Question

A firm has a $100,000 2-year variable interest loan with 180 day payment frequency. The firm decided to purchase a cap with X=6% and sells a floor with X=4%. The cap's price is $15,000 and the floor's price is $8000. Fill in the following table of interest payments based on the time t 180-day spot rates given (adding in the final loan repayment):

t		Loan interest payment	Call payoff	Put payoff	Net payment
0	3.50%	-	-	-	-
180	4.50%	-1750
360	5.50%
540	6.50%
720	-	-103250

The net income at t=0 (NPV) of the loan with the collar consisting of the long cap and short floor is .

The annualized IRR of the loan with the collar is . The annualize IRR of the loan without the collar would be .

Answer 1

t	interst rate	LOAN INTEREST PAYMENT	CALL PAYOFF	PUT PAYOFF	NET PAYMENT
180	3.5%	1750 100000*3.5%*180/360	0	250 100000*0.5%*180/360	2000
360	4.5%	2250 100000*4.5%*180/360	0	0	2250
540	5.5%	2750 100000*5.5%*180/360	0	0	2750
720	6.5%	3250 + 100000 100000*6.5%*180/360	-250 100000*0.5%*180/360	0	103000

THE NET INCOME AT t=O IS 93000 (100000-7000), AS 15000 IS PAID FOR CAP PRICE AND 8000 IS RECEIVED FOR FLOOR PRICE HENCE NET PAYMENT MADE IS 7000 and loan mount received is 100000, hence net income of the loan is 93000

NOW WE CALCULATE THE IRR FOR LOAN WITH COLLAR

  

now solving for x in above equation we get irr = 4.429% for 180.days, now we multiply by 2 to calculate per annum irr which is 8.856% p.a.

NOW WE CALCULATE THE IRR FOR LOAN WITHOUT COLLAR

now solving for x in above equation we get irr = 2.85% for 180.days, now we multiply by 2 to calculate per annum irr which is 4.97% p.a.