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

breakeven is the point at which Modern Artifacts has no profit no loss situation.To summarise this where revenue = cost.

a) accounting break even level of sales:-

   it means breakeven in accounting terms

accounting break even level of sales =    FIXED COST + DEPRICIATION / SALES PRICE - VARIABLE COST PER UNIT     

     where deprecitation = initial cost of investment/ life of investment   = 4000/5  = 800 per year

      so accounting break even = (1300+800) / (100-70) = 2100/ 30 = 70 unit per year

   hence in order to break even firm has to produce 70 units in a year.

b) NPV break even level of sales

   NPV = Present Value (PV) of Opertaing Cash Flow - Initial Investment

   at break even NPV should be 0 (zero)

Let Q be the quantity.

   OCF = Contribution - Fixed expenses

   = [ Q *(100-70) ] - 1300

   = 30Q -1300

(* we haven' t considered depreciation here because we are already considering Initial investment in NPV calculation, hence taking dep will have double deduction effect so we are avoiding here.)

   So Break even ,

   NPV = Present Value (PV) of Opertaing Cash Flow - Initial Investment

   NPV = OCF PVIAF ( i% , n) - I.I.

   0 = 30Q - 1300 PVIAF ( 12%, 5) - 4000

   4000 = (30Q- 1300 ) * 3.605

  4000 = 108.15 Q - 4686.5

8686.5 = 108.15 Q

So, Q = 8686.5 / 108.15 = 80.32 ~ 81 units approx a year

c) Accounting break even when tax rate is 30%

  tax rate has no effect on Accounting break even because taxes paid are zero, when pretax profit is zero.

hence ,  

accounting break even level of sales =    FIXED COST + DEPRICIATION / SALES PRICE - VARIABLE COST PER UNIT     

     where deprecitation = initial cost of investment/ life of investment   = 4000/5  = 800 per year

      so accounting break even = (1300+800) / (100-70) = 2100/ 30 = 70 unit per year

   hence in order to break even firm has to produce 70 units in a year.

d) NPV break even level of sales when tax rate rate is 30%

   tax rate will have effect on NPV break even because after tax cash flows changes with change in tax rate.(here tax rate becomes 30 from 0). here we earn depreciation tax shield ,because dep. saves tax and tax shield on expenses.

   OCF = [ Contribution ( 1-tax rate)} - expenses ( 1 - tax rate) ] + { Depreciation * Tax Rate }

   = [{Q (100 - 70) (1- .3 )} - 1300(1-.3)]  + { 800 * .3}

   = [{Q * 30 * 0.7 } - 910] + 240

   = 21Q -910 +240

   = 21Q -670

at break even NPV = 0

NPV = Present Value (PV) of Opertaing Cash Flow - Initial Investment

   NPV = OCF PVIAF ( i% , n) - I.I.

   0 = (21Q - 670) PVIAF ( 12%,5) - 4000

   4000 = (21Q - 670)* 3.605

   4000 = 75.705 Q - 2415.35

   4000+ 2415.35 = 75.705 Q

6415.35 = 75.705Q

Q = 6415.35/75.705 = 84.74 ~ approx 85 units a year

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