Pass-through and C corp outputs under TCJA

Hull, Robert Article Pass-through and C corp outputs under TCJA International Journal of Financial Studies Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Hull, Robert (2020) : Pass-through and C corp outputs under TCJA, International Journal of Financial Studies, ISSN 2227-7072, MDPI, Basel, Vol. 8, Iss. 3, pp. 1-32, https://doi.org/10.3390/ijfs8030046 This Version is available at: https://hdl.handle.net/10419/257713 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ International Journal of Financial Studies Article Pass-Through and C Corp Outputs under TCJA Robert Hull School of Business, Washburn University, Henderson Learning Center, 1700 SW College Avenue, Topeka, KS 66621, USA; [email protected] Received: 4 July 2020; Accepted: 24 July 2020; Published: 3 August 2020   Abstract: Corporate finance research focuses on C corps (CCs) neglecting pass-throughs (PTs). We answer this neglect by examining PT outputs for the categories of debt choice, valuation, and leverage gain. In the process, we expand on the nongrowth PT research and supplement the recent CC research on the same outputs. Before the Tax Cuts and Jobs Act (TCJA) became effective in January 2018, PTs had an after-tax valuation advantage over CCs. Under TCJA, we demonstrate this advantage has been reverse. This suggests that, ceteris paribus, a typical PT can now find it advantageous to switch to the CC ownership form. More importantly, we show that nongrowth firm values are comparable to growth firm values unless we assume a rise in growth consistent with projections under TCJA where tax rates are lower. We demonstrate this projected growth increase is the key to make businesses more profitable. Additionally, we show PTs achieve optimal debt-to-firm value ratios (ODVs) well below those for CCs; PTs generally attain slightly higher quality credit ratings at their ODVs compared to CCs; and, PTs have lower leverage gains outputs (in the form of the maximum gain to leverage and the percentage increase in unlevered firm value) compared to CCs. Keywords: pass-through; valuation; TCJA; growth; tax rate; debt choice; leverage gain JEL Classification: C02; G32; G35; K20; O43 1. Introduction Compared to C corp (CC) research, the study of the pass-through (PT) ownership form is a neglected area, given that taxation models focus on the corporate debt tax shield for CCs. For example, Henrekson and Sanandaji (2011) state that the literature on firm taxation has not sufficiently considered the taxation of owner-managed firms. The latter firms are characterized by the sole proprietorship ownership type, which is the largest ownership type among PT types. The purpose of this study is to overcome this neglect through a detailed examination of PT outputs for the three categories of debt choice, valuation, and leverage gain. In this study, we compare these categories of outputs for PT with those for CCs. This comparison is particularly important given the changes in tax laws caused by the Tax Cuts and Job Acts (TCJA) that was passed by the US congress on 22 December 2017, where most changes became effective on 1 January 2018. TCJA altered tax rates and brackets in a manner that favors CCs more than PTs. In response to this tax legislation, this study’s first major goal is to examine the decision as to whether PT managers should switch to the CC ownership form. Since a reason for TCJA was to increase growth, this study’s second major goal is to test the influence of projected increases in growth on the two for-profit business forms of PTs and CCs. To achieve our major goals, we explore the following research questions. What can we say about PT outputs for the three categories of debt choice, valuation, and leverage gain for two tax environments, namely, pre-TCJA and TCJA? What can we disclose about these PT outputs for conditions of nongrowth and growth within the two tax environments? What can we tell a typical PT manager about its optimal credit rating (OCR) and how this rating might change when favorable tax laws are enacted causing Int. J. Financial Stud. 2020,8, 46; doi:10.3390/ijfs8030046 www.mdpi.com/journal/ijfs Int. J. Financial Stud. 2020,8, 46 2 of 32 greater business growth to occur? How do the findings of our PT tests compare to the findings of the same CC tests and what does this comparison tell us about the most profitable ownership form? Answering these questions are crucial for managers who are charged with determining the capital structure mix that maximizes firm value, choosing the best ownership form, and understanding the impact of lower taxes on growth. To answer our research questions, this paper uses the Capital Structure Model (CSM) that was recently extended by Hull (2019) to incorporate PT equations within a framework that formerly only addressed CCs. By using the CSM, we avoid measurement problems found in agency models (Jensen and Meckling 1976;Jensen 1986) and pecking order models (Myers 1977;Myers and Majluf 1984). We also circumvent inherent problems in the tax-based models of Modigliani and Miller (1963), Miller (1977 ) that fail to fully incorporate the costs of borrowing as factors influencing the gain to leverage (G L ). The CSM formulations for G L include borrowing costs that increase with debt and allow for identification of the maximum G L (max G L ) and thus the maximum firm value (max V L ), since max VLequals max GLplus unlevered equity value. The CSM is also chosen because, in examining the current state of the corporate finance field, we find it contains the only equation that ties together the debt-equity and plowback-payout decisions. The CSM does through its innovation of the levered equity growth rate (g L ), which is a function of interest payments and earnings retained for growth. This innovation allows us to test different historical and future projected annual growth rates for the same target credit rating. In this paper, we test three annual growth rates. First, we test a historical sustainable growth rate of g L =3.12%, which is consistent with the annual compounded growth in real US GDP for the 70 years prior to TCJA with GDP data supplied by the US Bureau of Economic Analysis (2020). This usage assumes GDP is a result of the growth in businesses and, in particular, in the risk-taking residual equity ownership of businesses. Second, we test g L =3.90%, which is consistent with the Tax Policy Center, TPC, (2018) that cites sources predicting that TCJA, on average, will increase GDP by about 0.8%. Thus, and as also pointed out by Hull (2019), a g L of 3.90% is consistent with a growth rate of 3.12% increasing by about 0.8%. Third, we test g L =4.50%, which represents the two growth projections given by TPC that are at the high end. In regard to these two high end projections, TPC reports that the Congressional Budget Office (CBO) estimates the effect of TCJA will be an increase of 0.7% per year in GDP for the next ten years, while the Tax Foundation Taxes and Growth model projects an increase of 2.1%. The average of these two rates is 1.4%. This suggests a rate of about 4.50% when 1.4% is added to the long-run growth in real US GDP of 3.12% that occurred prior to TCJA. While these are projections for only ten years due to possible termination of certain TCJA provisions (especially for PTs), our tests assume permanency in these provisions. Unlike other key provisions, the drop to a flat corporate tax rate of 0.21 caused by TCJA (where the former maximum tax rate for CCs had been 0.35) is not set to expire. Besides the growth rates just described, our tests rely on government, market, and financial data. In terms of the latter, Damodaran (2020) most recently supplies credit spreads (based on credit ratings) matched to interest coverage ratios for the year 2019. As shown by Hull (2020), Damodaran’s data is useful for computing costs of borrowings associated with debt choices. Because our main tests use spreads for 2019, the results for these tests are subject to time-dependence, since spreads can change from year to year. Thus, we also report (when relevant) results from robust tests using spreads for 2017 and 2018. Due to disagreement about effective tax rates found in the literature, our robust tests also include conducting tests focusing on lower effective tax rates. Given the above, we now describe our major findings in terms of the outputs for the three categories of debt choice, valuation, and gain to leverage where these outputs are best viewed as those for a typical or average business. First, in terms of debt choice outputs, we find similar optimal debt-to-firm ratios (ODVs) for all PT tests, namely, pre-TCJA, TCJA, growth, and nongrowth. ODVs for PTs have a narrow range from 0.2226 to 0.2499 with an average of 0.2377. This contrasts with a higher CC range from 