Question

Ayden's Toys, Inc., purchased a $455,000 machine to produce toy cars. The machine will be fully depreciated by the straight-line method over its 5-year life. Each toy sells for $15. The variable cost per toy is $5 and the firm incurs fixed costs of $315,000 per year. The corporate tax rate for the company is 24 percent. The appropriate discount rate is 12 percent. What is the financial break-even point for the project?

Please Show the Work, I know it might be easy, but I appreciate it.

Answer 1

1. Initial Investment = 455000

2. calculation of depreciation and Tax saving on depreciation:

= 455000 / 5

=Depreciation = 91000

Tax saving on depreciation = 91000 x 0.24 = 21840

3. Cash inflow from Revenue. Let number of units sold be X

contribution = Selling price - Variable cost = 15-5= 10 per unit

Net cash inflows after taxes = [(Sales units x contribution per unit) - Fixed cost] x (1-taxes)

= [(X * 10) - 315000] x (1 -0.24)

= (10X -350000) x 0.76

= 7.6X - 266000

Total cash inflows after taxes = 7.6X - 266000 + 21840

7.6X - 244160

4. Equate PV of cash inflows with Initial investment to find value of x

Initial Investment = Annual after tax cashflows x Cumulative discounting factor @12% for 5 years

455000 = (7.6X - 244160) x 3.604776

126221.4351 = 7.6X - 244160

7.6X = 370381.4351

X = 48734.40 approx

Break even point of project = 48734 approx units.