Frost damage or drought?

My coprosma which I planted in autumn last year has developed dead, brown tips on its leaves. The whole plant is affected but I'm unsure if it has been caused by frost damage over the winter or a lack of water. There are other shrubs in the bed which seem to be thriving so I'm not convinced the leaf damage has been caused by drought. Any diagnosis would be welcome. Thanks. 

At first sight this seems to be frost damage or wind damage. This might have happened during the cold spell in February. However, we have had some dry periods after that so at root level it could be too dry. In that case it could do with watering.

How are the new leaves developing? Are they glossy and firm? It seems to me that I can see some new growth, which looks healthy, but with the dark foliage it is hard to tell.