I used a "Break Even Formula" to see if refinancing our house would make sense when closing costs could be recovered by the interest saved on the loan.

Keith Bunn from CavUSFinancialCoaching sent in this question:
I listened to podcast episode #36 "Should I Refi" and am wondering if we can use that same math formula for insurance? Tell me if I have the math right... these are made up numbers.
Car insurance example
$1920  current annual payment
- $1000  competitor's annual rate
= $920  saving per year
Would the Break Even formula work here? $1920 / $920 = 2.08 years you would have to go to break even, right?

And what would be the mathematical formula if someone took on more responsibly (insurance wise) to lower their premiums? How does someone figure out how many years they have to go without an accident in order for the increased responsibility to make sense?
When to use a Break Even Analysis
A break even analysis works best when calculating variables in debts, loan payoff dates, or assessing the exposure to risk.
Answering the car insurance example
Car insurance is an expense so a break even calculation doesn't really need to be performed. For example: A married couple uses Company A for their cable and spends $150 a month. The learn that they can get a comparable service from Company B for $100. In this case they are saving $50 a month instantly. There is no break even point, thus no analysis is necessary.

We could, however, say that the couple is getting 3 months of cable for the price of 2 (3x $100 a month is the same as 2X $150 a month, getting an additional month for the same price). In other words, if you can get the same coverage for less by switching to Geico then go for it.
Lower insurance, higher deductible
One way to save on insurance is to raise the deductible. A deductible is the "first dollars" that are used to pay for a bill (medical, auto, home, etc...) and the policy owner (you) is usually the one responsible to pay the "first dollars". This allows the insurance company to share the risk with you, and keep costs down.

Increasing the deductible means increasing your risk and decreasing the insurance company's risk. This will most certainly mean lower premiums for you. But how do you know if taking on more risk is a good decision?
The Break Even Formula
A simple equation: Additional risk / divided by savings = equals Break Even

For example: Joe Smith pays $1,200 a year to cover his $15,000 truck with a $1,000 deductible. He learns he can save $400 a year by raising the deductible to $4,000. In other words, he's taking on an additional $3,000 of risk to save $400 in annual premiums.
$3,000 (additional risk) / $400 (premium savings) = 7.5 years
He would have to go 7.5 years without backing into a pole or hitting someone's parked car just to break even. That's a lot of risk, especially when you consider that the truck might not even be worth $4,000 at the end of 7.5 years. (That was a joke)
It's not just for refinancing anymore
The Break Even analysis works for refinancing a home, car, even debt consolidation. Anywhere that will cost you money or time when changing terms or providers.
Also mentioned in Episode 62:

5 ways to cut expenses on The Worst of the Free Financial Advisor: Episode 8
Be a part of the MoneyPlan SOS podcast - I am asking podcast listeners to send in their "shout out", similar to Dustin Hartler's (used in this episode) for possible replay during the show. Here's the suggested script: "This is ____ from _____ and you are listening to Steve Stewart on the MoneyPlan SOS Podcast - helping everyday Americans pay attention, not interest". Record it on your computer, iPhone, or call into the MPSOS hotline 312-373-0767 and leave it as a voicemail.
The joke: What is the difference between someone that says "I have a degree IN ____" vs "I have a degree FROM _____"? About $20,000 to $40,000 in additional tuition expenses.