Should I Stay or Should I Go

Is ending a financially draining relationship worth the hit to assets?

Some tools to price staying vs going.

via GIPHY

Let's jump to the hypothetical.

(A)sh and (B)riar marry. B has a child from a previous relationship. Two years later, A and B have a child. 

After 3 years, they have a combined household net wealth of $800,000, mostly saved by A who is the sole earner. B does not work or do any domestic duties and spends $40,000 a year, increasing 3% above inflation.

A thinks of leaving, but how do they weigh up spiralling costs against a property division.

If I stay there will be trouble

The present cost of staying is the present value (PV) of a series of outflows.

To calculate, we need:

• Payment amount (PMT) - To be fair, A must consider B's non-financial contributions to the household. However, it's clear B contributes no domestic duties as payments in kind. In this case, -$40,000.  
• Number of Periods (t) - 15 years until their child turns 18 and A is off the hook for child support.
• Discount Rate (r) - A smaller discount rate will counter-intuitively increase the present value of the cash outflow as losses retain their value further into the future, and alternative investments are not much more attractive. In a negative cashflow situation r can be framed as the amount by which inflation beats outflow growth (i.e. inflation rate - outflow growth rate). In this case, -3%
• The Future Value (FV) is 0 as there is no salvage value. In fact, there is an exit cost.

Plug that into a spreadsheet and we get approx $772,000.

If the exit cost for A is less than that amount, exiting is financially worth more than staying.

The weakness of this approach is that it assumes that B will not change. Whether B can be coaxed to contribute more through frugality or labour is ultimately a subjective question for A.

And if I go it will be double

No one wants to see their wealth cut in half.

From A's perspective, they go from $800,000 to $400,000. 

But their household - and the number of mouths they must feed - also changes.

Exit costs in family breakdown are not straightforward and are highly contingent on care arrangements and property splits.

Assuming shared custody of their mutual child and B taking full responsibility of their child from their previous relationship, A's household size goes from 4 to 1.5.

To reflect differences in resource use, the OECD equivalises income with an equivalence factor derived from the square root of household size. A household of 4 (equivalence factor: 2) would need double the income of a lone adult household to experience a comparable standard of living.

Because wealth is linked to income, it can also be equivalised.

One day it's fine and next is black

Assume a 50:50 property split. A reasonable assumption, considering a child in common.

Equivalised household wealth:

• Before split: $400,000 ($800,000/√4)
• After split: ~$327,000 ($400,000/√1.5)
• Difference: -$73,000.

Before we proceed, I want to clear up a common assumption.

If you say that you are mine

Why am I using current household wealth and not starting from A's position before they entered the relationship? i.e. what if A was previously a wealthy single and 'brought in' the bulk of the assets?

Several reasons:

• The starting point should reflect the life that A is experiencing right now.
• B's assets will also form part of any property split.
• Even if B has no assets to their name they may have initially contributed in kind.
• A can be considered to have been content with the arrangement, no matter how draining, until recently. Is it 'fair' that through no fault of their own they lose a chunk of their life savings? Maybe, maybe not, but they would have been mindful of the possibility when entering the relationship, all ventures entail risk, and this is the flip-side of the chance of a happy marriage.
• A was single five years ago. The counterfactuals are too numerous and complicated to discern whether they would have been better off. They could have entered an even more trying relationship. They could have discovered crypto-currency or sports gambling.

Ultimately, you have to draw a starting line somewhere, and placing it earlier will lead to an unnecessary dredging up of the past.

Come on and let me know

For A:

Staying has a present value/cost of $772,000.

The equivalised cost of going is $73,000.

In this case, A would be financially better off leaving. 

Note that even if we had calculated A's exit cost to be $400,000 (i.e. A brought $800,000 into the relationship which is then halved) they would still be 'better off'.

This Indecision's Bugging Me

Take-aways:

There are a lot of variables. Time, cost, household size. Even discerning the variables is complicated.

Nevertheless, it can still be done. Established math is available to work out whether to stay in a loss-making venture or pay for an exit.