###### How Taxes Affect the Cost of Capital

Taxes can have a significant impact on the weighted average cost of capital... **Read More**

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.

The yield-to-maturity of a bond is the annual return that an investor earns on a bond if they purchase the bond 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 the 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:

*P _{0}* = 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

Suppose company A issues a new debt by offering a 20-year, $100,000 face value, 10% semi-annual coupon bond. Upon issuance, the bond sells at $105,000. What are 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

*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 =

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 the debt of a company 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 existing debt of the company.

Assume that company B has senior, unsecured debt with an average maturity of 5 years and the marginal tax rate of the company 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:

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

QuestionWhich 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 they purchase the bond today and hold it until maturity.

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

C. The yield-to-maturity of a bond is the return that an investor earns on a bond if they purchase the bond and sell it one year prior to maturity.

SolutionThe correct answer is B.

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

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

Option C is incorrect. The yield-to-maturity of a bond assumes that the investor holds the bond until maturity.

*Reading 33 LOS 33f: *

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