BREAKEVEN ANALYSIS Simply put it, breakeven analysis concerns the most straightf
ID: 2667564 • Letter: B
Question
BREAKEVEN ANALYSISSimply put it, breakeven analysis concerns the most straightforward question in
business: How many sales are needed to get revenues exceed costs? This exercise
provides an overview of this method. To fix idea, let’s consider some particular
numbers: A firm, called A, has purchased a $250,000 machine to produce certain
products. The machine will be fully depreciated by the straight-line method over
its five-year useful life. Each product sells for $25. The variable cost per product
is $6, and the firm incurs fixed costs of $360,000 each year. The corporate tax rate
for the company is 34%. The relevant discount rate is 12%.
(a) What is the depreciation of the machine at the end of each year? Note
the machine is fully depreciated by straight-line method, that is the resid-
ual value is 0 and the depreciation rate each year is 100% divided by the
useful time of the machine.
(b) Let n denote the number of sales each year, p denote the selling price per
unit, c denote the variable cost per unit, FC denote the fixed costs each year
and D denote the depreciation each year. Note that FC does not depend
on n, while in each year the total revenue is n x p and total variable cost is
n x c. Now, in a given year, the EBT , or earnings before taxes are
EBT = n(p - c) - FC - D
We call a sales level n to be the accounting profit break-even point if at this
sales level a firm’s accounting profit is zero. (Observer that for a sales level
greater than n, the accounting profit must be positive.) Then, what is n
of firm A? Hint: If the EBT is zero, then the income tax is zero, and the
accounting profit is zero as well. As a result, to find out n, one only needs to
solve the equation where EBT = 0.
(c) Of course, by now you should anticipate that we’re not in general interested
in the accounting profit. What do we care are cash flows. Let t further
denote the income tax rate. Recall that the operating cash flow OCF is
defined as
OCF = Sales’ Revenu-Total cost- Taxes:
First show that the tax payment is
T = [n(p - c)- FC- D]t
Hint: Note T = EBTt.
Next, show that the OCF has the following expression:
OCF = [ n(p - c )- FC](1 - t ) + Dt
Now you are asked to work out an expression for the cash flow break-
even point n which makes the OCF = 0. Observe that for any sales
level greater than n, the cash flow is greater than zero.
Finally, what is n of firm A?
(d) Up to now, we haven’t considered the role played by the initial cost for pur-
chasing the machine. It is always the case that when taking into account of
initial cost, the cash flow break-even point sales level will lead to a negative
NPV, since all cash flows are 0 in the subsequent periods.
Let r denote the discount rate. Then a fairly easy way to find out the so
called present value break-even point starts by first calculating the equivalent
annual cost EAC of the initial investment. In our case, EAC is defined by
the following equation
$250,000 = EAC x Ar^5
Then we could define the adjusted operating cash flow AOCF by including
EAC as one term of cost in each year
AOCF = OCF- EAC = [n(p - c) - FC](1 - t) + Dt - EAC.
The present value break-even point n is the solution of the equation be
setting AOCF = 0. Work out the expression of n using the above equation
and find out n of firm A.
Dalia Baptiste
Explanation / Answer
a). Depreciation of the machine at the end of the each year is as follows. Year Asset value Depreciation 1 250000 50000 2 250000 50000 3 250000 50000 4 250000 50000 5 250000 50000 b). EBT = n(p-c) - FC - D EBT is zero, FC is $360,000, D is 50,000, p is $25 , c is $6. 0 = n(25-6) - 360,000 - 50,000 n*19 = 410,000 n =410,000/19 =21578.95 Therefore no of sales in each year is 21,578.95. c). OCF = [ n(p - c )- FC](1 - t ) + Dt OCF is zero, then 0 = (n(25-6) - 360,000)(1- 0.34) + 50,000 * 0.34 0 =( n*19 - 360,000)*0.66 +17,000 0 =19n*0.66 - 360,000*0.66 + 17,000 12.54n = 237600 - 17,000 =220,600 n =220,600/12.54 =17,591.706 Therefore no of sales in each year is 17,591.706. d) $250,000 = EAC*(1+12%)^5 EVC = $250,000/1.12^5 = $141,856.7 AOCF = OCF- EAC = [n(p - c) - FC](1 - t) + Dt - EAC AOCF is zero. 0 =( n(25 - 6) - 360,000)(1-0.34) + 50,000*0.34- 141,856.7 0 =12.54n - 220,600 - 141,856.7 12.54n = 362,456.7 n = 362,456.7/12.54 =28,904.043 =Year Asset value Depreciation 1 250000 50000 2 250000 50000 3 250000 50000 4 250000 50000 5 250000 50000
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