Chapter 6, Problem 7QP

a)

Summary Introduction

To determine: The rate of return on each bond.

Explanation of Solution

Computation of rate of return on each bond is as follows:

1. (a) Bond 1:

$\begin{array}{c}\text{Present value}\left({\text{PV}}_1\right)=\text{ coupon amount}\times \frac{1-{\left(1+\text{YTM}\right)}^{-\text{n}}}{\text{YTM}}+\frac{\text{Face value}}{{\left(\text{1+YTM}\right)}^{\text{n}}}\\ =\$80\times \frac{1-{\left(1.10\right)}^{-10}}{0.10}+\frac{\$1,000}{{1.10}^{10}}\\ =\$877.11\end{array}$

$\begin{array}{c}\text{Present value}\left({\text{PV}}_2\right)=\text{ coupon amount}\times \frac{1-{\left(1+\text{YTM}\right)}^{-\text{n}}}{\text{YTM}}+\frac{\text{Face value}}{{\left(\text{1+YTM}\right)}^{\text{n}}}\\ =\$80\times \frac{1-{\left(1.10\right)}^{-9}}{0.10}+\frac{\$1,000}{{1.10}^9}\\ =\$884.82\end{array}$

$\begin{array}{c}\text{Rate of return}=\frac{\text{coupon amount}\text{+}\left({\text{PV}}_2-{\text{PV}}_1\right)}{{\text{PV}}_1}\\ =\frac{\$80+\left(\$884.82-\$877.11\right)}{\$877.11}\\ =0.100\text{or 10\%}\end{array}$

1. (b) Bond 2:

$\begin{array}{c}\text{Present value}\left({\text{PV}}_1\right)=\text{ coupon amount}\times \frac{1-{\left(1+\text{YTM}\right)}^{-\text{n}}}{\text{YTM}}+\frac{\text{Face value}}{{\left(\text{1+YTM}\right)}^{\text{n}}}\\ =\$120\times \frac{1-{\left(1.10\right)}^{-10}}{0.10}+\frac{\$1,000}{{1.10}^{10}}\\ =\$1,122.89\end{array}$

$\begin{array}{c}\text{Present value}\left({\text{PV}}_1\right)=\text{ coupon amount}\times \frac{1-{\left(1+\text{YTM}\right)}^{-\text{n}}}{\text{YTM}}+\frac{\text{Face value}}{{\left(\text{1+YTM}\right)}^{\text{n}}}\\ =\$120\times \frac{1-{\left(1.10\right)}^{-9}}{0.10}+\frac{\$1,000}{{1.10}^9}\\ =\$1,115.18\end{array}$

$\begin{array}{c}\text{Rate of return}\text{=}\frac{\text{coupon amount}\text{+}\left({\text{PV}}_2-{\text{PV}}_1\right)}{{\text{PV}}_1}\\ =\frac{\$120+\left(\$1,115.18-\$1,122.89\right)}{\$1,122.89}\\ =0.100\text{or 10\%}\end{array}$

Therefore, the rate of return of both bond 1 and bond 2 is 10%.

b)

Summary Introduction

To determine: Whtethr the higher-coupon bond give a higher rate of return over this period.

Explanation of Solution

The both bonds are giving the same rate of return irrespective of coupon rate of the bond.