Interest rate options

CFA Level III Derivatives
#1

R33. Ex11. Q01.

In this question the options is in the money and exercised, but the effective rate on loan (9.25) still ends up being higher than libor (6+3).

What makes it okay to exercise the option then? the combined cost of not exercising + option premium would make it steeper?

#2

Because it’s an annualized rate. If the payoff of the option was zero, the annual rate would be: ($5,112,500/$4,989,912)^(365/90) = 10.34%.

9.25% < 10.34%

#3

Thanks