GGM Residual Income

Can someone explain why the numerator in the GGM model, (ROE - r) x BV is the same as Earnings - (BV * r) The second formula makes sense because we are just subtracting an equity charge from earnings.

Well I mean the first one just subtracts the return they require ® from the return they receive and then multiplies that difference by the Book Value. Where as the second one subtracts the return/equtiy charge they require from the earnings they ‘receive’.

Earnings = NI = ROExBV Using substitution: (ROExBV) - (BVxR) Then using simple Algebra: BV(ROE - R)

^Thanks nielsendc, I was trying to work this out but so bust my mind was full of other crap, I just kept looking at earnings/equity and trying to come to the same conclusion, when I should of started with earnings = ROExBV