In perfect capital and product markets, investors will bid up the price of tax-favored assets until the after-tax returns on all assets (within the same risk class) are the same (tax arbitrage). The marginal investor is then indifferent between investing in a fully taxed asset, a partially taxed asset, or a tax-exempt asset. Consider the following valuation model with taxes.

The market value of equity (MVE) is given by:

(1) MVE = B × After-tax Income

where B is some valuation multiplier that equals 1/r and where r is Scholes and Wolfson’s (expected) rate of return. Note, in the SW-model r will be the same for all assets r=r*. The after-tax Income is given by:

(2) After-tax Income = Pre-tax Income – Tax Expense

The tax expense equals the product of the Effective Tax Rate and Pre-tax Income:

(3) Tax Expense = ETR × Pre-tax Income

where ETR is the Effective Tax Rate. Substitution of (3) in (2) for Tax Expense, and this transformed equation into (1) for After-tax Income solves to the following valuation model:

(4) MVE = (1/r) × (1 – ETR) × Pre-tax Income

Suppose further there are three firms A, B, and C. Each firm has a pre-tax income of 100. Firm’s A (benchmark firm) Effective Tax Rate equals the statutory tax rate (ETR=str) and equals 0.35. Firm’s B Effective Tax Rate equals 0.25 and firm’s C Effective Tax Rate equals 0 (Zero-Tax Firm). Finally, Firm’s A MVE equals 500.

Assume that Scholes and Wolfson’s tax arbitrage works perfectly and implicit taxes fully offset explicit tax benefits.

Exercise:

1. Calculate the after-tax returns, pre-tax returns, implicit taxes, explicit taxes, total taxes, and their respective tax rates for all three firms if the SW-model holds.
2. Discuss the practical implications of SW’s implicit tax concept.
3. How can a practitioner measure/identify whether implicit taxes are existent? And if so, how can she/he assess how strong this effect is?
4. Many high-tax countries such as the US or France are concerned that multinational companies will artificially shift income from high-tax to foreign low-tax countries in order to save taxes and reduce their ETRs. As a consequence, high-tax countries fear a loss in tax revenue and that they will lose investors to foreign countries. Discuss these concerns in the light of SW’s implicit tax model.
5. Imagine you are a professional investment banker. How would your knowledge about implicit taxes affect your investment decisions?
6. Many governments are issuing tax-exempt bonds. Why? Aren’t they simply losing tax revenues in doing so?

Hints for the solution

1. You always start with the benchmark asset. You have all info given to calculate the after-tax return for the benchmark asset: r*=((1 − str)×PI)/MVE which will give you a rate of 0,13 (=((1 – 0.35)×100)/500
2. You also have all info you need to calculate the benchmark firm’s pre-tax return. For this purpose simply calculate what the firm’s return would have been if the firm had paid no tax: 0,2 (=((1 – 0)×100)/500
3. You also know that if SW-model holds all firms have the same after-tax return of 0.13
4. Further, if the SW-model holds, you know that the benchmark firm will not be paying any implicit taxes. So, the implicit tax and the implicit tax rate will both be 0.
5. From this, it follows that the benchmark firm’s explicit tax rate (which is the statutory tax rate) will equal the total tax rate (Total tax Rate = Explicit Tax Rate + 0)
6. Having solved the case for the benchmark firm, you just need to apply the formulas explained in the lecture to calculate implicit taxes (tax rate) and explicit taxes (tax rates). NOTE: These metrics for the two alternative assets (partially taxed and tax-exempt) are always calculated relative to the benchmark asset as outlined in the SW equations.

Answer rating: 100% (QA)

Answer 1 Aftertax returns pretax returns implicit taxes explicit taxes total taxes and their respective tax rates for all three firms if the SWmodel holds Firm A Benchmark Firm Aftertax Return 013 1 0... View the full answer