risk management question

In this question, why is the payoff from the put of $875,000 not reducing the loan interest for the effective interest.

On 16 March 2012, First Citizen Bank (FCB) approached Silva for advice on a loan commitment. At that time, FCB had committed to lend $100 million in 30 days (on 15 April 2012), with interest and principal due on 12 October 2012, or 180 days from the date of the loan. The interest rate on the loan was 180-day Libor + 50 bps, and FCB was concerned about interest rates declining between March and April. Silva advised FCB to purchase a $100 million interest rate put on 180-day Libor with an exercise rate of 5.75% and expiring on 15 April 2012. The put premium was $25,000. Libor rates on 16 March 2012 and 15 April 2012 were 6% and 4%, respectively. The option was exercised on 15 April 2012, and the payoff was received on 12 October 2012. FCB has asked for a written evaluation of the success of the strategy.

The effective annual rate is calculated as follows:

Future value of put premium on 15 April:

$25,0001+(0.06+0.005)30360=$25,135.42" name=“QMK33379-E” resolution=“300” src=“http://www.analystforum.com/resources/399691/topicresources/590970413/QMK33379-E.png” style=“width: 307px; height: 38px” width=“315” />

Effective loan outlay = $100,000,000 + $25,135.42 = $100,025,135.42.

Loan interest is calculated as;

$100,000,000(0.04+0.005)180360=$2,250,000" name=“QMK33379-E___2” resolution=“300” src=“http://www.analystforum.com/resources/399691/topicresources/590970413/QMK33379-E___2.png” style=“width: 303px; height: 40px” width=“311” />

Put Payoff:

$100,000,000[max0,0.0575−0.04180360=$875,000" name=“QMK33379-E___3” resolution=“300” src=“http://www.analystforum.com/resources/399691/topicresources/590970413/QMK33379-E___37fe66983-4e29-4e41-a229.jpg” style=“width: 409px; height: 40px” width=“813” />

Effective interest = $2,250,000 + $875,000 = $3,125,000.

Effective annualized loan rate:

[100,000,000+3,125,000100,025,135]365180-1=0.0638" name=“QMK33379-E___5” resolution=“300” src=“http://www.analystforum.com/resources/399691/topicresources/590970413/QMK33379-E___5.png” style=“width: 265px; height: 46px” width=“310” />

CFA Level III

“Risk Management Applications of Option Strategies,” Don M. Chance

Section 3.2

The pay off from the put is a net benefit to the lender of the original 100m loan. The 2.2m is the interest on the loan @ libor +50bp PLUS the payoff from a put option going below 5.75, to 4.00. The 1.75% ITM option is a gain to the long holder, which is the bank in this case.

Most of the text takes the perspective of the borrower, not the lender.