Question

Consider a project to supply Detroit with 27,000 tons of machine screws annually for automobile production. You will need an initial $5,000,000 investment in threading equipment to get the project started; the project will last for 5 years. The accounting department estimates that annual fixed costs will be $1,200,000 and that variable costs should be $225 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the 5-year project life. It also estimates a salvage value of $575,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $332 per ton. The engineering department estimates you will need an initial net working capital investment of $480,000. You require a return of 11 percent and face a tax rate of 22 percent on this project. Calculate the accounting, cash, and financial break-even quantities

Answer 1

S = 332; V = 225, F = 1,200,000, Annual depreciation = D = 5,000,000 / 5 = 1,000,000, T = 22%

Let Q be the accounting break even quantity

Hence, Accounting profit = (S - V) x Q - (F + D) = 0

Hence, (332 - 225) x Q - (1,200,000 + 1,000,000) = 0

Hence accounting break even quantity = Q = 2,200,000 / 107 = 20,561 tons

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Let Q* be the cash break even quantity

Cash flow = NOPAT + D = [(S - V) x Q* - (F + D)] x (1 - T) + D = 0

Hence, [(332 - 225) x Q* - (1,200,000 + 1,000,000)] x (1 - 22%) + 1,000,000 = 0

Hence, (107Q* - 2,200,000) x 78% + 1,000,000 = 0

Hence, Q* = [-1,000,000 / 78% + 2,200,000] / 107 = 8,579 ton

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Let Q be the financial break even quantity. At this quantity NPV should be zero

Annual operating cash flows = C = NOPAT + D = [(S - V) x Q - (F + D)] x (1 - T) + D = [(332 - 225) x Q - (1,200,000 + 1,000,000)] x (1 - 22%) + 1,000,000 = 83.56Q - 716,000

Terminal cash flows = Ct = Post tax salvage value + release of working capital = 575,000 x (1 - 22%) + 480,000 = $ 928,500

Initial investment, C0 = machine cost + working capital = 5,000,000 + 480,000 = 5,480,000

Annuity factor over five years = A(1, r, n) = A (1, 0.11, 5) = 3.6959

PV factor for year 5 = PV(1, r, n) = PV (1, 0.11, 5) = 0.5935

Hence NPV = - C0 + C x Annuity factor over five years + Ct x PV factor for year 5 = 0

Hence, -5,480,000 + (83.56Q - 716,000) x 3.6959 + 928,500 x 0.5935 = 0

308.4596Q - 7,575,242.71 = 0

Hence, Q = 7,575,242.71 / 308.4596 = 24,558 Tons