Chapter 10, Problem 1P

a.

Summary Introduction

To calculate: The current price of the bond of The Lone Star Company.

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 1P

The current market price of the bond of The Lone Star Company, assuming a YTM of 6%, is $1,458.80

Explanation of Solution

Calculation of the current price of the bond:

$\begin{array}{c}\text{Current Price}=\text{Present value of interest payments}+\text{Present value of principal payment}\\ =\$\text{1},\text{1}47.00+\$3\text{11}.80\\ =\$\text{1},458.80\end{array}$

Working notes:

Calculation of the present value of interest payments:

$\begin{array}{c}{\text{PV}}_A=\text{A}\times \frac{\left\{\text{1}-\left[\frac{\text{1}}{{\left(\text{1}+i\right)}^n}\right]\right\}}{i}\\ =\$\text{1}00\times \frac{\left\{\text{1}-\left[\frac{\text{1}}{{\left(\text{1}+0.06\right)}^{\text{2}0}}\right]\right\}}{0.06}\\ =\$\text{1}00\times \text{11}.4699\text{2122}\\ =\$\text{1},\text{1}47.00\end{array}$

Calculation of the present value of the principal payment:

$\begin{array}{c}\text{PV}=\text{FV}\times \left[\frac{\text{1}}{{\left(\text{1}+i\right)}^n}\right]\\ =\$\text{1},000\times \left[\frac{\text{1}}{{\left(\text{1}+0.06\right)}^{\text{2}0}}\right]\\ =\$\text{1},000\times 0.3\text{11}80473\\ =\$3\text{11}.80\end{array}$

b.

Summary Introduction

To calculate: The current price of the bond of The Lone Star Company.

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 1P

The current market price of the bond of The Lone Star Company, assuming a YTM of 9%, is $1,091.28

Explanation of Solution

Calculation of the current price of the bond:

$\begin{array}{c}\text{Current Price}=\text{Present value of interest payments}+\text{Present value of principal payment}\\ =\$9,\text{12}.85+\$\text{1}78.43\\ =\$\text{1},09\text{1}.\text{2}8\end{array}$

Working notes:

Calculation of the present value of interest payments:

$\begin{array}{c}{\text{PV}}_A=\text{A}\times \frac{\left\{\text{1}-\left[\frac{\text{1}}{{\left(\text{1}+i\right)}^n}\right]\right\}}{i}\\ =\$\text{1}00\times \frac{\left\{\text{1}-\left[\frac{\text{1}}{{\left(\text{1}+0.09\right)}^{\text{2}0}}\right]\right\}}{0.09}\\ =\$\text{1}00\times 9.\text{12}854567\\ =\$9,\text{12}.85\end{array}$

Calculation of the present value of the principal payment:

$\begin{array}{c}\text{PV}=\text{FV}\times \left[\frac{\text{1}}{{\left(\text{1}+i\right)}^n}\right]\\ =\$\text{1},000\times \left[\frac{\text{1}}{{\left(\text{1}+0.09\right)}^{\text{2}0}}\right]\\ =\$\text{1},000\times 0.\text{1}7843089\\ =\$\text{1}78.43\end{array}$

c.

Summary Introduction

To calculate: The current price of the bond of The Lone Star Company.

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 1P

The current market price of the bond of The Lone Star Company, assuming a YTM of 13%, is $789.25

Explanation of Solution

Calculation of the current price of the bond:

$\begin{array}{c}\text{Current Price}=\text{Present value of interest payments}+\text{Present value of principal payment}\\ =\$70\text{2}.47+\$86.78\\ =\$789.\text{25}\end{array}$

Working notes:

Calculation of the present value of interest payments:

$\begin{array}{c}{\text{PV}}_A=\text{A}\times \frac{\left\{\text{1}-\left[\frac{\text{1}}{{\left(\text{1}+i\right)}^n}\right]\right\}}{i}\\ =\$\text{1}00\times \frac{\left\{\text{1}-\left[\frac{\text{1}}{{\left(\text{1}+0.\text{1}3\right)}^{\text{2}0}}\right]\right\}}{0.\text{1}3}\\ =\$\text{1}00\times 7.0\text{2}475\text{1}58\\ =\$70\text{2}.47\end{array}$

Calculation of the present value of the principal payment:

$\begin{array}{c}\text{PV}=\text{FV}\times \left[\frac{\text{1}}{{\left(\text{1}+i\right)}^n}\right]\\ =\$\text{1},000\times \left[\frac{\text{1}}{{\left(\text{1}+0.\text{1}3\right)}^{\text{2}0}}\right]\\ =\$\text{1},000\times 0.08678\text{22}9\\ =\$86.78\end{array}$