Question

On March 3, XYZ Company borrows $10,000,000 for one year with interest paid quarterly at LIBOR and also has a long position in an interest rate cap with an exercise rate of 9% for a premium of $50,000 in order to protect against rising interest rates. Given the following term structure, determine the effective cost of borrowing with and without the cap.

Date	Days in Period	LIBOR (%)
March 3		9
June 3	91	8
September 3	92	11
December 3	92	12
March 3	90	13

Answer 1

To calculate effective interest cost all we have to do is calculate interest in both cases i.e.
a) with cap

b) without a cap

Case a)

In case of cap interest rate maximum will be 9 %
which means period ending with
Month Actual % To be used %  

3 June 8 8
3 Sep 11 9
3 Dec 12 9
3 March 13 9

So final calculation will be

Principal	$10,000,000
Premium	$50,000
Interest June 3	$199,452
Interest sep 3	$226,849
Interest dec 3	$226,849
Interest march 3	$221,918
Total interest + premium	$925,068
effective cost	9.251

case b) without a cap
In this case, actual % will be used and no premium will be paid

Month Actual % To be used %  

3 June 8 8
3 Sep 11 11
3 Dec 12 12
3 March 13 13

So final calculation will be

Principal	$10,000,000
Premium	$0
Interest June 3	$199,452
Interest sep 3	$277,260
Interest dec 3	$302,466
Interest march 3	$320,548
Total interest + premium	$1,099,726
effective cost	10.997