Home prices are increasing while inventory is decreasing nationally, which presents a challenge for first-time homebuyers who might not have the cash for a hefty down payment. When you consider the ideal down payment is 20 percent in markets where housing values are rising, that goal only gets harder and harder to achieve.

A new study by LendingTree, a leading online loan marketplace, ranks the nation's 100 largest cities to determine the best options for first-time homebuyers.

In the study, LendingTree Chief Economist Tendayi Kapfidze used several down payment variables, among other criteria, to determine how favorable each city's housing market is for first-time homebuyers.

Here are the factors that contribute to a favorable housing market:

  • Average down payment amount: Putting down a big sum of cash up front isn't easy for most first-time homebuyers and it could take years to pull the funds together.
  • Average down payment percentage: The down payment is one of the biggest hurdles on the path to homeownership. Lower down payments make it easier for first-time buyers to take that first step.
  • The number of buyers financing with an FHA mortgage: Buyers using an FHA mortgage sometimes put as little as 3 percent down. This and other FHA benefits increase the likelihood of being approved.
  • Percentage of buyers with less than prime credit (below 680): Since first-time homebuyers might have a lower credit score than a current homeowner, they're likely to be more competitive in a market where many potential buyers also have credit scores below prime.
  • The "Housing Opportunity Index": Some cities are just too expensive for the median income family. The Housing Opportunity Index, which measures the number of homes sold that the median income family can afford, improves the ranking of cities that are still affordable for families with median incomes.
  • Average FHA down payment versus average down payment for other kinds of loans: This measure helps determine how much FHA borrowers are really saving on their reduced down payments.

So, what did the study reveal? Let's start with the bad news first.

The worst cities for first-time homebuyers:

  1. Denver
  2. New York City
  3. San Francisco
  4. Austin, Texas
  5. Las Vegas
  6. Los Angeles
  7. Oxnard, Calif.
  8. Boston
  9. Sacramento, Calif.
  10. Miami

San Francisco, Oxnard, and Sacramento are ranked as some of the top hardest real estate markets to break into in California.

The worst cities for first-time homebuyers have high-income inequality and higher home prices than the national average. This makes home loans inaccessible for many first-time homebuyers who already are stretched thin from paying high rental prices.

In Sacramento, a first-time homebuyer needs $55,102 for a down payment on a house, according to the study. Zillow calculates the average home in the Capitol City costs just over $314,000.

While a down payment in Sacramento averages 16 percent, slightly lower than the ideal 20 percent, the housing prices are much higher than the national average of $206,300.

High demand neighborhoods in Sacramento such as North Natomas, Midtown, and Land Park fetch closer to $400,000-$500,000 and above.

In addition, 30 percent of homebuyers in Sacramento have less than prime credit, making the market more competitive where many potential buyers also have credit scores below prime. There is also a lower percentage of buyers using an FHA mortgage in Sacramento, meaning fewer people are using benefits which could help them approved for a home.

Denver is the worst of the worst for first-time homebuyers, earning low scores in every category. Its crushing down payments average out at a whopping $66,806. Even the FHA down payment is particularly high at $22,841.

The best cities for first-time homebuyers:

  1. Little Rock, Ark.
  2. Birmingham, Ala.
  3. Grand Rapids, Mich.
  4. Youngstown, Ohio
  5. Winston, N.C.
  6. Dayton, Ohio
  7. Indianapolis
  8. Scranton, PA
  9. Pittsburgh
  10. Cincinnati

Opportunities abound in industrial states

Twelve of the top 15 cities are in Ohio, Pennsylvania, Michigan, and Indiana. The economies in these states are growing, but the homes have remained remarkably affordable, making cities like Indianapolis, Philadelphia, Detroit, and Dayton, Ohio, more accessible for first-time homebuyers.

What does this mean for you?

Limited home inventory leads to skyrocketing prices in many markets. First-time homebuyers also are seeing their buying power diminished by rising interest rates.

Sacramento is experiencing a housing shortage along with the rest of the state. The city cannot seem to keep up with the demand as people continue to move into the region from the Bay Area and other cities like Seattle.

But don't despair.

If homeownership is your goal, several programs are available to assist you. Be sure to consider all your options, including FHA loans.

"The down payment is the biggest obstacle to homeownership for first-time buyers, so it's best to start saving well ahead of the intended home purchase," said Tendayi Kapfidze, LendingTree's chief economist and author of the report.

Always shop around for mortgage lenders to compare rates and loan terms, and get the best offer. And take time now to improve your credit score, which can dramatically impact the rates you are offered.

MagnifyMoney is a price comparison and financial education website, founded by former bankers who use their knowledge of how the system works to help you save money.