Question

James, Inc., has purchased a brand new machine to produce its High Flight line of shoes. The machine has an economic life of 6 years. The depreciation schedule for the machine is straight-line with no salvage value. The machine costs $636,000. The sales price per pair of shoes is $94, while the variable cost is $42. Fixed costs of $330,000 per year are attributed to the machine. The corporate tax rate is 24 percent and the appropriate discount rate is 9 percent.

  

What is the financial break-even point?

Answer 1

Solution:

The financial break-even point for the machine is the point where its present value of cash inflows is equal to the Initial Investment in the machine

Thus it is that level of sales where the after tax discounted cash inflows is equal to the Initial Investment in the machine.

Calculation of Annual After cash Inflows :

The formula for calculating the annual after tax cash Inflow is

= [ (Sales - Variable cost - Fixed Cost - Depreciation ) * ( 1 - Tax rate ) ] + Depreciation

As per the information given in the question we have

Sales price per unit = $ 94   ; Let the units of sales be “x” units

Thus sales value = $ 94 * x = 94x

Variable cost per unit = $ 42   ; Let the units of sales be “x” units

Thus total variable costs = $ 42 * x = 42x

Cost of Machine = $ 636,000

No. of years of economic life = 6 years

Thus annual straight line depreciation = Cost of Machine / No. of years of economic life

= $ 636,000 / 6 = $ 106,000

Fixed Cost = $ 330,000 ; Tax rate = 24 % = 0.24

Applying the above information we have the annual after tax cash inflows

= [ ( 94x – 42x - $ 330,000 - $ 106,000 ) * ( 1 - 0.24 ) ] + $ 106,000

= [ ( 52x - $ 436,000 ) * 0.76 ) ] + $ 106,000                   

= [ 39.52x - $ 331,360 ] + $ 106,000                                  

= 39.52x - $ 225,360

Thus the annual after tax cash inflows = 39.52x - $ 225,360

Calculation of present value of after cash Inflows :

As per the information given in the question

Discount rate for the project = 9 %    ; No. of years of the project = 6 Years

The present value factor at 9 % for six years is = PVIFA(9 %, 6) = 4.485919

Thus the present value of after tax cash inflows of the project = Annual after tax cash inflows * PVIFA(9 %, 6)

= ( 39.52x - $ 225,360 ) * 4.485919

= 177.283503x – $ 1,010,946.613494

The present value of after tax cash inflows of the project = 177.283503x – $ 1,010,946.613494

Calculation of Financial break even point :

We know that at the Financial break even point the present value of after tax cash inflow of the project = Initial Investment

Thus we have

177.283503x – $ 1,010,946.613494 = $ 636,000

177.283503x = $ 1,010,946.613494 + $ 636,000

177.283503x = $ 1,646,946.613494

x = $ 1,646,946.613494 / 177.283503

x = 9,289.903395

x = 9,289.90 units ( when rounded off to two decimal places )

x = 9,290 units ( when rounded off to the nearest whole number )

Thus the financial break even point = 9,290 units