The clearest real-world example of sensitivity analysis that I have ever seen is one by oil
and gas company Shell about the impact of changes in the oil price.
The price sensitivity at Shell group level is $6 billion of cash flow from operations
per annum per $10 per barrel Brent oil price movement.
If the oil price goes up by $10 per barrel, they expect $6 billion of incremental cash
flow from operations.
If the oil price goes down by $10 per barrel, they expect a decrease of $6 billion of cash
flow from operations.
This sensitivity statement comes with a disclaimer: this price sensitivity is appropriate for
smaller price changes, and is best used for full-year numbers.
The “format” of this sensitivity analysis is: what is the effect of a change in absolute
terms of an input variable (oil price) on the absolute amount of a target variable (cash
flow from operations).
Commodity trading and mining company Glencore provides a sensitivity analysis in the part
of the annual report that discusses the review of assets for impairment.
For each cash generating unit with limited headroom relative to their estimated recoverable
value, a sensitivity impact of potential 10% movements in the most sensitive assumptions
is provided.
For Coal South Africa, a 10% fall in coal price assumptions would lead to a possible
impairment of $703 million.
For Mopani, a fall of 10% in the copper price assumption would lead to a possible impairment
of $181 million, while a 10% reduction in the estimated annual production over the life
of the mine could result in an impairment of $116 million.
Similar sensitivity analyses are done for cash generating units involved in the extraction
and production of nickel, oil, and zinc.
The “format” of this sensitivity analysis is: what is the effect of a change in percentage
terms of an input variable (10%) on the absolute amount of a target variable (millions of $ of
impairment charges).
These examples lead us to a definition of sensitivity analysis: the process of estimating
how target variables change in relation to changes in input variables.
What is the effect of a change in input variable x on target variable f(x)?
What is the effect of a change in the oil price on cash flow from operations?
What is the effect of a change in revenue on profitability?
What is the effect of a change in estimated project benefits on net present value?
The key to sensitivity analysis is to identify the most significant assumptions that affect
an output: which input variables have the strongest impact on the target variables?
Prior to starting a sensitivity analysis, you first need to decide what the key performance
indicators (target variables) are!
Here’s an example of sensitivity analysis.
Let’s start off with the base case on the left.
The projected income statement of a company has $1 million of revenue, minus $600K of
variable costs, which leads to $400K of contribution margin.
After deducting fixed costs of $200K, operating margin is $200K. What is the effect of a change
in revenue (more specifically a drop of 10%) on operating margin?
Wrong question!
Not every type of change in revenue has the same effect on operating margin.
Currently, the company expects to sell 100 thousand units of one single type of product
at $10 each.
If we want to analyze the impact of a change in revenue (input variable) on operating margin
(target variable), then we should either take a 10% decrease in volume, or a 10% decrease
in price, or even better: analyze the effect of each of these versus the base case side-by-side.
A 10% decrease in volume leads to revenue of $900K: 90 thousand units sold at $10 each.
A 10% decrease in price also leads to revenue of $900K, but with a different composition:
100 thousand units sold at $9 each.
So far, so good, so what?
That question is answered in the next line of the projected income statement.
Variable costs in the case of a 10% drop in volume are $540K: 90K units that cost $6 per
unit to make.
In other words, 90K units in revenue, and 90K units in variable costs.
If there is a drop in volume, then both revenue and variable costs drop by 10%.
Variable costs in the case of a 10% drop in price stay at $600K: 100K units at that cost
$6 per unit to make.
Revenue drops, but variable costs stay the same.
As a result, the contribution margin in the volume drop scenario is $360K (90K units times
$4 per unit), while in the price drop scenario it is only $300K (100K units times $3 per unit).
Deduct the fixed costs, which stay at $200K, the same as in the base case scenario.
Then take a look at operating margin: $160K in the 10% volume drop scenario, but only
$100K in the 10% price drop scenario.
From this, we learn that we can expect a 10% drop in volume to lead to a 20% drop in Operating
Margin, while a 10% drop in price would lead to a 50% drop in Operating Margin!
Be much more afraid of a drop in price than of a drop in volume!
What we have done so far is called a “one assumption at a time” scenario analysis:
analyzing the effect of varying one model input factor at a time while keeping all other fixed.
In real life, many assumptions may be linked, and move at the same time,
in the same direction, or in opposite directions.
What if both volume and price drop by 10% at the same time?
Our new revenue would be $810K: 90K units at $9 per unit.
Variable costs $540K: 90K units at $6 per unit.
Contribution margin $270K: 90K units at $3 per unit. Fixed costs $200K.
Operating margin $70K. What we learn from this, is that a 10% drop in volume AND a 10% drop in price at the same time
lead to an expected 65% drop in Operating Margin versus the base case!
In a lot of situations, people performing a sensitivity analysis mistakenly assume that
input variables and output variables are linked in a linear way: a 20% change in the inputs
is expected to have double the effect on the outputs versus a 10% change in the inputs.
A positive linear scenario on the left, a negative linear scenario on the right.
The impacts of input variables on target variables could however be exponential, not linear!
In the case of a “positive” scenario, this would be called convexity:
exponential growth in the target variable.
This is something you try to look for, and benefit from!
In the case of a “negative” scenario, this would be called concavity:
exponential decline in the target variable.
This is something you try to avoid, build defenses against, in order not to get hurt,
or “blow up”!
When doing a sensitivity analysis, try to detect the sensitivity of an outcome to different
sized shocks.
What does sensitivity analysis give us?
In the words of Nassim Taleb: performing sensitivity analysis on assumptions does not eliminate
the risk, but identifies which assumptions are key to conclusions, and thus merit close scrutiny.