Flat price/Full price and accrued interest-please help

CFA Level I Fixed Income
#1

Hi,

Can someone please help me with this question:

Today: Feb 10th 2021, Matures: 31 Dec 2040, Coupon:8% PA, YTM:12%

The coupon is paid semi-annually on 30th June and 31st Dec. It’s actual/actual

I calculate this way:
N=40, Pmt: 4, YTM:6%, FV=100 CPT PV. PV=69.907

Full price: 69.907x(1.06)^(140/360)=71.509
AI: 4x140/360=1.55
Flat price:71.509-1.55=69.95

Can you please point me what am I doing incorrectly here?
Answer: Full price:70.836, AI:0.906, Flat price: 69.93

Thanks so much!

#2

I used the BOND worksheet on my BAII:

2nd BOND
SDT 2.1021 enter
CPN 8 enter
RDT 12.3140
RV 100 enter
ACT (NOT 360: you say actual/actual above)
2/Y
YLD 12
PRI CPT 69.93015549
AI 0.906077348

I’ll try to put up some math in the next day or so.

#3

Thanks very much! Today, I learned how to calculate with bond function but I’ve not used it before so I don’t want to get stuck on the exam the following week. I’ll appreciate in a traditional way (some maths).

#4

A little math:

AI = 4 * 41/181 = 0.906077348

41 days from Dec 31 2020 to Feb 10 2021, 181 days from Dec 31 2020 to June 30 2021

PV bond at issue

2nd CLR TVM
P/Y=C/Y=2
40 N 12 I 4 PMT 100 FV CPT PV -69.90740626

Roll up bond PV with 41 days’ interest @ 6%

69.90740626 * (1.06 ^ 41/181) = 70.83623284

#5

thanks so much!!! I always get confused with the number of days (I know from the last coupon day to the settlement day). Is there any trick to count them correctly?

Have a nice day,
Rajni

#6

The BAII also has a DATE worksheet to calculate the difference in days between 2 dates!!