Question

): Evaluate the following pure-yield pickup swap: You currently hold a 20-yearm AA-rated, 9% coupon rate bond with yield to maturity of 11.0%, and face value $1,000. As a swap candidate, you are considering a 20-yearm AA-rated, 11% coupon rate bond with yield to maturity of 11.5%, assume reinvestment rate is 11.5% and coupon are paid semi-annually, please fill out the table below and you must show (explain) clearly how numbers in the table are obtained.

	Current Bond	Candidate bond
Dollar investment
Coupon
i on one coupon
Principal value at year end
Total accrued
Realized compound yield
Value of swap:		basis point in one year

Answer 1

Given Details:
Currently hold: 20 Year, 9% Coupon priced, 11% Yield Rate
Swap candidate: 20 Year, 11% Coupon priced, 11.5% Yield Rate
Price of the Current Bond:
Current Bond price	=[$90 PVIF(11%,20Y)] + [$1000 PVF(11%,20Y)]
	=[$45 PVIF(5.5%,40Y)] + [$1000 PVF(5.5%,40Y)]
	=[$4516.04612] + [$1000 0.11746]
	=$722.07 + $117.46
Current Bond price	= $839.53
Price of the Candidate Bond:
Current Bond price	=[$110 PVIF(11.5%,20Y)] + [$1000 PVF(11.5%,20Y)]
	=[$55 PVIF(5.75%,40Y)] + [$1000 PVF(5.75%,40Y)]
	=[$5515.5330] + [$1000 0.10685]
	=854.31+106.85
Current Bond price	= $961.61
Principal value at year end Current Bond:
Current Bond price	=[$90 PVIF(11%,19Y)] + [$1000 PVF(11%,19Y)]
	=[$45 PVIF(5.5%,38Y)] + [$1000 PVF(5.5%,38Y)]
	=[$4515.80474] + [$1000 0.13074]
	=$711.21 + $130.74
Current Bond price	= $841.95
Principal value at year end Candidate Bond:
Current Bond price	=[$110 PVIF(11.5%,19Y)] + [$1000 PVF(11.5%,19Y)]
	=[$55 PVIF(5.75%,38Y)] + [$1000 PVF(5.75%,38Y)]
	=[$5515.3131] + [$1000 0.11949]
	=842.22+119.49
Current Bond price	= $961.61
	Current Bond	Candidate Bond
Dollar investment	$839.53	$961.61
Coupon	$90	$110
i on one coupon	2.59	3.16
Principal value at year end	$841.95	$961.71
Total accrued	$934.54	$1,074.87
Realized compound yield	11.0125	11.4988
Value of Swap	= 48.6

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