New Zealand Law
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Child support is based on income, so if he starts a new venture with no income at first this will reduce his liable payments. But until his income actually drops, then you do not have to agree, unless you want to. If this is a private arrangement you may want to register the agreement with Inland Revenue, and then he must deal with them.
The amounts are assessed on your own incomes, and not dependent on what the other party has to pay. So your payments will remain the same, even if he has no income. I assume you have a joint parenting arrangement with different incomes as this the only way you may be liable.
You will still need to pay based on your income but not on his income. Your liability will not increase because his income drops
You can reach whatever private arrangement that works, but underpinning these are what you can get through Inland Revenue if the agreement is registered. The basic idea is to split the costs of raising the child of course, and the income through an IRD assessment will be based as I have described. So you need to look at the notional cost of looking after the child, and then divide this by the time he is with you. Equal care means an equal share, but you don't then have to subsidise the father if he chooses to reduce his income.