## Cost of debt

##### Published: Mar 2007

The cost of debt is the average interest rate that a company pays on all of its debt. It calculates the costs associated with each individual form of debt, for example of loans and bonds, and determines the average cost for the entire debt of the company.

The cost of debt is typically expressed after tax, as interest payments on debt are tax deductible and this will reduce the overall cost of borrowing. There are two general approaches to determine the cost of debt:

### 1. Calculating the yield to maturity and current market values of all outstanding debt

##### Debt securities

The cost of debt represents the opportunity cost of debt and what a company would have to pay on its debt if it was raising funds today. This means for debt securities that it is not the existing coupon on bonds and debentures, but the rate that the company would need to pay new purchasers of the security. A corporate bond’s current yield to maturity is the best approximation for the cost of debt capital:

$$YTM = \frac{Coupon \: + \: \frac{face \: value \: – \: Present \: value}{Number\: of \: coupon \: periods \: until \: maturity}}{\frac{face \: value \: + \: Present \: value}{2}}$$

For example, a ten year bond paying a 6% coupon with a face value of €1,000 is currently selling at €950 with eight years until maturity. Using the formula above, the yield to maturity and the cost of debt before tax is 6.79%:

$$YTM = \frac{60 \: + \: \frac{1000 \: – \: 950}{8}}{\frac{1000 \: + \:950}{2}} = \frac{66.25}{975} = 6.79\%$$

This calculation assumes a single annual coupon payment. The formula can be adapted for semi-annual or quarterly coupon payments.

##### Bank loans

In contrast to securitised debt, bank borrowings do not have a market price that can be related to the cost of debt. The interest rate of an existing loan can simply be taken as an approximation of the cost of debt.

### 2. Using the ‘debt risk premium’ method to estimate the cost of debt

This method estimates the cost of debt. According to the debt risk premium method, the cost of debt is the sum of a risk free rate and a risk premium for the risk of the company in question. Using this method, the risk free rate of a government bond, which matches the term structure of the corporate debt, would be used. Then, depending on the company’s credit rating, the appropriate risk spread would be derived from currently traded comparable bonds from the issuer with a similar credit rating and features. The sum of the risk-free rate and the risk premium is the estimated cost of debt.

#### After-tax cost of debt

To arrive at the after-tax cost of debt, the following formula can be used:

$$After-tax \: cost \: of \: debt = cost \: of \: debt \: before \: tax \: \times \: 1 \: – \: tax \: rate$$

Taking the example from above where the cost of debt on a bond is 6.79% and the applicable tax rate is 30%, the company’s after-tax cost of debt for the bond would be 4.753% (6.79% × (1-30%)).