Chapter 17, Problem 17.2STP

a)

Summary Introduction

To determine: The straight bond value of the bond.

Introduction:

The word conversion stands for the normal meaning as it is. The conversion feature states that the holder of the securities such as the specific bond, stock options or the warrants is able to convert these bonds or warrants into the normal common stock of the firm.

Explanation of Solution

Given information:

Par value of the bond is given as $1,000 and it is given that the bonds can be converted into 40 shares of common stock. The annual coupon rate is 11% and the interest rate is 13%. Maturity year is 25 years.

Formula to determine the straight bond value of the bond:

$B_0=\frac{I}{r_d}\times \left(1-\frac{1}{{\left(1+r_d\right)}^n}\right)+M\times \frac{1}{{\left(1+r_d\right)}^n}$

Here,

B₀ refers to the straight bond value

I refers to the discount value

r_d refers to the interest rate

M refers to par value

n refers to maturity year

Determine the straight bond value of the bond:

$\begin{array}{c}{B}_0=\frac{I}{r_d}\times \left(1-\frac{1}{{\left(1+r_d\right)}^n}\right)+M\times \frac{1}{{\left(1+r_d\right)}^n}\\ =\frac{\left(0.11\times 1000\right)}{0.13}\times \left(1-\frac{1}{{\left(1+0.13\right)}^{25}}\right)+1,000\times \frac{1}{{\left(1+0.13\right)}^{25}}\\ =\frac{110}{0.13}\times \left(1-\frac{1}{21.2305}\right)+1,000\times \frac{1}{21.2305}\end{array}$

$\begin{array}{c}=\left(846.1538\times 0.952898\right)+\left(1,000\times 0.047102\right)\\ =806.298+47.102\\ =853.4\end{array}$

Hence, the straight bond value is $853.4.

b)

Summary Introduction

To determine: The conversion value of the bond.

Introduction:

The word conversion stands for the normal meaning as it is. The conversion feature states that the holder of the securities such as the specific bond, stock options or the warrants is able to convert these bonds or warrants into the normal common stock of the firm.

Explanation of Solution

Given information:

Par value of the bond is given as $1,000 and it is given that the bonds can be converted into 40 shares of common stock. The annual coupon rate is 11% and the interest rate is 13%. Maturity year is 25 years. The market price of the stocks are given as $20, $25, $28, $35, and $50.

Determine the conversion value of the bond:

Market price	Conversion ratio	Conversion value
$20	40	$800
$25	40	$1,000
$28	40	$1,120
$35	40	$1,400
$50	40	$2,000

Computation of conversion value:

c)

Summary Introduction

To determine: The selling price of the bond for each stock price given in part (c).

Introduction:

The word conversion stands for the normal meaning as it is. The conversion feature states that the holder of the securities such as the specific bond, stock options or the warrants is able to convert these bonds or warrants into the normal common stock of the firm.

Explanation of Solution

Given information:

Par value of the bond is given as $1,000 and it is given that the bonds can be converted into 40 shares of common stock. The annual coupon rate is 11% and the interest rate is 13%. Maturity year is 25 years. The market price of the stocks are given as $20, $25, $28, $35, and $50.

Determine the selling price of the bond for each stock price given in part (c):

Market price	Conversion ratio	Conversion value
$20	40	$800
$25	40	$1,000
$28	40	$1,120
$35	40	$1,400
$50	40	$2,000

For each stock price, the bond should be sold at the conversion value. However, it should not be sold less than the straight value of the bond $853.4 (Calculation in Part (a)). Hence, for stock price $20, the bond should be sold at the price of $853.4. For stock price $25, $28, $35, and $50, the bond should be sold at the prices of $1,000, $1,120, $1,400, and $2,000 respectively.

d)

Summary Introduction

To determine: The least selling price for the bond.

Introduction:

The word conversion stands for the normal meaning as it is. The conversion feature states that the holder of the securities such as the specific bond, stock options or the warrants is able to convert these bonds or warrants into the normal common stock of the firm.

Explanation of Solution

Given information:

Par value of the bond is given as $1,000 and it is given that the bonds can be converted into 40 shares of common stock. The annual coupon rate is 11% and the interest rate is 13%. Maturity year is 25 years.

Determine the least selling price for the bond:

The selling price of the bond should not be less than the straight value of the bond $853.4. Hence, the least selling price is the straight bond value.