There are a few separate issues present in your question: the type of appraisal a lender may require, the LTV you need to qualify, and whether you should pay for an appraisal at this point.
Types of Appraisals
As you probably understand, the taxman's valuation of your property affects how much you have to pay in property taxes. When a tax assessor gives a specific dollar value to your home, it is the government's opinion of your home's fair-market value. However, the actual dollar assessment is not used by any mortgage lender, nor would you use it to determine a sale price for your property.
Mortgage lenders almost always some kind of an appraisal for a mortgage loan. There are different kinds of appraisals. However, for some loans, like an FHA Streamline refi, no appraisal may be required. Depending on your property and loan, a lender will generally require one of the following three types of appraisals:
- A full, formal appraisal: You pay for a licensed appraiser to come over and view the property. The appraiser submits a valuation, based on a professional analysis of how your property compares to homes in your area of a similar size and condition, based on what they sold for recently.
- A drive-by appraisal: A drive-by appraisal is also by a licensed appraiser. As the name indicates, the appraiser views the home from the outside, to look at its general condition. A drive-by is not as detailed as a full appraisal. It also involves a comparison to the value of similar homes in your area.
- An automated appraisal: An automated appraisal, also know as an AVM (automated valuation model) is not done by a licensed appraiser. Instead, it is produced by a mathematical model using a database with information such as the sale price of comparable homes and property tax assessments. It does not involve anyone viewing your property at all.
If your appraisal comes in below the value you believe your home is worth, first check and see that the basic information on the appraisal is correct (square footage, number of bedrooms, etc.). You can also appeal to the lender to have the appraisal reviewed or reconsidered.
In your case, you could choose to pay for a full appraisal, but that choice comes with a risk.
Appraised Value and Cash-out
You have two main options for taking cash out of your property, a new, cash-out first mortgage at a higher balance or a second mortgage, either a Home Equity Loan or a Home Equity Line of Credit (HELOC). The appraised value of your property is a key component in determining how much a lender is willing to lend you. LTV restrictions are different for a refinance loan, a purchase loan, or a HELOC. For instance, FHA purchase loans allow you to borrow up to 96.5% of the home's value. However, rules for cash-out refinancing are different. You will have a problem getting a new cash-out first mortgage, because of LTV limits.
- FHA cash-out: An FHA cash-out refinance is limited to an 85% LTV for a fixed-rate mortgage.
- Conventional loan cash-out: You're limited to 85% LTV for a Fannie Mae backed cash-out conventional, fixed-rate loan on a single family residence that is your primary residence. Fannie's allows a maximum 70% LTV for an adjustable-rate mortgage (ARM). LTV limits are lower for second homes and investment properties
CLTV and HELOC
Your ability to refinance is also affected by the combined loan-to-value (CLTV). The CLTV is based on the total percentage of your home's value and the total amount you owe of your first mortgage plus any other subordinate financing, second or third mortgages.
For example, a home worth $200,000 with a first loan of $140,000 and a HELOC of $20,000, would have a CLTV of 80% ($160,000 of mortgages against the $200,000 home value).
Any lender considering your application for a HELOC will not just look at the size of the HELOC loan you want, but at the CLTV. A general rule of thumb is that HELOCs will be capped at a 80-85% CLTV, depending on the lender and your compensating financial factors of debt-to-income ratio and assets.
There are a few barriers to accomplishing your goal of pulling out $25,000 in cash.
In your specific case, your current mortgage balance is $175,000. Four months ago your home was valued, in a formal appraisal, at $220,000. If it is worth that today, and you are restricted to 80% CLTV, the maximum you can borrow would be $176,000, so you would not qualify. If the lender allowed you an LTV of 85%, then you would be able to borrow $187,000. When the costs for the loan are figured in, you would likely net less than $10,000. Many lenders won't offer a HELOC for such a small amount.
The fact that you bought the home only four month's ago could be a problem. According to Fannie Mae's rules about cash-out refinances, "If the property was purchased within the prior six months, the borrower is ineligible for a cash-out transaction unless the loan meets the delayed financing exception" available if you paid cash for the house and then wanted to take cash out.
Don't Pay for an Appraisal
Paying for an appraisal, at this juncture, doesn't seem to make any sense. The average full appraisal costs about $400, though prices vary depending on the area of the country in which you're located and the complexity of your appraisal. For instance, if you live on an unusual property or a very expensive property, you can expect to pay a higher price.
Before you pay for an appraisal, I suggest that you speak with any prospective lender and find out the maximum LTV for your property. It does seem odd that the “robo appraisal” (an AVM) that your lender used came back with so much lower value than your formal appraisal of less than half a year earlier.
Keep in mind before paying for any appraisal ordered by a lender that the appraisal will belong to the lender, not to you, even though you paid for it. If you switch to another lender, because you find a better rate, for instance, be prepared to pay for another appraisal.