Calculating Cost of Debt Capital

The cost of debt is the cost of financing a debt whenever a company incurs a debt by either issuing a bond or taking 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

A bond’s yield-to-maturity is the annual return an investor earns on a bond if they purchase it today and hold it until maturity. It is the yield that equates the present value of the bond’s promised payments to its market price.

Assuming that a bond pays semi-annual interest and any intermediate cash flows are invested at the rate of r_d/2, then:

$$ { P }_{ 0 }=\left( \sum _{ t=1 }^{ n }{ \frac { { PMT }_{ t } }{ { \left( 1+\frac { { r }_{ d } }{ 2 } \right) }^{ t } } } \right) +\frac { FV }{ { \left( 1+\frac { { r }_{ d } }{ 2 } \right) }^{ n } }
$$

Where:

P₀ = The current market price of the bond.

PMT_t = The interest payment in period t.

r_d = The yield to maturity.

n = The number of periods remaining to maturity.

FV = The maturity value of the bond.

Example: Calculating the Before-tax Cost of Debt and the After-tax Cost of Debt

Suppose company A issues a new debt by offering a 20-year $100,000 face value and 10% semi-annual coupon bond. Upon issuance, the bond sells at $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.

$$ $105,000=\left( \sum _{ t=1 }^{ 40 }{ \frac { $5,000 }{ { \left( 1+\frac { { r }_{ d } }{ 2 } \right) }^{ t } } } \right) +\frac { $1,00,000 }{ { \left( 1+\frac { { r }_{ d } }{ 2 } \right) }^{ 40 } }
$$

Using a financial calculator to solve for r_d/2, the six-month yield, we get r_d/2 = 4.72%.

Note PV = -$105,000 when using the calculator instead of the formula.

The before-tax cost of debt is therefore r_d = 4.72% × 2 = 9.44%, and the after-tax cost of debt = r_d(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. This approach is applied whenever reliable, current market price data for a company’s debt is unavailable. In this method, the before-tax cost of debt is estimated by using the yield on comparably rated bonds for maturities that are closely aligned to the maturities of the company’s existing debt.

Example: Debt-rating Approach

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

$$ (1 – t) = 9\% (1 – 0.35) = 5.85\% $$

Question

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

1. A bond’s yield-to-maturity is the semi-annual return  an investor earns on a bond if they purchase the bond today and hold it until maturity.
2. A bond’s yield-to-maturity is the annual return  an investor earns on a bond if they purchase the bond today and hold it until maturity.
3. A bond’s yield-to-maturity is the return an investor earns on a bond if they purchase the bond and sell it one year prior to maturity.

Solution

The correct answer is B.

A bond’s yield-to-maturity is the annual return that an investor earns on a bond if they purchase the bond today and hold it until maturity.

A is incorrect. The yield-to-maturity is an annual return and not a semi-annual return.

 C is incorrect. A bond’s yield-to-maturity assumes that the investor holds the bond until maturity.