0.4132 to 0.4609 with an average of 0.4416. However, robust tests indicate the ODV gap is narrower than what we report from our main tests. ODVs for PTs occur at a debt choice that generates a Moody’s credit rating Int. J. Financial Stud. 2020,8, 46 3 of 32 of A3, which is an upper medium investment grade rating. The lone exception is the 4.50% growth rate test where the rating is Baa2, which is a lower medium IG rating. The larger ODV outputs for CCs lead to a rating of Baa2 for all tests, which is a slightly lower quality than typically found for PTs. Robust tests verify our credit rating findings but can produce occasional disagreements with our main tests. We conclude: ODVs for PTs are smaller than CCs and typically come with a slightly higher quality rating. Second, in terms of firm valuation outputs (where all firm values are after-tax values), we find the following. Whereas higher firm values are expected under TCJA with lower taxes, we show the precise valuation differences when compared to pre-TCJA firm values. To illustrate this preciseness, consider the pre-TCJA and TCJA max V L outputs when growth is 3.12%. For each $1,000,000 in before-tax cash flows, we find max V L for a PT is $10.390 M (M =million) for the pre-TCJA test and $10.758M for the TCJA test. For CCs, max V L is $9.476 M for the pre-TCJA test and $11.413M for the TCJA test. Whereas the increase in max V L for PTs is only 3.54% due to TCJA, the increase for CCs is 20.44%, which reflects the more favorable tax treatment for CCs under TCJA. When we compare pre-TCJA nongrowth max V L and growth max V L using a growth rate of 3.12%, we find that the PT growth max V L is slightly greater. In contrast, the pre-TCJA nongrowth max V L for CCs is comfortably larger than its pre-TCJA growth max V L . The latter outcome occurs because high CC tax rates in the pre-TCJA environment made internal growth unaffordable for a typical CC as internal funds (retained earnings) faced a high pre-TCJA corporate tax rate. When we repeat this comparison using the lower tax rates under TCJA for CCs, we now find the growth max V L is greater than the nongrowth max V L . When we test greater growth rates of 3.90% or 4.50% that are projected to occur under TCJA, we find the growth max V L outputs for both PTs and CCs are now much greater than those for nongrowth. We show that the average pre-TCJA max V L from all PT tests is $10.380 M, which is greater than the average of $9.754 M found for CCs. However, under TCJA, we find this advantage for PTs is reversed, as the average max V L of $11.802 M for CCs is greater than that of $11.163 M for PTs. This advantage slightly rises if we repeat our tests and use spreads for either 2017 or 2018 but lessens if we test lower effective tax rates. We conclude: CC firm valuation increases by much more than PTs under TCJA with one reason being that the relative lower tax rates under TCJA for CCs makes growth more affordable for CCs compared to PTs. This increase makes switching from a PT to a CC profitable under TCJA. If growth increases as projected under TCJA, PTs and CCs will both profit substantially. Third, with regard to leverage gain outputs, we find the following. First, PTs have lower maximum gain to leverage (max G L ) values compared to CCs. Second, PTs also have lower values for the maximum percentage increase in unlevered equity (max % ∆ E U ). Third, whereas PTs have lower values for the net benefit from leverage (NB) for the two pre-TCJA and nongrowth TCJA tests, we find that PT have greater NB values for the three TCJA growth tests, indicating that PTs add more value per dollar of new debt for TCJA growth tests. The values for leverage gain outputs can change as annual spread data changes. Robust tests using spreads for 2018 and lower tax rates generate lower values. The lower values for max %∆EUare consistent with empirical research. We conclude: While the superiority of PT compared to CCs depends on the leverage gain output being analyzed, CCs generally perform much better in the category of leverage gain outputs indicating greater gains from leverage compared to PTs. The remainder of this paper is as follows. In Section 2, we overview the literature related to ownership form, financing, and the effective tax rates. Section 3presents our research methodology used to produce outputs. This methodology is a trade-offmodel called the Capital Structure Model (CSM). Section 4provides the procedure to get credit spreads, ratings, and costs of borrowing Int. J. Financial Stud. 2020,8, 46 4 of 32 matched to debt-to-firm value ratios (DVs); gives the procedure to determine optimal outputs; presents introductory variables and computations used by the CSM; and, offers PT applications of the CSM that showcase outputs at ODV for nongrowth and growth tests under TCJA. Section 5provides figures that display G L and V L results for PTs when plotted against respective DVs and credit ratings. Section 6 gives results pertaining to optimal outputs for PTs and CCs, provides policy implications, and suggests possibilities for future research. Section 7offers a summary. 2. Literature Review This section provides a review of for-profit ownership forms, equity and debt financing, and effective (average) tax rates used in this study. 2.1. Ownership Forms A sole proprietorship is the most common business type for the pass-through (PT) ownership form. Other types include partnership (general or limited), limited liability company and S corp. While most PTs are small, they can also be large, global enterprises. Prior to the Tax Cuts and Job Acts (TCJA) that took effect in January 2018, PTs were viewed as having, on average, an after-tax valuation advantage over C corps (CCs). This valuation advantage was reflected in the choice of ownership form. For example, as noted by Hodge (2014), CCs had shrunk in number since the 1980s while PTs had tripled so that they outnumbered CCs by about 18 to 1. However, with the large drop in the corporate tax rate from the maximum rate of 0.35 to a flat rate of 0.21 under TCJA, the continuance of the forty-year trend of increasing the proportion of the PT ownership form is in jeopardy. Since TCJA, much has been written on PT switching its ownership form to a CC. For example, Robert (2019) writes about the advantage of an LLC switching to a CC, while Houston (2019) discusses the advantage of an S corp converting to a CC. Regardless of the PT type considering conversion to a CC, Grant Thorton International Ltd. (2019) notes that a crucial PT consideration for converting to a CC under TCJA is how much taxes will be paid on corporate earnings and equity dividends compared to what the PT pays in taxes at its personal level. In regard to this consideration, this study offers insight on the conversion of the PT ownership form to the CC form by computing after-tax firm valuation for pre-TCJA and TCJA tax environments. Another factor in conversion to a CC is that PT owners get a temporary twenty percent standard tax deduction on income under $315,000, if married filing jointly, or $157,500 for all other filing statuses. Even for PTs that earn below these limits, there are restrictions on who qualifies and questions as to if this deduction will last past 2024. Finally, as noted by numerous tax service companies, switching ownership forms is often more than just saving taxes. However, as suggested by Grant Thorton International Ltd. (2019), the savings on taxes will arguably be the paramount factor for most PTs that are considering switching to a CC. 2.2. Financing Forms Pass-throughs, like all for-profit businesses, rely on the two basic financing forms: equity and debt. Compared to CCs, PT financing manifests differences. One area of difference involves the legal treatment. For example, consider partnerships where the Tax Foundation (2019) reports that they account for 55.3% of PT net income. Dantzler (2017) notes that the distinction between equity and debt financing within the partnership framework is often blurred because there is much less law in the PT world for partnerships compared to CCs. Dantzler’s observations suggest that, at least for PTs that are partnerships, computing PT leverage ratios can be a difficult undertaking. However, there is also a difficulty in computing leverage ratios for CCs that use preferred stock as a form of financing. The difficulty lies in the fact that preferred stock is a hybrid security with both equity and debt features. While preferred stock is classified as equity, its dividend payment is recognized, like interest payment, as a highly prioritized payment. Int. J. Financial Stud. 2020,8, 46 5 of 32 Another area of difference involves the investor clienteles that inhabit different for-profit ownership forms. For example, unlike many CCs that issue equity shares involving thousands of