Question

Dan’s Motor Works is analyzing a 4-year project that has estimated annual sales of 3,400 units at a sales price per unit of $54. Fixed costs are estimated at $22,000 and estimated variable costs per unit are $37.80. The initial cost of the project is $92,000. What sales quantity is required for the firm to breakeven on a financial basis if the required return is 16.80 percent?

Answer 1

Solution:

The breakeven on a financial basis 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 )

As per the information given in the question we have

Sales price per unit = $ 54   ; Let the units of sales be “x” units

Thus sales value = $ 54 * x = 54x

Variable cost per unit = $ 37.80   ; Let the units of sales be “x” units

Thus total variable costs = $ 37.80 * x = 37.80x

Fixed Cost = $ 22,000 ;

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

= ( 54x – 37.80x - $ 22,000 )

= ( 16.20x - $ 22,000 )               

Thus the annual after tax cash inflows = 16.20x - $ 22,000

Calculation of present value of after cash Inflows :

As per the information given in the question

Discount rate for the project = 16.80 %    ; No. of years of the project = 4 Years

The present value factor at 16.80 % for four years is = PVIFA(16.80 %, 4) = 2.754080

Thus the present value of after tax cash inflows of the project = Annual after tax cash inflows * PVIFA(16.80 %, 4)

= ( 16.20x - $ 22,000 ) * 2.754080

= 44.616094x – $ 60,589.756796

The present value of after tax cash inflows of the project = 44.616094x – $ 60,589.756796

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

44.616094x – $ 60589.756796 = $ 92,000

44.616094x = $ 60589.756796 + $ 92,000

44.616094x = $ 82,589.756796

x = $ 82,589.756796 / 44.616094

x = 1,851.1203

x = 1,851 units ( when rounded off to the nearest whole number )

Thus the breakeven on a financial basis = 1,851 units