It seems like that accountant may not be doing a great job in accounting for the properties expenses. But that is opportunity for you! I would not rely on the accountant/seller's provided profit and loss statement (P&L) but verify as much as you can. I would want to see the rent roll to see what is actually coming in and from what units and the trailing 12 months expenses to track what is going out.
Once you have this info you can compare to the market. Likely the units are being under rented so do online research on places like zillow, apartments.com, etc. to find rent comps - also speak with a local property manager. If you use the local property manager they should be able to help with the due diligence items as well. If you find that units are rented for lower than market rents, run your projections implementing those upgrades. I analyze conservatively knowing that the units will probably need some repairs and vacancy will go up over the stabilization period until all the repairs are made and units are rented up to market rent. That is how you can optimize income (in a nutshell).
To figure out how to optimize expenses, look at what the current expenses are - it sounds like they are high in this case. I would look at their P&L and if their total expenses are less than 50% of the effective gross income, then they are probably reporting low. I would suggest using 50% or their reported expenses, whichever is higher (ex. if they report 60%, use 60%). From there look where you can cut back. It sounds like you have a good idea of the insurance - but still get several quotes. And beware of taxes, when you purchase they will likely go up because the seller will likely sell for higher than the current assessed value. Find out your area's tax percentage rate and the estimated purchase price to ballpark the new tax expense. Find what you can cut and implement a plan to cut it.
For the utilities you can look into implementing a RUBS system which is a way to calculate the expense each tenant generates for utilities each month and then you bill back the tenants that amount. This shifts the responsibility from you to the tenant on who pays utilities. Also look at other comparable properties and make sure they have separate utilities or else implementing RUBS may decrease the rental amount you can charge so you will have to look into that and weigh the costs if all landlords pay utilities in your area.
Next you need to determine the cap rate for that area. Call brokers, talk to other investors, ask people on BP to find the cap rate for your area on that size and class of property. This will come in handy in the next part.
Once you find the CURRENT income and expenses for the property, you can determine your NOI. Then divide that NOI by the cap rate you found by talking to brokers, etc. to determine the value of the property. The value you come up with will likely be lower than the asking price because either the actual income is less than the reported or the expenses are higher or both. But this is where in your offer you back it up with the data you used to find your price because apartments are valuated based on the NOI.
However, you also ran your own numbers with your projections based on the data you found doing all the above things. This should yield you a higher NOI. If it doesn't, it might not be a good deal. But if it does and you apply the same cap rate to the higher NOI the value you determined in your projection should be higher. To be more competitive you can increase your price closer to that number. Be careful though because this, in my opinion, is like paying the seller for the potential of the property and frankly like paying them for your effort. But if it helps you get the deal and the numbers still work then by all means do it because you have your plan on how to increase that value.
I hope all of that helped and that you can make the deal work!