Grey Company is considering replacing its existing cutting machine with a new machine that,according to the manufacturer,is more efficient in terms of energy consumption-a variable cost of production.In this regard,it would like to do some financial planning,including "what-if" analysis.Budgeted information regarding the two machines is as follows:

Question

Quizplus · Accepted Answer

Required:
(1)Determine the sales volume at which the costs are the same for both machines.
(2)What amount of sales,in dollars,for the new machine would produce a 10% profit margin (i.e.ratio of profit to sales = 10%)?
Please see Feedback for answers.
 Feedback: (1)Total cost equation (per month),existing machine: TC = $32,000 + $44X,where X = output Total cost equation (per month),new machine: TC = $40,000 + $40X,where X = output
Setting the two equations equal,we have: 11ea6e70_bce5_cace_8f54_1763b6b558fc_TB1699_00 (2)Required sales level,in dollars,to generate a target pre-tax profit of 10% on sales,under the new machine:
Let X = required sales level (in dollars)to earn targeted profit
Let Q = required sales volume in units to earn targeted profit
Then,given a sales price of $55 per unit,we have: X = $55Q
The basic profit equation is:
CM - FC = pre-tax profit
($55 - $40)Q - $40,000 = (10%)$55Q
$15Q - $5.5Q = $40,000
Q = [40,000/9.50] = 4,211 units 11ea6e70_bce5_cacf_8f54_21228bf8e6c9_TB1699_00 R = $55Q = $55 per unit x 4,211 units = $231,605

Grey Company Is Considering Replacing Its Existing Cutting Machine with a New