Chapter 10, Problem 6P

a.

Summary Introduction

To calculate: The price of the bond of Kilgore Natural Gas.

Introduction:

Bond Valuation:

It refers to a method of determining the value of a bond based on certain inputs, such as coupon rate, time to maturity, and yield to maturity. This technique calculates the present value of the future cash flows of the bond, which also includes its face value that is expected to be received at maturity.

Answer to Problem 6P

The price of the bond of Kilgore Natural Gas., assuming a maturity period of 30 years, will be $758.34

Explanation of Solution

Calculation of the price of the bond:

$\begin{array}{c}\text{Price of bond}=\text{Present value of interest payments}+\text{Present value of principal payment}\\ =\$7\text{2}4.96+\$33.38\\ =\$758.34\end{array}$

Working notes:

Calculation of the present value of interest payments:

$\begin{array}{c}{\text{PV}}_A=\text{A}\times \frac{\left\{\text{1}-\left[\frac{\text{1}}{{\left(\text{1}+i\right)}^n}\right]\right\}}{i}\\ =\$90\times \frac{\left\{\text{1}-\left[\frac{\text{1}}{{\left(\text{1}+0.\text{12}\right)}^{30}}\right]\right\}}{0.\text{12}}\\ =\$90\times 8.055\text{1}8397\\ =\$7\text{2}4.96\end{array}$

Calculation of the present value of the principal payment:

$\begin{array}{c}\text{PV}=\text{FV}\times \left[\frac{\text{1}}{{\left(\text{1}+i\right)}^n}\right]\\ =\$\text{1},000\times \left[\frac{\text{1}}{{\left(\text{1}+0.\text{12}\right)}^{\text{30}}}\right]\\ =\$\text{1},000\times 0.0333779\text{2}\\ =\$33.38\end{array}$

b.

Summary Introduction

To calculate: The price of the bond of Kilgore Natural Gas.

Introduction:

Bond Valuation:

It refers to a method of determining the value of a bond based on certain inputs, such as coupon rate, time to maturity, and yield to maturity. This technique calculates the present value of the future cash flows of the bond, which also includes its face value that is expected to be received at maturity.

Answer to Problem 6P

The price of the bond of Kilgore Natural Gas., assuming a maturity period of 15 years, will be $795.67.

Explanation of Solution

Calculation of the price of the bond:

$\begin{array}{c}\text{Price of bond}=\text{Present value of interest payments}+\text{Present value of principal payment}\\ =\$6\text{12}.98+\$\text{1}8\text{2}.69\\ =\$795.67\end{array}$

Working notes:

Calculation of the present value of interest payments:

$\begin{array}{c}{\text{PV}}_A=\text{A}\times \frac{\left\{\text{1}-\left[\frac{\text{1}}{{\left(\text{1}+i\right)}^n}\right]\right\}}{i}\\ =\$90\times \frac{\left\{\text{1}-\left[\frac{\text{1}}{{\left(\text{1}+0.\text{12}\right)}^{\text{1}5}}\right]\right\}}{0.\text{12}}\\ =\$90\times 6.8\text{1}086449\\ =\$6\text{12}.98\end{array}$

Calculation of the present value of the principal payment:

$\begin{array}{c}\text{PV}=\text{FV}\times \left[\frac{\text{1}}{{\left(\text{1}+i\right)}^n}\right]\\ =\$\text{1},000\times \left[\frac{\text{1}}{{\left(\text{1}+0.\text{12}\right)}^{\text{1}5}}\right]\\ =\$\text{1},000\times 0.\text{1}8\text{2}696\text{2}6\\ =\$\text{1}8\text{2}.69\end{array}$

c.

Summary Introduction

To calculate:The price of the bond of Kilgore Natural Gas.

Introduction:

Bond Valuation:

It refers to a method of determining the value of a bond based on certain inputs, such as coupon rate, time to maturity, and yield to maturity. This technique calculates the present value of the future cash flows of the bond, which also includes its face value that is expected to be received at maturity.

Answer to Problem 6P

The price of the bond of Kilgore Natural Gas., assuming a maturity period of 30 years, will be $973.21.

Explanation of Solution

Calculation of the current price of the bond:

$\begin{array}{c}\text{Price of bond}=\text{Present value of interest payments}+\text{Present value of principal payment}\\ =\$80.36+\$89\text{2}.85\\ =\$973.\text{21}\end{array}$

Working notes:

Calculation of the present value of the interest payment:

$\begin{array}{c}{\text{PV}}_A=\text{A}\times \frac{\left\{\text{1}-\left[\frac{\text{1}}{{\left(\text{1}+i\right)}^n}\right]\right\}}{i}\\ =\$90\times \frac{\left\{\text{1}-\left[\frac{\text{1}}{{\left(\text{1}+0.\text{12}\right)}^{\text{1}}}\right]\right\}}{0.\text{12}}\\ =\$90\times 0.89\text{2}857\text{1}4\\ =\$80.36\end{array}$

Calculation of the present value of the principal payment:

$\begin{array}{c}\text{PV}=\text{FV}\times \left[\frac{\text{1}}{{\left(\text{1}+i\right)}^n}\right]\\ =\$\text{1},000\times \left[\frac{\text{1}}{{\left(\text{1}+0.\text{12}\right)}^{\text{1}}}\right]\\ =\$\text{1},000\times 0.89\text{2}857\text{1}4\\ =\$89\text{2}.85\end{array}$