Question

Jed's Cars, Inc., just purchased a $450,000 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 $277,000 each year. The corporate tax rate for the company is 23 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 2 decimal places, e.g., 32.16.)

Answer 1

Solution

At financial breakeven point, NPV is zero.

NPV= PV of cash flows – initial investment

0 = OCF x PVIFA (n,R) – 450,000

OCF x PVIFA (n,R) = 450,000

OCF x PVIFA (6,11%)=450,000

OCF = 450,000/ 4.230537

OCF= 106,369.45

Now we need to compute quantity to arrive at this ocf.

Annual depreciation = 450,000/6

                                         = 75,000

Depreciation tax benefit = depreciation x tax rate

                                                = 75000 x 23%

                                                = 17,250

OCF = [(price – VC) x Q - FC] x(1- tax rate) + Depreciation tax benefit

106,369.45 = [(27-12) x Q -277,000](1-0.23) +26250

11.55Q = 106,369.45 -17250+ 213290

Q=302409.5/11.55

Q=26182.64