Using the Libor scenario shown in Exhibit 1 and under the assumption that the zero-cost collar is put in place, the effective interest due on AI’s loan for the semiannual period ended on 31 December 2013 is closest to: A. PEN1,911,000 B. PEN1,365,000 C. PEN2,062,667
Answer = A The effective interest in period t is: Loan balance × (Actual days in period/360) × [Libort1 + Spread + max(0,Libort– 1 – Cap rate) + max(0,Floor rate – Libort–1).
Can anyone explain how to to do this question? if the LIBOR rate is within the collar, there should be no payoff except he loan interest payment?
I believe that question is worded terribly. They’re using the LIBOR rate from June 2013 (2.0%) in which the interest payment is due on the semi-annual period ended December 2013 since interest is paid in arrears.
If you have a floating rate note outstanding, you should establish the collar by long floor and short cap. If libor decreases below strike of floor, you get some payoff to make up for the low interest received on the original note. If libor increases above the strike of cap, you will have to pay the cap owner but it’ll be offset by the higher interest on the original note.
But the answer guide’s formula looks like you are both long floor and cap. How do you establish zero-cost collar by going long on both cap and floor? What am I missing here?
it’s 2.25% + 90 bps - it uses the previous period to pay the dec '13 payment. The floor is 2.25% so you’re paying the 2% to the loan, and the .25% on the put. Is this typical treatment for a loan like this to have th eperiod delayed 1 per?
I calculate the interest as $120MM (182/360) x .029 = $1,759,334
I calculate the payoff on the floor as $120MM (182/360) x (.0225 - .02) = $151,666
This sums to $1,911,000 which is the answer but I got it wrong because I subtracted the payoff on the floor. If AI is long the floor and short the cap, then the 2.25% - $2.00% should be a credit against the interest on the loan. Why am I mistaken on this?
A few things are going on here. $1.9 million is the correct answer, but there is a minor typo in the solution as was suggested by @ov25.
The stated solution ADDS the payoff from both the interest rate call and put. (Which are the caplet and floorlet components of the collar.) Yet, to confirm straight from the CFA text: “A collar combines a long position in a cap with a short position in a floor.”
To keep the usual notation, recognize here that payments are outflows and receipts are inflows.
The interest on the loan itself is then -$1.759 million as pointed out by @joec19.
The second snippet of the solution should be: NP * (+ max{0, .02 - .047} - max{0, .0025 - .02}).
Notice the plus sign on the first term (the cap) and negative sign on the second (the floor), which the borrwer has sold short. The borrower will short the floor to finance the cap and protect itself from rate increases. In this case, for the payment made on 30-Dec-13, the rates for that period are determined using LIBOR as of 30-Jun-13. LIBOR on 30-Jun is 2.00%, below the floor of 2.25% which the borrower has sold short.
There is no payment on the cap, because rates didn’t rise through 4.7%. So the total cost (effective interest is):
-$1.759 million + 0 - $151,666 = -$1.911 million
I suggest the actual CFA text here by Don Chance, it’s well laid out and easy to follow.