Hi again boobee!!
a. What is the accounting break-even level of sales in terms of number
of diamonds sold?
The machinery costs $1 million a year and is depreciated straight-line
over 10 years to a salvage value of zero. That means Depreciations per
year:
$1,000,000 / 10 = $100,000 .
The point at which EBIT = 0 is the break-even level of sales.
In other words:
sales break-even point = level of sales necessary to cover operating
(not financial) costs.
At the break-even level of sales:
EBIT = Revenues - Variable costs - Fixed costs - Depreciation = 0 ;
then:
Revenues - Variable costs = Fixed costs + Depreciation
If q = quantity; 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.
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?
Revenues = q.p = 5,978 x $100 = $597,800
Variable expenses (or variable costs) = q.v = 5,978 x $30 = $179,340
Fixed Expenses = $200,000
Total Expenses = $179,340 + $200,000 = $379,340
Depreciation (straight-line)= $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 (PVcf)= Cash Flow x Annuity factor
The 12%, 10-year annuity factor is 5.650 , then:
PVcf = $176,999 x 5.650 = $1,000,044.35
NPV = PVcf - Initial Investment
NPV = $1,000,044.35 - $1,000,000 = $44.35
This error is acceptable, you can see that walking the reverse way:
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
$141,991.15 = 0.65 . q . ($100 - $30) - $130,000
Then
$271,991.15 = 0.65 . q . $70
then q = $271,991.15 / (0.65 . $70) = 5977.83 diamonds; this quantity
must be rounded to 5978 diamonds (this is the origin of the $44.35
error).
I hope this helps. If something in the answer is obscure or unclear
please post a request of a clarification before rating this answer.
Regards.
livioflores-ga |
Request for Answer Clarification by
boobee-ga
on
10 Jul 2003 19:02 PDT
Hi livioflores
I inputted your calculations into my excel workbook and got the
following. It states that if the figures are correct that the npv
will be approx. 0. Please advise.
In part a, enter the formula to calculate the break-even point. In
part b, enter the formulas to calculate
all the unknown items (you will know that your formulas are correct if
the NPV is approximately equal to 0.
a. What is the accounting break-even level of sales in terms of number
of diamonds sold?
Accounting break-even point 4,286 diamonds
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?
Number of diamonds 5,978
Annuity factor 5.650
Revenue $597,800
Variable Expenses $179,340
Depreciation $1,000,000
Fixed expenses $200,000
Cash Flow $176,999
Present value of cash flow $1,000,083.83
Net present value $83.83
|
,
0 Comments
)