The impact of tax legislation on lot-sizing and sourcing

strategies

Hua Jin, Dr Patrick Beullens

Southampton Business School, University of Southampton , United Kingdom

CMS-MMEI, 29th March 2019, Chemnitz

Content1. Introduction

– Corporate tax (CT), Value Added Tax (VAT), Import Duties (ID)

– Literature & Research questions

2. Economic Order Quantities with CT and VAT

– NPV based EOQ

– CT and VAT schemes and their impact

– CT and VAT Adjusted EOQ

– Numerical results

3. Acquisition (Acquire products from EU) with CT and VAT

4. Import (Global sourcing) with CT and VAT

5. Conclusion2

1. Introduction: Taxes

• Corporate Tax (CT)

• Import Duties (ID)

• Value Added Tax (VAT)

As most firms wish to make decisions that maximise future profits after tax, these additional expenses should in principle be accounted for.

3

1. Introduction: Taxes in supply chain

4

Raw material producer manufacturer

Retailer Customer

Sells 100+VAT(20)

20

Reclaims VAT

charged by

producer, sells

finished goods to

retailer for

200+VAT(40)

20

40

Reclaims VAT charged from

upstream, sells finished goods

to customer for 400+VAT(80)

4080

HM Revenue & customs

Producer-Collect 20

Manufacturer-collect 20

Retailer-collect 40

80 Output VAT for Retailer

40 Input VAT for Retailer

1. Introduction: OR literature

• There is an increased awareness in the literature of the importance of taxes to the firms and the management of supply chains.

• Very few papers in the inventory literature consider taxes

– Gurnani (1983) develops EOQ with CT and NPV criterion, but optimal lot-size independent of CT. No VAT.

– Michalski (2013) derives a modified “NPV” EOQ model with CT tax benefit on costs to maximise firm value. Optimal lot-size decreases. No VAT.

– Hsu and Zhu (2011) & Xiao et al. (2015) analyse production models under Chinese export-oriented VAT policy and CT. Optimal decision depend on purpose of the product of the tax policy. No NPV.

No literature has examined impact of timing of taxes

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1. Introduction: Why CT and VAT are ignored?

• CT 𝑀𝑎𝑥 ( 1 − 𝜖 𝑝 − 𝑐 𝑦)

= 𝑀𝑎𝑥 (𝑝 − 𝑐)𝑦

• VAT 𝑀𝑎𝑥 ( 1 + 𝜏 𝑝 𝑦 − 1 + 𝜏 𝑐 𝑦 − 𝜏𝑝𝑦 + 𝜏𝑐𝑦)

= 𝑀𝑎𝑥 (𝑝 – 𝑐)𝑦

• If lot sizing models are based on average cost, it seems that both CT and VAT would not impact decisions.

• This is no longer true when looking at the processes by which most governments collect VAT and CT cash-flows.

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1. Introduction: Research Question

• Based on the NPV criteria, how should the financial parameters in the model to be specified so that its application ensures compatibility with the NPV optimization of profits after tax ?

• Is there a rational for embedding taxation rules and processes in inventory control , further for supplier selection based on the Economic order quantity assumptions?

As most firms wish to make decisions that maximise the Net Present Value (NPV) of future profits after tax, these additional cash-flows

and their timing should in principle be accounted for.

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1. Introduction: Sourcing Strategy

8

UK Domestic

Buyer

global supplier

EU supplier

UK domestic customer

EU customer

Acquisition

Import

1 Domestic Purchasing

2 Acquisition

3 Import

Applied UK and EU tax rules that applied

in 2015-2016 as the basis on our

Understanding of relevant legislation.

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2. EOQ derived from NPV criterion

AS=p y- ( s + w y T )σ𝑖=1∞ 𝑒(−𝑖𝑎𝑇) - FOC = p y -

𝑎( 𝑠+𝑤𝑦𝑇)

1−𝑒−𝑎𝑇-FOC

෪𝐴𝑆=( p – w ) y -𝑠

𝑇- a

𝑠

2- a w

𝑦𝑇

2- FOC

Q* =2𝑠𝑦

𝑎𝑤

• In general term, CT is charged as a percentage of Operating Profit (OP) in an accounting year.

𝑂𝑃 = 𝐺𝑟𝑜𝑠𝑠 𝑃𝑟𝑜𝑓𝑖𝑡 (𝐺𝑃) − 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝐸𝑥𝑝𝑒𝑛𝑠𝑒𝑠 (OE)

• In operational business function expressed in EOQ model:

𝑂𝑃 = 𝑁𝑒𝑡 𝑆𝑎𝑙𝑒𝑠 − 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝐸𝑥𝑝𝑒𝑛𝑠𝑒𝑠 −𝐶𝑂𝐺𝑆

𝑝𝑦𝑠

𝑇+ 𝐹𝑂𝐶 𝑤𝐼0 + 𝑤 𝑦 − 𝐼0 + 𝐼1 − 𝑤𝐼1 = 𝑤𝑦

In the EOQ model, the amount of products purchased may differ from demand ydue to the lot size decision and the times when the accounting year starts and ends relative to the inventory cycle, however, for the constant purchase price w, the effect can cancel out.

