Factoring policy with constant demand and limited capital

• Author: Yanhai Li,Chaocheng Gu
• Published date: 01 November 2020
• DOI: http://doi.org/10.1111/itor.12514
• Date: 01 November 2020

Intl. Trans. in Op. Res. 27 (2020) 3104–3122

DOI: 10.1111/itor.12514

INTERNATIONAL

TRANSACTIONS

IN OPERATIONAL

RESEARCH

Factoring policy with constant demand and limited capital

Yanhai Liaand Chaocheng Gub,∗

aSchool of Business Administration, Guangdong University of Finance and Economics, Guangzhou 510320, China

bDepartment of Administrative Management, Jinan University, Guangzhou 510632, China

E-mail: xgliyh@163.com [Li]; guchaocheng@jnu.edu.cn [Gu]

Received 18 April 2017; received in revised form 3 October 2017; accepted 3 January2018

Abstract

The conventionof selling on credit (to customers) results in mass accumulation of accounts receivable(AR) on

the balance sheet of firms. However, capital-constrainedfir ms do not have enough capital to investin AR and

cover the production cost incurred during the credit period. To finance future business, a capital-constrained

firm can employ factoring—a financing scheme wherein firms sell AR to a financial institution (called a

factor) at a discount—to advance cash from AR. By formulating a time-continuous model with constant

demand over an infinite horizon, we study the factoring policy of firms in two practice-based discounting

schemes: automatic discounting and manual discounting. In the automatic discounting scheme, AR should be

discounted at the same age,whereas this requirement is relaxed in the manualdiscounting scheme and how long

in advance to discount the AR is contingent over time. In both discounting schemes, the firm needs to choose

the timing of discounting in order to reach a capital-unconstrained state as soon as possible. In the automatic

discounting scheme, we approximate the firm’s objective function with a quasi-convex function whose error

is demonstrated to be small. Based on this approximation, the firm’s optimal decision and the factor’s profit

can be calculated more easily. When manual discounting is adopted, the firm should meet all the demand by

exploiting factoring if the profit marginunder immediate discounting is nonnegative. Giventhe same factoring

discount rate, manualdiscounting is always more attractive to the firm than automatic discounting. However,

the preference of the factor over the two discounting schemes depends on the factoring discount rate.

Keywords:accounts receivable; factoring; discounting; payment delay; credit period

1. Introduction

Firms often sell to customers under a trade credit contract that results in mass accumulation of

accounts receivable (AR) on their balance sheets. For instance, the aggregate trade credit reached

nearly US$5.6 trillion in 2012, with the average firm extending approximately 19% (17%) of its

sales (assets) in the form of AR (Ghoul and Zheng, 2016). It is estimated that trade credit financed

∗Corresponding author.

C

2018 The Authors.

International Transactionsin Operational Research C

2018 International Federation ofOperational Research Societies

Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148,

USA.

Y. Li and C. Gu / Intl. Trans. in Op. Res.27 (2020) 3104–3122 3105

roughly two-thirds of the global trade in the year 2014 (Breza and Liberman, 2017). To leverage

AR-based assets for financing future business, firms can employ factoring, which is a financial

arrangement that allows firms to sell their AR to a financial institution (called a factor) at a

discount, to advance cash and increase their capital position. Factoring has emerged as one of the

most important sources of financing for small and medium-sized enterprises (Bakker et al., 2004).

The total worldwide factoring volume increased from €1.28 trillion in 2010 (Milenkovic-Kerkovic

and Dencic-Mihajlov, 2012) to €2.35 trillion in 2014 (Auboin et al., 2016).

Factoring facilities are traditionally made on a whole turnover basis (Mizan, 2011; Ramage,

2012), whereby the entire sales ledger of a company must flow through the factor in the contract

period, irrespective of the firm’sfinancial need. Therefore, the wholeturnover factoring arrangement

is referred to as automatic discounting. An automatic discounting contract often specifies the

remaining payment days, which is fixed over the whole contract period. For example, the firm

may allow all AR to be discounted automatically at the earliest possible moment (Vliet et al.,

2015). By contrast, in recent years more and more factoring facilities provide selective discounting

(e.g., spot factoring) arrangements wherein single receivables are sold to a factor and the firm

can choose when and which AR to discount. Therefore, the selective discounting is referred to as

manual discounting. Manual discounting appears to be increasingly popular with the emergence of

information technology and new business models. For example, MarketInvoice, a rising star of the

U.K.-based Fin-tech start-ups, utilizes advanced data analysis approaches and online peer-to-peer

(P2P) platform to provide manual discounting (selective discounting) as well as the traditional

automatic discounting (whole turnover) based factoring service to its clients.

Regardless of whichdiscounting arrangement applies, one common advantage of factoring is that

the capital-constrained firms can employ this financing scheme to alleviate their underinvestment

problem (Sopranzetti, 1999), and raise working capital to finance the production of next orders

(Auboin et al., 2016). The main disadvantage of factoring is that the profit margin of a firm shrinks

further because of the relatively high factoring cost. For example, Klapper (2006) found that the

average factoring cost rate is 5 percentage points above the bank rate, while the effective annual

cost rate of factoring can be as high as 50 percentage points (Michalski, 2014). Therefore, a capital-

constrained firm experiences the following trade-off in deciding the optimal timing of discounting:

selling the AR earlier to finance future business to alleviate demand loss, or holding the AR to a

later timing to save financing cost and retain a higher profit margin.

Before choosing the discounting timing, firms and factors should consider which discounting

scheme (automatic or manual discounting) suits them best. A recent survey found that 63% of

the firms prefer automatic/whole-turnover discounting to manual/selective discounting, while the

remaining 37% hold the opposite preference (Blackman, 2013). From the perspective of factors,

the niche for manual discounting has induced a rising number of traditional factors (that were

used to allow whole-turnover discounting only) to provide selective factoring facilities. Meanwhile,

the reverse can also be true. For example, MarketInvoice, one of the largest manual discounting

providershas expanded its business into the automatic discounting segment of factoring market. The

cost effectiveness of the twodiscounting schemes differs. In the manual discounting scheme,the fir m

sells AR only when in shortage of cash. In the automaticdiscounting scheme there is continuing cost

in the whole contract period, usually forthree months or longer, even if the firm’scash flow improves

to the extent that finance is not actually required (Kirkby, 1976). Few studies have examined the

effect of cost effectiveness on the firm’s and factor’s preference over the two discounting schemes.

C

2018 The Authors.

International Transactionsin Operational Research C

2018 International Federation of OperationalResearch Societies