In: Finance
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)
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% (Cashflow*PVF@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