Question

A bond has 8 years until maturity and a coupon rate of 8.9% payable annually and sells for $1030. The face value of the bond is $1000. What are the current yield and yield to maturity? What do these two numbers represent?

Answer 1

The formula for yield to maturity is:

Yield to maturity = C + F - P /n / F + P / 2

where, C is the coupon payment, F is the face or par value of the bond = $1000, P is the current price of the bond = $1030 and n is the no. of years to maturity = 8.

Coupon payments = $1000 * 8.9% = $89

Putting the values in the above formula, we get,

Yield to maturity = $89 + ($1000 - $1030) / 8 / ($1000 + $1030) / 2

Yield to maturity = $89 + (-$30 / 8) / ($2030 /2)

Yield to maturity = $89 - 3.75 / $1015

Yield to maturity = $85.25 / $1015

Yield to maturity = 8.37%

The formula for current yield is:

Current Yield = C / P * 100

where, C is the coupon payment, P is the current price of the bond = $1030

Putting the values in the above formula, we get,

Current yield = $89 / $1030 * 100

Current yield = 8.64%

Yield to maturity represents the rate of return a person will receive if the bond is hold till maturity. Yield to maturity is the return or yield when the bond becomes mature.

Current yield is the rate of return or yield of the bond at present moment. It is based on the current bond price.