Recently, someone on this board stated that Mgt wanted to reduce total costs by 25% and they further said that if all costs were absorbed by labor then the labor cost reduction would be 50%. Well, it appears it's actually worse than that. By the way he also said that labor costs were 40% of total costs. It turns out that if all this is true then the labor reduction will be, sadly enough, 62.5%. Here is the breakdown in numbers:
where T = Total Cost
L = Labor Cost
O = Other Cost
r = percent Reduction in Labor Cost if Total Cost is
reduced by 25%
T - .25T = L - r(L) + O
.75T = L(1 - r) + O
= L(1 - r) + T - L
= L(1 - r) - L + T
= L((1 - r) - 1) +T
0 = L((1 - r) - 1) + T - .75T
-L(1 - r - 1) = .25T
rL = .25T
r = .25( T/L ) where L = .4T (Labor is 40% of Total)
r = .25 (T/.4T)
r = .25/.4
r = .625
r = 62.5%
where T = Total Cost
L = Labor Cost
O = Other Cost
r = percent Reduction in Labor Cost if Total Cost is
reduced by 25%
T - .25T = L - r(L) + O
.75T = L(1 - r) + O
= L(1 - r) + T - L
= L(1 - r) - L + T
= L((1 - r) - 1) +T
0 = L((1 - r) - 1) + T - .75T
-L(1 - r - 1) = .25T
rL = .25T
r = .25( T/L ) where L = .4T (Labor is 40% of Total)
r = .25 (T/.4T)
r = .25/.4
r = .625
r = 62.5%