# Loans vs. Cashflow

August 15, 2013

In a standard installment loan, given the parameters: principal, periodic interest rate, and number of payment periods, we can solve for payment amount using the following equation:

But what if we know the payments but not the interest rate? There is a specific kind of "loan" where this happens. It's known as a cash flow.

An example of a cash flow would be as follows: an individual has won a lottery prize or a legal settlement which promises to pay the individual $1,000 per month for the next 10 years. The individual wants his money right now. So, he goes to a company that offers to purchase his settlement for a straight purchase of $100,000. Now, the company knows that it is going to get $1,000 per month for the next 120 months, which is a total of $120,000, and the $20,000 profit over the next ten years will be that company's income on this deal.

This is accounted for as a loan with a principal amount of $100,000, with 120 monthly payments of $1,000. So, we have the variables Pr, n, and P in the equation above, but we do not have i. We don't know what the interest rate is, and there is no mathematical way to solve the above equation for i. The interest rate (i) in this case is known as the internal rate of return (IRR).

The internal rate of return is important to the "lender" (the company purchasing this cash flow) because it will help to define how much of each $1,000 payment received each month is income and how much is paying down the initial $100,000 investment.

The Nortridge Loan System uses an iterative method, involving the amortization schedule to determine the IRR. Basically, if we take an amortization schedule involving a loan of $100,000 amortized at some interest rate, with monthly payments of $1,000 for 120 months, we are going to have some number at the end of 120 months for the remaining balance (or Net Present Value). If we set the IRR too high, the Net Present Value after 120 months will be a positive number, and if we set the IRR to low it will be a negative number. We simply adjust the IRR value on this amortization schedule until we arrive at a net present value at the end of 120 months as close to zero as possible.

NLS does this all automatically if you set up a special kind of loan that allows you to configure the cash flow and calculate the IRR.

Incidentally, the IRR on the loan we have been discussing is: (drumroll)... 3.73701%.

The math may be complicated, but the system handles it all automatically, so for you, it's easy.