= error term ε t = year index, year 1997 - 2001 i = firm index, range 1 95 – This way of determining the and comparing this normal level to the actual level is in ‘normal’ addition used for COGS, inventory growth and production costs as variables for the other methods of manipulation. The normal level of COGS is expressed by: COGSi,t/Ai,t-1 = a0 + a1*(1/Ai,t-1) + b*(Si,t/Ai,t-1) + εt COGS = Cost of Goods Sold A = Assets S = Sales a0, a1, b = regression coefficients = error term ε t = year index, year 1997 - 2001 i = firm index, range 1 - 95 Comparable to the determination of normal level of COGS is the normal level of the change in inventory determined. The difference between the determination of the normal levels is the addition of the variable change in sales in the previous year scaled by total assets in the previous year. = a0 + a1*(1/Ai,t-1) + b1*(ΔSi,t/Ai,t-1) + b2*(ΔSi,t-1/Ai,t-1) + ΔINVi,t/Ai,t-1 εt = change in inventory ΔINV A = total assets = change in Sales ΔS a0, a1, b1, b2 = regression coefficients = error term ε t = year index, year 1997 - 2001 i = firm index, range 1 - 95 With the use of the equations of COGS and change in inventory can the equation of the production costs be determined. Roychowdhury (2006) defines production costs as the sum of COGS and the change of inventory, which is expressed in the following equation (Roychowdhury 2006, p 345): PRODi,t/Ai,t-1 = a0 + a1*(1/Ai,t-1) + b1*(Si,t/Ai,t-1) + b2*(ΔSi,t/Ai,t-1) + b3*
ε = error term t = year index, year 1997 - 2001 i = firm index, range 1 – 95 This way of determining the ‘normal’ and comparing this normal level to the actual level is in addition used for COGS, inventory growth and production costs as variables for the other methods of manipulation. The normal level of COGS is expressed by: COGSi,t/Ai,t-1 = a0 + a1*(1/Ai,t-1) + b*(Si,t/Ai,t-1) + εt COGS = Cost of Goods Sold A = Assets S = Sales a0, a1, b = regression coefficients ε = error term t = year index, year 1997 - 2001 i = firm index, range 1 - 95 Comparable to the determination of normal level of COGS is the normal level of the change in inventory determined. The difference between the determination of the normal levels is the addition of the variable change in sales in the previous year scaled by total assets in the previous year. ΔINVi,t/Ai,t-1 = a0 + a1*(1/Ai,t-1) + b1*(ΔSi,t/Ai,t-1) + b2*(ΔSi,t-1/Ai,t-1) + εt ΔINV = change in inventory A = total assets ΔS = change in Sales a0, a1, b1, b2 = regression coefficients ε = error term t = year index, year 1997 - 2001 i = firm index, range 1 - 95 With the use of the equations of COGS and change in inventory can the equation of the production costs be determined. Roychowdhury (2006) defines production costs as the sum of COGS and the change of inventory, which is expressed in the following equation (Roychowdhury 2006, p 345): PRODi,t/Ai,t-1 = a0 + a1*(1/Ai,t-1) + b1*(Si,t/Ai,t-1) + b2*(ΔSi,t/Ai,t-1) + b3*