P $12-5$ Product pricing using the cost$-$plus approach concepts; differential analysis report for accepting additional business

Obj. $1,2,3$Twilight Lumina Company recently began production of a new product, the halogen light, which required an investment of $$1,200,000$ in assets. The costs of producing and selling $20,000$ halogen lights are estimated as follows:

Variable cost Fixed cost:

Direct materials $$30$ per unit Factory overhead $$340,000$

Direct labor $10$ Selling and admin exp $160,000$

Factory overhead $6$

Selling and admin $,$exp. $4$

Total $$50$ per Unit

Details

Variable costs per unit are Direct materials: $$30$ Direct labor: $10$ Factory overhead: $6$ Selling and admin. exp.: $4$ Total: $$50$ Fixed costs are Factory overhead: $$340,000$ Selling and admin. exp.: $160,000$

Twilight Lumina Company is currently considering establishing a selling price for the halogen light. The president of Twilight Lumina Company has decided to use the cost$-$plus approach to product pricing and has indicated that the halogen light must earn a $20\%$ rate of return on invested assets.

Instructions

$1.$ Determine the amount of desired profit from the production and sale of the halogen light.

$2.$ Assuming that the total cost concept is used, determine $($a$)$ the cost amount per unit, $($b$)$ the markup percentage, and $($c$)$ the selling price of the halogen light.

ANSWER

Check Figure: Markup percentage, $16\%$

$3.$ Assuming that the product cost concept is used, determine $($a$)$ the cost amount per unit, $($b$)$ the markup percentage $($round to the nearest two decimal places$),$ and $($c$)$ the selling price of the halogen light $($round to the nearest cent$).$

$4.$ Assuming that the variable cost concept is used, determine $($a$)$ the cost amount per unit, $($b$)$ the markup percentage, and $($c$)$ the selling price of the halogen light.

$5.$ Comment on any additional considerations that could influence establishing the selling price for the halogen light.

$6.$ Assume that $15,000$ units of the halogen light have been produced and sold during the current year. Analysis of the domestic market indicates that $2,000$ additional units of the halogen light are expected to be sold during the remainder of the year at the normal product price determined under the total cost concept. Twilight Lumina Company received an offer from Contech Inc. for $3,000$ units of the halogen light at $$52$ each. Contech Inc. will market the units in Southeast Asia under its own brand name, and no selling and administrative expenses associated with the sale will be incurred by Twilight Lumina Company. The additional business is not expected to affect the domestic sales of the halogen light, and the additional units could be produced using existing capacity.

a$.$ Prepare a differential analysis report of the proposed sale to Contech Inc.

b$.$ Based on the differential analysis report in part $($a$),$ should the proposal be accepted?