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Kids Inc. just purchased a $350,000 machine to launch its 4-year project of toy

ID: 2618511 • Letter: K

Question

Kids Inc. just purchased a $350,000 machine to launch its 4-year project of toy car production. The machine will be fully depreciated to zero by the straight-line method over its 7-year economic life, and will be sold for $200,000 at the termination of the 4-year project. There is an initial net working capital investment of $80,000 that Kids Inc. can recover 92% of the amount at the termination of the project. The variable cost is $22 per toy car, and annual fixed production costs are $250,000. The expected unit price of the toy car is $40, and Kids Inc.'s marginal tax rate is 21%. The risk premium on this project is 12%. and the inflation rate and the risk-free rate are, respectively, 3% and 4% Calculate explicitly (step i) the annual break-even operating cash flow, and then (step 11) the minimum number of toy cars needed to be sold annually to justify the acceptance of this 4- year project according to the objective of a firm stated in the lecture materials. You are required to follow the 2-step procedure presented in the lecture materials but NOT the goal seek function) to answer both parts of this problem

Explanation / Answer

Machine cost = 350,000

Annual depreciation = 350,000/7 = 50,000

Salvage value at year 4 = 200,000

Book value at year 4 = 350,000 - 4*50,000 = 150,000

After-tax SV = SV - (SV - BV)*Tax = 200,000 - (200,000 - 150,000)*0.21 = 189,500

Required interest rate = 3 + 4 + 12 = 19%

Net initial investment = 350,000 + 80,000 - 189,500/1.19^4 - 80,000*0.92/1.19^4

Net initial investment = 298,800.25

Now compute equivalent annual cash flow

PV = 298,800.25, N = 4, r = 19%, FV = 0; compute PMT = 113,242.59

Annual break even cash flow = 113.242.59

Let the quantity of cars = Q, which just satisfy to breakeven.

CF = [(40 - 22)Q - 250,000]*(1 - 0.21) + 40,000*0.21

CF = (18Q - 250,000)*0.79 + 8400

CF = 113.242.59 (given from above)

18Q - 250,000 = (113,242.59 - 8400)/0.79 = 132712.14

Q = 21,261.7855 or 21,262 toys car