Video Games:
Reason and Revenue in a Blockbuster Promotion
Part 2
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Lee Humphries

Understanding the Values

A value of 1 or greater.  Whenever the breakeven ratio equals 1 or greater, the store will lose revenue on the promotion.  That's because those values require the number of additional turnovers to equal or exceed the number of exercised discounts.   This is impossible: Not all discounts will produce additional turnovers.  Here's why. 

Without a promotion, all early returns (of the videos we're considering) turn over again the same day; if they didn't, the promotion would be pointless.  These are regular turnovers; they always occur—promotion or no promotion.  With a promotion, the number of early returns increases; these additional early returns result in additional turnovers.  For every early return there is a discount, but only the additional early returns generate additional turnovers.  There are always fewer additional turnovers than discounts.  If each discount is exercised, the ratio of additional turnovers to exercised discounts must be less than 1.

A value less than 1.  Theoretically, a store can achieve any breakeven ratio whose value is less than 1 and greater than or equal to 1/3 (the bottom of the range).  But practical considerations reduce the upper limit.

To get some perspective, we'll do three things.

•     First, we'll determine a likely range of values for the breakeven ratio.

•     Having done that, we'll introduce a second kind of number, the additional early-return factor (defined below), which is derived from the breakeven ratio.

•     Finally, we'll evaluate the range of additional early-return factors that corresponds to the range of breakeven factors.  That will be revealing.

How the rental mix affects the breakeven ratio.  Recall that the breakeven ratio is determined by the value of the expression

(average Next Rental fee)  -  (discounted Next Rental fee)
(New Release fee)  -  (average Fallback Rental fee)

In this expression, there are two variables: the average Next Rental fee and the average Fallback Rental fee.  (The other items are constants.)  The average Next Rental fee is determined by the mix of New and Old Release rentals in Subset A.  The average Fallback Rental fee is determined by the mix of Tradedowns and Forgone Rentals in Subset B.

For Subset A, it is reasonable to assume that New Releases comprise roughly 50% to 70% of the rental mix.  (New Releases are more popular than Old Releases.)

Constraints on forgone rentals.  Subset B is more complicated.  As we learned above, the breakeven ratio must have a value that is less than 1. 

The lower limit.  When we combine that fact with the fact that Subset A's New Release rentals lie in the 50%-to-70% range (i.e., the average rental fee is somewhere between $2.50 and 2.70), the mathematical outcome is this:  Forgone Rentals must comprise more than 25% of Subset B's Fallback Rental mix; 25%+ is the lower limit for Forgone Rentals in the Fallback mix.

Why 25%?  Without the promotion, at least 50% of Subset A's rentals are assumed to be New Releases, so the average rental fee is no lower than $2.50.   As each Subset A patron substitutes a $1.00 Discounted Rental for his Average Rental, the store gives up $1.50 in revenue.  This $1.50 loss must be recaptured from Subset B renters, whose average Tradeup must contribute $1.50, or more, in offsetting revenue.  When a Subset B renter trades up from a Forgone Rental, the store collects $3 in new revenue ($3 - $0 = $3); when a Subset B renter trades up from an Old Release, the store collects $1 in new revenue ($3 - $2 = $1).  If 25% of Subset B renters trade up from a Forgone Rental, the average offsetting revenue per rental will be $1.50—which equals 25%($3) + 75%($1)—and the breakeven ratio will be exactly 1, an impossible value to achieve, as previously discussed.  Therefore, for the breakeven ratio to fall below 1, Forgone Rentals must comprise more than 25% of Subset B's Fallback Rental mix.

The upper limit.  The upper limit for Forgone Rentals is constrained by practical considerations.  Consider this: If Forgone Rentals are 100% of the fallback mix, all patrons who found their high-demand preference out of stock rented nothing to replace it.  Most customers don't behave this way; rather than return home empty-handed, they'll rent some other title as a substitute.  So, an upper extreme of 100% is virtually impossible.

Let's be overly generous and say that as many as 70% of Subset B patrons forgo a rental when they find their New Release preference out of stock.  That limits Forgone Rentals to a range whose bottom exceeds 25% and whose top doesn't climb above 70%.

Constraints on the breakeven ratio.  The promotion is now fenced in by three conditions:

•     The breakeven ratio must be less than 1.

•     The percentage of new Next Rentals in Subset A must be in the 50%-to-70% range.

•     The percentage of forgone Fallback Rentals in Subset B must be within the 25%-to-70% range.

These conditions yield breakeven ratio values ranging from a high of .9444 to a low of .625.  We will now relate these values to early returns.

The Additional Early Returns Factor  

Corresponding to every breakeven ratio value is another number, the additional early returns factor.  The additional early returns factor is the multiple by which pre-promotion early returns must increase if the promotion is going to generate breakeven revenue.  This multiple is equal to the expression

breakeven ratio              - 1
1 - breakeven ratio

Inserting into this expression the value .9444, the highest value arising from the three preceding conditions, we get a multiple of 16 times the regular number of early returns: [.9444/(1-.9444)] -1 = [.9444/.0556] -1 = 17-1 = 16.  At the highest breakeven ratio, the promotion will have to increase early returns (of promoted titles) by an astounding 1600% to achieve breakeven revenue.

Now let's drop down to the other end of the range.  Inserting into the expression the value .625, the lowest value arising from the three preceding conditions, we get a multiple of 2/3 times the regular number of early returns: [.625/(1-.625)] -1 = [.625/.375] -1 = 1.67 –1 = .67 = 2/3.  Even at the bottom of the range, the promotion will have to increase early returns by an unlikely 67%. 

Furthermore, all additional early returns must turnover again the same day.  If the store fails on either count, it will lose revenue.

Other negative factors.  The situation grows worse.  Other negative factors are also at work.  Our practical minimum breakeven ratio of .625 corresponds to 50% New Releases in the Next Rental mix, 70% Forgone Rentals in the Fallback Rental mix.  But in reality, the percentage of New Releases will likely be higher; the percentage of Forgone Rentals, lower.

The mathematical dynamics of the promotion are such that the additional early returns factor must rise as: (1) the percentage of New Releases in the Next Rental mix increases and/or (2) the percentage of Forgone Rentals in the Fallback Rental mix decreases.  So in all likelihood, the actual additional early-returns factor for breakeven revenue will exceed the practical-range minimum of 67%. 

What are the chances that a store can increase early returns by more than 67%?  Not very good.

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