# Interest rate put example - CFAI erratum?

CFAI Books - Volume 5 - page 318 - Example 12…

Halfway into the first paragraph “Current Libor is 7.125%, which is the rate it could borrow at now for any period less than 180 days.”

In the solution: \$475,000 [1 + (.07125 + .01) (65/360)] = \$481,968

Why are we adding .01 to the borrowing cost of the option premium? Every Kaplan question i’ve seen uses the “current” borrowing rate, not the future borrowing rate. Shouldn’t it be \$481,111?

No errata found on CFAI website in volume 5 that addresses this question.

Is this supposed to be an erratum? Or do we use future borrowing costs? I’m confused. Thanks.

Loan is being taken at

since Put is for protection of the loan interest rate payments - that rate applies to the Put as well.

Doesn’t the option pay off at expiration on day 65? Aren’t we just hedging between time 0 and day 65?

Day 0 - we “borrow” the funds at LIBOR

Day 65 - the option is either ITM or OTM ( payoff time , so we can “pay down” the “borrowed” premium)

Day 247 - we close out the remaining \$100m position (irrelevant to option premium)

IE: Isn’t day 65 - option expiration? (or at least an American option that we sell for current value). Assuming we’re ITM, couldn’t we pay back the premium amount that we “borrowed” and use the difference to reduce our \$100m lending amount?

I’m not getting why we’re using the borrowing rate from day 65 - 247 if the option is no longer outstanding during that time frame.

The loan of 100,000,000 is the underlining. The put option would be exercised on day = 65, the 100,000,000 loan would be lent out at the existing libor + spread.

So the firm is making 6% on the 100m loan but they also made an agreement with a put writer who was helping the lender lock in a floor libor rate with the stipulation if the rate fell below this floor the put writter would compensate the buyer of the put with the difference between the strike and the actual libor on day =65 with the underlining being the 100m loan.

The firm paid 481k as an insurance policy to protect the 100m loan from earning a rate lower than the strike of the option.

Galli… My question is: Does the option premium cost \$481,968 or \$481,111 ?

The CFAI book says \$481,968…shouldn’t it be \$481,111 ?

Halfway into the first paragraph “Current Libor is 7.125%, which is the rate it could borrow at now for any period less than 180 days.”

Am I wrong?

Seems like “Current Libor is 7.125%, which is the rate it could borrow at now for any period less than 180 days.” is a bit imprecise/borderline wrong.

They borrow at LIBOR + 100bps, so you need to add 100bps to that.

The 100bps is an opportunity cost for not lending out the \$481,111 at the + spread rate they usually receive.