Question

6 years ago you bought a bond with a par value of $1000 for $950. The...

6 years ago you bought a bond with a par value of $1000 for $950. The bond has a coupon rate of 5%. You purchased the bond for $950. You collected the first coupon five years ago and you reinvested it at a rate of 5%. The coupon you collected four years ago was reinvested at 6%. The one you collected three years ago was reinvested at 3%. The coupons collected two years ago and last year were not invested. Now, after collecting the current coupon, you sold the bond for $1100. What the realized yield of this investment?

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Answer #1

Coupon Annual = 5% * 1000 = 50

Value of Coupon reinvested 5 years ago = 50 * (1+0.05)^5 = 63.814078125

Value of Coupon reinvested 4 years ago = 50 * (1+0.06)^4 = 63.123848

Value of Coupon reinvested 3 years ago = 50 * (1+0.03)^3 = 54.63635

Value of Coupon received 2 years ago = 50

Value of Coupon received 1 years ago = 50

Value of coupon collected just now= 50

Total Value of Coupon today = 63.814078125 + 63.123848 + 54.63635 + 50 + 50 + 50 = 331.57

Realized Return = Coupons + Capital Gain / Purcahse Price

= 335.57 + (1100 - 950) / 950

= 485.57 / 950

= 51.11%

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