Today I will explain fifth freedom flights for Air New Zealand(NZ).
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Frequent Flyer Programme of NZ

The Frequent Flyer Programme of NZ, Airpoints, is bit complicated programme.

https://www.airnzpoints.co.nz/

You would better to credit any other partner airlines’ programme.

For instance, if you fly with the booking class A ;

If you credit to ANA(NH) :
( 5490(NRT-AKL) + 5490(AKL-NRT) ) * 100 % = 10,980 miles
　
If you credit to Cathay Pacific(CX) :
( 5490(NRT-AKL) + 5490(AKL-NRT) ) * 110 % = 12,078 miles

If you fly with the booking class S, G or K, you cannot earn any air miles with NH nore CX, but with UA you can earn :

S class : 50%
G/K class : 25%

AKL – LAX – LHR

LAX <-> LHR(5456 miles)
NZ1/2
27JAN – 02FEB
C : JPY356,280 –

AKL – RAR – LAX

RAR <-> LAX(4670 miles)
NZ18/19
27JAN – 04FEB
C : JPY379,650 –

SYD – RAR

SYD <-> RAR(3102 miles)
NZ60/61
27MAR – 07APR
Y : JPY92,080 –

SYD – NLK

SYD <-> NLK(1044 miles)
NZ762/763
27MAR – 07APR
Y : JPY42,330 –

Apparently no business class seats on this flight.

BNE – NLK

BNE <-> NLK(911 miles)
NZ764/765
08APR – 15APR
Y : JPY38,930 –
Apparently no business class seats on this flight.

Conclusion

I think New Zealand has the similar weather with Japan, also there are lots of hot springs.

I have been there once with NZ, visited Auckland(AKL), Christ Church(CHC) and the Lake Tekapo, all of them were very nice.

I would love to visit Wellington(WLG) and Rarotonga(RAR), Cook Islands :

I want to take “Skycouch”, only NZ has in the world, too.