Question

Ayden’s Toys, Inc., just purchased a $490,000 machine to produce toy cars. The machine will be fully depreciated by the straight-line method over its 7-year economic life. Each toy sells for $22. The variable cost per toy is $7 and the firm incurs fixed costs of $350,000 per year. The corporate tax rate for the company is 21 percent. The appropriate discount rate is 9 percent. What is the financial break-even point for the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Solution:

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

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

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 = $ 22   ; Let the units of sales be “x” units

Thus sales value = $ 22 * x = 22x

Variable cost per unit = $ 7   ; Let the units of sales be “x” units

Thus total variable costs = $ 7 * x = 7x

Cost of Machine = Cost of asset = $ 490,000

No. of years of economic life = 7 years

Thus annual straight line depreciation = $ 490,000 / 7 = $ 70,000

Fixed Cost = $ 350,000 ; Tax rate = 21 % = 0.21

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

= [ ( 22x – 7x - $ 350,000 - $ 70,000 ) * ( 1 - 0.21 ) ] + $ 70,000

= [ ( 15x - $ 420,000 ) * 0.79 ) ] + $ 70,000                   

= [ 11.85x - $ 331,800 ] + $ 70,000                                  

= 11.85x - $ 261,800

Thus the annual after tax cash inflows = 11.85x - $ 261,800

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 = 7 Years

The present value factor at 9 % for seven years is = PVIFA(9 %, 7) = 5.032953

Thus the present value of after tax cash inflows of the project = Annual after tax cash inflows * PVIFA(9 %, 7)

= ( 11.85x - $ 261,800 ) * 5.032953

= 59.640491x – $ 1,317,627.0522

The present value of after tax cash inflows of the project = = 59.640491x – $ 1,317,627.0522

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

59.640491x – $ 1,317,627.0522 = $ 490,000

59.640491x = $ 1,317,627.0522 + $ 490,000

59.640491x = $ 1,807,627.0522

x = $ 1,807,627.0522 / 59.640491

x = 30308.721793

x = 30,308.72 units ( when rounded off to two decimal places )

Thus the financial break even point for the project = 30,308.72 units