Question

Problem 1 You are consulted by Inventors, Inc., a group of scientists who have designed a new product. They have estimates of the costs of materials, labor, overhead, and other expenses for 2018 but need to know how much to charge for each unit to earn a profit in 2018 equal to 15% of their estimated investment of $4,000,000 (ignore income taxes). Their plans indicate that each unit of the new product requires the following: Direct Material 3 lb. of a material costing $11.25 per lb. Direct labor 4 hrs. of a welder's time at $16.85 per hr. 2 hrs. of an operator's time at $15.15 per hr. Major items of production overhead include annual rent of $96,000 on the factory building, $25,000 of machinery depreciation, and indirect material of $22,500. Other production overhead is an estimated 40% of total direct labor costs. Selling expenses are an estimated 25% of total sales, and non-factory administrative expenses are 15% of total sales. The consensus at Inventors is that, during 2018, 14,000 units of product should be produced for selling and 3,000 units should be produced for the next year's beginning inventory. Also, an extra 9,000 pounds of material should be purchased as beginning materials inventory for the next year. Because of the nature of the manufacturing process, all units started must be completed, so work in process inventories are negligible. Required: 1. Compute the cost per unit using the assumptions provided above. 2. Determine the selling price necessary to earn the desired profit.
Solutions are given, please show how they were calculated. Thank you!

Answer 1

1. Calculation of cost per unit :

Materials:
Inward:
for production	17000 units*(3*11.25)	573750
Extra	9000lbs *11.25	101250
Total		675000
Indirect Material (given)		22500
Direct Material for production	573750-22500	551250
Closing stock (i.e. Extra)		101250
WIP:
Materials	as calculated above	551250	551250
Labour
(a)	17000*4*16.85	1145800
(b)	17000*2*15.15	515100	1660900
OH
Rent		96000
Depreciation		25000
Indirect Material		22500
Production O/H	40%(1660900)	664360	807860
Total Cost of Production			3020010
No. of units produced			17000
Cost p.u	3020010/17000		177.65

2. Calculation of Selling Price p.u.

Required Profit	4000000*15%		600000
Cost of Goods sold	177.65*14000		2487067
Selling Expense	25% (sales)		0.25 * 14000x	3500	x
Non-Factory Admin Expense	15% (sales)		0.15 *14000 x	2100	x
Sales	let S.P p.u =x		14000x
Profit + Costs =Sales
Therefore,
600000+2487067+3500x+2100x=14000x
3087067=8400x
x=3087067/8400
x=367.51