Question

L.J.’s Toys Inc. just purchased a $510,000 machine to produce toy cars. The machine will be fully depreciated by the straight-line method over its six-year economic life. Each toy sells for $27. The variable cost per toy is $12, and the firm incurs fixed costs of $287,000 each year. The corporate tax rate for the company is 35 percent. The appropriate discount rate is 11 percent. What is the financial break-even point for the project? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Answer 1

Cost of machine = $ 510,000

Life of machine,n = 6 years

Selling Price of toy = $ 27

Fixed Cost = $ 287,000 per year

Variable Cost = $ 287,000

Tax Rate = 35 %

Discount rate, r = 11 %

Depreciation is a non-cash expense and the owner of machine can save tax on it.

Annual Depreciation = Cost of Machine / Life of Machine = $ 510,000 / 6 = $ 85000

Year	Fixed Cost	Depreciation	Tax Savings ( 35% 0f Depreciation)	Net Cash Flows = Tax Savings - Fixed Cost	Discounted Cash Flows = { NCF / ( 1 + r ) ^ n }
1	$287,000	$85,000	$29,750	($257,250)	-231757
2	$287,000	$85,000	$29,750	($257,250)	-208790
3	$287,000	$85,000	$29,750	($257,250)	-188099
4	$287,000	$85,000	$29,750	($257,250)	-169459
5	$287,000	$85,000	$29,750	($257,250)	-152665
6	$287,000	$85,000	$29,750	($257,250)	-137536

Note: n is the corresponding year ( 1 - 6) , r is the discount rate

Sum of Discounted Cash Flows = 1,088,306

Total Fixed Cost incurred during life of machine = Cost of Machine + Sum of Discounted Cash Flows

   = $ 510,000 + $ 1,088,306 = $ 1,598,306

$Break Even Point = \frac{Total Fixed Cost}{Sales Price Per Unit- Variable Cost Per Unit}$

= $ 1,598,306 / ( $ 27 - $ 12 )

= $ 1,598,306 / $ 15

= 106553.73

= 1,06,554 units