There are major expenses in setting up with all the necessary gear for multi-day hiking.
Buying gear from new it’s not unreasonable for a ballpark budget:
$400 footwear
$400 pack
$400 raingear
$400 sleeping bag
$400 woollen clothing
$400 stove and cooking, headlight and other bits and pieces
(How come everything seems to be around $400?)
Even with a solitary week or so tramp a year, for ten years, that ain’t so bad. Or, stack it against the more transitory expenses of an international fling. It’s not so extreme. And once you’ve got the gear, at least it’s reusable.
Actually, in keeping with the NZ making-do way, you can always start somewhat compromised and build up the kit as you work out exactly what you need.
The next biggest expense is transportation and accommodation on each side of your trip, and, I guess, that varies considerably as to where you are from and where you are going.
Food and fuel are more predictable but will depend on your preferences. You can pay $16 for a commercial dehydrated dinner, or cobble something healthy with sufficient calorific value from a base of rice or spaghetti. Dehydrating your own dinners is the best value.
Hut passes or tickets, well, you can work that out easy enough.
Think of it as an investment in your health and your physical and mental well-being.