Video Games:
Reason and Revenue in a Blockbuster Promotion
Part 3
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Lee Humphries

Extra Rentals

The promotion has another aspect that still might save the day for Blockbuster.

The promotion requires early returnees to exercise their discounts at the same time they return their promoted videos.  This "use it or lose it" rule induces some people to rent their Next Rental sooner than usual.

If enough early returnees treat their Discounted Rental as an Extra Rental (a cheap title rented in addition to their usual Next Rental), their Extra Rental will offset the revenue lost when other early returnees treat their Discounted Rental as their Next Rental (a cheap title rented in lieu of their usual, higher-priced selection).

What percentage of early returnees must exercise their discount as an Extra Rental for the store to generate the same revenue with the promotion as without it?  The percentage varies and is affected by several things:

•     the rental fees for different classes of videos,

•     the average rental fee,

•     the proportion of additional turnovers (if any) to early returns, and

•     the source of those additional turnovers—Are they from patrons who previously substituted an Old Release for an unavailable New Release, or from patrons who forwent a rental altogether?

As you can see from the last two points, additional turnovers play a critical role in determining the breakeven percentage of Extra Rentals.

A store will encounter one of four situations with respect to turnovers: (1) no additional turnovers; (2) additional turnovers, all of which come from Forgone Rentals; (3) additional turnovers, all of which come from substituted Old Releases; and (4) additional turnovers, coming from both Forgone Rentals and substituted Old Releases.

A mathematical model of the promotion.  All four situations are covered by the following equation, which models the conditions for breakeven revenue.  The equation gives the percentage of Extra Rentals, X, required for the promotion's revenue to offset the cost of the discount.

X = ( 1 + ge - { [D + (f + g)eN] / A} )

where:

All input and output percentages are expressed as their decimal equivalents.

e is the percentage increase in early returns; this increase is the additional early returns.

f is the percentage of additional early returns resulting in turnovers by customers who previously substituted nothing for an out-of-stock New Release; f = 1-g.

g is the percentage of additional early returns resulting in turnovers by customers who previously substituted an Old Release for an out-of-stock New Release; g = 1-f.

D is the Discounted Fee.

N is the New Release Fee.

A is the Average Rental Fee.

            A is equal to n[New Release Fee]+[1-n][Old Release Fee],
                  where:

                  n is the percentage of New Releases in the pre-promotion rental mix, and

                  (1-n) is the percentage of Old Releases in the pre-promotion rental mix.

(Were a store to rent no New Releases, the average rental fee would equal the Old Release fee.  Under these conditions the promotion would be impossible and the X value would be meaningless.)

Let us reiterate.  For the promotion to achieve breakeven revenue, X percent of early return discounts must be exercised as Extra Rentals.

The equation for this breakeven X reveals that X must increase as:

•  the ratio of additional early returns to all early returns decreases (i.e., as e decreases),

•  the ratio of substitute rentals to forgone rentals increases (i.e., as g increases),

•  the average rental fee, A, increases.

The discount exercise period.  If the promotion is to succeed, a critical percentage of discounts must be exercised as Extra Rentals.  However, the percentage of Extra Rentals that a store can achieve is constrained by the duration of the discount exercise period.

As the discount exercise period grows longer, the likelihood that customers will use the discount for an Extra Rental grows smaller—the pressure to "use it or lose it" decreases.  More customers will find that the longer discount exercise period includes the date when, as a matter of course, they would transact their Next Rental.   Thus, a longer discount exercise period lets more customers rent on their regular schedule and still take advantage of the discounted title (selecting a discounted title in lieu of their normal, more expensive Next Rental).  This threatens revenue.

Blockbuster must have recognized the threat since it required patrons to exercise the discount at the time of the early return.  The requirement, however, is a double-edged sword.  A shorter discount exercise period indirectly reduces the percentage of additional turnovers, e. Customers who can't use another video within the limited discount exercise period won't inconvenience themselves to return their promoted videos early.  That will reduce the supply of additional early returns (on which additional turnovers depend).

The discount exercise period can be shortened to increase the percentage of Extra Rentals or it can be lengthened to increase the percentage of additional early returns.  But it cannot be adjusted to make the two rise simultaneously.  Any plan to increase Extra Rentals and additional turnovers in tandem is logically flawed.

Is the Promotion Viable?

Applying the equation.  To assess the overall viability of the promotion, we will use the above equation to evaluate two different scenarios, determining for each the percentage of Extra Rentals, X, needed for breakeven revenue.  The scenarios differ in the values we assign to e, g, and A.  (We don't adjust D and N; they're constants.  And we don't need to worry about f; since f = 1-g.)

Best-case scenario.  In the best-case scenario, we make the following assumptions about a store:

§         50% of the early returns are e, additional early returns (i.e., early returns generated by the promotion).

§         50% of the additional turnovers are g, tradeups from an Old Release to a New Release.

§         The average rental fee, A, is $2.50 (which is to say, prior to the promotion 50% of the rentals were New Releases; 50% were Old Releases: (.5*$3) + (.5*$2) = $1.50 + $1.00 = $2.50.

The promotion is unlikely to encounter values more favorable to its cause than these.  To achieve breakeven revenue with these values, 25% of the discounts need to be exercised as Extra Rentals: X = 25%.

Reasonable-case scenario.      In the reasonable-case scenario, we make these, more realistic, assumptions about a store:

§         10% of the early returns are e, additional early returns (i.e., early returns generated by the promotion).

§         75% of the additional turnovers are g, tradeups from an Old Release to a New Release.

§         The average rental fee, A, is $2.60 (which is to say, prior to the promotion 60% of the rentals were New Releases; 40% were Old Releases: (.6*$3) + (.4*$2) = $1.80 + $0.80 = $2.60.

To achieve breakeven revenue with these more realistic values, 57.5% of the discounts must be exercised as Extra Rentals: X = 57.5%. 

Conclusion.     It is most improbable that the promotion could induce more than half of the participants to rent an Extra video, as required by the reasonable-case scenario.  Indeed, it would be a feat if the promotion could induce even a quarter of the participants to rent an Extra video, as required by the best-case scenario.

Our calculations strongly suggest that the promotion will lower—not increase—revenue.  Perhaps Blockbuster came to realize this as well.  Several months after my first encounter with the promotion, I ran into it again in another part of the country.  Things had changed.  The reward for an early return was no longer a Discounted Rental.  It was a bag of popcorn.

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