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We present a re-analysis of the XMM-Newton and NuSTAR observing campaign forthe well-studied, X-ray-bright AGN MCG-06-30-15. In particular, we consider adisc model with finite thickness. By fitting the disc reflection spectra in thedata, we obtain a black hole spin of 0.87--0.99 (90\% confidence range) aftertaking the thickness of the disc into consideration. Spectral models with agrid of mass accretion rate from 0 to $30\%\dot{M}_{\rm Edd}$ are calculatedfor MCG-06-30-15. This result is obtained by considering a free disc reflectionfraction parameter $f_{\rm refl}$ and is consistent with previous measurementsbased on razor-thin disc models. Besides, an isotropic, point-like geometry,i.e. the `lamppost' geometry, is assumed for the corona in our model. We findthat such a geometry overestimates $f_{\rm refl}$ in the data. Therefore, thindisc models with consistent `lamppost' values of $f_{\rm refl}$ provide a worsefit than ones with a free $f_{\rm refl}$ parameter. We discuss possible reasonsfor the discrepancy between the observed and theoretical values of $f_{\rmrefl}$ at the end of the paper. Modifications for the over-simplified lamppostmodel might be needed when the thickness of the thin disc is considered infuture work.

Black Hole Spin Measurements Based on a Thin Disc Model with Finite Thickness I. An example study of MCG-06-30-15