Chapter 11, Problem 1PROB

Summary Introduction

YTM is the yield to maturity. It is the rate earned by the investor if he holds the bond till maturity.

Calculate the YTM by using the following formula:

${\text{P}}_0=\frac{\text{INT}}{{\left(1+\text{YTM}\right)}^1}+\mathrm{...}+\frac{\text{INT}+\text{M}}{{\left(1+\text{YTM}\right)}^{\text{n}}}$

Where,

${\text{P}}_0$ is the current price of the bond,

${\text{r}}_{\text{d}}$ Or YTM is the before tax cost of debt,

M is the par value or face value,

INT is the dollar interest payment,

N is the number of years of interest payment.

After tax cost of debt: Interest expenses are tax deductible. So, after tax cost of debt is obtained after deducting the tax expenses from the cost of debt.

Calculate the after tax cost of debt by using the following formula:

${\text{r}}_{\text{dt}}={\text{r}}_{\text{d}}\times \left(1-\text{T}\right)$

T is the tax rate,

${\text{r}}_{\text{d}}$ is YTM is the before tax cost of debt,

${\text{r}}_{\text{dt}}$ is the after tax cost of debt,

G products is plan to issue new bonds for new growth opportunity. Interest payment is $60, maturity 10 years, current price is $1,077 and tax rate is 40%

Explanation of Solution

a.

Calculate the YTM as follows:

$\begin{array}{l}{\text{P}}_0=\frac{\text{INT}}{\left(1+\text{YTM}\right)}+\mathrm{...}+\frac{\text{INT}+\text{M}}{\left(1+\text{YTM}\right)}\\ \$1,077=\frac{\$60}{{\left(1+\text{YTM}\right)}^1}+\frac{\$60}{{\left(1+\text{YTM}\right)}^2}+\frac{\$60}{{\left(1+\text{YTM}\right)}^3}+\mathrm{...}+\frac{\$60+\$1,000}{{\left(1+\text{YTM}\right)}^{10}}\end{array}$

Using Excel calculate YTM:

Therefore, the YTM is $\boxed{5.0\%}$.

a.

Calculate the after tax cost of debt as follows:

$\begin{array}{c}{\text{r}}_{\text{dt}}={\text{r}}_{\text{d}}\times \left(1-\text{T}\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}=5\%\times \left(1-40\%\right)\\ =3\mathrm{\%\hspace{1em}\hspace{1em}\hspace{1em}}\end{array}$

Therefore, the after tax cost of debt is $\boxed{3.0\%}$.