Question

Ayden's Toys, Inc., just purchased a $332,000 machine to produce toy cars. The machine will be fully depreciated by the straight-line method over its four-year economic life. Each toy sells for $23. The variable cost per toy is $10, and the firm incurs fixed costs of $285,000 each year. The corporate tax rate for the company is 40 percent. The appropriate discount rate is 10 percent. What is the financial break-even point for the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Break-even point _____ units

Answer 1

Let X = Number of units need to break even

Contribution = X * (23 - 10) = 13X

Earnings before depreciation and tax = 13X - 285000

After tax earnings = (13X - 285000) ( 1 - 0.40) = 7.8X - 171000

OCF = Operating cash flow = (7.8X - 171000) + 83000 * 0.4 = 7.8X -137800

Tax advantage with depreciation = 332000 / 4 years ; and 83000 * 0.40 is the tax advantage is added to profits after tax to get the operating cashflow.

PV ( OCF) = (7.8X - 137800) * [ 1 - (1.10)^-4 / 0.10 ] = 332000 ......... this is the condition for Financial Break even

7.8X - 137800 * (3.169865) = 332000

7.8X - 137800 = 332000 / 3.169865 = 104736

7.8 X = 242536

X = 31094.40 Units ......... is the financial break even point