Hi mbastu!!
a. What is the accounting break-even level of sales in terms of number
of diamonds sold?
The machinery cost of $1 million is depreciated straight-line over 10
years to a salvage value of zero. That means the Depreciation per year
is:
D = $1,000,000 / 10 = $100,000
The break-even level of sales is the sales point at which EBIT = 0 ;
in other words:
sales break-even point = level of sales necessary to cover operating costs.
At the break-even level of sales:
EBIT = Revenues - Variable costs - Fixed costs - Depreciation = 0
then:
Revenues - Variable costs = Fixed costs + Depreciation
If we call:
q = quantity sold;
p = price per unit;
v = variable cost per unit,
then
Revenues = q.p and Variable costs = q.v
We will have:
Revenues - Variable costs = q.p - q.v = q.(p - v)
Revenues - Variable costs = q.(p - v) = Fixed costs + Depreciation
Then:
q = (Fixed costs + Depreciation) / (p - v)
q = ($200,000 + $100,000) / ($100 - $30) = $300,000 / $70 = 4285.71
The break-even level of sales in terms of number of diamonds sold is
4,286 diamonds.
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b. What is the NPV break-even sales assuming a tax rate of 35 percent,
a 10-year project life and a discount rate of 12 percent?
At the break even point:
Revenues = q.p = 5,978 x $100 = $597,800
Variable costs = q.v = 5,978 x $30 = $179,340
Fixed costs = $200,000
Total Costs = $179,340 + $200,000 = $379,340
Depreciation = $1,000,000 / 10 years = $100,000 per year.
Tax rate (T) = 0.35
Cash Flow = (1-T)*(Revenues - Total Expenses) + T * Depreciation =
= 0.65*($597,800 - $379,340) + 0.35*$100,000 =
= $141,999 + $35,000 =
= $176,999
Present value of cash flow (PV)= Cash Flow * Annuity factor
The 12%, 10-year annuity factor is 5.650 , then:
PV = $176,999 x 5.650 = $1,000,044.35
NPV = PV - Initial Investment =
= $1,000,044.35 - $1,000,000 =
= $44.35
NOTE:
The above value is a good aproximation to zero, and the error is a
result of some hidden roundings, you can see that taking the reverse
way:
At the breakeven point the NPV is zero, then:
NPV = 5.650 x (0.65 .(q.p - q.v - FC) + 0.35 . D ) - $1,000,000 = 0
then:
$1,000,000/5.650 - 0.35*$100,000 = 0.65*q*(p-v) - 0.65*$200,000
then:
$141,991.15 = 0.65*q*($100 - $30) - $130,000
then:
$271,991.15 = 0.65*q*$70
==> q = $271,991.15 / (0.65*$70) = 5977.83 diamonds; this result must
be rounded to 5978 diamonds (this is the origin of the non zero result
of the NPV).
I hope this helps. If you find something unclear or missed please do
not hesitate to request for a clarification, I will be glad to give
you further assistance on this before you rate this answer.
Best regards.
livioflores-ga |