Schweser V1 Exam 2 Afternoon Test Question 46

[topgun0728]

Hi!

The more I think about this question, the more I am confused and am more and more tempted to discount the $7,500 (see the first part of the solution below) by the 4.4% Fixed Rate PAY instead of the LIBOR rate (correct answer). I *mechanically* came up with the following solution (based on my Level II experience, and yes, FRA was never 100% clear to me then as well as now) but still don’t get why I need to use LIBOR instead of the 4.4% Fixed Rate PAY to arrive at the EXPECTED payment TO Canopy. After all, isn’t the whole point of this exercise to HEDGE OUT LIBOR so that I can PAY FIXED at 4.4%? Then why am I discounting by LIBOR as if I am still PAYING LIBOR?

I need the help of an FRA guru to explain this to me why so that I can retain my sanity. I suppose it’s better to be correct and insane than to be wrong and sane on exam day (the saving grace here is that the answers are close enough given the answer choices).

Thanks in advance,

———-

Canopy Managers has also contracted to take out a 9-month loan for $5 million in three months at LIBOR. Canopy’s chief financial officer has become concerned that interest rates might increase and has asked Thomas to investigate the possibility of hedging the position with a forward rate agreement. Thomas finds a forward rate agreement is available with the same maturity as Canopy’s loan and a forward rate of 4.40%. The risk free rate is 3.8%, and LIBOR has increased to 4.60%.
The potential credit risk to Canopy from the FRA agreement is closest to:
A) $7,183.
B) $7,250.
C) $7,292.
- First, under the terms of the FRA, Canopy will receive LIBOR and pay fixed. So the FV (IMPORTANT) of the EXPECTED payment TO Canopy = $5M Loan Amount * 9-month Loan / 12-months * (4.6% LIBOR Rate RECEIVE - 4.4% Fixed Rate PAY) = $7,500
- Next, find the EXPECTED payment TO Canopy (FRA payment) by discounting it BACK by the LIBOR rate (not the Fixed Rate PAY since Canopy will be paying LIBOR on the $5M loan): $7,500 / (1 + 4.6% * 9-month Loan / 12-months) = $7,249.88
- Finally, to find the potential credit risk, calculate the PV (IMPORTANT) of the EXPECTED payment TO Canopy (FRA payment) discounted at the risk-free rate (RFR): $7,249.88 / [(1 + 3.8%) ^ (3-months from now / 12-months)] = $7,182.60

 

[myriam2222]

I would say that a discount rate has to be a market rate. Time value of money is a notion of opportunity cost. This rate of 4.4% was set at the beginning of the contract. Later on, it does not exist anymore on the market, only in the contract. But the market rate is 4.6% and no one would have accepted to pay you 4.6% to get 4.4% in exchange if they had known at the time that market rate would end up being 4.4%.
Once you get the information on the market rate, you use it to discount. The other rate only continues to exist in the contract. It is not the actual relevant measure of time value of money.

 

[topgun0728]

This makes sense. I suppose this is the same concept as what I did in the final part of the solution when I calculated the PV of the EXPECTED payment TO Canopy by discounting at the risk-free rate (RFR) of 3.8%. You are absolutely right that the market rate should be used to discount (come to think of it, this is USUALLY the case and I cannot even think of an example where the market rate is NOT used). This is the important concept here.
Thank you so much Myriam2222!
So to edit my original post:
Instead of:
(not the Fixed Rate PAY since Canopy will be paying LIBOR on the $5M loan)
I should say:
(not the Fixed Rate PAY since market rate is the relevant discount rate to use for determining the EXPECTED payment TO Canopy (FRA payment).

 

[myriam2222]

You are welcome!
Yes, agree!