Modern Artifacts can produce keepsakes that will be sold for $100 each. Nondepreciation fixed costs are $1,800 per year, and variable costs are $45 per unit. The initial investment of $2,000 will be depreciated straight-line over its useful life of 5 years to a final value of zero, and the discount rate is 12%.
(For all the requirements, do not round intermediate calculations. Round your answer to the nearest whole number.)
a. What is the accounting break-even level of sales if the firm pays no taxes?
b. What is the NPV break-even level of sales if the firm pays no taxes?
c. What is the accounting break-even level of sales if the firm’s tax rate is 20%?
d. What is the NPV break-even level of sales if the firm’s tax rate is 20%?
First of all lets calculate depreciation
Depreciation = Initial investment / Useful life
=2000/5 = 400 $
a) Accounting break even point = (Non depreciation fixed cost + Depreciation) / ( Selling price per unit - variable cost per unit)
=(1800+400) / (100-45)
=2200/55
=40 units
b) Let sales unit be X
Statement showing PV of cash inflow (where tax rate is 0)
Particulars | 1 to 5 |
Selling price per unit | 100 |
Less: variable cost per unit | 45 |
Contribution per unit | 55.00 |
Sales units | X |
Total contribution | 55X |
Less: Fixed cost | 1800 |
Cash flow | 55X-1800 |
PVIFA(12%,5) | 3.6048 |
PV of cash inflow | 198.2627X - 6488.5972 |
NPV break even means PV of cash inflow = PV of cash out flow
198.2627X - 6488.5972 = 2000
198.2627X = 8488.5972
X = 42.81 i.e 43 units
c) if tax rate is 20%
Accounting break even point = (Non depreciation fixed cost + Depreciation) / ( Selling price per unit - variable cost per unit)
=(1800+400) / (100-45)
=2200/55
=40 units
d) if tax rate is 20%
Let sales unit be x
Statement showing PV of cash inflow (where tax rate is 20%)
Particulars | 1 to 5 |
Selling price per unit | 100 |
Less: variable cost per unit | 45 |
Contribution per unit | 55.00 |
Sales units | X |
Total contribution | 55X |
Less: Fixed cost | 1800 |
Less: Depreciation | 400 |
PBT | 55X-2200 |
Tax @ 20% | 11X - 440 |
PAT | 44X - 1760 |
Add: Depreciation | 400 |
Cash flow | 44X - 1360 |
PVIFA(12%,5) | 3.6048 |
PV of cash inflow | 158.6112X - 4902.528 |
NPV break even means PV of cash inflow = PV of cash out flow
158.6112X - 4902.528 = 2000
158.6112X = 6902.528
X = 43.519 i.e 44 units
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