We present an analysis of Spitzer IRAC (3.6–8 μm) and MIPS (24 μm) imaging of members of the 16 Myr old open cluster NGC 1960 (M36). Models of terrestrial planet formation indicate that rocky planets are likely to achieve their final masses at around 10–30 Myr, and thus this cluster is at an interesting epoch for planet formation. We find 21 B–F5 type stars and 14 F6–K9 type stars which have 24 μm excess emission, and thus determine that >30 per cent of B–F5 type stars and >23 per cent of F6–K9 type stars in this cluster have 24 μm excess emission. These excess frequencies are similar to those observed in other clusters of similar age. Three early-type stars have excesses at near-infrared wavelengths. Analysis of their spectral energy distributions confirms that these are true debris discs and not remnant primordial or transitional discs. None of the 61 Sun-like stars has confirmed near-infrared excess, and we can place a limit on the frequency of 8 μm excess emission around Sun-like stars of <7 per cent. All of the detected excesses are consistent with emission from debris discs and are not primordial.