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Estimating Gift Certificate Liability: An Actuarial Approach CAS 2003 Annual Meeting New Orleans, Louisiana November 9-12, 2003 Harry T. Garland, Ph.D. [email protected] Garland Actuarial LLC. Terminology.

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Estimating Gift Certificate Liability:

An Actuarial Approach

CAS 2003 Annual MeetingNew Orleans, LouisianaNovember 9-12, 2003

Harry T. Garland, [email protected]

Garland Actuarial LLC

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Terminology

Liability* – Expected value of all future gift certificate redemptions from those already issued.

Breakage – Expected value of issued gift certificates that will never be redeemed.

Breakage Factor – Percentage of total value of issued gift certificates contributing to Breakage.

Escheat Law – Legal basis in some states to claim from the issuer the dollar value of unredeemed gift certificates.

* Auditors may take other factors into account when determining liability for accounting purposes

Garland Actuarial LLC

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The Problem

Let TI = Total value of certificates issued

Let TR = Total value of certificates redeemed

Let L = Liability

Let B = Breakage

Then,

TI – TR = L + B

For unredeemed certificates how do you estimate those that will be redeemed at some future time (L) vs. those that will never be redeemed (B)? And what if the company does not have accurate records to be able to determine TI and TR?

Garland Actuarial LLC

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The Process

Actuary

Analysis

Analysis

Accountant

Attorney

Data

Company

Escheat Law Compliance

Balance Sheet Liability

Garland Actuarial LLC

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Sample Company Data

Garland Actuarial LLC

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Analytical Approach

1) Build a model that predicts monthly certificate redemptions from historical monthly certificate sales.

2) Determine breakage from the model.

3) Determine liability from the model

Garland Actuarial LLC

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Building the Model

1) Assume that certificate redemptions in any month can expressed as a linear combination of certificate sales for that month and all past months.

2) Express the model as a redemption vector with elements RV(0), RV(1), RV(2)… where

RV(0) is the percentage of dollar value issued in the current month contributing to redemptions in the current month.

RV(1) is the percentage of dollar value issued in the immediately preceding month contributing to redemptions in the current month.

And so on. The length of the vector should be determined by when the contribution of certificates issued in more distant months becomes immaterial to current redemptions.

Garland Actuarial LLC

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Techniques for Calculating the Redemption Vector

  • If transaction data on redemptions by issue date is available, build an actuarial triangle of redemptions by age of month of issue.
  • If only cumulative sales and redemption data is available consider multiple regression analysis and/or exponential decay model.

Garland Actuarial LLC

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Example of Regression Matrix

Dollar amount redeemed each month is modeled as a linear combination of the dollar amounts issued in preceding months. The regression coefficients form the elements of the redemption vector. Assumption for this example is that there are no significant redemptions from certificates more than one year old.

Garland Actuarial LLC

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Regression Vector

for Sample Company Data

For this example, the elements of the redemption vector are the coefficients of the regression.

RV = (33.2%, 27.9%, 8.9%, 6.1%, 4.3%, 2.9%, 2.4%, 2.3%, 1.8%, 0.2%. 0.1%, .06%)

Garland Actuarial LLC

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Calculating Breakage Factor

Since each element of the redemption vector, RV(n), represents the percentage contribution to monthly redemption of those certificates issued n months prior to the redemption month, then the sum of all the elements of the redemption vector represents the percentage of certificate sales that is estimated to be redeemed. The breakage factor then is given by:

Garland Actuarial LLC

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Calculating Liability

  • Convolution of the redemption vector with the vector of monthly certificate sales yields the vector of estimated monthly certificate redemptions.
  • Convolution of the liability vector with the vector of monthly certificate sales yields the vector of estimated liabilities (as of the end of each month.)
  • The liability vector models what has not yet been redeemed. It can be derived from the redemption vector as follows:

For a redemption vector with n+1 elements RV(0), RV(1), … RV(n), the liability vector, LV, can be formulated as an n-element vector where each element (x ranging from 0 to n-1) is given by:

Garland Actuarial LLC

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Summary

We have shown how actuarial techniques can be used to help a company estimate future gift certificate liabilities. This information is needed to help the company determine its balance sheet liability for gift certificates and its escheat obligations (which vary form state to state.)

Companies may have very poor records regarding their paper gift certificate transactions (e.g. no redemption data by issue date.) Companies that have merged or acquired other companies may have incomplete historic data. As a result, a variety of techniques may be needed to accurately model redemptions.

Many companies are replacing their gift certificates with magnetically-striped gift cards. Use of gift cards will facilitate the acquisition of data for actuarial analysis.

Garland Actuarial LLC

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