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I'm Larry Walter.
This is principlesofaccounting.com Chapter 18 and
this module extends the examples and
thought processes we developed in the previous module related to CVP Analysis.
And now we're going to look more specifically at sensitivity analysis where
we assume changes in variable cost or changes in fixed cost, or
even blended changes or changes in revenue functions.
So recognize that cost structures can change over time and management
must carefully analyze these changes to determine the effect on the business.
Let's revisit Leyland Sports from the previous module.
Remember in the Leyland Sports example, we needed sales of $2 million to break even.
There was a 60% contribution margin and a fixed cost pool of $1,200,000.
Now, in revising this example, we're going to assume we hire a sales manager at
an annual fixed cost of $120,000.
And that would increase our fixed cost pool to 1,320,000.
If we divide that by our 0.60 contribution margin ratio,
we come up with our revised break-even sales of $2,200,000.
In other words, this is the same break-even calculation we did previously,
but we've added additional fixed cost into the equation.
This simply means that by adding the sales manager,
we're going to have to see a $200,000 increase in sales
to justify the expenditure to at least cover that fixed cost.
We can also look at changes in variable costs.
If Leyland adds a sales manager but
instead of paying them a salary instead pays them a commission of 4% of sales,
the the revised break even is 2,142,857.
This results by dividing the continuing fixed cost
of 1,200,000 by the revised contribution margin ratio of 0.56.
In other words, instead of having a 60% contribution
margin we only have a 56% contribution margin, because each additional baller
of sales incurs another $0.4 of cost or commission for the sales manager.
And so the commission structure may appear to be more logical, because our breakeven
sales point is $2,142,000 instead of $2,200,000.
I've graphed this to do an analysis however and recognized that,
that's not a constant, it really depends on the level of sales that are generated.
So here i've plotted the sales managers fixed salary at $120,000 and
done an analysis to determine the managers total compensation,
its constant no matter the level of sales.
In the alternative I also prepared a plot of the commission, the sloping line.
If, instead of a fixed salary we have a commission,
if there are no sales we pay nothing but on the other hand if sales are very high
out here at say $6 million then we're paying $240,000 to the sales manager.
So whether we're better off or worse off really depends on the level of sales.
What the previous analysis does not show however is that human behavior also needs
to be considered.
Commissions may provide an inducement for
the sales manager to perform at a higher level.
At $6,000,000 in sales, for example, the commission based manager makes twice as
much as they would at the fixed cost of $120,000.
The businesses might even be much better off with the $6 million sales level
all things considered.
And so sometimes the lowest cost option is not the best cost option
in terms of effecting the total profitability of the business.
In the previous example for Leyland Sports,
we first modified the fixed cost and did an analysis.
And then we modified the variable cost and
did an analysis to see what the effect is on break even, okay?
Many costs changes how we're gonna involve both fixed and
variable component shifting, s Such is the case for Flynn Flying Service.
Flynn has a jet but it currently earns and operates and it costs $3 million
fixed costs to operate it, but the contribution margin is only 30%.
They're offered an even exchange for a new jet that has a higher $4 million
fixed cost operations per year, but it's variable cost is lower and
it has a higher contribution margin at 50% of sales.
Assuming Flynn expects 9 million in revenue, is it better to exchange or not?
And so, Flynn should make this deal, the break-even on the old jet is $10 million.
In other words, the $3 million in fixed cost divided by the 30%
contribution ratio tells us that we need ten million in sales to break even,
whereas the new jet only needs $8,000,000 in sales to break even.
That's calculated as the $4,000,000 in fixed costs divided by
the 50% contribution margin ratio.
So now perhaps you're beginning to appreciate how significant the value is
of understanding your contribution margin ratio and your fixed cost structure and
how quickly you can do an analysis of business decisions.
Of course, this could be a double-edged sword.
If volume levels did not reach the $9 million volume level or
drop below the $8 million level, we may run an analysis and
find we're better off keeping the existing jet.
So, our assumptions need to be valid for our analysis to be valid.
Finally, we looked at cost shifts.
We have not talked about revenue shifts and so I'm going to look at an example
where we have a 10% increase in sales price for Leaping Lemming.
We looked at Leaping Lemming in the previous module as well.
Here we've got sales of 10,000 units at $1,000 per unit,
total revenues would be $10 million.
If we're able to increase the sales price by 10% to $1,100 per unit,
total sales will be $11 million.
So it's only a 10% increase in sales price but look what it does to our net income.
We go from a $500,000 income to a $1,500,000 income.
I think you would agree that's a significant change in
the profitability of the business.
Again, this behavior,
this profitability behavior is a function of our cost structure.
Now, the analysis I just looked at assumed rather cavalierly that we could get away
with raising prices 10%, however customers may be very sensitive to pricing,
it could be that we'll see a significant drop in demand if we raise our prices 10%,
and so further analysis may be required.
A company needs to assess how volume drops can be absorbed when prices increase.
For example if Lemming desires to at least maintain its $500,000 of profit when it
increases its price, what level of sales drop could be absorbed?
And we could actually see sales be cut in half to only 5,000 units.
In other words, our fixed cost of $500,000 plus our $500 target income.
That's our proval of cost and profit we need to be able to cover,
divided by the $200 per unit contribution margin,
would tell us that 5,000 units would allow us to achieve our target income level.
Another issue to consider are cost plus pricing agreements
that seek to provide the seller with an assured margin but no more.
In other words, you may be buying a product and say,
look we think it's fair to allow you to make a 15% profit.
And so let's agree that the selling price for
our transaction will be based on cost plus 15%.
However those agreements can have unintended consequences
as we will now see.
Heap and Pioneer have entered into an agreement that provides Pioneer with
a contribution margin of 20% on 1 million bags delivered.
Originally the bags were anticipated to cost Pioneer $1 to produce and
fixed cost worth $100,000.
However, assume there was a huge increase from
the price of petroleum which is a base raw material for plastic bags.
And so that the variable production cost rose to $3 per unit
instead of $1 per unit.
So let's see what happens in this case.
First of all looking at the $1 scenario, I've calculated sales at $1,250,000.
That allows us to recover our variable costs of $1
a unit times the 1 million units.
And gives us our contribution margin of $250,000, which is 20% of sales.
>From which we subtract our $100,000 of fixed costs, and
profitability that we anticipate is $150,000.
But we're entitled to pass on our cost increases with the $3 scenario
variable costs are now $3 million, 1 million units at $3 a unit.
This requires us to charge the sales price at 3
million 750,000 to get us our 20% contribution margin, that is 20% of $3,
750,000, our fixed cost are unaffected,
however, so our net income is now $650,000,
a large increase from the $150,000 we previously expected.
And so this should illustrate quite clearly why costs
plus contracts can be dangerous.
The seller has very little concern about controlling costs because
they're passing them through, and indeed, if those increase in cost are all
variable in nature, there's no change in fixed cost,
the seller can actually make a great deal more as variable costs go up.
So, one needs to be very careful in dealing with cost plus contracts.
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