"Mr. Smith acquired a property consisting of one acre of land and a two-story building five years ago for $100,000. He also obtained an $80,000 mortgage loan from ACE Bank to provide financing to complete the purchase. This year, Mr. Smith constructed another building on the property with his own funds at a cost of $20,000. Mr. Smith has decided after completing the building to approach Duce Bank to borrow and mortgage the new building with a $16,000 loan. Is Duce Bank likely to provide the $16,000 in financing? What other options may Mr. Smith have to consider?"

To determine whether Duce Bank is likely to provide the $16,000 in financing, we need to consider a few factors:

1. Equity: The equity is the portion of the property's value that is owned outright by Mr. Smith. Initially, Mr. Smith acquired the property for $100,000 with an $80,000 mortgage loan. Therefore, the equity at the time of purchase was $20,000 ($100,000 - $80,000). After constructing the new building for $20,000, the overall value would have increased. Let's assume the new building also adds $20,000 in value. So, the total value of the property would now be $140,000 ($100,000 + $20,000 + $20,000).

2. Loan-to-Value (LTV) Ratio: LTV ratio is used by banks to assess the risk associated with a loan. It is the ratio of the loan amount to the appraised value of the property. Lenders typically prefer a lower LTV ratio, usually around 80% or lower. To calculate the LTV ratio, divide the loan amount by the appraised value of the property and multiply by 100.

Now, assuming Duce Bank uses the same appraised value of $140,000, we can calculate the LTV ratio for Mr. Smith's request for a $16,000 loan:
LTV = ($16,000 / $140,000) * 100 ≈ 11.43%

Based on a low LTV ratio of 11.43%, it is likely that Duce Bank will provide the $16,000 in financing. This is because the requested loan amount is relatively small compared to the appraised value of the property.

However, Mr. Smith should also consider other options:

1. Increase the loan amount: If Mr. Smith needs more funds beyond $16,000, he could inquire about borrowing a larger amount from Duce Bank or explore other lending options.

2. Refinance the existing mortgage: Mr. Smith could consider refinancing his existing mortgage with ACE Bank to release additional equity and provide funds for his new project.

3. Seek financing from other lenders: Mr. Smith can approach other banks or financial institutions to compare loan terms, interest rates, and eligibility criteria.

4. Self-financing: If Mr. Smith has sufficient funds or savings, he may choose to finance the building construction himself without taking a loan.

Ultimately, the availability of financing and the best option for Mr. Smith will depend on his creditworthiness, the specific policies of Duce Bank, and other factors unique to his financial situation. It is advisable for Mr. Smith to consult with financial advisors and lenders to explore all available options and choose the most suitable one.