Question

The following data have been obtained.

Cash operating costs	$10,000 / year	Life	5 years
Labor per hour	$16.00	First Cost	$60,000
Production rate	25 hour	Salvage	$10,000
Depreciation	SL	Tax rate	42%
Selling price	$1.47/unit	Debt ratio	37%
Interest on debt	8.35%	Return on equity	14.7%

How many parts must be produced each year to just break even? (Use the AEC equation)

Answer 1

Let X number parts must be produced for break even.

Per year analysis

So Annual revenue TR=1.47*x=1.47X

Annual operating cost TC=10000+16*X/25=10000+0.64X

Given

Interest on debt rd=8.35%

return on equity re=14.7%

D/E=37%

T=42%

WACC r={(1-0.42)*0.37*8.35%+1*14.7}/1.37=12.04%

P=$60000

S=$10000

n=5

Annual equivalent Cost=Equivalent annual cost of initial investment P for 5 years-Equivalent annual cost of Salvage value S for 5 years+Annual cost TC

Equivalent annual cost of initial investment P for 5 years=P*r/(1-(1+r)^-n)=$13884.23

Equivalent annual cost of initial investment S for 5 years=S*r/((1+r)^n-1)=$1572.85

Annual equivalent Cost=13884.23-1572.85+10000+0.64X=22311.38+0.64X

For break even quantity

Annual equivalent Cost=Annual total revenue

22311.38+0.64X=1.47X

X=26881.20 (26882 parts) per year