Question

Derby Phones is considering the introduction of a new model of headphones with the following price and cost characteristics.

Sales price	$	21	per unit
Variable costs		9	per unit
Fixed costs		26,000	per month

Assume that the projected number of units sold for the month is 6,000. Consider requirements (b), (c), and (d) independently of each other.

Required:

a. What will the operating profit be?

b. What is the impact on operating profit if the sales price decreases by 10 percent? Increases by 20 percent?

c. What is the impact on operating profit if variable costs per unit decrease by 10 percent? Increase by 20 percent?

d. Suppose that fixed costs for the year are 10 percent lower than projected, and variable costs per unit are 10 percent higher than projected. What impact will these cost changes have on operating profit for the year? Will profit go up? Down? By how much?

Answer 1

a.  

Operating profit = (Sales price - variable cost) * units - Fixed cost

= ($21 - $9) * 6,000 - $26,000

= $72,000 - $26,000

= $46,000

b.

Sales price decrease by 10%

New sales price = $21* 0.9 = $18.90

Operating profit = (Sales price - variable cost) * units - Fixed cost

= ($18.90 - $9) * 6,000 - $26,000

= $59,400 - $26,000

= $33,400

Operating profit decreases by ($46,000 - $33,400) $12,600

Sales price increases by 20%

New sales price = $21 * 1.20 = $25.20

Operating profit = ($25.20 - $9) * 6,000 - $26,000

= $97,200 - $26,000

= $71,200

Operating product increases by ($71,200 - $46,000) $25,200

c.

Variable cost per unit decrease by 10%

New variable cost = $9 * 0.9 = $8.10

Operating profit = ($21 - $8.10) *6,000 - $26,000

= $77,400 - $26,000

= $51,400

Operating profit increases by ($51,400 - $46,000) $5,400

Variable cost increases by 20%

New variable cost = $9 * 1.20 = 10.80

Operating profit = ($21 - $10.80)* 6,000 - $26,000

= $61,200 - $26,000

= $35,200

Operating profit decreases by ($46,000 - $35,200) $10,800

d.

New fixed cost = $26,000 * 0.90 = $23,400

New variable cost = $9 * 1.1 = $9.9

Operating profit = ($21 - $9.9) * 6,000 - $23,400

= $66,600 - $23,400

= $43,200

Operating profit go down by ($46,000 - $43,200) $2,800