Question

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%?

Answer 1

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