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Modern Artifacts Inc. can produce keepsakes that will be sold for $80 each. Non-depreciation fixed costs...

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

What is the accounting break-even analysis if the firm pays no taxes?
What is the NPV break-even analysis if the firm pays no taxes?
What is the accounting B/E level of sales if the firm has a 40% tax rate?
What is the NPV B/E level of sales if the firm’s tax rate is 40%?

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Expert Solution

Deprciation = 3000 / 5 = 600

Accounting Breakeven = ( Fixed costs + depreciationn ) / ( Sales value - variable cost )

= ( 1000 +6 00) / ( 80 - 60 ) = 1600 / 20 = 80 units

NPV break even is a point at which NPV = 0

as there are no taxes we have equation as below

[ Sales value - variable cost ) * No of units - 1000 ] * [ 1 - ( 1+r)^-n ]/ r - Initial Investment = 0

[ 20* no of units - 1000 ] * [ 1 - 1.1^-5 ] / 0.1 - 3000 = 0

[ 20 * units - 1000] * 3.79 -3000 = 0'

75.82 units - 3790.79 - 3000=0

no of units = 6790.79 / 75.82 = 89.57 units

Npv breakven units if no taxed = 89.57 units

The accounting breakeven level will remain the same 80 units

accounting B/E level of sales if the firm has a 40% tax rate = 80*80 = 6400

Now the Npv breakevn will change as tax has been brought in

{(Sales value - variable cost ) *No of units -1000 } ( 1 - tax rate )*+ Depreciation tax shield ] * Annuity factor -+ initial investment = 0

[ { 20*no of units - 1000 } * 0.6 + 600*0.4 ] * 3.79 - 3000 = 0

[ 12* units - 600 + 240 ] *3.79 - 3000 = 0

45.49 units - 1364.68 -3000 = 0

units = 4364.68 / 45.49 =95.95

NPV B/E level of sales if the firm’s tax rate is 40% = 96 * 80 = 7680 ( rounded off)

jeff jeffy answered 1 year ago

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