Citibank issued bonds few years ago. Investor John sells $100 par of the bonds mid-accrual period...

Citibank issued bonds few years ago. Investor John sells $100 par of the bonds mid-accrual period settlement on 8/19/2020.
Givens:

Coupon = 6%

Coupon Payment Frequency = Semi-annual

Interest Payment Dates are March 31 and Sept 30th

Maturity Date September 30th, 2023

Day Count Convention = 30/360

Yield-to-Maturity 4%

What are the Full (Dirty) proceeds of the sale of this bond closest to on August 19th, 2020?
(bond does not accrue interest on 8/19)

Solutions

Expert Solution

Full proceeds of the sale of this bond on Sep 30th 2020 = Present value of future cashflow of coupon & maturity proceed.

Period	Type	Cashflow	PVF @ 2%	*DCF @ 2% (CashflowPVF@2%)**
Mar 31 2021	Coupon	100*6%/2 = $3	1/1.02 = 0.9804	$2.9412
Sep 30 2021	Coupon	100*6%/2 = $3	0.9804/1.02 = 0.9612	$2.8836
Mar 31 2022	Coupon	100*6%/2 = $3	0.9612/1.02 = 0.9424	$2.8272
Sep 30 2022	Coupon	100*6%/2 = $3	0.9424/1.02 = 0.9239	$2.7717
Mar 31 2023	Coupon	100*6%/2 = $3	0.9239/1.02 = 0.9058	$2.7174
Sep 30 2023	Coupon+Maturity	100+3 = $3	0.9058/1.02 = 0.8880	$91.4640
				$105.6051

Full proceeds of the sale of this bond on Sep 30th 2020 = $105.6051
Discount rate for 11 days (Aug 19th to sep 30th) = 4%*30/360*11 = 0.036667%

Full proceeds of the sale of this bond closest to on Aug 19th 2020 = (Full proceeds of the sale of this bond on Sep 30th 2020+coupon on sep 30th 2020)/(1+discount rate for 11 days) = ($105.6051+$3)/(1+0.00036667) = $108.6051/1.00036667 = $108.5327

jeff jeffy answered 1 year ago

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