Cost of debt

The cost of debt represents the cost to a company of its debt finance.

A distinction must be made between the required return of debt holders / lenders (K_d) and the company's cost of debt (K_d(1-T)). Although in the context of equity the company's cost is equal to the investor's required return, the same is not true of debt. This is because of the impact of tax relief.

The cost of debt needs to be determined as part of calculating a weighted average cost of capital for use as a discount rate for investment appraisal.

 V_e and V_d are the market values of equity and debt respectively.

k_e and k_d are the returns required by the equity holders and the debt holders respectively.

T is the corporation tax rate.

k_e is the cost of equity.

k_d(1-T) is the post tax cost of debt.

Using the Dividend Valuation Model to determine the cost of debt

The dividend valuation model can be applied to debt as follows:

Bank loans / overdrafts

Post tax cost of debt  =  k_d(1-T) = Bank interest rate × (1 - T)

Irredeemable bonds

K_d (1-T) = I (1-T) / MV

where

I = the annual interest paid,

MV =  the current bond price.

Redeemable bonds

If the redemption value of the bonds happens to be the same as the current market value, then for calculation purposes the bonds can be treated as if they were irredeemable.

If not, then an IRR calculation is required:

k_d (1-T) = the Internal Rate of Return (IRR) of

• the bond price
• the interest (net of tax)
• the redemption payment

Convertible debt

To calculate the cost of convertible debt you should:

(1)Calculate the value of the conversion option using available data. Note: share prices can be assumed to grow in the future in line with the growth in dividends.

(2)Compare the conversion option with the cash option. Assume all investors will choose the option with the higher value.

(3)Calculate the IRR of the flows as for redeemable debt, treating the value of the conversion option (shares or cash) as the redemption value in the calculation.

Note: the is no tax effect on redemption whichever option is chosen at the conversion date.

Using credit spreads and credit rating agencies to determine the cost of debt

However, an important technique for deriving cost of debt in practice is based on an awareness of credit spread (sometimes referred to as the "default risk premium"), and the formula:

k_d (1-T) = (Risk free rate + Credit spread) (1-T)

The credit spread is a measure of the credit risk associated with a company. Credit spreads are generally calculated by a credit rating agency and presented in a table like the one below:

What is credit risk?

Credit or default risk is the uncertainty surrounding a firm's ability to service its debts and obligations.

It can be defined as the risk borne by a lender that the borrower will default either on interest payments, the repayment of the borrowing at the due date or both.

The role of credit rating agencies

If a company wants to assess whether a firm that owes them money is likely to default on the debt, a key source of information is a credit rating agency.

They provide vital information on creditworthiness to:

• potential investors
• regulators of investing bodies
• the firm itself.

The assessment of creditworthiness

A large number of agencies can provide information on smaller firms, but for larger firms credit assessments are usually carried out by one of the international credit rating agencies. The three largest international agencies are Standard and Poor's, Moodys and Fitch.

Certain factors have been shown to have a particular correlation with the likelihood that a company will default on its obligations:

• The magnitude and strength of the company's cash flows.
• The size of the debt relative to the asset value of the firm.
• The volatility of the firm's asset value.
• The length of time the debt has to run.

Using this and other data, firms are scored and rated on a scale, such as the one shown here:

Calculating credit scores

The credit rating agencies use a variety of models to assess the creditworthiness of companies.

In the popular Kaplan Urwitz model, measures such as firm size, profitability, type of debt, gearing ratios, interest cover and levels of risk are fed into formulae to generate a credit score.

These scores are then used to create the rankings shown above. For example a score of above 6.76 suggests an AAA rating.

Credit spreads

There is no way to tell in advance which firms will default on their obligations and which won't. As a result, to compensate lenders for this uncertainty, firms generally pay a spread or premium over the risk-free rate of interest, which is proportional to their default probability.

The yield on a corporate bond is therefore given by:

Yield on corporate bond = Yield on equivalent treasury bond + credit spread

Table of credit spreads for industrial company bonds:

Note: the figures are given in basis points (100 basis points = 1%)

Simple illustration

The current return on 5-year treasury bonds is 3.6%. C plc has equivalent bonds in issue but has an A rating. What is the expected yield on C's bonds and the post tax cost of debt for C plc, given it pays tax at 30%?

Solution

From the table the credit spread for an A rated, 5-year bond is 65.

This means that 0.65% must be added to the yield on equivalent treasury bonds.

So yield on C's bonds = 3.6% + 0.65% = 4.25%.

The post tax cost of debt will then = 4.25 × 0.7 = 2.975%

Determining credit spreads

The two main ways of calculating credit spreads are as follows:

• Using option pricing theory
• Using probabilities and expected value.

Using CAPM to determine the cost of debt

The CAPM can be used to derive a required return as long as the systematic risk of an investment is known.

In the case of equity an equity beta can be used to derive a required return on equity. Similarly, if the debt beta is not zero (for example if the company's credit rating shows that it has a credit spread greater than zero) the CAPM can also be used to derive k_d as follows:

kd = R_f + β_debt (E(R_m) - R_f)

Then, the post tax cost of debt is kd (1-T) as usual.

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