儲值票卡發行公司可運用資金之研究

Abstract

摘要 儲值票卡的持有人以先付款後消費的方式使用票卡進行消費，因此發行儲值票卡的單位將可因票卡銷售，而有一項預收款餘額，若能妥善運用，此一款項將可衍生投資收益。另外，在票卡遺失、毀損或過期的情況下，持卡人無法繼續使用卡內剩餘儲值金額，則票卡未被使用餘額將成為卡片發行公司的另一項利得。這兩項利得在服務費率不高時，亦即發卡公司無法對業者收取足以反映成本及合理利潤所需的服務費率時，將成為是否能夠回收設備投資成本的關鍵因素。 儲值票卡的卡內金額與存貨類似，因此，用於分析存貨耗用情形的圖形，應可用於分析儲值票卡的卡內金額耗用情形，類似的套用也曾出現在Baumol（1952）的目標現金餘額決定。本研究利用存貨分析圖形發展出模式的分析單元，並由分析單元的組合形成票卡的收入流與消費流，此對儲值票卡發行公司的預收款餘額與票卡未被使用餘額的估算非常有幫助。 儲值票卡發行公司的預收款餘額為發卡公司每一期淨現金流入之累積值，其中，現金流入來自於票卡收入，而現金流出則來自於其與服務提供機構間的帳款清算，其值主要受卡內儲值金額被使用之速度、卡內儲值金額是否被用罄，以及發卡公司與服務提供機構間的帳款清算方式影響。儲值票卡發行公司的預收款餘額除了會隨票卡收入的增減而增減外，亦會隨上述因素之不同，而有變化，本研究利用這四個影響因素作為模式分析的主要情境構面，來建構預收款餘額模式。 本研究先建構連線即時的基本模式，再以該模式為基礎，每次僅變動一個構面值，來推演其他適用於單一服務提供機構的預收款餘額模式。至於多服務提供機構的預收款餘額模式之構建，本研究係以消費者過去花用在各服務提供機構的消費比例分解每日票卡收入，然後以分解後的每日票卡收入與前述用於單一服務提供機構之預收款餘額模式，依與個別服務提供機構之帳款清算方式求算預收款餘額，最後再將這些個別求算出來的每期預收款餘額加總，而得出多服務提供機構之預收款餘額模式。 本研究也以模擬數值帶入前述所提之所有預收款餘額模式中，並據以畫出預收款餘額時序圖與投資收益時序圖，以瞭解各模式之特性與異同，另以比較靜態分析探討預收款餘額與各影響變數之變動方向，再以圖形綜合之，以瞭解預收款餘額對各影響變數之相對彈性。結果發現，預收款餘額會隨每日票卡收入、每日票卡收入增加率、票卡使用期限、票卡未被使用率，以及帳款清算週期的增加而增加，而隨卡內金額被使用速度之增加而減少。本研究亦發現，預收款餘額與各影響變數間的相對彈性，會因變數值與期別的不同而使某些變數的彈性排序產生變化，然大體而言，以每日票卡收入對預收款餘額的影響最大，而以卡內金額被使用速度對預收款餘額的影響最小。 至於票卡未被使用餘額的估算，本研究係以票卡收入流與票卡消費流的關係，先找出票卡未被使用率的估計式，再計算票卡未被使用餘額。結果發現，票卡未被使用率的估計式不受卡內儲值金額被使用的速度影響，可是票卡收入的成長型態如果改變，其票卡未被使用率的估計式也會隨之而變。

Abstract Stored value card is pre-paid card. A holder of stored value cards pays before consumption. The stored value cards issuing company might gain investment benefit due to the unused prepaid amount. Furthermore, an issuing company could obtain the balance for voided card if stored value cards are lost, broken or beyond the time limit. These benefits are the key factors for an issuing company to recover the cost if the service charge is regulated. The value contained in stored value card is similar to the characteristics of inventory. Therefore, the diagram used for analyzing the consumption of inventory may be suitable for analyzing the consumption of stored value cards. The diagram has been adopted in determining the Target Cash Balance by Baumol (1952). In this study, the diagrams are used to develop the analysis unit of model. By combining all analysis units, we could get the revenue flow and consumption flow of stored value card, which are conducive to the estimates of the unused prepaid amount and balance for issuing company. The unused prepaid amount of stored value cards per period equals the cumulative value of net cash inflow per period for issuing company. The cash inflow comes from the ticket revenue and the cash outflows are paid to the service providers through clearing account. The cash outflow is affected by the usage rate of stored value cards and the clearing pattern agreed by stored value cards issuing company and service-providing units. We take four factors -- the ticket revenue, the using speed of stored value cards, whether the full amount of stored value card is used up, and the clearing pattern between stored value cards issuing company and service-providing units – in this work to study the voided amount. One possible value from each dimension is employed to construct the basic model. The value of one dimension per time is changed to construct other models. The proposed models are suitable for the cases with one service provider or multiple service providers, when the clearing patterns are similar. If the clearing patterns or the clearing days are different, we must divide the ticket revenues into various amounts proportional to the consumption in each service for each day. With classified ticket revenue and the corresponding consumption in each day, we formulate the cash flows accordingly. The cash flow for this case could be obtained through combining all cash flows. Besides, we take value into those analysis models. We draw the timing diagrams of voided amount of stored value cards and its investment benefit. The comparative static study for voided amount of stored value cards is implemented. It is found that voided amount of stored value cards increases when ticket revenue per day, the adding rate of ticket revenue per day, the used cycle of ticket, the balance ratio of ticket or the clearing cycle increases. This value has opposite change direction with the using speed of stored value cards. Furthermore, the elasticity and its order among some variables for unused prepaid amount of stored value cards change if the value of variables or period changes. In general, the unused prepaid amount of stored value cards is deeply affected by ticket revenue per day, while it is lightly affected by the using speed of stored value cards. After analyzing the revenue flow and consumption flow of stored-value tickets, a method is proposed to estimate the value for voided tickets. Balance ratio could be applied to reach a good result in the process of estimation. It is shown that the estimator of balance ratio remains the same for constant and accelerated consumption rates. However, balance ratio will change if the ticket revenue is growing.