Counting coupons to go when firm issues bond

CFA Level I FRA
#1

Hi everyone,

I am struggling on a stupid thing on the calculation of interest expenses, carrying value, etc. when a company issues a bond, and more precisely about the coupons counting and the coupons payment date(s).

I compared two similar exercices and I got confused:

The first exercice:

on 1 January 2014, the market rate of interest on a company’s bonds is 5%, and it issues a bond with the following characteristics:

face value: 50 mios

coupon rate, paid annually 4%

time to maturity 10 years (31.12.2023)

Issue price (per 100) 92.28

if the company uses IFRS, its interest expense in mios in 2014 is:

correct answer is: 2’307 (0.05*46’140). you can find 46’140 by doing 0.9228*50 mios

I found the 46’140 by performing the following with my calculator: FV= 5 MIOS I/Y=5 PMT=2 MIOS N=10 PV=?

However, I don’t understand why N=10, because I did N=9 at the beginning because I thought that there is 9 “coupons to go”.

Could someone help me here?

Thanks

#2

Why did you think that there is 9 coupons instead 10?

#3

Also confused as to why you used 9 rather than 10. Maybe a mistake due to the years of the issue and maturity (2023 - 2014 = 9)?

Note that the issue was in January with the maturity in December, so I would have used N = 10 in this calculation.

#4

because I thought that they wanted to know the interest expense at the end of 2014, and the coupon is paid the 31.12.2014… that’s why

#5

let me give you another exercice (that I answered correctly) and which confuses the whole thing for me.

By the way, sorry, don’t want to confuse anyone, just trying to understand the whole stuff

a company prepares its financial statement sin accordance with IFRS issues a USD 5 mios face value 10-year bonds on 1 January 2013 when market interest rates for such bonds are 5.50%. The bonds carry a coupon of 6.50%, with interest paid annually on 31 December. The carrying value of the bonds as of 31.12.14 is:

correct answer is: 5’316’000

Can be found with calculator (PMT=325’000, I/Y=5.5, N=8,FV=5 MIOS, CPT PV–>)

Here I totally understand because as of 31.12.14, two coupons have been paid, so there is 8 coupon that still have to be paid til maturity.

But for the first exercice, I thought that at the end of 2014, already one coupon would be paid, so this is why I thought it would be N=9…

#6

46,140 is the carrying value of the bonds as of 1 Jan 2014. Since the market rate of interest is 5%, the interest expense for the year 2014 using the effective interest method is 5% * 46,140 = 2,307. FV should be 50 in your BAII inputs, as well as P/Y = C/Y =1.

#7

Ok, it’s just I wasn’t clear for me whether the first coupon has already been paid or not. I misunderstood the question.

Thank you for all your answers.

Have a nice evening ahead.

#8

You can also think of the interest expense as the cash coupon paid + amortization of discount = 2,000 + 307. The amortization amount is the difference between the bond carrying value on Jan 1, 2015 and Jan 1, 2014.