Question

Consider a project to supply Detroit with 25,000 tons of machine screws annually for automobile production. You will need an initial $4,500,000 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 $1,075,000 and that variable costs should be $200 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 $450,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $302 per ton. The engineering department estimates you will need an initial net working capital investment of $430,000. 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

Cash Break Even Point (BEP)= Fixed costs- Non-cash expenses/Selling price per unit - variable cost per unit
Accounting BEP=Fixed Cost/(Selling price per unit - variable cost per unit)
Financial BEP=(Gross profit - cost of sales - operating expenses)/No. of outstanding common shares
Proposed quantity of machine screws to be supplied to Detroit	25,000	tons
Initial investment in threading equipment	45,00,000	$
Life of threading equipment	5	years
Fixed cost	10,75,000	$
Variable cost per ton	200	$
salvage value	4,50,000	$
Method of depreciation	straight line
Therefore depreciation per annum=(4500000-450000)/5	8,10,000	$
initial net working capital investment	4,30,000	$
selling price per ton	302	$
required rate of return	11%
Tax rate	22%
Pre-tax rate of return=11%/(1-tax rate)	14%
Fixed costs = Fixed cost + Depreciation	18,85,000
Therefore Accounting BEP=1885000/(302-200)	18,480	units
Cash BEP=Fixed cost excluding depreciation as depreciation is non cash expense/(Selling price per unit-variable cost per unit)
=1075000/(302-200)	10,539	units
Financial BEP
The PV of the Operating Cash Flow (OCF) must be equal to the initial investment at the financial breakeven since the NPV is zero at the break even point, so
Initial investment=OCF(PVIFA^r,n)
Here initial investment=investment on threading machine+investment on net working capital
=(4,500,000+430,000)=OCF(PVIFA^14%,5)	Note: Please refer to working below for PVIFA calculation
=OCF=(4,500,000+430,000)/3.433081
Therefore OCF=1,436,028
We can now use this OCF in the financial breakeven equation to find the financial breakeven sales quantity
Financial Break even unit=Fixed Cost+OCF/(Selling price per unit-Variable cost per unit)
=1,075,000+1,436,028/(302-200)
24,618	units
	Working Construct a table for calculating present value interest factor of annuity (PVIFA) using the following formula PVIFA=1-(1+R)^-N/R 0.01 0.02           0.03           0.04           0.05           0.06           0.07           0.08           0.09           0.10           0.11                  0.12           0.13                   0.14 n/i 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 1 0.990099 0.980392 0.970874 0.961538 0.952381 0.943396 0.934579 0.925926 0.917431 0.909091 0.900901 0.892857143 0.884956 0.877192982 2 1.970395 1.941561 1.91347 1.886095 1.85941 1.833393 1.808018 1.783265 1.759111 1.735537 1.712523 1.69005102 1.668102 1.646660511 3 2.940985 2.883883 2.828611 2.775091 2.723248 2.673012 2.624316 2.577097 2.531295 2.486852 2.443715 2.401831268 2.361153 2.321632027 4 3.901966 3.807729 3.717098 3.629895 3.545951 3.465106 3.387211 3.312127 3.23972 3.169865 3.102446 3.037349347 2.974471 2.913712304 5 4.853431 4.71346 4.579707 4.451822 4.329477 4.212364 4.100197 3.99271 3.889651 3.790787 3.695897 3.604776202 3.517231 3.433080969