Question

An investor purchases a just-issued 30-year, 10.500% semiannual coupon bond at 108.235 percent of par value and sells it after 15 years. The bond’s yield to maturity is 9.655% at time of sale, and falls to 9.100% immediately after the purchase but before the first coupon is received. All coupons are reinvested to maturity at the new yield to maturity. Does the investor realize a capital gain or loss on the sale, and by what amount expressed in % of PAR?

	A.	capital loss of 4.710 % of PAR
	B.	capital gain of 4.710 % of PAR
	C.	capital loss of 3.100 % of PAR
	D.	capital gain of 3.100 % of PAR

Answer 1

     

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Value of Bond at 9.655%

Value of Bond =

Where r is the discounting rate of a compounding period i.e. 9.655% / 2 = 0.048275

And n is the no of Compounding periods 15 years * 2 = 30

Coupon 10.50% / 2 = 0.0525

=

= 1066.25

Value at 9.10%

Value of Bond =

Where r is the discounting rate of a compounding period i.e. 9.10% / 2 = 0.0455

And n is the no of Compounding periods 15 years * 2 = 30

Coupon 10.50% / 2 = 0.0525

=

= 1113.35

% Capital Loss of PAR = 1066.25 - 1113.35 / 1000 = 4.71%

Option A is correct.

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