Question

Hi,

Can you provide the exact answers in details for this problem:

Calculate the accounting, cash, and financial break-even quantities.

Here is the problem:

Consider a project to supply Detroit with 27,000 tons of machine screws annually for automobile production. You will need an initial $5,300,000 investment in threading equipment to get the project started; the project will last for 6 years. The accounting department estimates that annual fixed costs will be $1,275,000 and that variable costs should be $240 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the 6-year project life. It also estimates a salvage value of $650,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $350 per ton. The engineering department estimates you will need an initial net working capital investment of $510,000. 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.

Thank you,

Carol

Answer 1

1)	Contribution margin per unit = 350-240 =	$                 110
	Fixed costs = Depreciation+Other fixed operating cost = 5300000/6+1275000 =	$     21,58,333
	Accounting BEP in units = Total fixed costs/CM unit = 2158333/110 =	19621	Units
2)	Cash BEP in units = Cash fixed costs/CM unit = 1275000/110 =	11591	Units
3)	Financial BEP in units, is the number of units that will result in 0 NPV.
	The PV of known Cash flows are:
	INITIAL INVESTMENT:
	Cost of the equipment	$     53,00,000
	Increase in NWC	$        5,10,000
	Total initial investment	$     58,10,000
	TERMINAL NON OPERATING CASH INFLOWS:
	After tax salvage value = 650000*(1-25%) =	$        4,87,500
	PV of after tax salvage value = 487500/1.14^6 =	$        2,22,098
	PV of after tax fixed costs = 1275000*75%*(1.14^6-1)/(0.14*1.14^6) =	$     37,18,538
	PV OF DEPRECIATION TAX SHIELD:
	= (5300000/6)*25%*(1.14^6-1)/(0.14*1.14^6) =	$        8,58,747
	NPV of known cash flows = -5810000+222098+858747 =	$    -84,47,693
	The PV of the after tax annual contribution margin should be	$     84,47,693
	Annual after tax contribution margin = 8447693*0.14*1.14^6/(1.14^6-1) =	$     21,72,388
	Before tax contribution margin = 1216138/75% =	$     28,96,517
	Number of units to be sold = 2896517/110 =	26332	Units
	CHECK:
	Total CM = 26332*110 =	$     28,96,517
	Depreciation = 5300000/6 =	$        8,83,333
	Other fixed costs	$     12,75,000
	NOI	$        7,38,183
	Tax at 25%	$        1,84,546
	NOPAT	$        5,53,638
	Add: Depreciation	$        8,83,333
	OCF	$     14,36,971
	PV of OCF = 1436971*(1.14^6-1)/(0.14*1.14^6) =	$     55,87,902
	PV of after tax salvage value = 487500/1.14^6 =	$        2,22,098
	Total PV of cash inflows	$     58,10,001
	Less: Initial investment	$     58,10,000
	NPV	$                      1
		Almost 0