Salem Electronics currently produces two products: a programmable calculator and a tape recorder. A recent marketing study indicated that consumers would react favorably to a radio with the Salem brand name. Owner Kenneth Booth was interested in the possibility. Before any commitment was made, however, Kenneth wanted to know what the incremental fixed costs would be and how many radios must be sold to cover these costs.

In response, Betty Johnson, the marketing manager, gathered data for the current products to help in projecting overhead costs for the new product. The overhead costs based on $30,000$ direct labor hours follow. $($The high$-$low method using direct labor hours as the independent variable was used to determine the fixed and variable costs.$)$

Fixed Variable

Materials handling $ $$ $$18,000$

Power $22,000$

Engineering $100,000$

Machine costs $30,000*80,000$

Inspection $40,000$

Setups $60,000$

$*$All depreciation.

The following activity data were also gathered:

Calculators Recorders

Units produced $20,00020,000$

Direct labor hours $10,00020,000$

Machine hours $10,00010,000$

Material moves $120120$

Kilowatt$-$hours $1,0001,000$

Engineering hours $4,0001,000$

Hours of inspection $7001,400$

Number of setups $2040$

Betty was told that a plantwide overhead rate was used to assign overhead costs based on direct labor hours. She was also informed by engineering that if $20,000$ radios were produced and sold $($her projection based on her marketing study$),$ they would have the same activity data as the recorders $($use the same direct labor hours, machine hours, setups, and so on$).$

Engineering also provided the following additional estimates for the proposed product line:

Prime costs per unit $$18$

Depreciation on new equipment $18,000$

Upon receiving these estimates, Betty did some quick calculations and became quite excited. With a selling price of $$26$ and just $$18,000$ of additional fixed costs, only $4,500$ units had to be sold to break even. Since Betty was confident that $20,000$ units could be sold, she was prepared to strongly recommend the new product line.

Required:

$1.$ Reproduce Betty's break$-$even calculation using conventional cost assignments.

Variable overhead rate: $fill in the blank $1$

$4\mathrm{.}00$

per direct labor hour

Unit variable cost: $fill in the blank $2$

$22\mathrm{.}00$

Break$-$even: fill in the blank $3$

$4,500$

units

How much additional profit would be expected under this scenario, assuming that $20,000$ radios are sold?

$fill in the blank $4$

$62,000$

$2.$ Use an activity$-$based costing approach, and calculate the break$-$even point and the incremental profit that would be earned on sales of $20,000$ units. In your computation for break$-$even point, round amounts to the nearest cent and round your final answer to the nearest whole unit. In your analysis assume that the expected engineering hours, inspection hours, and setups are realized and that depreciation is a fixed cost.

I need help with #$2$