Question

Derby Phones is considering the introduction of a new model of headphones with the following price and cost characteristics. Sales price $ 18 per unit Variable costs 8 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

Solution

Let us list down the important values

Original sales estimate = 6000 units

Sale price per unit = $ 18

Original Fixed Cost = $ 26,000

Original Variable Cost per unit = $ 8

A)

Total Revenue = 18 x 6,000

= $ 108,000

Total Cost = Fixed + Variable Cost

= 26,000 + 8 x 6,000

= 26,000 + 48,000

= $ 74,000

Operating Profit = 108,000 - 74,000

Operating profit = $ 34,000

B)

• Operating profit when sale price is 10% lesser

i.e. sale price is 90% of 108,000 = 108,000 x 0.90

Sale price = 97,200

Operating profit = 97,200-74,000

Operating profit = $ 23,200

• Operating profit when sale price is 20% higher

i.e. sale price is 120% of 108,000 = 108,000 x 1.20

Sale price = 129,600

Operating profit = 129,600-74,000

Operating profit = $ 55,600

C)

• Operating profit when variable cost per unit is 10% lesser :

i.e. Variable cost is 90% of 48,000 = 48,000 x 0.90

Variable Cost = 43,200

Operating profit = 108,000 - (43,200+ 26,000)

Operating profit = $ 38,800

• Operating profit when Variable cost per unit is 20% Higher

i.e. Variable cost is 120% of 48,000 = 48,000 x 1.20

Variable Cost = 57,600

Operating profit = 108,000 - (57,600 + 26,000)

Operating profit = $ 24,400

D)

Fixed cost is 10% Lower than projected

i.e. Fixed Cost is 90% of 26,000 = 26,000 x 0.90 = 23,400

Variable cost is 10% higher than projected

i.e. Variable Cost is 110% of 48,000 = 48,000 x 1.10 = 52,800

Therefore Total cost = Fixed + variable cost

= 23,400 + 52,800

= 76,200

Operating profit = 108,000 - 76,200

= 31,800

Difference in operating profit between projected and modified = 34,000 - 31,800

= $2,200 lesser

Hence in this situation, the operating profit has gone down by $ 2,200.