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Hull chapter 7 , question 7.1

shivanin

Member
Q. "Companies A and B have been offered the following rates per annum on a $20 million five-year loan: Fixed Rate Company A Floating Rate 5.0% Company B LIBOR+0.1% 6.4% LIBOR+0.6% Company A requires a floating-rate loan; company B requires a fixed-rate loan. Design a swap that will net a bank, acting as intermediary, 0.1% per annum and that will appear equally attractive to both companies. "

As per the solution company A receives 5.3 %..... But I got the answer as 5.4%

I think that and here is 5.3% because 0.1% margin of the bank. But didn't we already subtracted it from difference of differentials of two rates to get the net profit for each?
I.e. 1.4 - 0.5 - 0.1%=0.8% divided by 2. So y are we again subtracting 0.1% from interest payment to company A???:oops:
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi @shivanin We're updating the big Hull study note so I entered this into our dynamic swap XLS (see screen below, although I am not quite happy yet with the presentation, I don't think it's clear enough yet :(); the XLS is here https://www.dropbox.com/s/xh6mbl7mm3cwm29/swap-comparative-advantage-v2.xlsx?dl=0

My XLS approaches the problem very much like Hull's answer to 7.1, specifically:
  1. the gross advantage = 1.4% - 0.5% = 0.90%
  2. The intermediary bank collects 0.1% such that 0.90% - 0.1% = 0.8% remains as the net advantage to be shared between the companies
  3. If the advantage is split evenly (per the 50% assumption), then each Company gain 0.40%
  4. Therefore, Company A (who transforms to floating) must gain 0.40%, from L+0.10% to L-0.30%, which must be achieved by receiving fixed 5.30% in the swap
  5. Therefore company B (who transforms to fixed) must gain 0.40%, from 6.40% fixed to 6.0% fixed, which must be achieved by paying 5.40 in the swap% (which in turn must be +0.1% higher than the 5.30%). I hope that is helpful!

 
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David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
@zekrom That 0.10% is to compensate the intermediary (financial institution) per the given assumption (this is Hull's question 7.1): "Design a swap that will net a bank, acting as intermediary, 0.1% per annum and that will appear equally attractive to both companies." Please note that if we change this assumption to zero, while the Interim placeholder remains, then we have the solution for swap directly between the two counterparties (see below). In the case, the solution is to swap a fixed 5.35% because we are still dividing the total benefit equally; the total benefit of 0.90% implies a gain of 0.45 for each. I hope that helps!
 
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