Application of Derivatives - Mamani

[agulani]

Hey, has anyone done the practice multiple choice questions for derivatives?
For questions 4/6 in relation to Application of Derivatives Mamani the passage states this for the question
Another of Mamani’s clients, Arequipa Industries (AI), is about to borrow PEN120 million for two years at a floating rate of 180-day Libor (currently 3.25%) plus a fixed spread of 90 basis points with semiannual resets, interest payments based on actual days/360, and repayment of principal at maturity. AI’s management is worried that Libor might rise during the term of the loan and asks Mamani to recommend strategies to reduce this risk. Mamani suggests a zero-cost collar on 180-day Libor with a cap of 4.70% and a floor of 2.25%, payment dates matching the loan payments (on 30 June and 31 December, with the first payment on 31 December), and interest based on actual days/360. She develops various examples of the collar’s impact, including one using the interest rate scenario in Exhibit 1.
Rates are
Jun-12 2.6% (182 days)
Dec-12 2.25% (183days)
Jun-13 2% (183days)
Dec-13 2.5% (182 days)
Answers
a)PEN1,911,000
b)PEN2,062,667
c)PEN1,365,000
In the question, it says they are worried that Libor might rise and are talking about using a zero cost collar, so that means they are buying a cap and selling a floor, but the answer subtracts the floor amount from interest paid since its a loan?
Can somone explain?
The answer is below
Incorrect.
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).

 

[crosstheevil]

I’m not sure if I understand you question correctly but it seems to me that because Libor does not increase, the company has to bear the burden of a “short put” (i.e. they sold a floor before)

 

[agulani]

So the client took a loan out and has to pay floating interest on the loan, but to hedge the risk of rates increasing he buys a cap and to reduce the cost of the hedge he sells a floor (short put), creating a zero cost collar.
When calculating interest paid and the payoff of a caps/floors that are in the money, you must calculate current period interest payment and the previous periods gain/loss from the cap or floor.
In this case, he was short the put (floor) and the previous period the rate was below the floor so that would mean he would have to pay additional (loss on the floor) which would increase his total interest paid, why are they deducting the floor payment from interest? they should be adding it.

 

[crosstheevil]

+ max(0,Floor rate – Libort–1)
I think this means they are adding it … without this portion, interest payment would only be 1,759,333

 

[agulani]

The answer is A, 1,911,000
the formula should read
120,000,000 x (182/360) x (0.025 + 0.009) = $2,062,666 (Total Interest Paid on the Loan)
What needs to be paid on the floor
120,000,000 (182/360) x (0.0225-0.02) = $151,666.67
This is a loss on the floor (he is short the put because its a zero cost collar), and he is paying interest since he took out a loan
so it should be 151,666.67 + 2,062,666 = $2,214,332
Can someone explain? unless they were affriad of interet rates going up and decided to buy a floor and sell a cap? which makes no sense

 

[MrSmart]

agulani wrote:
The answer is A, 1,911,000
the formula should read
120,000,000 x (182/360) x (0.025 + 0.009) = $2,062,666 (Total Interest Paid on the Loan)
What needs to be paid on the floor
120,000,000 (182/360) x (0.0225-0.02) = $151,666.67
This is a loss on the floor (he is short the put because its a zero cost collar), and he is paying interest since he took out a loan
so it should be 151,666.67 + 2,062,666 = $2,214,332
Can someone explain? unless they were affriad of interet rates going up and decided to buy a floor and sell a cap? which makes no sense

The interest rate is 2.09%, not 2.59%

 

[agulani]

yea that was typo, the answer they provided is still wrong

 

[crosstheevil]

agulani wrote:
The answer is A, 1,911,000
the formula should read
120,000,000 x (182/360) x (0.02 + 0.009) = $1,759,333 (Total Interest Paid on the Loan)
What needs to be paid on the floor
120,000,000 (182/360) x (0.0225-0.02) = $151,666.67
This is a loss on the floor (he is short the put because its a zero cost collar), and he is paying interest since he took out a loan
so it should be 151,666.67 + 1,759,333 = $1,911,000

You can use Excel to double check.