Optimal Revision Rules of Cost-Based Transfer Prices in a Multi-Period Production Setting

Abstract

This paper investigates standard cost-based transfer prices in a two-period setting. We analyze whether and how firms should use cost information observed after the first period to revise the transfer price for the second period. Updating the transfer price improves trading decisions if realized cost helps predict future costs, but it causes underinvestment in cost reduction. We find that firms benefit from revising the transfer price based on realized cost instead of keeping it fixed for both periods. Moreover, optimally balancing trade and investment efficiency requires that the firm commits ex ante to a transfer price that does not fully use the information contained in past cost observations to update expected costs in future periods.

Keywords:

• Transfer pricing
• Long-term investments
• Multi-period model
• Commitment

JEL Classifications:

• D82
• D83
• M41

Acknowledgements

We thank Robert Göx (editor), two anonymous reviewers, and Gunther Friedl for their helpful comments and suggestions that greatly helped improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Many firms use cost-based transfer prices for internal pricing. According to Ernst & Young (2010, p. 13), cost-based transfer prices are adopted by 30% of respondent companies for tangible good pricing and by as much as 52% for service transaction pricing.

2 Feinschreiber (2004, p. 29) notes that ‘a standard cost system must change over time to reflect new facts. A standard cost system that remains static leads to a proliferation of variances that may become unwieldy. [··· ] However, frequent changes in the standard cost system mean that the standards are not standard.’

3 Göx and Schiller (2006) and Baldenius (2009) provided an overview of the transfer pricing literature. Cost-based versus negotiated transfer prices were compared by, for example, Wagenhofer (1994), Anctil and Dutta (1999), Baldenius et al. (1999), and Dikolli and Vaysman (2006). Arya and Mittendorf (2008) researched controllable market-based versus cost-based transfer pricing without intra-firm coordination problems arising from specific investment problems and cost uncertainty. Johnson et al. (2018) compared alternative market-based transfer prices. Other authors that have investigated the effectiveness of different transfer pricing mechanisms include Harris et al. (1982), Amershi and Cheng (1990), Vaysman (1996), and Johnson (2006).

4 In a dynamic setting, Dutta and Reichelstein (2010) investigate the hold-up problems that emerge with capacity investments, but they do not compare the effectiveness of different pricing mechanisms and flexibility choices.

5 Alternatively, we could assume that fixed costs of the investment are verifiable but include white noise so that no transfer pricing rule can be contingent on $I$. Our results remain unchanged if the buyer cannot observe the supplier's investment level.

6 Our results remain unchanged if the buyer cannot observe the supplier's cost information and if the supplier cannot observe the buyer's revenue information.

7 The structure of the conditional expectation resembles a linear regression of ${\theta }_{c2}$ on ${\theta }_{c1}$. Because we assume equal variances, the regression coefficient $\beta =\frac{\mathrm{Cov}({\tilde{\theta }}_{c1},{\tilde{\theta }}_{c2})}{{\sigma }_c^2}=\rho$ equals the correlation coefficient.

8 Choosing the support of ${\tilde{\theta }}_{\mathrm{ct}}$ and ${\tilde{\theta }}_{\mathrm{rt}}$ such that $\underset{\_}{{\theta }_r}>\overline{{\theta }_c}$ ensures positive quantities. Choosing the support of ${\tilde{\theta }}_{\mathrm{ct}}$ such that $\underset{\_}{{\theta }_c}>\frac{2m{y}^2}{1-2y^2}$ ensures positive cost in each period. Finally, restricting $y<\frac{1}{\sqrt{2}}$ ensures finite investment and quantities.

9 This flexibility gain resembles the value of information measured as the expected profit increase by solving a decision problem using a posterior rather than prior expectation of a relevant parameter after observing an informative signal (e.g., Feltham 1968).

10 In the following sections, the superscript S denotes decisions and results under fixed standard-cost transfer pricing, F under flexible standard-cost transfer pricing, and W under the generalized updating mechanism with the optimal weight on realized cost.

11 Baldenius (2000) found that the optimal standard cost-based transfer price in a binary trade setting includes a positive markup over the expected cost. This is because the traded quantities are continuous in our analysis and binary in Baldenius' setting.

12 Under Bayesian updating, headquarters weights the realized cost from the first period by the marginal effect of the uncontrollable cost component ${\theta }_{c1}$ on the corresponding later period's cost component ${\theta }_{c2}$, i.e., $\frac{\mathrm{d}E[{\tilde{\theta }}_{c2}|{\theta }_{c1}]}{\mathrm{d}{\theta }_{c1}}=\rho$. Because headquarters only observes the joint effects of ${\theta }_{c1}$ and $I$, the cost decrease that is achieved by the supplier's investment inevitably decreases the second period's transfer price with the factor ρ.

13 We derive the full equilibrium solution in the proof of the proposition.

14 We show that ${\alpha }^F<1$ for $\rho \in (0,1)$ in the proof of Corollary 1 in the Appendix.

15 In the survey by Ernst & Young (2013, p. 20), 19% of respondent companies reported that they monitor their financial results for compliance with transfer pricing policies on either a real-time or a monthly basis. Thirty-eight percent reported that they reviewed their results quarterly, and 36% said they did so only annually.