Chapter 7, Problem 7.1CTF

Summary Introduction

To discuss: The current yield

Introduction:

A bond refers to the debt securities issued by the governments or corporations for raising capital. The borrower does not return the face value until maturity. However, the investor receives the coupons every year until the date of maturity.

The current yield of the bond is the annual coupon of the bond divided by the price of the bond.

Answer to Problem 7.1CTF

The current yield of the bond is 7.76%.

Explanation of Solution

Given information:

The face value of an 8 percent bond is $1,000. The coupon payment is semiannual. The present market value of the bond is $1,030.

The formula to calculate annual coupon payment:

$\text{Annual coupon payment}=\text{Face value of the bond}\times \text{Coupon rate}$

The formula to calculate the current yield:

$\text{Current yield}=\frac{\text{Annual coupon payment}}{\text{Current price of the bond}}$

Compute the annual coupon payment:

$\begin{array}{c}\text{Annual coupon payment}=\text{Face value of the bond}\times \text{Coupon rate}\\ =\$1,000\times 8\%\\ =\$80\end{array}$

Hence, the annual coupon payment is $80.

Compute the current yield:

$\begin{array}{c}\text{Current yield}=\frac{\text{Annual coupon payment}}{\text{Current price of the bond}}\\ =\frac{\$80}{\$1,030}\\ =0.0776\text{ or }7.76\%\end{array}$

Hence, the current yield is 7.76%.