Question

You are considering investing in a company that cultivates abalone for sale to local restaurants. Use the following information:

Sales price per abalone	=	$44.80
Variable costs per abalone	=	$11.35
Fixed costs per year	=	$506,000
Depreciation per year	=	$104,000
Tax rate	=	23%

The discount rate for the company is 15 percent, the initial investment in equipment is $936,000, and the project’s economic life is 9 years. Assume the equipment is depreciated on a straight-line basis over the project’s life and has no salvage value.

a.	What is the accounting break-even level for the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b.	What is the financial break-even level for the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Solution:

a.Calculation of Accounting Break – even level for the project :

The formula for calculating the Accounting Break – even level is

= ( Fixed costs per year + Depreciation per year ) / Contribution per unit

Where Contribution per unit = Sales price per unit - Variable costs per unit

As per the information given in the question we have

Fixed costs per year = $ 506,000 ; Depreciation per year = $ 104,000

Sales price per unit = $ 44.80 ; Variable costs per unit = $ 11.35

Thus Contribution per unit = $ 44.80 - $ 11.35 = $ 33.45

Applying the above information in the formula we have

= ($ 506,000 + $ 104,000 ) / $ 33.45

= $ 610,000 / $ 33.45

= 18236.1734

= 18,236.17 ( when rounded off to two decimal places )

Thus the accounting break even level = 18,236.17 abalone

b.Calculation of Financial Break – even level for the project :

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.

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 = $ 44.80   ; Let the units of sales be “x” units

Thus sales value = $ 44.80 * x = 44.80x

Variable cost per unit = $ 11.35   ; Let the units of sales be “x” units

Thus total variable cost = $ 11.35 * x = 11.35x

No. of years of economic life = 9 years    ; Depreciation per year = $ 104,000

Fixed Cost = $ 506,000 ;          Tax rate = 23 % = 0.23

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

= [ ( 44.80x – 11.35x - $ 506,000 - $ 104,000 ) * ( 1 - 0.23 ) ] + $ 104,000

= [ ( 33.45x - $ 610,000 ) * 0.77 ) ] + $ 104,000           

= [ 25.7565x - $ 469,700 ] + $ 104,000                           

= 25.7565x - $ 365,700

Thus the annual after tax cash inflows = 25.7565x - $ 365,700

As per the information given in the question

Discount rate for the project = 15 %    ; No. of years of the project = 9 Years

The present value factor at 15 % for nine years is = PVIFA(15 %, 9) = 4.771584

Thus the present value of after tax cash inflows of the project = Annual after tax cash inflows * PVIFA(15 %, 9)

= ( 25.7565x - $ 365,700 ) * 4.771584

= 122.899301x – $ 1,744,968.239446

The present value of after tax cash inflows of the project = 122.899301x – $ 1,744,968.239446

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

122.899301x – $ 1,744,968.239446 = $ 936,000

122.899301x = $ 1,744,968.239446 + $ 936,000

122.899301x = $ 2,680,968.239446

x = $ 2,680,968.239446 / 122.899301

x = 21,814.348923

x = 21,814.35 units ( when rounded off to two decimal places )

Thus the financial break even point for the project = 21,814.35 abalone