:

With market value debt ratios: 15% (0.9) + 5% (0.1) = 14% With book value debt ratios: 15% (.7) + 5% (.3) = 12%

14 There are some who argue that stock prices are much more volatile than the underlying true value. Even if this argument is justified (and it has not conclusively been shown to be so), the difference between market value and true value is likely to be much smaller than the difference between book value and true value.

Third, it is claimed that lenders will not lend on the basis of market value, but this claim again seems to be based more upon perception than fact. Any homeowner who has taken a second mortgage on a house that has appreciated in value knows that lenders do lend on the basis of market value. It is true, however, that the greater the perceived volatility in the market value of an asset, the lower is the borrowing potential on that asset.

### Estimating the Market Values of Equity and Debt

The market value of equity is generally the number of shares outstanding times the current stock price. If there other equity claims in the firm such as warrants and management option, these should also be valued and added on to the value of the equity in the firm.

The market value of debt is usually more difficult to obtain directly, since very few firms have all their debt in the form of bonds outstanding trading in the market. Many firms have non-traded debt, such as bank debt, which is specified in book value terms but not market value terms. A simple way to convert book value debt into market value debt is to treat the entire debt on the books as one coupon bond, with a coupon set equal to the interest expenses on all the debt and the maturity set equal to the face-value weighted average maturity of the debt, and then to value this coupon bond at the current cost of debt for the company. Thus, the market value of \$1 billion in debt, with interest expenses of \$60 million and a maturity of 6 years, when the current cost of debt is 7.5% can be estimated as follows:

Estimated Market Value of Debt = 60

1.0756 0.075

1.0756

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