individuals and institutional investors, PTs often rely on a small number of investors (partners or venture capitalists) as their most common source of equity funding. Although some question the wisdom of government participation (Florida and Smith 1993), venture capitalists can also include government entities. Smaller PTs (like the sole proprietorship type) can get debt financing by simply using a credit card or, like all businesses, acquiring some form of trade credit. Like CCs, larger PTs can take on debt by issuing notes, bonds, and other obligations. As noted by Hull and Price (2015), while large CCs can float large bond issues and undertake a variety of large short-term borrowings, PT debt financing often includes regional and national mezzanine borrowings that permit the issuance of unsecured and subordinated notes at high interest rates. Hull (2019) writes that PTs can also borrow from individuals, banks, savings and loans, credit unions, commercial finance companies, and Small Business Administration (SBA) guaranteed loans where the latter have methods of encouraging bank and non-bank lenders to make long-term loans to PTs. Compared to CC debt, PT debt is less likely to be assigned a credit rating by a major credit rating company. Arguments can be offered that debt is less valuable for PTs compared to CCs. For example, PTs are more likely to be smaller owner-managed enterprises where the owner and manager functions are joined. This situation avoids principal-agent conflicts between owners and managers found in larger entities where many managers are not primary owners and so have interests that are different from the residual equity owners (Jensen and Meckling 1976). This means debt can be more valuable to equity owners in larger firms (most often CCs) because interest payments limit the available cash flows that can be wasted by self-serving managers (Jensen 1986). In addition, PTs are less likely to raise equity funds with negative signaling as accompanies large public offerings of equity where the company is suspected of issuing overvalued securities (Masulis 1983;Asquith and Mullins 1986). Thus, negative signaling for large public equity issues (mostly by CCs) can serve to make debt more valuable by issuing debt to avoid the negative signaling from an equity issuance. In conclusion, we can find arguments that suggest CCs should have higher leverage ratios compared to PTs. As will be seen, these arguments are consistent with this study’s findings. PTs, like CCs, are subject to market conditions so that tests can be conducted base on different market risk scenarios affecting cost of financing. While this paper does not look at different market risk scenarios like prior PT research (Hull and Price 2015), we do implicitly assume there are risk classes of PTs that are similar to CCs. In particular, the tests we conduct assume that PTs and CCs have a risk class resembling the market as the optimal leverage ratio occurs near the market beta of one for all of our tests. This risk class generates the same costs of borrowings for equity and debt financing for both PTs and CCs. These borrowing costs are tied to credit spreads and ratings but achievable at different leverage ratios based on the firm’s size classification (as described in Section 4.1). With the same costs of borrowings matched to the same credit ratings, differences in our PT and CC outputs revolve around discrepancies in leverage ratios (based on size) and dissimilarities in tax rates (based on the ownership form). 2.3. Effective Tax Rates We now describe what we mean by an effective tax and then discuss the assignment of tax rates used in our tests. 2.3.1. Effective Tax Rate Described For a PT owner, who is an individual income tax filer, the average tax rate is total personal taxes paid divided by taxable income. An average personal tax rate can also be defined in terms of taxes paid divided by variables other than taxable income. Such variables include gross income (GI), adjusted gross income (AGI), or modified AGI (MAGI). The latter three variables represent amounts larger than taxable income. Thus, an average personal tax rate defined in in terms of these three variables Int. J. Financial Stud. 2020,8, 46 6 of 32 will be lower and so a researcher must be aware of the differences when reviewing sources to ensure consistency in estimating an average personal tax rate. For a CC, the average corporate tax rate is corporate taxes paid divided by taxable income where the accounting term, earnings before tax (EBT), is commonly used for a CC’s taxable income. The federal corporate tax rate under TCJA is a flat rate of 0.21 (the pre-TCJA maximum was 0.35). Besides corporate taxes, CC owners pay personal taxes on debt income and equity distributions where the latter is EBT minus corporate taxes. Debt income comes in the form of interest (where more interest leads to a lower EBT) and capital gains for debt owners that are subject to taxation at the PT or personal federal tax rate with a TCJA maximum of 0.37 (the pre-TCJA maximum was 0.396). However, if debt is held more than one year, capital gains are subject to federal tax rates of 0, 0.15, and 0.2 with a 0.038 investment tax added if MAGI exceeds certain thresholds. Equity distributions are dividends and capital gains. Qualified dividends (which are stocks held at least 60 days) are subject to the same federal tax treatment as capital gains for equity and debt. Otherwise, dividends for CCs are taxed like PT personal business income with the TCJA maximum of 0.37. In conclusion, the total taxes paid by CCs can differ from PTs because CC earnings are taxed twice, albeit almost always at lower maximum tax rates at both the corporate and personal levels compared to PTs that are taxed only once on its taxable income. In keeping with common usage, this paper refers to an average tax rate as an effective tax rate where, for our purposes, the effective tax rate includes only federal income taxes thus ignoring other taxes paid that a for-profit business often incurs such as state, city, county, sales, property, unemployment, social security, and Medicare. Inclusion of other taxes paid lead to a higher effective tax rate. Unless a flat federal tax rate is operative, the use of a marginal federal tax rate will also lead to a higher tax rate as income climbs until it reaches the maximum statutory rate. This is because a marginal tax rate reflects the dollars of taxes paid at the highest statutory rate after all prior dollars were taxed at lower rates. Thus, unlike the use of GI,AGI, or MAGI that lead to a lower tax rate, the addition of other taxes paid or the use of a marginal tax rate will lead to higher tax rates. 2.3.2. Effective Tax Rates for Main Tests For our tests, we allowed tax rates to change in their predicted direction given by Hull (2014) for increasing Pchoices where a Pchoice refers to the proportion of unlevered equity (E U ) retired with debt (D). Hull argues the corporate tax rate (T C ) and the personal equity tax rate (T E ) decrease with greater debt-for-equity transactions while personal debt tax rates increase. While Hull’s original arguments were for a CC, they are applicable to PTs since T E for PTs moves in the same direction as both T C and T E for CCs. However, T E for PTs is more akin to T C for CCs as both are business tax rates on net income, whereas the T E for CCs is the rate on equity payouts in the form of dividends and capital gains. For our tests, we used a 0.03 change in tax rates for each of the fifteen increasing Pchoices where each Pchoice corresponds to one of the fifteen Moody’s ratings used by Damodaran (2020). As described below, the use of 0.03 in conjunction with the setting of unlevered tax rates achieved effective levered tax rates that we expected to occur at the optimal debt-to-firm value ratio (ODV). From federal data supplied by the Tax Policy Center (2016) on the distribution of PT business income for 2016 (where the maximum T E is 0.396), an effective T E for a pre-TCJA tax environment can be estimated at of 0.32. However, earlier sources (SBA 2009;National Federation of Independent Business 2013) suggest an effective T E that would be below 0.32 with variations based on the pre-TCJA years examined. Given this information, we selected an effective T E of 0.30 at ODV for pre-TCJA tests. Given this pre-TCJA estimate, a TCJA approximation for an effective T E at ODV would be about 0.28 due to the slight fall in personal tax rates caused by TCJA. Because we begin with an unlevered firm and allow tax rates to change when debt increases as described by Hull (2014), our pre-TCJA tests start with an unlevered T E of 0.35. This starting point enables us to achieve as an effective levered T E that is near 0.30 at ODV for pre-TCJA tests. For TCJA tests, we started with