Modern Artifacts can produce keepsakes that will be sold for $80 each. Nondeprec

Question

Modern Artifacts can produce keepsakes that will be sold for $80 each. Nondepreciation fixed costs are $1,000 per year, and variable costs are $60 per unit. The initial investment of $3,000 will be depreciated straight-line over its useful life of 5 years to a final value of zero, and the discount rate is 10%.

What is the accounting break-even level of sales if the firm pays no taxes? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

What is the NPV break-even level of sales if the firm pays no taxes? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

What is the accounting break-even level of sales if the firm

Modern Artifacts can produce keepsakes that will be sold for $80 each. Nondepreciation fixed costs are $1,000 per year, and variable costs are $60 per unit. The initial investment of $3,000 will be depreciated straight-line over its useful life of 5 years to a final value of zero, and the discount rate is 10%.

Explanation / Answer

Part a)

Accounting break even level of sales without taxes is calculated with the use of Fixed Cost including Depreciation. The formula for calculating accounting break even point =

Accounting Break Even Point = (Fixed Cost + Depreciation)/(Selling Price - Variable Cost)

______________

Solution:

Here Depreciation = Cost/Estimated Life = $3,000/5 = $600, Fixed Cost = $1,000, Selling Price = 80 and Variable Cost = 60. Using these value in the above formula, we get,

Accounting Break Even Point = (1,000 + 600)/(80 - 60) = 80 units

_______________________________

Part b)

To calculate NPV break even sales level, we need to calculate the cash flow. With no taxes, the amount of cash flow will be = Units*(Selling Price - Variable Cost) - Fixed Cost

______________

Solution:

Let us assume that the NPV break even sales level be denoted by Q

Cash Flow = Q*(80 - 60) - 1,000

Since, we have to calculate the break even sales level where NPV is 0, we get the following equation:

NPV = 0 = Present Value of Cash Flows - Initial Investment

Present Value of Cash Flows = Cash Flow*Present Value Interest Factor for An Annuity at 10% for 5 Years

Using the Present Value Interest Factor for An Annuity table we get,

NPV = 0 = (20Q -1,000)*3.7908* - 3,000

Q = (3,000 + 1,000*3.7908)/(20*3.7908) = 90 units (NPV break even level of sales)

_______________________________

Part c)

Accounting break even point will be same as in part a) irrespective of whether taxes are paid or not, because taxes are zero when the profit is 0 and at the break even point, profits are zero.

The formula for calculating accounting break even point =

Accounting Break Even Point = (Fixed Cost + Depreciation)/(Selling Price - Variable Cost)

______________

Solution:

Here Depreciation = Cost/Estimated Life = $3,000/5 = $600, Fixed Cost = $1,000, Selling Price = 80 and Variable Cost = 60. Using these value in the above formula, we get,

Accounting Break Even Point = (1,000 + 600)/(80 - 60) = 80 units

_______________________________

Part d)

To calculate NPV break even sales level, we need to calculate the cash flow from operations after taxes, the amount of cash flow will be = [Units*(Selling Price - Variable Cost) - Fixed Cost]*Tax Rate + Depreciation*Tax Rate

______________

Solution:

Let us assume that the NPV break even sales level be denoted by Q

Operating Cash Flow = [Q*(80 - 60) - 1,000]*(1-35%)+ 600*35%

Since, we have to calculate the break even sales level where NPV is 0, we get the following equation:

NPV = 0 = Present Value of Cash Flows - Initial Investment

Present Value of Cash Flows = Cash Flow*Present Value Interest Factor for An Annuity at 10% for 5 Years

Using the Present Value Interest Factor for An Annuity table we get,

NPV = 0 = [(20Q -1,000)*65% + 600*35%]*3.7908 - 3,000

3,000 = (13Q -440)*3.7908

3,000 = 13Q*3.7098 - 440*3.7908

Q = (3000 + 440*3.7908)/(13*3.7908) = 95 units (NPV break even level of sales)

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