Loan Options and Incremental Cost Analysis

Home Equity Loan (Second Trust Deed / Second Loan): This is a second, separate loan taken out on a property, additional to the initial, larger mortgage.
Home Equity Line of Credit (HELOC):
- Functions exactly like a credit card; a physical credit card may even be issued.
- It is always securitized by the house, meaning the house is the collateral. Failure to pay can result in the loss of the property.
- Tax Deductibility (Primary Residence):
  - Currently, interest accrued on home loans up to 750,000 can be written off annually against taxes.
  - If the Tax Reform Act of 2016 were to reset, this limit would revert to 1,000,000.
  - For a full equity line of credit, the maximum amount of interest that can be written off is capped at the interest on 100,000. This is why lenders will often cap the principal amount of a HELOC at a level that would generate interest equivalent to this cap, rather than allowing a much larger loan amount.

Purpose: These loans are utilized when an individual or entity needs additional funds (e.g., an extra 300,000) but does not want to refinance their original, existing loan (perhaps due to a favorable, low interest rate) and cannot secure a second mortgage (a common constraint in many commercial real estate transactions).
Mechanism:
- A new lender provides a "wrap-around" loan that encompasses both the principal balance of the original loan (e.g., 1,000,000) and the additional funds needed (e.g., 300,000), totaling a new, larger loan (e.g., 1,300,000).
- The borrower makes a single, consolidated payment (e.g., 6,500 per month based on the 1,300,000 wrap-around loan) directly to the new lender.
- The new lender then has a legal and contractual obligation to take a portion of that payment and send the required payment to the original lender for the initial loan. This ensures the original loan remains current.
- It's generally not the same company providing both the original and wrap-around loans.

Scenario (Max, the Investor, and Chaz, the Lender):
- Max has 300,000 in liquid assets, earning a 9\% annual return (his opportunity cost).
- He aims to purchase a 1,000,000 property.
- Lenders (like Chaz) often attempt to convince borrowers to take larger loans by highlighting a slightly higher overall interest rate (e.g., an additional 0.5\%) while allowing the borrower to retain more cash. This sales pitch is often misleading as it doesn't represent the true cost of the additional borrowed capital.
Objective of Incremental Cost Analysis: To accurately determine the actual interest rate and cost of borrowing only the additional amount of money (e.g., the extra 100,000 borrowed when moving from an 80\% loan to a 90\% loan).
Importance: A seemingly small increase in the overall interest rate (e.g., 0.5\%) on a larger loan is applied to the entire larger loan sum (e.g., 0.5\% on 900,000), not just the incremental 100,000. The incremental cost reveals how expensive that marginal 100,000 truly is.

Calculate Payment for Both Loan Options: Determine the monthly payment for both the larger loan scenario and the smaller loan scenario.
- Example: Payments calculated were -5,643.4115 for the big loan and -5,346.1794 for the smaller loan.
Subtract Payments: Calculate the difference between the larger loan's payment and the smaller loan's payment (Payment{Big} - Payment{Small}). This represents the incremental monthly payment.
Calculate the Incremental Interest Rate (IRR): Using a financial calculator, determine the internal rate of return (interest rate) for the additional amount borrowed, considering:
- \text{PV}: The additional principal amount borrowed (e.g., 100,000).
- \text{PMT}: The incremental payment calculated in Step 2.
- \text{N}: The total number of payments (e.g., 360 months for a 30-year loan).
- \text{FV}: The residual balance of the incremental loan at the end of the holding period or loan term. If the property is held for a shorter period, calculate the difference in outstanding balances of the two loans at the point of sale. If held to maturity, FV is 0.
- Example Result: The additional 100,000 might realistically cost 10.25\% to borrow, significantly higher than the perceived 0.5\% increase.
- Common Error: An incorrect approach is assuming the incremental principal corresponds directly to the incremental payment without using IRR, or incorrectly setting up the cash flow for the incremental calculation.

Compare Incremental Loan Cost to Opportunity Cost:
- Opportunity Cost: The return Max can make on his cash if he chooses not to use it for a larger down payment (e.g., his 9\% investment return).
- Decision:
  - If Incremental\ Loan\ Cost > Opportunity\ Cost (e.g., 10.25\% > 9\%), it is financially advantageous to make a larger down payment (thus taking a smaller loan). This is because the cost of borrowing the extra money is higher than the return he can generate from his own investment capital.
  - If Incremental\ Loan\ Cost < Opportunity\ Cost (e.g., hypothetical 8\% < 9\%), it is financially advantageous to borrow more (take a bigger loan) and retain his cash for investment. This is because he can earn a higher return on his cash than the cost of borrowing additional funds.

Often, loan officers may not fully understand the underlying math of incremental cost. They are generally trained by sales teams to emphasize certain aspects of loans to encourage borrowers to take larger amounts, not necessarily with malicious intent, but due to a lack of complete financial expertise in this specific area.

If the borrower (Max) plans to sell the property before the loan matures (e.g., in 10 years, or 120 months), the incremental cost analysis must be adjusted.
Modification to Step 2: In addition to calculating the difference in monthly payments, it's crucial to calculate the remaining loan balances (Future Value) for both the larger and smaller loan options at the time of the planned sale (e.g., after 120 months).
These future balances will then be incorporated into the incremental cost calculation as the respective \text{FV} components, and the term (\text{N}) for the calculation will be the holding period (e.g., 120 months).

Sideways HP financial calculators typically have a maximum frequency of 90 for inputting cash flows. This can require breaking down longer cash flow sequences (e.g., a 360-month loan) into segments for calculation.