The impact of tax legislation on lot-sizing and sourcing strategies - - PowerPoint PPT Presentation

The impact of tax legislation

• n lot-sizing and sourcing

strategies

Hua Jin, Dr Patrick Beullens

Southampton Business School, University of Southampton , United Kingdom

CMS-MMEI, 29th March 2019, Chemnitz

Content

• 1. 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. Conclusion

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• 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.

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• 1. Introduction: Taxes in supply chain

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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) 40 80 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

• n 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

𝑁𝑏𝑦 ( 1 − 𝜗 𝑞 − 𝑑 𝑧) = 𝑁𝑏𝑦 (𝑞 − 𝑑)𝑧

• VAT 𝑁𝑏𝑦 ( 1 + 𝜐 𝑞 𝑧 − 1 + 𝜐 𝑑 𝑧 − 𝜐𝑞𝑧 + 𝜐𝑑𝑧)

= 𝑁𝑏𝑦 (𝑞 – 𝑑)𝑧

• 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

• rder 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

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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 )σ𝑗=1

∞ 𝑓(−𝑗𝑏𝑈) - FOC = p y - 𝑏( 𝑡+𝑥𝑧𝑈) 1−𝑓−𝑏𝑈

• FOC

෪ 𝐵𝑇=( p – w ) y -

𝑡 𝑈 - a 𝑡 2 - a w 𝑧𝑈 2 - FOC

Q* =

2𝑡𝑧 𝑏𝑥

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

accounting year. 𝑃𝑄 = 𝐻𝑠𝑝𝑡𝑡 𝑄𝑠𝑝𝑔𝑗𝑢 (𝐻𝑄) − 𝑃𝑞𝑓𝑠𝑏𝑢𝑗𝑜𝑕 𝐹𝑦𝑞𝑓𝑜𝑡𝑓𝑡 (OE)

• In operational business function expressed in EOQ model:

𝑃𝑄 = 𝑂𝑓𝑢 𝑇𝑏𝑚𝑓𝑡 − 𝑃𝑞𝑓𝑠𝑏𝑢𝑗𝑜𝑕 𝐹𝑦𝑞𝑓𝑜𝑡𝑓𝑡 −𝐷𝑃𝐻𝑇 𝑞𝑧

𝑡 𝑈 + 𝐺𝑃𝐷

𝑥𝐽0 + 𝑥 𝑧 − 𝐽0 + 𝐽1 − 𝑥𝐽1 = 𝑥𝑧 In the EOQ model, the amount of products purchased may differ from demand y due 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. 𝑃𝑄 = 𝑞𝑧 −

𝑡 𝑈 − 𝐺𝑃𝐷 −𝑥𝑧

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• 2. EOQ and CT cash-flows (1)

Firms with a taxable profit of £𝟐. 𝟔 𝒏𝒋𝒑 or less, pay CT 9 months (and one day) after the end of the accounting year.

Amount need to pay at time 0: є 𝑃𝑄 𝑓− 12+9 𝑏𝑈𝑤

ASє = −є 𝑃𝑄 𝑓− 12+9 𝑏𝑈𝑤 σ1=1

∞

𝑏 𝑓−𝑗𝑏𝑈𝑏

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9month 9month 9month

NPV= −є 𝑃𝑄 𝑓− 12+9 𝑏𝑈𝑤 σ𝑗=1

∞

𝑓−𝑗𝑏𝑈𝑏

year year year year

• 2. EOQ and CT cash-flows (2)

Firms with a taxable profit above £𝟐. 𝟔 𝒏𝒋𝒎𝒎𝒋𝒑𝒐 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' = є

𝑓−𝑏(12+9)(1/12) 1−𝑓−𝑏𝑈𝑏

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

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• 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 +

𝑡τ 𝑈 ) – 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* =

2𝑡𝑧 𝑏𝑥

TQ* =

2𝑡𝑧 𝞭′𝑥

• 3. Acquisition and Tax

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

𝑏 ( 1+τs) 1−𝑓−𝑏𝑈 − wYT 𝑏 1+τw 1−𝑓−𝑏𝑈

−(1- δ) FOC (1+ τ)– δ FOC Q1* =

2𝑡𝑧(1+τ−ϵ′−τ′) 𝑏𝑥(1+τ)

(UK sourcing) Q4* =

2𝑡𝑧(1−ϵ′) 𝑏𝑥

(EU sourcing)

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UK Domestic Buyer EU supplier EU customer UK domestic customer Ponyon =output VAT Poryor = No output VAT

• 3. Acquisition and Tax: sourcing strategy

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− s

𝑏 ( 1+τs) 1−𝑓−𝑏𝑈 − wYT 𝑏 1+τw 1−𝑓−𝑏𝑈

• 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) −[ wYT𝑓𝑏𝑀𝐽 + xs𝑓𝑏𝑀𝑡 + (wYT +xs)ϴ𝑓𝑏𝑀𝑂 + (wYT+xs) )(1+ ϴ)τ1𝑓𝑏𝑀𝑂 + (1-x) s (1+ τs ) ] σ𝑗=1

∞ 𝑓(−𝑗𝑏𝑈)

−(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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