Estimating monthly expenses for the lender when modifying a loan – Better to over estimate or under estimate?

I called BofA before I was late on my mortgage to request a loan modification. I had been borrowing frequently from credit cards to help pay the loan. The woman asked me what my monthly expenses were, and I was not prepared because I thought she would mail me out a packet. I over estimated thinking that would make the need seem greater. She advised me that I did not qualify because I owed quite a bit more then I made. I then decided to stop making the payment and now that I am going on three months delinquent I again requested a modification, and this time I am faxing them the information. Am I correct to assume that after calculating (mortgage calculator) what I desire (realistically) in a payment, that it is best that my expenses when subtracted from my net pay should leave me with, for example, $ 200-$ 300, above what I would want me mortgage payment to be? That way showing that after the payment and monthly expenses I at least a have a couple of hundred dollars left over for the month.

I recently read about a gift equity loan on yahoo answers and am a little confused on how it can work best for me.

My parents bought a home for 350K and put 20K into the home and have rented it for 3 years. With the rent they have received, they have been breaking even with the bank and only owe 310,000. They want to sell me the home for the 310K so in this situation what is the best way to go about this, would using a gift equity loan be the best option and could you explain why?

Annual salary: 380,000 (before taxes)
Im willing to put a downpayment of around 60,000
Good credit
No debts, car payments, or student loans

Also, I have heard that banks will give around 3x your annual salary as a loan which in my case would be close to 250K and with my 60K down payment that works out perfectly but if I can save my down payment to put towards fixing up the home or other things that would be amazing so any ideas?

Ive used a few mortgage calculators and without the gift of equity loan I will pay around 1600 a month including taxes and hazard insurance so can someone tell me how much I might pay with the gift of equity loan?
Wow another great answer tax lady, if you read this again, could you edit your response and let me know what YOU think the best way to go is for my parents and I?

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