MARGINAL LIKELIHOOD OF SHUTTING DOWN? 267
Marginal likelihood of shutting down?
Would you sell your product for less than it cost? Does this sound likely? Obviously, you
should sell one more coconut only if the revenue from that sale exceeds its cost to you.
But what, exactly, is the cost?
Think about the problem. Let’s talk coconuts again. Recall that you buy coconuts for
one peso each and sell them for five pesos and you have operating expenditure of 80
pesos a day for renting the stall.
If you sell just one coconut in a day, your total, average and marginal costs were 81
pesos. If you sell two nuts, total costs edge up to 82 pesos, average total cost per nut slips
to 42 pesos and marginal cost per husk plummets to one peso.
Marginal cost is the expense associated with selling one more item. In this example, the
total cost will rise steadily, the average cost will continue falling, and the marginal cost of
every nut after the first one will remain fixed at one peso. Except that it won’t. At some
point the marginal cost will start rising due to limited supply of coconuts or the additional
3% chance of
failing to obtain
85 000
Probability
Telephones
97% chance of
sourcing more than
85 000
100 00085 000
Figure 11.4 Not enough telephones?
Break even in your business plan
Most readers will check your business plan for your break even analysis. I have
taken you a little beyond the usual ‘straight-line analysis’ to give you a head start
in the hard world of business planning and funding. However, even if you just draw
two straight lines and identify where they cross you will have aided understanding
of your business case. Expand on this by assigning probabilities and you will boost
your credibility and your perceived ability to manage.
t
268 CHAPTER 11 MANAGING RISKS
costs of employing staff, renting more stalls, trucking more nuts – the law of diminishing
returns nearly always rears its ugly head sooner or later.
At sales of 40 coconuts a day the average total cost has slipped to three pesos. Suppose
that rationing pushes up the amount that you have to pay for the 41st nut to four pesos
(and your buying costs per unit will continue to increase thereafter). Marginal cost has
gone back above average cost, so average cost must rise. This is obvious if you think
about the way that an average is calculated.
If you were to plot these trends, you would see a chart similar to Figure 11.5. I have
cheated by making the curves smoother than the coconut example implies. Corporate life
is somewhat more complex than selling nuts at the roadside and there are rather more
factors at play. However, if you follow through this analysis, you will spot two key figures
from Figure 11.5.
Always, always sell coconuts for more than one peso – in other words,
always price above marginal cost – except for very special promotions or to
gain goodwill.
t
Minimum
price for
profit
Cost per unit
QuantityMinimum
quantity
Minimum
profitable
quantity
Shutdown
price
Marginal cost
Average
total cost
Average
variable cost
Figure 11.5 Shut down or expand?
MARGINAL LIKELIHOOD OF SHUTTING DOWN? 269
1 Shutdown price. If your income per unit is less than minimum average variable cost
per unit (less than the point where marginal cost = average variable cost) you are
not covering your variable costs. In other words, if gross revenue per coconut is less
than one peso, you might as well close the stall and spend your days on the beach.
2 Minimum economic price. If your income per unit is less than the lowest point in
your average total cost curve (where average total cost = marginal cost) you are not
covering fixed and variable costs. If you sell coconuts for less than three pesos, you
will make a net loss.
If you are selling between your shutdown and minimum economic prices, you are covering
the variable costs of the product, but not your fixed costs. You are making a loss, but at least
you are earning more than if you did nothing. For example, if you are selling coconuts for
between one and three pesos and have paid for your stall rental today, you are recovering
some of the rental. You need to develop a sales strategy in order to move to full profitability.
MARGINS AND THE NORMAL
As you will have spotted already, you can apply the normal to marginal analysis and cal-
culate the likelihood of various outcomes. It is exactly the same as all the other examples
of using the normal – so I won’t labour this one. An interesting exercise, if you feel so
inclined, is to assume that costs are distributed normally around the central expectation
and establish a range of probable outcomes.
Stall holders at hot dusty bazaars in the Middle East know all about
marginal analysis. Their haggling will go all the way down to just above
their shutdown price. They would rather make a sale at just above average
variable costs – never mind their fixed costs – than see you buy from their
neighbour. Small retailers in smart shopping malls sometimes sit idle, without
recognising this, while lost custom drifts past.
t
Marginal notes for your business plan
You certainly want to think about marginal analysis when you plan and run your
business. The calculations are usually more complex than the example here, but the
conclusions will hit you like a coconut falling from the palm tree. Remember that
average costs are not static. Watch for them to jump about when the stall owner
suddenly increases the rent. It is a rare – and advanced – business plan that includes
much marginal analysis. Nevertheless, you may find it useful to say a word or two
about marginal costs, not least to demonstrate that you understand costs and
prices – and that you have them well under control.
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