Question

Dillon, Jones, and Kline, Ltd. is studying the acquisition of two electrical component insertion systems for producing its sole product, the universal gismo. Data relevant to the systems follow. Model A: Variable costs, $16.00 per unit Annual fixed costs, $986,500 Model B: Variable costs, $11.80 per unit Annual fixed costs, $1,113,700 The selling price is $66 per unit for the universal gismo, which is subject to a 10 percent sales commission. (In the following requirements, ignore income taxes.)

1. How many units must the company sell to break even if Model A is selected? 2. Calculate the net income of the two systems if sales and production are expected to average 46,000 units per year. 3. Assume Model B requires the purchase of additional equipment that is not reflected in the preceding figures. The equipment will cost $420,000 and will be depreciated over a five-year life by the straight-line method. How many units must the company sell to earn $975,000 of income if Model B is selected? As in requirement (2), sales and production are expected to average 46,000 units per year. 4. Ignoring the information presented in part (3), at what volume level will the annual total cost of each system be equal?

Answer 1

1)Sales commission: 66* 10% = 6.6

Variable cost for model A: 16+6.6 = 22.6

BEP (units) =Fixed cost /(price -variable cost)

          = 986500 / (66- 22.6)

             = 986500 / 43.4

              = 22730.41 units [rounded to 22731 units]

2)

	MOdel A	Model B
sales [46000*66]	3036000	3036000
less:variable cost	(1039600)    [22.6*46000]	(846400)    [18.4*46000]
contribution	1996400	2189600
fixed cost	(986500)	(1113700)
Net Income	1009900	1075900

3)Annual depreciation : cost /useful life

         = 420000/ 5 = 84000

Total fixed cost : 1113700+84000= 1197700

variable cost : 11.8+6.6 = 18.4

Desired unit sales for model B: [fixed cost+ desired profit ]/[price- variable cost]

     =[1197700+975000]/[66-18.4]

     = 2172700/47.6

     = 45644.96 units [rounded to 45645]

4)Indifference point : [change in fixed cost ]/[change in variable cost

        =[1113700-986500]/[22.6-18.4]

          = 127200/4.2

            = 30285.71   [rounded to 30286 units]