Chapter 6, Problem 15PROB

Summary Introduction

The bond has a maturity value of $1,000 and coupon rate of 7%. The bond was selling for $996 one year ago and today it Is selling for $1006.

Yield to maturity (YTM) of a bond is the required rate of return expected on holding the bond till maturity. When the YTM of the bond is higher than the coupon value, the bond is said to be trading at a discount and when it is lower than the coupon value, then the bond is trading at a premium.

YTM calculation is a trial and error process, however, we can calculate YTM using a financial calculator as follows:

INT = PMT = coupon amount

FV = M = maturity value

PV = Price of the bond (input as a negative value)

N = number of periods

Current yield is the annual income on the bond relative to the current price of the bond. It is calculated as the coupon divided by the price of the bond.

$\begin{array}{l}\text{Current Yield = }\frac{Int}{V_{d,Begin}}\\ where,\\ \text{Int=annual interest or coupon on the bond}\\ V_{d,Begin}=\text{Value at the beginning of the period}\end{array}$

Value of a bond keeps changing depending on the prevailing interest rates. As the interest rate increases, the value of the bond decreases on the contrary as the interest rate decreases, price of the bond increases. Capital gains is calculated based on this changing bond prices.

$\begin{array}{l}\text{Capital gains yield = }\frac{V_{d,End}-V_{d,Begin}}{V_{d,Begin}}\\ where,\\ V_{d,End}=\text{Value at the end of the period}\\ V_{d,Begin}=\text{Value at the beginning of the period}\end{array}$