A bond that has a face value of $1,500 and coupon rate of 4.40% payable semi-annually...

A bond that has a face value of $1,500 and coupon rate of 4.40% payable semi-annually was redeemable on July 1, 2021. Calculate the purchase price of the bond on February 10, 2015 when the yield was 4.65% compounded semi-annually.

Round to the nearest cent

Solutions

Expert Solution

As Bond is Redeemable on July 1, 2021 and Coupons are paid Semi-Annually,

Coupon Dates are Jan 1 and July 1 of every year.

Last Coupon paid was on Jan 1, 2015 and Remaining Coupons are Jul 1, 2015 to Jul 1, 2021 i.e. 13

Coupon = Par Value*Coupon Rate/2 = 1000*4.4%/2 = $22

Semi-Annual Yield = 4.65%/2 = 2.325%

Period	Cash Flow	Discounting Factor [1/(1.02325^year)]	PV of Cash Flows (cash flows*discounting factor)
1	22	0.97727828	21.50012216
2	22	0.955072837	21.0116024
3	22	0.933371939	20.53418266
4	22	0.912164123	20.06761071
5	22	0.891438185	19.61164008
6	22	0.871183176	19.16602988
7	22	0.851388396	18.73054472
8	22	0.832043387	18.30495452
9	22	0.813137931	17.88903447
10	22	0.794662038	17.48256484
11	22	0.77660595	17.0853309
12	22	0.758960127	16.69712279
13	22	0.741715247	16.31773544
13	1000	0.741715247	741.7152474
		Price of the Bond = Sum of PVs	986.113723

Therefore, Price as on Jan 1, 2015 = $986.11

Price as on Feb 10, 2015 = Price as on Jan 1, 2015 + Accrued Coupon for Jan 2 to Feb 10 i.e. 40 days = $986.11 + (1000*4.4%*40/365) = 986.11+4.82 = $990.93

jeff jeffy answered 1 year ago

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