Interest Rate Options and Effective Annual Rate

[cook29]

Why do we subtract the call premium+interest from the loan amount in determining the effective annual rate? Aren’t we still still borrowing the full loan amount? Can anyone conceptualize that for me? For instance, Schweser has on page 185 a blue box problem noting $10M needs to be borrwed in 31 days for 90 days. A call is bought on the libor expiring in 31 days. Then it goes on to find the EAR but subtracts the call premium ($5,000) plus the interest on that call premium from the principal amount to be borrowed ($10M). TIA.

 

[cipherap15]

Dont have the example in Front of me. But essentially from the Borrower we’re solving for x where:
(Amount Borrowed) * (1 + X) ^T/365 = (Amount We have to pay Back)
Since we’re getting a loan of say 5 million and want to protect ourselves from interest rate risk, we would purchase a Interest Rate Call option. This Option say costs 10000. Therefor we’re really only borrowing 4,990,000 bucks because we have to pay for the Call Option.
These questions usually the loan is in the future so we compound the 10000 forward to when we’re actually getting the loan and subtract that amount from the Loan Amount to get the effective amount

 

[myriam2222]

If your option is in the money and you benefit from a more favorable interest rate thanks to it, you will overestimate such a benefit if you don’t also take into account what it did cost you. If the option is just breakeven (i.e. just slighty in the money to offset the premium), it makes no difference that you took this option, but it will seem like it does if you omit the premium when calculating the effective rate.
All cash outflows and inflows should be taken into account.
You should see this effective rate computation as a kind of IRR because it should make all discounted cash inflows and outflows add up to zero.