Valuation of Floating Rate Note

Discussion in 'SP5' started by Sendo, Sep 28, 2019.

  1. Sendo

    Sendo Member

    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:

    upload_2019-9-28_11-10-50.png

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

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  2. Gresham Arnold

    Gresham Arnold ActEd Tutor Staff Member

    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
     
  3. Sendo

    Sendo Member

    Thanks Gresham, that explains it perfectly.
     

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