an unlevered tax rate of 0.33 to attain an effective levered TEthat approaches 0.28 at ODV. Int. J. Financial Stud. 2020,8, 46 7 of 32 The Tax Foundation (2014)reveals the effective T C ranges from about 0.24 to 0.34 for a ten-year pre-TCJA period from 2001 through 2010. This suggests an effective T C of about 0.29 for the pre-TCJA tax environment. To achieve this rate, we set an unlevered T C at its maximum statutory rate of 0.35. The maximum corporate tax rate (T C ) under TCJA is 0.21, which is also its minimum since 0.21 is a flat rate. Given that the estimated effective T C of 0.29 is 0.06 under the pre-TCJA maximum T C of 0.35, a value with the same drop of 0.06 in a TCJA environment would be 0.21 − 0.06 =0.15. However, a proportional fall would be (0.29/0.35)0.21 =0.174. Considering that T C is a flat rate under TCJA and tax credits and deductions may be more difficult to attain under TCJA, we considered an effective T C near 0.18 at ODV to be more reasonable and could be achieved with an unlevered T C of 0.21. As noted by Hull (2020) for his CC study under TCJA, an effective T C of 0.18 is consistent with the estimate of 0.18 given by the Penn Wharton Budget Model (2017) under TCJA. As described next, our tax rates on debt and CC equity income under TCJA were also consistent with Hull (2020). Interest distributions for debt owner are taxed at the personal debt tax rate (T D ) for both PTs and CCs where T D has a pre-TCJA maximum of 0.396 and a TCJA maximum of 0.37. If debt is held longer than three years, any capital gains is taxed at a lower capital gains rate where the typical maximum T D is 0.2. However, as noted by Hull (2020), wealthier investors often avoid paying taxes on for-profit debt by investing in nontaxable bonds because the taxable equivalent yield is higher. Given the above, we set T D at 0.22 as a reasonable effective tax rate for a typical PT or CC debt owner under a pre-TCJA tax environment. Under TCJA, we expect a slightly smaller T D and so set an effective T D at 0.21 as does Hull (2020). Unlike T C and T E that fall with leverage, T D rises with leverage. Thus, to achieves effective T D values near 0.22 and 0.21 at ODV, we set unlevered T D values at 0.19 and 0.18, respectively, for pre-TCJA and TCJA tests. Unlike PTs, most CCs have many investors who buy and sell public shares and receive dividends and capital gains. These investors are subject to different personal tax laws on equity income than PT owners. For CC investors who buy equity and receive qualified dividends and capital gains, the maximum T E is typically only 0.2 and not the much higher personal statutory maximum for PTs. As mentioned by Hull (2020), investors have the ability to defer capital gains so that, through charitable contributions and inheritance, T E can be zero. For this reason, we advocate an effective personal tax rate (T E ) on dividends and capital gains of about 0.14 for CC owners. To achieve an effective T E near 0.14 at ODV, the unlevered T E is set at 0.165. This rate holds for both pre-TCJA and TCJA tax environments since TCJA did not change the tax rates governing dividends and capital gains on equity. 2.3.3. Effective Tax Rates for Robust Tests The above estimates used for our main tests, can be subject to error due to the variations that occur in estimates of tax rates. These estimates can weight tax provisions differently. For example, suppose we assign significant weight to the tax provision where PTs can receive a 0.20 reduction in taxes paid until at least 2024. Whereas this deduction helps smaller PTs who qualify, the bulk of taxes are paid by larger PTs who earn too much to qualify. Thus, the impact of this deduction on the effective T E may be small. Regardless, if such a provision is an important factor, then our estimate of T E for PTs is too high. In addition, PTs can buy shares in publicly traded companies or achieve capital gains on assets. If so, they pay taxes on qualified dividends and capital gains at the typical maximum T E of 0.2. Besides the above arguments for a lower effective tax rate for PTs, Hull and Price (2015) cite studies suggesting lower effective tax rates for both PTs and CCs. In light of the above factoids, we tested a set of lower effective tax rates on business income for PTs and CCs. Below we describe these effective tax rates. To overcome potential inflation of T E , we performed robust tests where we seek a levered T E that is about 0.04 below that of our main PT tests. Similarly, we sought a levered T C that, on average, is about 0.04 below our main CC tests. To achieve the PT goal, we set the unlevered T E so it is 0.05 below that of our main PT tests. This serves to yield effective T E values for PTs near 0.26 and 0.24 for our respectively pre-TCJA and TCJA tests and thus 0.04 below the corresponding values of 0.30 and 0.28 for our main PT tests. Just like T E , disagreements can also be found for T C , as it also can vary from Int. J. Financial Stud. 2020,8, 46 8 of 32 year to year with values often lower than what we use in our main tests. In response, our robust tests, that use a lower T E for PTs, also utilized a lower T C for CCs. While we lowered unlevered T E by the same amount (namely, 0.05) for both pre-TCJA and TCJA tests for PTs, such is not the case for CCs where the TCJA fall for T C is much greater than found for T E . Thus, we found it more appropriate to lower the unlevered T C for pre-TCJA tests by 0.07 and the unlevered T C for TCJA tests by only 0.03. The average of these values of 0.07 and 0.03 is 0.05. This average is like the PT tests where the unlevered T E is set 0.05 below for all of our main tests. Setting the unlevered T C (as just described) yields effective levered T C values at ODV that are 0.23 and 0.15 for respective pre-TCJA and TCJA tests. These levered T C values are about 0.06 and 0.02 below those for respective pre-TCJA and TCJA tests with an average of 0.04. Besides robust tests that use lower effective tax rates, we performed robust tests that use spreads for 2017 and 2018. For these tests, we used the same tax rates described in Section 2.3.2 that are utilized for our main tests. Since these tests generate more results, for brevity’s sake, these results are only reported when relevant, especially if they produce differences from our main tests. The results for our lower effective tax rate tests are briefly summarized in Section 6.2. 3. Methodology After discussing major capital structure models, this section identifies and describes the model best suited to represent the methodology that generates this study’s outputs for the three categories of debt choice, valuation, and leverage gain. Besides the methodology described in this section, we also use two procedures when illustrating the nongrowth and growth applications of the CSM in the next section. The first procedure matches costs of borrowings to debt choices (Section 4.1) and shows how key inputs for the CSM are obtained. The second procedure determines how we identify optimal outputs (Section 4.2) for nongrowth and growth tests. 3.1. Capital Structure Models Trade-offcapital structure models (Baxter 1967;Kraus and Litzenberger 1973;DeAngelo and Masulis 1980;Berk et al. 2010) argue that an interior ODV exists. Baxter was one of the first researchers to provide the major trade-offargument. At that time, the trade-offargument stated that, as leverage increases, negative effects from financial distress costs will eventually outweigh the positive effects from the debt tax shield. Since this formulation by Baxter, the trade-offargument has been modified to incorporate other leverage related effects such as those posited by agency theory ( Jensen and Meckling 1976 ;Jensen 1986). While the mainline trade-offmodels focus on CCs, the Capital Structure Model (CSM) provides a trade-offframework that covers both CCs (Hull 2018) and PTs (Hull 2019). Since Baxter (1967), the main innovation in capital structure models is arguably that given by developers of agency models. Agency models fall under the umbrella of trade-offmodels as agency theory offers a structure that leads to an ODV with or without taxes. Jensen and Meckling (1976) demonstrate how an ODV can result simply from principal-agent valuation effects. Subsequent agency theory researchers (Gay and Nam 1998;D’Melloa and Miranda 2010) describe two principal-agent problems, underinvesting and overinvesting, that are related to financing of projects where projects serve to advance the wealth of either debt ownership or equity ownership at the expense of the other ownership. Besides the conflicts between equity and debt owners, agency models address valuation effects when debt enters the capital structure. For example, consider an all-equity firm with an excess of cash flows that leads to managerial waste. Jensen (1986) argues that such an enterprise can add value by issuing debt because interest obligations serve to discipline the spending of managers so that fewer cash flows will be spent on suboptimal and wasteful undertakings. Additionally, agency models cover the conflicts between principle-agents in the form of owners-managers. These conflicts are prevalent in large companies as embodied by CCs where owners and managers often have interests Int. J. Financial Stud. 2020,8, 46 15 of 32 debt even when lower quality ratings occur. As shown later in Section 6, we find this notion to be valid as the average ODV is 0.2377 for PT tests compared to 0.4132 for CC tests. As also shown later, some of our findings are subject to change when we tested spreads for 2017 and 2018 but not so much when we tested lower effective business tax rates for PTs and CCs. 4.3. Introductory Variables and Computations Used by Capital Structure Model (CSM) Appendix Apresents introductory CSM variables and their computations when a PT manager achieves a credit rating of Moody’s A3, which is the unambiguous OCR for nongrowth and growth tests when g L is 3.12%. The computations use the Capital Structure Model (CSM) of Hull (2019) for PTs with tax rates under TCJA. The computations featured in Appendix Aare as follows. First, Appendix Aprovides computations for two coefficients first derived by Hull (2014) for CCs to capture the effects of tax rates. Hull (2019) updates these coefficients so they apply to PTs. The first coefficient ( α1 ) is the Miller (1977) alpha that was first derived by Farrar and Selwyn (1967) and updated by Hull to account for changes in tax rates as leverage changes. The second coefficient ( α2 ) is the Hull alpha. Because the same tax rates occur with each Pchoice for all PT tests, values for α1 and α2 are the same for all PT tests and are respectively found in the 1st and 2nd components of the G L equations for PTs. The latter also holds for CC tests, albeit alpha values for CCs are different because they have slightly different formulas due to the extra layer of corporate taxes. Regardless, α1 and α2 values increase with leverage for both PT and CC tests. Appendix Acomputes α1 and α2 when the PT achieves its OCR at Moody’s A3 under TCJA. As seen in this appendix, these alpha values are α1 =0.905586 and α2 =1.069579. For a nongrowth G L equation, an increasing α1 makes the 1st component more positive while an increasing α2 makes the 2nd component more negative. For a growth G L equation, an increasing α1 makes the 1st component more positive but then reverses its effect, while an increasing α2 lessens its negative effect on the 2nd component and then makes this 2nd component more positive until the growth constraint is violated. Second, when computing unlevered firm value (E U ) under TCJA, Appendix Aoffers a PT nongrowth example and a PT growth example for g L =3.12%. The starting point to compute E U is $1,000,000 in before-tax cash flow 1 . For the nongrowth example where PBR =0 and the unlevered personal equity tax rate (T E1 )=0.33, the nongrowth E U was computed as $9,922,251. For the growth example where the optimal PBR is 0.3435 at ODV, the growth E U was shown to be $10,030,170 and thus growth adds $107,919. While our pre-TCJA test where T E1 =0.35 is not shown in Appendix A, we obtained a nongrowth E U of $9,626,064 and a growth E U of $9,638,148 with a PBR of 0.3515 and so only $12,084 was now added from growth. Thus, an increase of T E1 from 0.33 to 0.35 made the difference in nongrowth EUand growth EUfall from $107,919 to $12,084. If we continued to increase TE1, then the nongrowth E U would become greater than a growth E U and value would be subtracted instead of added with growth. This reflects the fact that RE used for growth becomes more expensive as it is taxed at higher tax rates. Is there a way of knowing when the nongrowth E U will be greater than the growth E U ? The answer lies in the discussion by Hull (2010,2018) of the relation between taxes on retained earnings (RE) and PBR. Hull proves the nongrowth E U is greater than the growth E U when the cost of internal equity financing is greater than PBR. For Hull, the cost of using internal equity financing involves the business taxes paid on RE before it can be used to finance growth. As illustrated in the prior paragraph for the TCJA test, when the cost of unlevered T E1 is 0.33 and thus lower than PBR of 0.3435, an unlevered firm added $107,919 in value through growth. However, the nongrowth E U and growth E U were similar for a pre-TCJA environment with only $12,084 in value added when the cost of unlevered 1 By before-tax, we mean after all expenses (including replacement costs) have been paid except for federal tax expenses. Thus, expenses include all applicable non-federal taxes (such as state taxes, payroll taxes, property taxes, sales taxes, and so forth). Since we begin with an unlevered firm, interest on debt is not yet an expense. Int. J. Financial Stud. 2020,8, 46 16 of 32 T E1 increases from 0.33 to 0.35 (with the PBR increasing from 0.3435 to 0.3515, which is about 3/8 as much of an increase compared to T E1 ). As will be seen later in Section 6for the pre-TCJA tests for CCs, the nongrowth max V L of $10.032 M is greater than the growth max V L of $9.476 M when g L =3.12%. This reflects the fact that the unlevered nongrowth E U is greater than the unlevered growth E U where RE is taxed at the pre-TCJA unlevered corporate tax rate (T E2 ) of 0.35, which is greater than the PBR of 0.3366. In conclusion, PBR must be greater than the business level tax rate on RE if growth to enhance nongrowth E U . If it cannot, then the nongrowth max V L is more likely to be greater than the growth max V L . This is why TCJA is important as expectations are that growth will increase beyond 3.12%, causing PBR to increase so that it will be greater than the unlevered tax rate (T E1 for PTs and T E2 for CCs) and make growth more affordable for firms. 4.4. Pass-Through Applications: Nongrowth and Growth under TCJA We now provide nongrowth and growth applications for pass-throughs (PTs). These two applications serve as respective examples of this study’s four nongrowth and eight growth tests. Like Appendix A, these applications use tax rates for TCJA tests as covered in Section 2.3. Appendix Breports a nongrowth pass-through (PT) application under TCJA using the PT nongrowth G L equation of Hull (2019). This appendix includes a table that reports values for variables for eleven of the sixteen Pchoices where the sixteen Pchoices consist of an unlevered Pchoice of zero and fifteen interior Pchoices corresponding to the fifteen interest coverage ratios (ICRs) with matching ratings and spreads supplied by Damodaran (2020) for the year 2019. The bold print column in the table in Appendix Bwith the OCR of A3 provides optimal values ranging from P=0.2582 in the top row to ODV =0.2409 in the bottom row. As seen in the table accompanying Appendix B, negative G L values first occur when the nongrowth PT goes from a non-investment grade credit rating (Moody’s Ba1) to a lower quality non-investment rating (Moody’s Ba2). The next lower quality rating (Moody’s B1) is a highly speculative credit rating. An even lower quality rating of B2 is in the last column. While not shown in Appendix B, if we were to issue enough debt to achieve a Moody’s Caa rating (which is a rating that indicates extreme speculation bordering on default), the PT nongrowth constraint would be violated. This constraint is breeched at high debt levels when the firm no longer has the cash flows to cover interest (I) with part of the reason being lower (or even negative) G L values. Whereas positive G L values can provide funds to pay I, negative GLvalues lower funds that could otherwise be used to pay I. In the bottom half of Appendix B, we show computations for optimal values for variables in the bold print column of the accompanying table where the PT attains a max V L of $10.633M (M =million) at its ODV of 0.2409. For example, the max % ∆ E U was computed as 7.16% at this ODV. This percentage of 7.16% indicates leverage adds, on average, 7.16 cents to unlevered firm value (E U ) for every dollar of debt issued to retire E U when a nongrowth PT is at this ODV. The net benefit from leverage (NB) was computed as 27.74%, indicating that each dollar of debt, on average, adds 27.74 cents to G L when the PT is at its ODV. A greater value for NB indicates greater efficiency per dollar of debt issued. Appendix Cis like Appendix Bbut replaces a nongrowth PT with a growth PT using an annual growth rate of 3.12% under TCJA. As noted earlier, this rate was captured in the CSM by using a levered equity growth rate (g L ) of 3.12%. This appendix uses the PT growth G L equation of Hull (2019) . The growth OCR (achieved with a PBR