John Key has made claims about the costs of Labour’s early childhood education policy in Key: No big Budget spend-up (NZ Herald):

Mr Key cited Labour’s promise to increase early childhood education from 20 free hours a week for three and four years old to 25 hours a week.

The policy doesn’t take effect until July 2017 but Labour has costed it at $57 million in the first year and about $60 million after that.

Mr Key said the cost was more likely to be $600 million, $700 million or $800 million.

Rob Salmond at Polity has disputed this in Key in self-parody about lying (mk 2):

So Key thinks this policy will cost at least ten times as much as Labour does. That’s a very big claim.

He does some calculations:

• The policy is for 5 extra hours free, each week of the year. That’s up to 260 extra free hours per child.
• The Free ECE funding rates range from $4.91/hr to $11.56/hr, including GST, depending on what kind of centre you are using. Let’s assume everyone is in the top category and gets $11.56 an hour. After removing the GST that the government gets back in the end, the per hour cost could be up to $10.
• So, at absolute maximum, the policy could cost 260 hours X $10/hr = $2,600 per child. (In reality, of course, it won’t come close to this average.)

Here’s the problem: there are only around 120,000 three and four year olds in New Zealand!

That looks about right from this 2013 census chart:

120,000  x $2,600 = $312,000,000

That, at a maximum, is about half of Key’s lowest claim. It’s likely to be much lower.

Key looks to have grossly exaggerated the potential costs.