Break Even Analysis - Marginal Costing, Cost Management Video Lecture | Cost Management - B Com

let us look at the break-even analysis
using graphical method on your screen
you can see a graph with units sold on
the x-axis and the dollar amount on the
y-axis now we know that there are three
main components involved in the
break-even analysis the first one is
fixed cost
second is the variable cost
and the third is revenue so let us
understand how we can plot these three
on this graph let us first take the
fixed cost now we know that by
definition fixed cost is the cost which
does not vary by the volume of
production so irrespective of the number
of units sold the fixed cost will remain
constant so on the graph if we have to
plot the line basically the cost will be
the same if the number of units sold is
10 20 30 40 50 or 60 so what this gives
us is a straight line parallel to the
x-axis so let us draw that line so let's
say that the fixed cost is two thousand
dollars so the line representing the
fixed cost will be starting from two
thousand dollars and parallel to the
x-axis
so this line here represents the fixed
cost so what this line means is that the
fixed cost is two thousand dollars
whether the number of units sold is 5 10
15 20 up to any other number of units
sold now let us move to variable cost so
variable cost varies by the number of
units sold so if we have to plot the
variable cost so let's say this is the
graph with units sold on the x-axis and
dollar amount on the y-axis now if we
don't produce anything that is if we
have number of units as 0 then there is
no cost so there is no cost because we
are not producing anything so the line
for variable cost will start from here
and it will go like this this will be
representing the variable cost the slope
of this line will depend on the cost per
unit now again on this graph the fixed
cost will be aligned like this so this
will represent the fixed cost now if we
add the 2 the variable cost and the
fixed cost then we get the total cost so
if we have to draw the line for total
cost on this graph basically at this
point when the number of units sold is 0
the variable cost is also 0 while there
is a certain amount of fixed cost so the
total cost will start from here and will
go like this so this line will represent
the total cost and basically on this
total cost line at any point let's say
this point the total cost is the
addition of the variable
cost and the fixed cost at that number
of units sold so let's use this concept
to draw the line for total cost on this
main graph so as mentioned earlier since
the variable cost at zero units is zero
however fixed cost is two thousand so
the total cost will start from two
thousand and then as we keep on adding
the variable cost to the fixed cost we
will get the line for our total cost now
let's say that the variable cost is
equal to 120 dollars per unit so at the
point where number of units is forty
let's find out the total variable cost
so if quantity is equal to forty the
total variable cost is equal to 120
multiplied by 40 12 fours are 48 so
forty eight hundred dollars is the
variable cost at forty units so for
drawing the line for total cost we
already have one point which is here at
two thousand dollars intercepting at the
y-axis and the second point is at forty
units the variable cost is forty eight
hundred and if we add to this amount the
fixed cost so total cost will be equal
to forty eight hundred which is the
variable cost plus fixed cost which is
two thousand so this becomes $6,800 so
the second point is forty and sixty
eight hundred let's say it is here
somewhere so with these two points let's
draw the line for total cost
so this line here represents the total
cost
now the third line which we have to draw
is for revenue let's say that each unit
is being sold at a selling price of $200
per unit so selling price is $200 per
unit so at a point where zero units are
sold the total revenue will be zero now
let's find out the total revenue at a
point where 40 units are sold so the
total revenue will be equal to 200
multiplied by 40 which is equal to four
twos are eight thousand dollars so at 40
units sold the total revenue will be
equal to eight thousand dollars so now
we have two points one is zero and the
other one is eight thousand dollars and
40 units so let us draw the line for our
total revenue so let's say the point is
somewhere here eight thousand and forty
now again this graph is not at scale so
let us draw the line for total revenue
so this represents the total revenue so
on this graph the point at which the
total revenue is equal to the total cost
is this point here where both of them
are intersecting each other and this
point is known as the break-even point
so this is the break-even point now if
we draw a line parallel to the y-axis
touching the x-axis then the point here
on the x-axis will represent the
break-even point in terms of units sold
and if we draw a line parallel to the
x-axis touching the y-axis like this
then this point here will represent the
break-even point in terms of dollars now
again since this graph is not on scale
so these numbers may not be accurate but
these are representative of how you can
actually achieve the break-even point
using graphical method now this region
here below the break-even point
represents the area of loss while this
region here above the break-even point
represents the area of profit now one
question that comes to mind is that how
do we know that these lines are linear
or straight in nature so let us take the
example of the total cost line to
understand this now we know that the
total cost is equal to the fixed cost
plus the variable cost and the variable
cost is equal to the number of units
multiplied by the unit variable cost so
T is equal to F Plus let's say Q is the
number of units and small C represents
the unit variable cost now we know that
the formula for a straight line is
is why is equal to M X plus C here C is
a constant that is a numerical value M
represents the slope of the line and X
is the variable so in this equation for
a straight line C is the point where the
line intercepts on the y-axis so now
let's put the equation for total cost in
terms of a straight line so we get T is
equal to C Q plus F so here f is the
constant or the y-intercept so if we
look at the graph the total cost line
intercepts the y-axis at a point which
is equal to the fixed cost which is in
our case $2,000 so f is the y-intercept
or the constant small C represents the
slope so basically the unit cost of the
product determines the slope of the
total cost line and Q is the variable
now let's do the same thing for the
total revenue line now we know that
total revenue is equal to the quantity
of units sold multiplied by the unit
selling price now the equation for a
straight line is y is equal to M X plus
C so if we try to put the equation of
total revenue in this terms we get total
revenue is equal to P multiplied by Q
+0 now as we know C is the point at
which the line intercepts the y-axis and
the total revenue line intercepts the
y-axis at zero so this is the constant
in this case P is the unit selling price
which represents the slope and Q is the
variable so basically this proves that
the total revenue line is also supposed
to be a straight line as the total cost
line