of 0.3435), like the nongrowth OCR seen in Appendix B, has a Moody’s upper medium rating of A3. The bold print column of the table that accompanies Appendix Cprovides optimal values ranging from P =0.2554 in the top row to ODV =0.2381 in the bottom row. The last two columns are in gray-shade to signify that their values are unfeasible, as the growth constraint is violated once we achieve a Moody’s credit rating of B1, which is a highly speculative rating. In the bottom half of Appendix C, we compute the optimal values found in the bold print column of the table that accompanies this appendix. To illustrate, the max % ∆ E U was computed as 7.25%, indicating the unlevered firm value increases by 7.25% when the optimal amount of debt is issued. Int. J. Financial Stud. 2020,8, 46 17 of 32 This is a bit above the 7.16% achieved for the nongrowth situation. While we can note other differences in nongrowth versus growth values when comparing the accompanying tables in Appendices Band C, these differences are also small. For example, we found slightly larger values with growth for the outputs of max G L ,max V L , and NB when compared to nongrowth values. The value for ODV of 0.2381 with growth was slightly lower than the ODV of 0.2409 for nongrowth. This slightly lower ODV is explained by the greater equity value for growth as the fifteen debt values are the same for either a nongrowth test or a growth test. They are the same because debt values are derived from interest coverage ratios (ICRs) and the same ICR values are used for all PT tests (as described in Section 4.1). Finally, while a growth rate of 3.12% does not produce noteworthy differences with nongrowth outputs, Section 6will show that this is not the case for higher growth rates of 3.90% and 4.50%. 5. Pass-Through Results in Graphical Form This section provides three PT figures. Somewhat similar figures for CCs can be found in Hull (2020). Figure 1plots the gain to leverage (G L ) and its two components against debt-to-firm value ratios (DVs) under TCJA when there is nongrowth. Figure 2repeats Figure 1but replaces the nongrowth values with growth values using the historical growth rate of 3.12%. Figure 3plots firm value (V L ) against credit ratings for the TCJA nongrowth test and the three TCJA growth tests. As first described in Section 1, these three growth tests involve growth rates of 3.12%, 3.90%, and 4.50%. Figure 3only considers the feasible Pchoices for growth tests causing the three growth trajectories to have different plot points. Unfeasible choices are not possible due to violation of the growth constraint. Whereas growth trajectories only consider feasible points, the nongrowth trajectory is truncated in that all of its feasible points are not shown. Int. J. Financial Stud. 2020, 8, x FOR PEER REVIEW 17 of 32 derived from interest coverage ratios (ICRs) and the same ICR values are used for all PT tests (as described in Section 4.1). Finally, while a growth rate of 3.12% does not produce noteworthy differences with nongrowth outputs, Section 6 will show that this is not the case for higher growth rates of 3.90% and 4.50%. 5. Pass-Through Results in Graphical Form This section provides three PT figures. Somewhat similar figures for CCs can be found in Hull (2020). Figure 1 plots the gain to leverage (GL) and its two components against debt-to-firm value ratios (DVs) under TCJA when there is nongrowth. Figure 2 repeats Figure 1 but replaces the nongrowth values with growth values using the historical growth rate of 3.12%. Figure 3 plots firm value (VL) against credit ratings for the TCJA nongrowth test and the three TCJA growth tests. As first described in Section 1, these three growth tests involve growth rates of 3.12%, 3.90%, and 4.50%. Figure 3 only considers the feasible P choices for growth tests causing the three growth trajectories to have different plot points. Unfeasible choices are not possible due to violation of the growth constraint. Whereas growth trajectories only consider feasible points, the nongrowth trajectory is truncated in that all of its feasible points are not shown. 5.1. Gain to Leverage versus Debt-to-Firm Value Ratio The trajectory in Figure 1 uses the PT nongrowth GL equation of Hull (2019) that is illustrated in Appendix B. This trajectory ends with DV = 0.3691, which corresponds to a Moody’s credit rating of B1. While not shown, the last feasible DV of 0.5201 corresponds to a rating of B3. As was seen in Section 4, the next rating below B3 in quality is Caa and this latter rating is where the nongrowth constraint is violated. The 1st component given by the top trajectory (dotted line) has an upward trend until the first downward bump occurs at DV = 0.3037. The bottom trajectory (dashed line), representing the 2nd component, is decreasing with the drop-off becoming steeper as more debt is issued. These trajectories are consistent with the notion that the 1st component captures the positive leverage effects from tax and agency benefits related to debt while the 2nd component capture the negative leverage effects from financial distress and agency costs. Figure 1. Nongrowth Pass-Through Gain to Leverage (G L ) Versus debt-to-firm value ratios (DVs) under Tax Cuts and Job Acts (TCJA) with g L of 0% and optimal credit rating (OCR) of A3. Gain to Leverage (GL), solid line; 1st Component, dotted line, and 2nd Component, dashed line. 5.1. Gain to Leverage versus Debt-to-Firm Value Ratio The trajectory in Figure 1uses the PT nongrowth G L equation of Hull (2019) that is illustrated in Appendix B. This trajectory ends with DV =0.3691, which corresponds to a Moody’s credit rating of B1. Int. J. Financial Stud. 2020,8, 46 18 of 32 While not shown, the last feasible DV of 0.5201 corresponds to a rating of B3. As was seen in Section 4, the next rating below B3 in quality is Caa and this latter rating is where the nongrowth constraint is violated. The 1st component given by the top trajectory (dotted line) has an upward trend until the first downward bump occurs at DV =0.3037. The bottom trajectory (dashed line), representing the 2nd component, is decreasing with the drop-offbecoming steeper as more debt is issued. These trajectories are consistent with the notion that the 1st component captures the positive leverage effects from tax and agency benefits related to debt while the 2nd component capture the negative leverage effects from financial distress and agency costs. The G L nongrowth trajectory (given by the solid line) of Figure 1is concave in shape and peaks at the ODV of 0.2409 where the OCR is Moody’s A3 rating. There is asymmetry in the G L nongrowth trajectory where the fall offis greater after the maximum G L (max G L ) of $0.710M (M =millions) is reached where $0.710M is per $1,000,000 in before-tax cash flows. G L first becomes negative for a rating of Ba2 with a DV of 0.3353, which is before it enters the highly speculative rating of B1 where DV =0.3691. From here the negativity in G L continues as debt choices rise until the nongrowth constraint is violated, at which point all outputs are unattainable. As noted above, the last feasible DV (before the constraint violation occurs) is 0.5201, which corresponds to a Moody’s rating of B3. All ratings of lower quality than B3 are unfeasible and cannot support the debt choice associated with such a low quality rating. Figure 2repeats Figure 1but replaces nongrowth with growth using the PT growth G L equation of Hull (2019). Results for this equation are illustrated in Appendix C. Figure 2contains only feasible plot points because values after DV =0.3152 are unattainable as the growth constraint is violated. A DV of 0.3152 corresponds to a Moody’s rating of Ba2, which is the second non-investment or speculative rating given by Damodaran (2020). The 1st component in Figure 2has a trajectory (dotted line) that is concave in shape like the 1st component in Figure 1except it has a greater drop-offafter its peak is reached at DV =0.1936. The 2nd component in Figure 2has an upward trajectory (dashed line) that is concave upward but does not exhibit full concavity. This trajectory contrasts with the downward trajectory of the 2nd component in Figure 1. Regardless, this trajectory’s first three plot points are negative and its later positive plot points are offset by negative plot points in the trajectory for the 1st component. Int. J. Financial Stud. 2020, 8, x FOR PEER REVIEW 18 of 32 Figure 1. Nongrowth Pass-Through Gain to Leverage (GL) Versus debt-to-firm value ratios (DVs) under Tax Cuts and Job Acts (TCJA) with gL of 0% and optimal credit rating (OCR) of A3. Gain to Leverage (GL), solid line; 1st Component, dotted line, and 2nd Component, dashed line. The GL nongrowth trajectory (given by the solid line) of Figure 1 is concave in shape and peaks at the ODV of 0.2409 where the