My immediate instinct is to build an optimization moel around this question. By building a model
with configurable variables, we’ll be able to evaluate various scenarios based on different
assumptions.
First, we outline the data we have:
● Prevailing rate: Drivers - $19, Riders - $25, take rate- $6
○ 60% match rate
● Drivers: 100 rides/month, 20% churn
● Riders: 1 ride/month, typically 10% churn, 33% in cases of match failure
● Reducing Lyft's take from $6 to $3 boosts match from 60% to 93%
Side Notes:
Questions:
Immediate questions: What does it look like if we can
influence supply? How does it impact churn? Where is
equilibrium reached if we assume a linear relationship
between driver pay and match rate?
Second order questions: What does it look like if we
adjust growth rates? What does it look like if we can
influence demand? What does it look like if we can
influence driver churn or frequency?
Scope/Goal
At this point, in an actual
consulting scenario, I would
confirm the scope/goal of the
exercise. Other KPIs we
might want to consider
optimizing for could include: #
of riders on the platform, # of
drivers on the platform, # of
rides driven/ridden, GMV, etc.
Absent the chance to discuss
goal setting, we reiterate that
we are solving for how much should we pay drivers to maximize Lyft’s Net Revenue in the
Toledo market for the airport-downtown route over 12 months.
Solution:
To start, lets work backward and think about the assumptions we might be able to make about
Step 1: Before we get into more complex analysis of optimization using Microsoft Excel solver,
we’d like to rule out the most simple approaches by building a very small and limited model to
identify the critical levers and serve as a foundation for further analysis.
This first model will limit our evaluation to just month 1, ignoring the impact of churn
momentarily, and holding # of ride requests constant.
Assumptions:
● We’ll assume initially that we cannot influence demand or rider growth rate through cost
cuts (i.e. rider activity is fixed at 1 ride per rider per month)
● We’ll assume initially that 10% churn is the lower bound, and we cannot influence that
further via pricing
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●
Because we only have two datapoints regarding the impact of driver-pay on match rate,
we’ll exclude any form of sophisticated regression analysis. For the purposes of this step
(and later steps), we will assume a linear relationship between driver-pay on match rate.
We will start by evaluating the simplest approach, by identifying the linear relationship
between take rate and match rate to determine the impact of the upper limit, a 100%
match rate, on net income.
Using the algebraic equation:
m=
y 2− y 1
Where, the points on the graph are (3,93) and (6,60)
x 2−x 1
We find that the slope is
60−93
=−11
6−3
y=−11 x +126
From here we can infer Lyft’s revenue per ride of $2.36 when the match rate hits the
upper limit of 100%
●
If we assume a simple model where churn is only realized at the end of the month
(rather than on some form of rolling basis),and we assume that ride requests remain
constant in month 1 (i.e. irrespective of match rate or take rate), we quickly see that in
an isolated scenario where ride requests are denoted by some constant R, the negative
relationship between take rate and match rate suggests a optimal solution near 60% fill
@ $6 as 0.6($6)R>0.93($3)R>1($2.36)R. (Note:Admittedly, with a higher degree of
precision, we may be able to find a solution which provides even greater returns than $6,
although this ‘rounding error’ could improve the results by 1% at most.)
We also note that the linear relationship between take rate and match rate may not hold
above $6, at which point the driver pay would become uncompetitive with the prevailing
market rate.
Finally, we have demonstrated the necessity of evaluating churn as a necessary variable
to evaluate in the subsequent step.
Step 2: We’ll now evaluate the impact that churn may have on this relationship, over a 12
month period. We will continue to use the linear relationship discovered above as the basis for
the impact of take rate, in a scenario where rider churn continues unabated (i.e. there are no
new riders added to the platform at any point in the 12 month study)
Assumptions:
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●
●
●
●
●
●
We will assume the linear relationship between take rate and match, and that it will not
hold above $6. We also assume that Lyft is not interested in subsidizing riders/drivers so
negative take rate is not an option. Additionally, since we get 100% match at $2.36, our
range of potential take rate is $2.36-$6
We’ll assume that rider activity is fixed at 1 ride per rider per month (i.e. we cannot
influence demand through cost cuts) and that there are 100,000 riders on the platform
initially
We’ll assume that 10% churn is the lower bound, and we cannot influence that further
via pricing
For all of the above assumptions, we will assume they are static (uniform) across all
days of the month and there is no variability as a result of day of the week, seasonality,
etc.
For the time being, we will ignore driver churn, and that there are sufficient drivers to
maintain the match rate >= 60% subject to the linear equation identified above
Finally, we will assume that the take rate can vary over time
Results: See tab ‘Unabated Churn #1’
We ran an analysis using Excel’s solver function where the independent variable is the take rate
and the dependent variable is the match rate. Since our model optimizes for cumulative net
revenue at the end of 12 months, Excel prioritizes reducing rider churn in the early months via a
low take rate, and gradually moves toward maximizing take rate in month 12 (at which point we
are no longer concerned with rider churn).
Admittedly, this model has limited utility in practice because we need to optimize beyond 12
months and the many assumptions we’ve made. However it sets a foundation for further
analysis.
Step 3: Given that each driver can service 100 riders (at the current rate of 100 drives per
month), maintaining drivers is critical. We’ll assume this is the upper limit of driver capacity for
the time being. This means that our previously established solution will have insufficient drivers
due to churn following the first month.
Although we previously assumed that match rate was entirely a function of take rate, we must
now consider the feedback loop that driver churn has on influencing take rate.
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Specifically, with each subsequent month of churn, the maximum number of rides the platform
can accommodate fluctuates with the drivers available.
Results: See tab ‘Unabated Churn #2’
Assuming a platform in terminal decay (which I’m not happy about assuming, but given we have
positive churn, we’ll roll with it for now), each month, there will be 20% fewer drivers than the
prior month.
This time, since there is an evolving feedback loop, we will once again let the take-rate vary
from month-to-month as riders and drivers exit the platform.
Instead, we will set the # of riders matched <= number of rides available on the platform.
This leads us to the following conclusion:
For total platform revenue of $1,815,850 in FY1
Conclusion & Bonus Model:
Since the assumption of a platform in terminal decline didn’t quite sit well with me, I decided to
use the model I built and assume some negative churn. Using the same assumptions regarding
a 33% churn for unmatched riders, and the linear formula for take-rate to match %, I modified
the typical rider churn to -10% and the driver churn to -3% to demonstrate what a platform
undergoing growth could look like.
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Results: See tab ‘Bonus Sheet’
It’s admittedly imperfect; Like the previous model, churn accelerates as the model gradually
moves toward maximizing take rate in month 12 (at which point we are no longer concerned
with rider churn).
A more sophisticated model could assign some sort of dollar penalty for each churned user
(perhaps as some function of CaC).
However that model, and this additional model, both seem to be out of scope for the time being.
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