Chapter 9, Problem 9.4P

a.

Summary Introduction

To discuss:

To calculate the before-tax and after –tax cost of debt using approximation formula.

Introduction:

The before -tax cost debt is the rate of return the firm must pay on a new borrowing. The after-tax cost of a debt is the cost after deducting the tax amount.

When after tax cost of the debt is r_i and r_d is the before-tax cost of a debt, with the tax rate of the firm T, before-tax cost can be converted to after -tax cost by using the following equation,

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

Using the approximation the before-tax cost of the debt is calculated when the annual interest payment in dollars (I), the net proceeds from the sale of a bond (N_d) and term of the bond in years (n) , using the equation,

${\text{r}}_{\text{d}}\text{=}\frac{\left(\text{I}+\left(\frac{\text{[(\$1,000}-{\text{N}}_{\text{d}}\text{)]}}{\text{n}}\right)\right)}{\left(\frac{{\text{(N}}_{\text{d}}+\text{\$1,000)}}{\text{2}}\right)}$

b.

Summary Introduction

To discuss:

Comparison between the two approaches.

Introduction:

The before -tax cost debt is the rate of return the firm must pay on a new borrowing. The after-tax cost of a debt is the cost after deducting the tax amount.

When after tax cost of the debt is r_i and r_d is the before-tax cost of a debt, with the tax rate of the firm T, before-tax cost can be converted to after -tax cost by using the following equation,

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