Valuation of Floating Rate Note

[Sendo]

This question is from the recent South African exam (course similar to SP5):

Happy Credit (HC) extends 3-, 4- and 5-year personal loans with the variable interest rate being linked to the prime rate, and capital being repaid over the loan term. HC funds its operations by issuing 3-year Floating Rate Notes (FRNs) at par, paying the 3-month Johannesburg Interbank Average Rate (JIBAR) plus 1% p.a.

At present the annual, continuously compounding JIBAR 3-month rate is 9% and the 6-month rate, 10%.

Calculate the value of a FRN that was issued by HC, with six months outstanding, on a principle of R10 million.

I don't quite understand the memo which reads:



Why is there a -1 part to the equation?
This seems like a very simple question, but am struggling to understand the concept.

 

[Gresham Arnold]

Hi Sendo, so there are two payments remaining on this FRN:

- in 6 months' time: a payment consisting of the coupon (which will be (11%+1%)/4) and the principal of the FRN

- in 3 months' time: a payment consisting of the coupon (which will be (9%+1%)/4) only

So in the formula, when we calculate the value of the payment in 3 months' we have a '-1' term, because no principal is being paid.

(In other words e^((0.09+0.01)x0.25) = 1.0253, so we need to deduct 1, otherwise we are effectively assuming the payment is of interest AND principal. We can then multiply this interest payment by a discount factor (e^(-0.09x0.25) to calculate the present value.)

Hope that helps

Gresham

 

[Sendo]

Thanks Gresham, that explains it perfectly.