𝑂𝑃 = 𝑝𝑦 −𝑠

𝑇− 𝐹𝑂𝐶 −𝑤𝑦

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2. EOQ and CT cash-flows (1)

Firms with a taxable profit of £𝟏. 𝟓 𝒎𝒊𝒐 or less, pay CT 9 months (and one day) after the end of the accounting year.

Amount need to pay at time 0: є 𝑂𝑃 𝑒− 12+9 𝑎𝑇𝑣

ASє = −є 𝑂𝑃 𝑒− 12+9 𝑎𝑇𝑣 σ1=1∞ 𝑎 𝑒−𝑖𝑎𝑇𝑎

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9month 9month 9month

NPV= −є 𝑂𝑃 𝑒− 12+9 𝑎𝑇𝑣 σ𝑖=1∞ 𝑒−𝑖𝑎𝑇𝑎

0

year year year

year

2. EOQ and CT cash-flows (2)

Firms with a taxable profit above £𝟏. 𝟓 𝒎𝒊𝒍𝒍𝒊𝒐𝒏 pay CT in quarterly instalment , and these payments are due at times of middle 6; 9; 12; and 15 (in months) from the start of the accounting year.

Firms with a taxable profit above £20 million pay CT earlier, so tax due is the third, sixth, ninth and 12th months of the period.

We define the CT effect

It is an adjustment of an adopted CT rate and which is account for the

time-dependent CT schemes . Є' = є𝑒−𝑎(12+9)(1/12)

1−𝑒−𝑎𝑇𝑎

Corporation Tax-adjusted annuity stream function ASє = Є′ OP 12

2. EOQ and CT cash-flows (3)

The firm’s expected annual VAT liabilities to the government are net difference:

NVAT=OVAT-IVAT=p y τ – (w y τ + 𝑠τ𝑇

) – τ(1- δ) FOC

We define the VAT tax effect :

It is adjustment to an adopted VAT tax rate which account for the time-dependent VAT schemes used by firms.

Annual VAT accounting scheme

Standard VAT accounting scheme

Tax-exchange Annunity stream function depend on schemes

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2. EOQ and VAT cash-flows

• AS version of EOQ model in which the impact of CT and VAT is included, hence, the objective function is given by:

Linear approximation of the VAT CT adjusted EOQ:

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2. EOQ model with CT and VAT effects (1)

• The effect of taxes significantly increase the opportunity cost of capital to be used in the EOQ formula.

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2. EOQ and Tax – Analysis

Q* =2𝑠𝑦

𝑎𝑤TQ* =

2𝑠𝑦

𝞬′𝑤

3. Acquisition and Tax

ASio = py (1+ τ) + ponyon(1+ τ) + poryor (1+ τ)

− s 𝑎 ( 1+τs)1−𝑒−𝑎𝑇

−wYT𝑎 1+τw1−𝑒−𝑎𝑇

−(1- δ) FOC (1+ τ)– δ FOC

Q1* =2𝑠𝑦(1+τ−ϵ′−τ′)

𝑎𝑤(1+τ)(UK sourcing)

Q4* =2𝑠𝑦(1−ϵ′)

𝑎𝑤(EU sourcing)

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UK Domestic

Buyer

EU supplierEU customer

UK domestic customer

Ponyon =output VAT Poryor = No output VAT

3. Acquisition and Tax: sourcing strategy

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− s 𝑎 ( 1+τs)1−𝑒−𝑎𝑇

−wYT𝑎 1+τw1−𝑒−𝑎𝑇

3. Acquisition and Tax: Impact of Sales

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py (1+ τ) + ponyon(1+ τ) + poryor (1+ τ)

4. Import and CT with VAT

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ASio = py (1+ τ) + ponyon(1+ τ) + poryor (1+ τ)

−[ wYT𝑒𝑎𝐿𝐼 + xs𝑒𝑎𝐿𝑠 + (wYT +xs)ϴ𝑒𝑎𝐿𝑁

+ (wYT+xs) )(1+ ϴ)τ1𝑒𝑎𝐿𝑁

+ (1-x) s (1+ τs ) ] σ𝑖=1∞ 𝑒(−𝑖𝑎𝑇)

−(1- δ) FOC (1+ τ)– δ FOC

4. Guide price for global sourcing

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5. General conclusions

• Tax rate & schemes - when the firm pays tax to the government, are both important to the inventory decisions.

• Tax adjusted inventory model decreases set up cost, but increases holding cost. Optimal order level is smaller than those arrives at when using the unadjusted values of set up cost s and holding cost aw.

• If marginal profit is low, logistics decision are important, and thus also tax considerations.

• Impact on order quantity decisions, impact on supplier selection, impact on sale strategy.

• Government role is introduced in the logistic decision.

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Thank you for your attention !

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