Depending, of course, on what benefits you see from paying for a mission.[fn1] But, from a tax perspective, it makes way more sense for you to pay.
My answer is subject to all sorts of caveats, of course. I’m assuming, among other things, that you’re a U.S. taxpayer,[fn2] that you are in favor of your child’s serving a mission, and that you are in at least as good a position as your child to save and pay for your child’s mission.
Why should you pay rather than your child? Because the amount you pay to support missionaries (whether your own child or payments to the General Missionary Fund) are tax-deductible.
So? you may ask. Can’t my child take a tax deduction?
Sure. But, unless you child makes more money than you, and continues to earn that money during his or her mission, the deduction is more valuable than you.
Think of it this way: assume your daughter earns $7,250.[fn3] Meanwhile, you and your spouse collectively earn $52,762 during the year.[fn4] That puts your daughter in the 10% tax bracket, and you (assuming you file jointly) in the 15% bracket.
With missions costing $4,800/year, your daughter could reduce her tax bill by $480. You, on the other hand, would reduce your tax bill by $720.
Which is to say, for tax purposes,[fn5] you should pay for your child’s mission.
[fn1] Note that I’m talking solely about paying for a mission—saving for a mission is something else entirely, and, imho, you should have your child save for a mission. What happens to that money after his or her mission is up to you guys.
[fn2] I’m sorry to be U.S.-centric here. I assume the same answer applies in at least some other countries, but I’m not a comparative tax guy, so I can’t say for sure.
[fn3] That’s working 20 hours a week for 50 weeks of the year at the federal minimum wage of $7.25/hour.
[fn4] That is, the median household income in the U.S. in 2007-2011.
[fn5] People tell me there are purposes beyond tax purposes, but I’m not entirely sure I believe them.