Is the NIB Holdings Limited share price a buy?

The NIB Holdings Limited (ASX: NHF) share price has risen by 14% since 9^th June 2017, is it a buy?

NIB is one of the largest private health insurers in Australia alongside Medibank Private Ltd (ASX: MPL) and Bupa. Its share price has been on a rollercoaster over the last year but it has been a good growth stock over the longer term.

Here is my bull and bear case for NIB in the medium-term:

Bull case

NIB has shown the rest of the private health insurance industry how to grow policyholders effectively. In its latest report for the six months to 31 December 2016 it reported that total policyholders had grown from 706,226 to 751,629. Management haven't been afraid of working with other businesses like Qantas Airways Limited (ASX: QAN) to help growth using different avenues.

The private health insurance industry's overall growth is sluggish at best. However, NIB has succeeded at taking most of the new business thanks to effective marketing.

The government need the private health insurance sector to succeed to take the weight off the public health sector. There will always be some form of government support for the private health industry.

Bear case

The rising cost of health is turning off younger policyholders who are paying for increasing premiums but not getting as much benefit back. Wage growth has become so low that it will soon only be people in the high tax brackets that think it's worthwhile to get health insurance.

There are reports that hospital claims are going up recently. Public hospitals are asking patients if they have private health insurance and treating them as a private patient if they say they have insurance. This doesn't help the affordability of private health insurance and is only going to make things worse.

Foolish takeaway

NIB is currently trading at 22x FY17's estimated earnings with a grossed-up dividend yield of 4.24%. I think this is a pretty reasonable price to pay for a long-term investment. In the short-term the share price could be quite volatile as the market gets to grips with the health insurance industry's general woes.