# Cost of Debt

Cost of debt (k_{d}) 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 avialable. 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. interest and principal payments) to equal the market price of the debt. Where the market price is not available, yield to maturity can't be worked out but a relative approach can be used to estimate cost of debt. Under this approach, called the bond rating approach, cost of debt equals the average yield to maturity of similarl 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 as follows:

Current Market Value of Debt = Coupon Payment × | 1−(1+r)^{-n} | + | Face Value of Debt |

r | (1+r)^{n} |

Where,

Coupon Payment = | Stated Rate on the Bond | × Face Value of Debt |

Number of Payments per Year |

r = | Yield to Maturity |

Number of Periods per Year |

n = Number of Coupon Payments = Number of Periods per Year × Maturity in Years |

Cost of debt is then expressed as an annual APR i.e. cost of debt is equal to number of payments per year times r.

Apart from the yield to maturity approach and bond rating approach, current yield and coupon rate can also be used to estimate cost of debt.

## 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 times 1.15%)

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