Question

The capital required for a start-up is $2 million. This capital can be depreciated by the straight-line method over 10 years. It’s fixed and variable costs total $250,000 per year. The company is expected to have a 10-year life. The marginal tax rate is 40%. It expects to pay $450,000 in feedstock costs per year. What annual revenue is needed for a 10% return on the business?

Answer 1

Working notes:

• Annual depreciation = $2,000,000 / 10 = $200,000
• Taxable income (TI) = Revenue (R) - Total cost - Depreciation = R - 250,000 - 450,000 - 200,000 = R - 900,000
• After-tax income = TI x (1 - tax rate) = (R - 900,000) x (1 - 0.4) = (R - 900,000) x 0.6 = 0.6R - 540,000
• After-tax cash flow = After-tax income + Depreciation = 0.6R - 540,000 + 200,000 = 0.6R - 340,000

Therefore,

Initial cost = PW of after-tax cash flow

(0.6R - 340,000) x P/A(10%, 10) = 2,000,000

(0.6R - 340,000) x 6.1446 = 2,000,000

0.6R - 340,000 = 325,489

0.6R = 665,489

R = $1,109,148.41