The decision of whether to rent or to buy is often not purely a financial consideration, it may well be about flexibility and lifestyle or as seems more common at the moment the access to that deposit is limiting the opportunity to purchase.
If the financial consideration is a big driver of the decision then you will be pleased to know there is an excellent online tool published by The New York Times that helps to answer the question "when is it financially better to rent than to buy". To be clear the online tool is primarily built for renters to help better to see the point at which it becomes better to buy than to rent.
The beauty of the app is that there are a wide variety of inputs that dynamically allow the calculation to be personalised and whilst it is a US app it can be just as relevant to the NZ market.
The app requires some inputs to begin with which you are key to the calculation such as real estate fees, mortgage rates. inflation, investment rates, local and personal taxes as well as current inflation in property prices and rents. With all of these inputted then the key factors to examine are how long you plan to stay in the house and what is the price of the type of house you are looking to buy. It is also valuable to then go back and see the impact of property price inflation and rent increases as to how they impact the decision threshold.
Before you have a go with the app I would recommend you have a watch of this screencast I have published which walks you through the app together with advice around the input levels.