OCR is Moody’s A3 rating. There is asymmetry in the GL nongrowth trajectory where the fall off is greater after the maximum GL (max GL) of $0.710M (M = millions) is reached where $0.710M is per $1,000,000 in before-tax cash flows. GL first becomes negative for a rating of Ba2 with a DV of 0.3353, which is before it enters the highly speculative rating of B1 where DV = 0.3691. From here the negativity in GL continues as debt choices rise until the nongrowth constraint is violated, at which point all outputs are unattainable. As noted above, the last feasible DV (before the constraint violation occurs) is 0.5201, which corresponds to a Moody’s rating of B3. All ratings of lower quality than B3 are unfeasible and cannot support the debt choice associated with such a low quality rating. Figure 2. Growth Pass-Through GL Versus DV under TCJA with gL of 3.12% and OCR of A3. Gain to Leverage (GL), solid line; 1st Component, dotted line, and 2nd Component, dashed line. Figure 2 repeats Figure 1 but replaces nongrowth with growth using the PT growth GL equation of Hull (2019). Results for this equation are illustrated in Appendix C. Figure 2 contains only feasible plot points because values after DV = 0.3152 are unattainable as the growth constraint is violated. A DV of 0.3152 corresponds to a Moody’s rating of Ba2, which is the second non-investment or speculative rating given by Damodaran (2020). The 1st component in Figure 2 has a trajectory (dotted line) that is concave in shape like the 1st component in Figure 1 except it has a greater drop-off after its peak is reached at DV = 0.1936. The 2nd component in Figure 2 has an upward trajectory (dashed line) that is concave upward but does not exhibit full concavity. This trajectory contrasts with the downward trajectory of the 2nd component in Figure 1. Regardless, this trajectory’s first three plot points are negative and its later positive plot points are offset by negative plot points in the trajectory for the 1st component. Despite differences in the trajectories of the 2nd components in Figures 1 and 2, the GL growth trajectory (solid line) in Figure 2 is concave in shape like the GL nongrowth trajectory in Figure 1. The GL growth trajectory peaks at the ODV of 0.2381 where max GL = $0.728 M. While not shown, similar trajectories for GL and its two components occur if we increased the annual growth rate to gL = 3.90% or gL = 4.50%. However, as will be seen in Figure 3, full concavity becomes more difficult to achieve as the growth rate continues to increase. Figure 2. Growth Pass-Through G L Versus DV under TCJA with g L of 3.12% and OCR of A3. Gain to Leverage (GL), solid line; 1st Component, dotted line, and 2nd Component, dashed line. Int. J. Financial Stud. 2020,8, 46 19 of 32 Despite differences in the trajectories of the 2nd components in Figures 1and 2, the G L growth trajectory (solid line) in Figure 2is concave in shape like the G L nongrowth trajectory in Figure 1. The G L growth trajectory peaks at the ODV of 0.2381 where max G L =$0.728 M. While not shown, similar trajectories for G L and its two components occur if we increased the annual growth rate to g L = 3.90% or g L =4.50%. However, as will be seen in Figure 3, full concavity becomes more difficult to achieve as the growth rate continues to increase. In summary form, Figure 2is different from Figure 1in four ways. First, a growth trajectory in Figure 2stops at a lower DV compared to a nongrowth trajectory in Figure 1. This is because the growth constraint in Figure 2sets in after DV reaches 0.3152 while the nongrowth constraint in Figure 1occurs at a much higher DV. Although not shown in Figure 2, the violation occurs at DV =0.6168 (as can be seen in Section 4). Second, the growth trajectory for the 1st component (dotted line) has an interior maximum at the DV of 0.1936 before the ODV of 0.2381 is reached. This differs from the nongrowth trajectory for the 1st component that is still rising at its ODV.Third, the growth trajectory for the 2nd component (dashed line) trends upward, while the nongrowth trajectory for the 2nd component trends downward. Fourth, a close comparison of Figures 1and 2reveals that nongrowth G L values were similar to growth G L values until we reached the optimal Pchoices, at which point growth G L values became greater and continued to increase relative to nongrowth values until the growth constraint was violated. 5.2. Pass-Through Firm Value versus Credit Ratings Figure 3plots firm value (V L ) versus credit ratings for the nongrowth PT tests under TCJA and three growth PT tests under TCJA. This figure differs from the prior two figures by replacing G L with V L along the vertical axis and DV with Moody credit ratings, as used by Damodaran (2020), along the horizontal axis. For Figure 3, we only include credit ratings up to Ba2. As seen in this figure, the two trajectories for the two greatest growth rates (3.90% and 4.15%) cannot reach this rating of Ba2, as the growth constraint is violated at quality ratings greater than Ba2. For the nongrowth PT trajectory (dotted line at bottom), violation of the nongrowth constraint occurs at the extremely speculative rating of Caa, which is well below Ba2 in quality as was shown in Section 4. For the growth trajectory (small dashed line) when g L =3.12%, violation of the growth constraint first occurs with a rating of B1, which is a rating just below Ba2 in quality. For the growth trajectory (solid line) when g L =3.90%, violation of the growth constraint occurs at a rating of Ba2 and so this trajectory ends at a rating of Ba1. For the growth trajectory (large dashed line at top) when g L =4.50%, violation starts with Ba1 so the trajectory stops at Baa2. Given this pattern, we concluded that greater growth leads to violations at higher quality credit ratings. For the dotted line trajectory representing the nongrowth test in Figure 3, we find max V L = $10.633 M at the OCR of A3. For the dashed line trajectory where g L =3.12%, the plowback ratio (PBR) of 0.3435 yields g L =3.12% for an OCR of A3 with max V L =$10.758 M. The latter max V L is a $0.125 M larger than the nongrowth max V L of $10.633 M in the dotted line trajectory. In percentage form, the increase is only 1.18%. The small difference of $0.125 M is not caused by the choice of credit ratings. For example (and as alluded to in our discussion in Section 4.2), if we set PBR so that g L =3.12% for both lower and higher quality credit ratings, all V L values are lower than the growth max V L of $10.758 M that occurs at A3. Thus, a lower or higher quality credit rating does not necessarily lead to increased firm value, even when growth is the same. Thus, at least for this growth test, targeting the correct credit rating as OCR is important. Int. J. Financial Stud. 2020,8, 46 20 of 32 Int. J. Financial Stud. 2020, 8, x FOR PEER REVIEW 19 of 32 In summary form, Figure 2 is different from Figure 1 in four ways. First, a growth trajectory in Figure 2 stops at a lower DV compared to a nongrowth trajectory in Figure 1. This is because the growth constraint in Figure 2 sets in after DV reaches 0.3152 while the nongrowth constraint in Figure 1 occurs at a much higher DV. Although not shown in Figure 2, the violation occurs at DV = 0.6168 (as can be seen in Section 4). Second, the growth trajectory for the 1st component (dotted line) has an interior maximum at the DV of 0.1936 before the ODV of 0.2381 is reached. This differs from the nongrowth trajectory for the 1st component that is still rising at its ODV. Third, the growth trajectory for the 2nd component (dashed line) trends upward, while the nongrowth trajectory for the 2nd component trends downward. Fourth, a close comparison of Figures 1 and 2 reveals that nongrowth GL values were similar to growth GL values until we reached the optimal P choices, at which point growth GL values became greater and continued to increase relative to nongrowth values until the growth constraint was violated. 