# Cost of Debt

Cost of debt is the required rate of return on debt capital of a company. Where the debt is publicly-traded, cost of debt equals the yield to maturity of the debt. If market price of the debt is not available, cost of debt is estimated based on yield on other debts carrying the same bond rating.

The yield to maturity approach is useful where the market price of debt is available. Yield to maturity (YTM) equals the internal rate of return of the debt, i.e. it is the discount rate that causes the debt cash flows (i.e. coupon and principal payments) to equal the market price of the debt. Where the market price is not available, yield to maturity cannot be worked out but a relative approach can be used to estimate cost of debt. Under the relative approach, called the bond-rating approach, cost of debt equals the average yield to maturity of similar bonds, i.e. bonds carrying the same credit rating.

Cost of debt is an important input in calculation of the weighted average cost of capital. WACC equals the weighted average of cost of equity and after-tax cost of debt based on their relative proportions in the target capital structure of the company.

## Formula

Under the yield to maturity approach, cost of debt is calculated by solving the following equation for r:

 Bond Price = c × F × 1 − (1 + r)-t + F r (1 + r)t

Where,
c is the periodic coupon rate (i.e. annual coupon rate ÷ number of coupon payments per annum),
F is the face value of the debt, and
t is the number of coupon payments outstanding till maturity.

There is no algebraic solution to the above equation, but we can employ the hit-and-trial method. We can also use Excel YIELD function. Please see the article on YIELD TO MATURITY to study alternative methods for solving for r.

Cost of debt is then expressed as an annual percentage rate i.e. cost of debt is equal to number of payments per year times r. If c is for a semi-annual period, r is also for semi-annual period.

Apart from the yield to maturity approach and bond-rating approach, current yield and coupon rate (nominal yield) can also be used to estimate cost of debt but they are not the preferred methods.

## Example

Lockheed Martin Corporation has \$900 million \$1,000 per value bonds payable carrying semi-annual coupon rate of 4.25%. They are maturing on 15 November 2019. The bonds have a market value per bond of 112.5 as at 15 November 2012. If the tax rate is 35%, find the before tax and after-tax cost of debt.

Before tax cost of debt equals the yield to maturity on the bond. Yield to maturity is calculated using the IRR function on a mathematical calculator or MS Excel. Semiannual yield to maturity in this example is calculated by finding r in the following equation:

 \$1,125 = \$21.25 × 1−(1+r)-2×7 + 1 r (1+r)2×7

r comes out to be 1.15%. Relevant annual before tax cost of debt is just the relevant APR which his 2.3% (2 × 1.15%)

Corresponding after tax cost of debt is 1.495% (2.3% × (1 − 35%)).