Question

A process plant making 5000 kg/day of a product selling for $1.75/kg has annual variable pro- duction costs of $2 million at 100 percent capacity and fixed costs of $700,000. What is the fixed cost per kilogram at the breakeven point? If the selling price of the product is increased by 10 percent, what is the dollar increase in net profit at full capacity if the income tax rate is 35 percent of gross earnings?

Answer 1

a. Breakeven point = Fixed cost / Contribution margin

Contribution margin = Selling price - Variable costs per unit

Variable cost per unit = 2,000,000 / (5,000 * 365 days)

= $1.10

Contribution margin = 1.75 - 1.10

= $0.65

Breakeven point = 700,000 / 0.65

= 1,076,923 kg

Fixed cost per kilogram at those units is:

= 700,000 / 1,076,923

= $0.65

_________________________________________________________

b. Net profit at original prices:

= (Contribution margin * units produced) - Fixed costs

= (0.65 * 5,000 * 365) - 700,000

= $486,250

Less taxes:

= 486,250 * (1 - 35%)

= $316,062.50

Net profit after price increase:

New selling price = 1.75 * 1.1

= $1.93

Net profit = ((Selling price - Variable cost) * units sold) - fixed cost

= ( (1.93 - 1.10) * 5,000 * 365) - 700,000

= $814,750

After tax:

= 814,750 * (1 - 35%)

= $529,587.50

Dollar increase:

= 529,587.50 - 316,062.50

= $213,525