Question

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Alex purchased a $1,000 par value bond one year ago at a price of $1,008. At the time of purchase, the bond had 14 years to maturity and a 6 percent, semiannual coupon. Today, the yield to maturity of changed to 6.5 percent and he sold the bond. What is his realized yield as of today?

Answer 1

Face Value = $1000

Semi-Annual Coupon payment = $1000*6%*1/2

= $30

No of years to maturity from today = (14 - 1) = 13 years

n = 13 yrs*2 = 26

Yield to maturity (YTM) = 6.5%

Semi-annual YTM = 6.5%/2 =3.25%

Calculating the Price of Bond:-

+ ... Coupon Payment (1+YTM)" Price Coupon Payment Coupon Payment + (1+YTM) (1 + YTM2 FaceValue (1+YTM)

Price 30 30 (1 + 0.0325)1. (1+0.0325)2 30 1000 (1 + 0.0325 26 . (1 + 0.0325 26

Price = $521.196+ $435.37

Price = $956.57

So, Bond Sold for $956.57

Purchase Price = $1008

Coupon payment received during the year = $30*2

= $60

Calculating Realized Yield today:-

Realized Yield =[(Sale Price - Purchase Price) + Coupon Income]/Purchase Price

=[($956.57 - $1008) + $60]/$1008

= 0.85%

So, Realized Yield today is 0.85%

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