5.2. Pass-Through Firm Value versus Credit Ratings Figure 3 plots firm value (VL) versus credit ratings for the nongrowth PT tests under TCJA and three growth PT tests under TCJA. This figure differs from the prior two figures by replacing GL with VL along the vertical axis and DV with Moody credit ratings, as used by Damodaran (2020), along the horizontal axis. For Figure 3, we only include credit ratings up to Ba2. As seen in this figure, the two trajectories for the two greatest growth rates (3.90% and 4.15%) cannot reach this rating of Ba2, as the growth constraint is violated at quality ratings greater than Ba2. For the nongrowth PT trajectory (dotted line at bottom), violation of the nongrowth constraint occurs at the extremely speculative rating of Caa, which is well below Ba2 in quality as was shown in Section 4. For the growth trajectory (small dashed line) when gL = 3.12%, violation of the growth constraint first occurs with a rating of B1, which is a rating just below Ba2 in quality. For the growth trajectory (solid line) when gL = 3.90%, violation of the growth constraint occurs at a rating of Ba2 and so this trajectory ends at a rating of Ba1. For the growth trajectory (large dashed line at top) when gL = 4.50%, violation starts with Ba1 so the trajectory stops at Baa2. Given this pattern, we concluded that greater growth leads to violations at higher quality credit ratings. Figure 3. Nongrowth firm value (VL) (dotted line), 3.12% Growth VL (smaller dashed line), 3.90% Growth VL (solid line), and 4.50% Growth VL (larger dashed line) Versus Moody’s Credit Ratings for Pass-Throughs under TCJA with OCR of A3 target except for top trajectory where OCR is Baa2. Figure 3. Nongrowth firm value (V L ) (dotted line), 3.12% Growth V L (smaller dashed line), 3.90% Growth V L (solid line), and 4.50% Growth V L (larger dashed line) Versus Moody’s Credit Ratings for Pass-Throughs under TCJA with OCR of A3 target except for top trajectory where OCR is Baa2. As just seen in the small increase of only 1.18% with growth of 3.12%, we inferred that a PT would have to achieve an annual growth rate greater than the historical long-run rate (for a seventy-year period) of 3.12% to make growth more profitable relative to a nongrowth. This inference holds as seen in the solid line trajectory where V L is $11.506 M when g L =3.90% at a rating of A3 with a PBR of 0.3934. This V L of $1.506 M is an 8.22% increase over nongrowth max V L of $10.633 M. Furthermore, the V L of $11.506 M for g L =3.90% is 6.95% greater than the max V L of $10.758 M when g L =3.12%. However, this solid line trajectory reveals that the greatest V L is not $11.506 M that occurs at A3, but $11.527 M where the latter is attained at a rating of Baa2. Nevertheless, if the largest sustainable growth rate is 3.90%, we could not consider $11.527 M as the max V L because it is attained with g L =4.33%. Thus, we concluded that $11.506 M is still the likely candidate for max V L if 3.90%. Below we explore this candidacy. If we set PBR so that g L =3.90% occurs for a lower quality rating of Baa2, we found V L =$11.056 M, which is below $11.506 M when g L =3.90% for a rating of A3. If we set g L =3.90% for a higher quality rating of A2, we found V L =$11.588 M, which is above $11.506 M when g L =3.90% for a rating of A3. While this test yields a larger V L , other tests of higher quality ratings often yield either lower V L values or unfeasible outcomes where the latter occurs because higher quality ratings can lead to the growth constraint being violated. Regardless, if a PT manager can achieve growth of 3.90% at a higher quality rating, then greater firm value can result and determining max VLand OCR becomes a question as to what is the highest quality credit rating that can be attained by a PT when g L =3.90%. Achieving a higher V L for a higher quality credit rating than A3 for g L =3.90% differs from what we just saw for the lower growth rate of g L =3.12% where achieving 3.12% for a higher quality rating than A3 did not increase max V L . Given the difficulty of attaining and maintaining higher quality credit ratings, we would argue that a typical PT has an OCR of A3 if it can attain g L =3.90%. However, a stronger PT should be able to achieve an OCR of higher quality than A3 when g L =3.90%, while a weaker PT would have to settle for an OCR of lower quality than A3. The top trajectory with the larger dashed line uses g L =4.50%. As described in Section 1, a rate of 4.50% is consistent with the high end of the growth spectrum cited by the Tax Policy Center (2018) Int. J. Financial Stud. 2020,8, 46 21 of 32 under TCJA. For this trajectory, we use an OCR of Baa2 because an A3 rating with a growth rate of 4.50% is not feasible. This is because the growth constraint is violated when an A3 rating (or any rating of higher quality than Baa2) is used with g L =4.50%. The difficulty in achieving the higher quality rating of A3 is consistent with what we found in the real world, where higher quality ratings are unachievable for an average firm. The V L of $11.756 M in the top trajectory for a Baa2 rating when g L =4.50% is greater than the V L value of $11.506 M that occurs when g L =3.90% at an A3 rating in the solid line trajectory. It can be pointed out that the V L value of $11.712 M for an A3 rating in the top trajectory is achieved with an annual growth rate of 4.06% and this value of $11.712M is also higher than $11.506 M achieved at g L =3.90% with a rating of A3 in the solid line trajectory. As seen in the top trajectory, the firm values of $11.299 M and $11.498 M for credit ratings of A1 and A2 (with respective growth rates of 3.69% and 3.84%) are lower than $11.506 M achieved at g L =3.90% with a rating of A3. When we tried to target a Ba1 or lower quality rating when g L =4.50%, we found that V L values fell. From the 4.50% growth tests (just like the 3.90% growth test), we deduced that firm value can depend on the quality of the rating that is achievable for a higher growth rate projected under TCJA. While not shown in Figure 3, we also examined PT trajectories for a pre-TCJA nongrowth test and a pre-TCJA growth test with g L =3.12%. As expected (and shown next in Section 6), pre-TCJA tests yield smaller max V L values than those for TCJA since the pre-TCJA cash flows are taxed at greater levels. Regardless, there are similarities in all pre-TCJA and TCJA trajectories in that we find concave relations between V L and credit ratings. The pre-TCJA nongrowth max V L for PTs is only $0.019 M less than its growth max V L . This pre-TCJA difference of $0.019 M is smaller than the difference of $0.125 M for the same TCJA comparison for PTs. Since pre-TCJA tax rates are higher for PTs than TCJA tax rates, we surmised that higher pre-TCJA business tax rates make it more difficult for growth V L values to compete with nongrowth V L values. This is because RE is used for growth only after it is taxed and a pre-TCJA environment has greater business level tax rates, making the use of RE more expensive. This will be better seen in the next section, when we present CC results where the pre-TCJA business level corporate tax rate is significantly higher than that for TCJA. 6. Results for Pass-Throughs and C Corps This section reports results for pass-through (PT) and C corps (CC) outputs at ODVs and compares them. We also overview policy implications and suggest avenues for future research. 6.1. Optimal Outputs for the Three Categories of Debt Choice, Valuation, and Leverage Gain Table 2reports optimal values for seven outputs covering the three categories of debt choice, valuation and leverage gain. Panel A includes output for six PT tests consisting of two pre-TCJA tests and four TCJA tests where the latter four tests were described when presenting Figure 3. These tests use PT tax rates and interest coverage ratios (ICRs) for the small firm classification of Damodaran (2020). Panel B consists of outputs for six CC tests that repeat the six PT tests. These tests are identical except for the use of CC tax rates and ICRs for Damodaran’s large firm classification. As described in Section 2.3, we aimed to achieve effective levered tax rates at ODV. This goal is reasonably achieved as now described. For PTs in Panel A, we attained the following effective tax rates: T E =0.3006 and T D =0.2203 for the two pre-TCJA tests in the first two rows; T E =0.2834 and T D =0.2087 for the first three TCJA tests in the next three rows, and T E =0.2749 and T D =0.2149 for the last test (where g L =4.50%). For CCs in Panel B, we have T C =0.2915, T E =0.1374, and T D =0.2269 for the two pre-TCJA tests in the first two rows and T C =0.1749, T E =0.1374, and T D =0.2149 for the four TCJA tests in the last four rows. Table 2provides optimal results in terms of three categories of outputs: debt choice, valuation, and leverage gain. Since the averages in the last row of each panel often mirror the comparisons between the six rows in each panel, we focus on these averages when analyzing the seven columns of optimal outputs in this table. Because Table 2reports outputs using only the most recent credit spreads for 2019, we also provide, when relevant, outputs using ratings for 2017 and 2018 albeit we have less Int. J. Financial Stud. 2020,8, 46 22 of 32 confidence in applying 2017 data2. In addition, Section 6.2 overviews outputs using a lower effective tax rate scheme, as described in Section 2.3.3. Table 2. Seven Optimal Outputs. P Choice ODV EUMax VLMax GLMax %∆EUNB Panel A. Pass-Throughs (PTs) Nongrowth: Pre-TCJA 0.2559 0.2375 $9.626 $10.371 $0.745 7.74% 30.24% Growth (gL=3.12%): Pre-TCJA 0.2556 0.2371 $9.638 $10.390 $0.752 7.80% 30.51% