This mortgage broker is incorrectly calculating a number that may be of critical importance to a borrower's decision. First, it ignores differences in the loan balance in the two cases.
Money paid today is worth more than money paid in the future.
Third, the broker's approach ignore taxes, which affect the answer because points and interest are treated differently by the tax code. On a home purchase transaction, points are fully deductible in the year the loan is made whereas interest payments are deductible in future years as they are paid. To calculate it properly, the cost must includes points, monthly payments, the lost interest earnings on both the points and the monthly payments using the borrower's investment rate, less tax savings and less the reduction in the loan balance. Pulling all these factors together to calculate a correct breakeven period is not rocket science, but you can't do it in your head or with a standard calculator. I would guess that not one loan officer in a hundred has access to the technology needed to do this calculation.