You bought a bond of GM on December 1, 2005. The Yield to Maturity at the time o

Question

You bought a bond of GM on December 1, 2005. The Yield to Maturity at the time of purchase was 7.4%. The bond had following characteristics: Term = 20 years, Coupon = 6% semi-annual, Face Value = $1,000.

On June 1, 2009 GM declared bankruptcy, and as part of the bankruptcy deal (worked with the help of US Government) the bond was renegotiated as follows.

Beginning June 1, 2009 no interest will be paid for next 6 years.

Afterwards, interest will be paid at 30% of the original coupon interest for the reminder of the term.

Determine the following.

Assuming you still own that bond until maturity and assuming there are no surprises in the future, what would be the true yield earned by you for the bond that you purchased on 12/1/2005.

Explanation / Answer

Yield to maturity = 7.4% p.a. or 3.7% for semi annual.

Coupon rate = 6% p.a. or 3% for semi annual.

Semi-annual Coupon Interest = $ 1000 x 3% = $ 30

No. of Interest payments = 20 years x 2 instalments p.a = 40

current price of the bond = coupon interest x PVIFA (3.7%, 40) + Par value x PVIF (3.7%, 40)

= $ 30 x 6.0692 + ($30 x 30%) x 7.2329 + $ 1000 x 0.2338 = $ 480.9721

True yield earned = $ 1000 - $ 480.9721 = $ 519.0279

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