The value of debt is that it allows you to profit from the return of equity beyond the amount of actual net equity you own. Of course, this only works if the cost of borrowing is less than your return on equity. Market timing matters a great deal but isn't accounted for in this view. For my answer I would like to hand-wave away market timing considerations. One plausible justification is that you could default on your current home and then immediately go buy one of equal value. If you buy a new home of a lesser value (due to lack of funds) and then prices appreciate, then you missed some opportunity cost but probably not $100k worth of it.
Moving on, here are some helpful assumptions I'll make.
- You currently have a net worth of P
- Borrowing with good credit (which you have now) costs you R1 % yield, with a limit of A1
- You simply don't borrow at all if you have bad credit
- The time value of money to you, or your average investment yield is R2 %
- You make S dollars per year at your job more than what you spend
- You will retire in X years.
I'll ignore performance of your portfolio after retirement and only seek to optimize F, which will be your net worth upon retirement. In either case, your current net worth is earning the R2 rate. We can convert this for both your current net worth and future savings using conversion formulas.
Present to future value
F = P (1+R2)^x
Annual to future value
F = S ( (1+R2)^x - 1 ) / R2
Adding these together is sufficient to obtain F in the case that you have no borrowing power. The case where you do not default and maintain your credit score is different due to an initial $100k penalty and the amortized value of borrowing power. In a completely theoretical sense, you get an effective (R2-R1) yield on all borrowed money. The future value will be the following:
F = A1 (1+R2-R1)^x
One step is missing, however, which is to convert this value (the value of having a good credit score) into present value to compare to value of your defaulting.
P of borrowing power = F / (1+R2)^x = A1 { (1+R2-R1)/(1+R2) }^x
Now, let's put some specific values in. Say that you can borrow $300k with your good credit history and this applies for the next 25 years, after which you retire. The borrowing rate is 7% and the time-value of money to you is 10%. I would then calculate:
P of borrowing power = $58 k < $100 k
This indicates that it would be more economical to default. Of course, some people might point out that it will be removed from your record after 7 years. If you plug 7 years instead of 25 years into the equation, almost no assumptions about rates will lead to the option of keeping your house being preferable.
So in a nutshell, the value of your credit is probably less than $100k in a purely mathematical sense. But there are other factors too. If you don't have that borrowing ability maybe you wouldn't be able to borrow money to start the business of your dreams. If you are a rock star entrepreneur, then time-value of money to you could be 1,000% yield, sure, then maybe you could make the above numbers work (to favor keeping the house). I've also neglected ethics. As other people point out, it would be like stealing from the bank.