## Cost of Debt Capital

The cost of debt is the cost of debt financing whenever a company incurs debt by either issuing a bond or taking out a bank loan. Two methods for estimating the before-tax cost of debt are the yield-to-maturity approach and the debt-rating approach.

## Yield-to-Maturity Approach

The yield to maturity of a bond is the annual return that an investor earns on the bond if the investor purchases the bond and holds it until maturity. It is the yield which equates the present value of the bond’s promised payments to its market price.

Assuming that the bond pays semi-annual interest and that any intermediate cash flows are invested at the rate rd/2; expressed as an equation –

Where:

P0 = the current market price of the bond

PMTt = the interest payment in period t

rd = the yield to maturity

n = the number of periods remaining to maturity

FV = the maturity value of the bond

## Example

Suppose company A issues new debt by offering a 20-year, \$100,000 face value, 10% semi-annual coupon bond. Upon issuance, the bond sells for \$105,000. What is company A’s before-tax cost of debt and after-tax cost of debt if the marginal tax rate is 40%.

Solution

Given –

PV = \$105,000

FV = \$100,000

PMT = (10% of \$100,000)/2 = \$5,000

N = 20 * 2 = 40

Using a financial calculator to solve for

rd/2, the six-month yield, we get

rd/2 = 4.72%.

The before-tax cost of debt is therefore r= 4.72% x 2 = 9.44%, and the after-tax cost of debt = rd(1 – t) = 9.44% (1 – 0.40) = 5.66%.

## Debt-Rating Approach

The debt-rating approach is a method for estimating the before-tax cost of debt for a company whenever reliable current market price data for its debt is unavailable. In this method, the before-tax cost of debt is estimated by using the yield on comparably rated bonds for maturities which are closely aligned with the maturities of the company’s existing debt.

## Example

Suppose company B has senior, unsecured debt with an average maturity of 5 years and the company’s marginal tax rate is 35%. If the company’s debt rating is BBB- and the yield on similar senior, unsecured debt with the same debt rating and maturity is 9%, then the company’s after-tax cost of debt is:

(1 – t) = 9% (1 – 0.35) = 5.85%

## Question

Which of the following statements gives an accurate definition of yield to maturity?

A. The yield to maturity of a bond is the semi-annual return that an investor earns on a bond if the investor purchases the bond today and holds it until maturity.

B. The yield to maturity of a bond is the annual return that an investor earns on the bond if the investor purchases the bond today and holds it until maturity.

C. The yield to maturity of a bond is the return that an investor earns on the bond if the investor purchases the bond and sells it one year prior to maturity.

Solution

The yield to maturity of a bond is the annual return that an investor earns on the bond if the investor purchases the bond today and holds it until maturity. A is incorrect because the yield to maturity is an annual return and not a semi-annual return. C is incorrect because the yield to maturity of a bond assumes that the investor holds the bond until maturity.

Calculate and interpret the cost of debt capital using the yield-to-maturity approach and debt-rating approach

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