Canton Corp. produces a part using an expensive proprietary machine that can only be leased. The leasing company offers two contracts. The first (unit-rate lease) is one where Canton would pay $4 per unit produced, regardless of the number of units. The second lease option (flat-rate lease) is one where Canton would pay $60,000 per month, regardless of the number produced. The lease will run one year and the lease option chosen cannot be changed during the lease. All other lease terms are the same.

The part sells for $40 per unit and unit variable cost (excluding any machine lease costs) are $20. Monthly fixed costs (excluding any machine lease costs) are $200,000.

a. What is the monthly break-even level assuming:

1. The unit-rate lease?
2. The flat-rate lease?
b. At what volume would the operating profit be the same regardless of the lease option chosen?

c. Assume monthly volume of 20,000 units. What is the operating leverage assuming:

1. The unit-rate lease?
2. The flat-rate lease?
d. Assume monthly volume of 20,000 units. What is the margin of safety percentage assuming:

1. The unit-rate lease?
2. The flat-rate lease?

Explanation:

a)

1. Unit rate lease

Unit Contribution margin = Unit Selling price – Unit Variable cost

= 40 - 24 =  $16

Break even point (units) = Fixed cost/Contribution margin per unit

= 200,000/16  = 12,500

2. Flat rate lease

Unit Contribution margin = Unit Selling price – Unit Variable cost

= 40 - 20  = $20

Break even point (units) = Fixed cost/Contribution margin per unit

= 260,000/20  = 13,000

b.)

Let at X units produced profit margin is same under both the lease options

40X - 24X - 200,000 = 40X - 20X - 260,000

16X - 200,000 = 20X - 260,000

4X = 60,000

X = 15,000

If 15,000 units are produced, profit margin will be same under both the lease options.

c)

1. Unit rate lease

Contribution margin income statement

Sales (20,000 x 40)  800,000

Variable cost (20,000 x 24)  - 480,000

Contribution margin  320,000

Fixed cost  - 200,000

Operating income  120,000

Operating leverage = Contribution margin/Operating income

= 320,000/120,000  = 2.67

2. Flat rate lease

Contribution margin income statement

Sales (20,000 x 40)  800,000

Variable cost (20,000 x 20)  - 400,000

Contribution margin  400,000

Fixed cost  - 260,000

Operating income  140,000

Operating leverage = Contribution margin/Operating income

= 400,000/140,000  = 2.86

d)

1. Unit rate lease

Margin of safety = Actual sales - Break even sales

= 20,000 x 40 - 12,500 x 40

= 800,000 - 500,000

= $300,000

Margin of safety (%) = Margin of safety/Actual sales

= 300,000/800,000  = 37.5%

2. Flat rate lease

Margin of safety = Actual sales - Break even sales

= 20,000 x 40 - 13,000 x 40

= 800,000 - 520,000

= $280,000

Margin of safety (%) = Margin of safety/Actual sales

= 280,000/800,000  

= 35%

a manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. at the end of december, the company wishes to forecast sales for january. the estimate of trend through november has been 200 additional boards sold per month. average sales have been around 1000 units per month. the demand for december was 1100 units. the company uses α = 0.20 and β = 0.10. make a forecast including trend for the month of january.