Question

Modern Artifacts can produce keepsakes that will be sold for $80 each. Nondepreciation fixed costs are $1,200 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%.

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 35%? (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 35%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Answer 1

a) Depreciation per year = $3000 / 5 = $600

Total fixed costs per year = Depreciation + other fixed costs = $600 + $1200 = $1800

Contribution per unit = Sales price per unit - variable cost per unit = $80 - $60 = $20

Accounting break - even sales = Total fixed costs / Contribution per unit = $1800 / $20 per unit = 90 units

b) Let the break even level of sales be "p". Now, NPV break even is the level of sales at which NPV is zero or the present value of cash inflows are equal to the initial investment.

Sales (p x $80)	80p
Less: variable cost (p x $60)	60p
Less: Non depreciation fixed costs	1200
Less: Depreciation	600
Earnings before tax	20p - 1800
Less: Tax@0%	0
Earnings after tax	20p - 1800
Add: depreciation	600
Cash inflows per year	20p - 1200
PVIFA (10%, 5)	3.79078676939

Present value of cash inflows = Initial investment

or, Cash inflows per year x PVIFA (10% , 5) = 3000

or, (20p - 1200) x 3.79078676939 = 3000

or, p = 99.5696 units or 100 units

c) Accounting break even is not affected by taxes. Therefore, accounting break even sales is still 90 units.

d)

Let the break even level of sales be "p". Now, NPV break even is the level of sales at which NPV is zero or the present value of cash inflows are equal to the initial investment.

Sales (p x $80)	80p
Less: variable cost (p x $60)	60p
Less: Non depreciation fixed costs	1200
Less: Depreciation	600
Earnings before tax	20p - 1800
Less: Tax@35%	7p - 630
Earnings after tax	13p - 1170
Add: depreciation	600
Cash inflows per year	13p - 570
PVIFA (10%, 5)	3.79078676939

Present value of cash inflows = Initial investment

or, Cash inflows per year x PVIFA (10% , 5) = 3000

or, (13p - 570) x 3.79078676939 = 3000

or, p = 104.7225 units or 105 units