Question

Break-even calculations are most often concerned with the effect of a shortfall in sales, but they could equally well focus on any other component of cash flow. Dog Days is considering a proposal to produce and market a caviar-flavored dog food. It will involve an initial investment of $90,000 that can be depreciated for tax straight-line over 10 years. In each of years 1 to 10, the project is forecast to produce sales of $100,000 and to incur variable costs of 50% of sales and fixed costs of $30,000. The corporate tax rate is 30%, and the cost of capital is 10%


a. Calculate the NPV and accounting break-even levels of fixed costs. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Please find FIXED COST at NPV breakeven! not just NPV

Answer 1

a. NPV : $ 12,614.82

Fixed costs at NPV break-even : $ 32,932.85

Fixed operating costs for accounting break-even (other than depreciation expense): $ 41,000

Solution:

Annual depreciaion = $ 90,000 / 10 = $ 9,000

Total fixed costs = $ 30,000 + $ 9,000 = $ 39,000

Contribution margin ratio = ( 1 - variable cost ratio ) = ( 1.00 -0.50) = 0.50

Accounting break-even sales revenue = Total Fixed Costs / Contribution Margin Ratio = $ 39,000 / 0.50 = $ 78,000

EBITDA = 100,000 x 50 % - $ 30,000 = $ 20,000

Annual operating cash flows after taxes = EBITDA x ( 1 -t ) + Depreciation x t = $ 20,000 x 0.70 + $ 9,000 x 0.30 = $ 16,700

PVA _{10%, n=10} = [ { 1 - ( 1/1.10 ) ¹⁰ } / 0.10) = 6.1446

NPV = $ 16,700 x 6.1446 - $ 90,000 = $ 12,614.82

NPV break-even occurs when NPV = 0

Let the fixed cost at NPV break-even be F

[( 50,000 - F ) x 0.70 + 2,700 ] x 6.1446 ] - 90,000 = 0

or ( 37,700 - 0.70 F ) x 6.1446 = 90,000

or F = $ 32, 932.85

[(50,000 - F ) x 0.70] + 9,000 ] x 6.1446 = 90,000

or (35,000 - 0.70 F + 9,000 ] = 14,647

or 44,000 - 0.70 F = 14,647

or F = $ 41,932.86