Question

Consider a project to supply Detroit with 28,000 tons of machine screws annually for automobile production. You will need an initial $4,800,000 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 $1,150,000 and that variable costs should be $215 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 $525,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $320 per ton. The engineering department estimates you will need an initial net working capital investment of $460,000. You require a return of 14 percent and face a tax rate of 25 percent on this project.

  

Calculate the accounting, cash, and financial break-even quantities. (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.)

Answer 1

Answer:

Let us calculate cash flows and NPV:

Contribution per ton = 320 - 215 = $105

Total annual fixed costs = 1150000 + 960000 = $2,110,000

Cash fixed cost = $1,150,000

(A) Accounting break-even quantity = Fixed costs /Contribution per ton = 2110000 / 105 = 20,095 Tons

Accounting break-even quantity = 20,095 Tons

(B) Cash break-even quantity = Cash Fixed costs /Contribution per ton = 1150000 / 105 = 10,952 Tons

Cash break-even quantity = 10,952 Tons

(C) Financial break-even quantity:

Financial break-even quantity is quantity at which NPV = 0

PV of annual cash flow = Initial investment - PV of terminal cash flow

= 5260000 - 443411

= $4,816,589

Annual cash flow = PV of annual cash flow / PV of $1 annuity for 5 years at 14% rate

= 4816589 / 3.433081

= 1402993.11

Let us assume financial break-even quantity = X

Hence:

(X * Contribution per unit - Fixed cost) * (1 - Tax rate) + Depreciation tax shied = 1402993.11

=> (105X - 1150000) * (1 - 25%) + 960000 * 25% =1402993.11

=> 78.75X = 1402993.11 - 240000 + 862500

=> X = 25721 Tons

Financial break-even quantity = 25,721 Tons