How many units of TEES and ROOS would the company have to produce and sell to the above customer in order to maintain the normal operating income after taxes ($275,000)?
Note: Contribution Margin/Unit = Revenue/Unit – Variable Costs/Unit
In this case, Overhead Costs, Direct Materials, Direct Labor, and Machine Hours are all Variable Costs
“B” Coefficient (Production/Overhead Costs)
Direct Labor Hours
$18.20 X 2.5 hours/unit = $45.50/unit
$18.20 X 4.0 hours/unit = $72.80/unit
$21.40 X 0.6 hours/unit = $12.84/unit
$21.40 X 0.2 hours/unit = $4.28/unit
Now that we have determined the Contribution Margin/Unit of the two products called “TEES” and “ROOS” available to produce and sell, we must determine the number of units of “TEES” and “ROOS” using the operating income of $275,000 after taxes (our Fixed Cost)
Note that there is a ratio of 3:7 (TEES: ROOS) and a tax rate of 45%, so factoring it into the weighted average contribution margin:
(3)(16.16) + (7)(11.42) / (3+7) = $12.842
Required Sales = [$375,000 + ($275,000 / (1-0.45)]/$12.842 = 68,135.80 = 68,136 units in total
Sales of TEES = 68,136 X 3/10 = 20,441 units
Sales of ROOS = 68,136 X 7/10 = 47,695 units
Therefore, Scooter Company would need to produce and sell 20,441 units of TEES and 47,695 units of ROOS to the customer in order to maintain the normal operating income after taxes.
i) Construct a 95% confidence interval of what operating income could be after taxes if the customer were to order a total of 60,000 units of TEES and ROOS.
y= $375,000 + $1.50 Unit + $18.20 DLH + $21.40 MH
References: MedCalc. (2013, January 2). Values of the t-distribution (two-tailed). Retrieved January 18, 2013 from http://www.medcalc.org/manual/t-distribution.php