Modern Artifacts can produce keepsakes that will be sold for $100 each. Nondepre

Question

Modern Artifacts can produce keepsakes that will be sold for $100 each. Nondepreciation fixed costs are $1,300 per year, and variable costs are $70 per unit. The initial investment of $4,000 will be depreciated straight-line over its useful life of 5 years to a final value of zero, and the discount rate is 12%.

a. 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.)

b. 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.)

c. What is the accounting break-even level of sales if the firm’s tax rate is 30%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

d. What is the NPV break-even level of sales if the firm’s tax rate is 30%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Explanation / Answer

Break-Even Point is the point at which a firm experiences no profit - no loss situation. Hence, at break-even point, the firm is just able to cover all its costs. So at Break-Even Point, Total Revenue = Total Cost.

Calculation of Break-Even Point of Sales (in Units):

Break-Even Sales = Total Fixed Cost/ Contribution Margin p.u.

Total Fixed Cost = Depreciation Fixed Costs^ + Non-Depreciation Fixed Costs = $800 + 1,300 = $2,100

^Depreciation has been calculated by Straight Line Method as (Cost – Salvage Value)/Useful Life of Asset

Depreciation = ($4000 – 0)/ 5 = $800 per year

Contribution Margin per unit = Sales Price p.u. – Variable Cost p.u.

= $100 – 70 = $30 p.u.

Variable Costs are $70 p.u., while Sales Price is $100 p.u., reflecting 70% of Total Sales Price. Therefore, Contribution Margin Reflects at 30% of Sales Price = 30% = (0.30 X Sales)

Break-Even Sales (in Units) = Total Fixed Cost/ Contribution Margin p.u.

                                                     = $2,100/ 30 = 70 Units

NPV Break-Even means a point at which Net Present Value of a Project is 0.

For Calculation Purposes, Cash Flow Details from Project are also Required.

Cash Flow in this case = (Contribution Margin – Non-Depreciation Fixed Costs)

                                           = [(0.30 x Sales) – 1,300]

Assuming Sales as x. Then, Cash Flow = [0.30x – 1,300]

Also, the Discounting Rate has been given as 12% for an annuity of 5 Years.

The Discounting Factor comes at 3.60478.

Given Required NPV = 0,

Present Value of Cash Flows – Initial Investment = 0

Plugging Figures,

or [3.60478 x (0.30x -1,300)] - $4,000 = 0

or [1.08143x – 4,686.214] – 4,000 = 0

or 1.08143x = 4,000 + 4,686.214

or Sales (x) = 8,686.214/1.08143 = $8,032.16

Converting Sales Amount into Units = $8,032.16/ $100 p. u. = 80.32 Units = 80 Units approx.

There will be no impact on Accounting Break-Even Point, since at Break-Even Point the Firm is Earning Zero Profits. Since Taxes are Levied on Profits, and there are No Profits, there arises no question of Payment of Taxes and its Impact on BEP Point.

Hence, the BEP will remain Same as in Case – (a) above = 70 Units

In this case, Taxes have also been Provided and Required to be Factored In.

Inclusion of Tax Rate will affect Calculation in Two Ways:

- Firstly, It will affect the Incoming Sales Revenue Cash Flow by Reducing it by Tax Percentage.

- Secondly, It Will Add Income by Depreciation Tax Shield, i.e. Additional Cash Inflow by Depreciation x Tax Rate

Cash Flow = [(1- Tax Rate) x (Contribution Margin – Non-Depreciation Fixed Costs) + Depreciation Tax Shield]

= [(1 – 0.30) x {(0.30 x Sales) – 1300}] + (0.30 x 800)

Assuming Sales as x. Then, Cash Flow = [0.70 x (0.30x – 1,300}] + 240 = [0.21x – 670]

Annuity Factor is unchanged at 3.60478

So New Equation for Required NPV = 0,

or [3.60478 x (0.21x – 670)] - $4,000 = 0

or [0.75700x – 2415.2026] – 4,000 = 0

or 0.75700x = 4000 + 2415.2026

or Sales (x) = 6415.2026/ 0.7570 = $8,474.5080

Translating Sales Amount into Units = $8,474.51/ $100 p. u. = 84.74 Units = 85 Units

Please feel free to ask for any clarifications! :)

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