CVP, sensitivity analysis

The Derby Shoe Company produces its famous shoe, the Divine Loafer that sells for $70 per pair. Operating income for 2013 is as follows:

Sales revenue ($70 per pair) $350,000
Variable cost ($30 per pair) 150,000
Contribution margin 200,000
Fixed cost 100,000
Operating income $100,000

Derby Shoe Company would like to increase its profitability over the next year by at least 25%. To do so, the company is considering the following options:

Required:
1. Replace a portion of its variable labor with an automated machining process. This would result in a 20% decrease in variable cost per unit but a 15% increase in fixed costs. Sales would remain the same.
2. Spend $25,000 on a new advertising campaign, which would increase sales by 10%.
3. Increase both selling price by $10 per unit and variable costs by $8 per unit by using a higher-quality leather material in the production of its shoes. The higher-priced shoe would cause demand to drop by approximately 20%.
4. Add a second manufacturing facility that would double Derby's fixed costs but would increase sales by 60%.

Evaluate each of the alternatives considered by Derby Shoes. Do any of the options meet or exceed Derby's targeted increase in income of 25%? What should Derby do?

Contribution margin per pair of shoes = $70 – $30 = $40
Fixed costs = $100,000
Units sold = Total sales ÷ Selling price = $350,000 ÷ $70 per pair = 5,000 pairs of shoes

1. Variable costs decrease by 20%; Fixed costs increase by 15%
Sales revenues 5,000 $70 $350,000
Variable costs 5,000 $30 (1 – 0.20) 120,000
Contribution margin 230,000
Fixed costs $100,000 1.15 115,000
Operating income $115,000

2. Increase advertising (fixed costs) by $30,000; Increase sales 20%
Sales revenues 5,000 1.10 $70.00 $385,000
Variable costs 5,000 1.10 $30.00 165,000
Contribution margin 220,000
Fixed costs ($100,000 + $25,000) 125,000
Operating income $ 95,000

3. Increase selling price by $10.00; Sales decrease 20%; Variable costs increase by $8
Sales revenues 5,000 0.80 ($70 + $10) $320,000
Variable costs 5,000 0.80 ($30 + $8) 152,000
Contribution margin 168,000
Fixed costs 100,000
Operating income $ 68,000

4. Double fixed costs; Increase sales by 60%
Sales revenues 5,000 1.60 $70 $560,000
Variable costs 5,000 1.60 $30 240,000
Contribution margin 320,000
Fixed costs $100,000 2 200,000
Operating income $120,000

Alternative 4 yields the highest operating income. Choosing alternative 4 will give Derby a 20% increase in operating income [($120,000 – $100,000)/$100,000 = 20%], which is less than the company's 25% targeted increase. Alternative 1also generates more operating income for Derby, but it too does not meet Derby's target of 25% increase in operating income. Alternatives 2 and 3 actually result in lower operating income than under Derby's current cost structure. There is no reason, however, for Derby to think of these alternatives as being mutually exclusive. For example, Derby can combine actions 1 and 4, automate the machining process and decrease variable costs by 20% while increasing fixed costs by 15%. This will result in a 38% increase in operating income as follows:

Sales revenue 5,000 1.60 $70 $560,000
Variable costs 5,000 1.60 $30 × (1 – 0.20) 192,000
Contribution margin 368,000
Fixed costs $200,000 1.15 230,000
Operating income $138,000

The point of this problem is that managers always need to consider broader rather than narrower alternatives to meet ambitious or stretch goals.