Investment distortions and the value of the government's tax claim

Abstract

This article integrates the government in the context of company valuation. Our framework allows to analyse and to quantify the risk-sharing effects and conflicts of interest between the government and the shareholders when firms follow different financial policies. We provide novel evidence that firms with fixed future levels of debt might invest more than socially desirable. Economically, this happens if the gain in tax shields is big enough to outweigh the loss in the unlevered firm value. Our findings have implications for the practice of investment subsidy programmes provided by the government to avoid fostering investments beyond the socially optimal level.

Keywords:

• government tax claim
• company valuation
• optimal investment
• corporate overinvestment

JEL Classification:

• G31
• G32
• G38
• H21
• H25

Notes

1 While Galai (1998) and this article focus on the government's income by assessing the value and riskiness of the government's tax claim, Novy-Marx and Rauh (2011), for instance, are concerned about the riskiness and the value of government's liabilities.

2 For a generic tax shield valuation function which is not tied to a specific financial policy, see also Barbi (2012).

3 Otherwise arbitrage opportunities would exist. This proposition is consistent with the Modigliani–Miller Proposition I without taxes, which states that the value of a firm with fixed investments is independent of the distribution of the firm's cash flows.

4 All calculations are based on the valuation date t = 0. For simplicity, we suppress the unconditional expectation operator E(.) and we usually omit time subscripts when referring to the first valuation period t = 1. In general, stock variables (e.g. C) are associated with their actual value at the beginning of a period, and flow variables (e.g. CFBT) are associated with their expected value at the end of a period.

5 Fernandez (2004) reaches the same conclusion (see Equation 10 in Fernandez, 2004, p. 148). However, his further analysis of a levered company is flawed, since he does not recognize the principal payments’ role. He presents the non-growing perpetuity case in his Equation 12 by assuming that independent from the financial policy, no principal payments have to be made. But this is true only for a fixed debt policy (Cooper and Nyborg, 2006, p. 220).

6 The effect of leverage on the government's risk position has also been recognized by Miller and Modigliani (1966). They state: ‘[...] while the government can claim τ per cent of the profits, it must also bear τ per cent of the risk, including the risk introduced by leverage.’

7 One could expect that new investments are financed from retained earnings instead of NOPAT. However, note that the analysis focuses on the entity approach and such NOPAT is the appropriate choice. Outside financing can be introduced, but does not change the economic implications of the model (Gordon and Gould, 1978).

8 See Gordon and Shapiro (1956) and Lintner (1963). An in-depth analysis of this assumption can be found in Elton and Gruber (1976).

9 In the following analysis, the notation is simplified by not explicitly stating that irr and irr′ are functions of b.

10 It is important to note that the government's optimal retention ratio depends on the tax rate. This follows from the fact that the retention ratio is defined with respect to NOPAT, which also depends on the tax rate. Moreover, the IOS parameters a and q also depend on the tax rate since irr is the internal rate of return after tax. However, the government's optimal level of investment does not depend on the tax rate. This result stems from government's calculus to maximize the before-tax value C which does not depend on taxes. Hence, the government's optimal chosen level of net investments is also independent of taxes. This can be easily verified as the government's maximization problem can be equivalently formulated on a before-tax basis with a before-tax retention ratio b_BT and a before-tax internal rate of return irr_BT . Then, both the optimal before-tax retention ratio and the optimal level of net investments are required to be independent of taxes. A formal derivation is available upon request.

11 All other solutions of b lie outside the admissible parameter space; four of them are complex, and the fifth equals 2.281.

12 The HR function of an unlevered firm is equal to the RHS in Equation 38 where WACC reduces to the unlevered cost of equity (k).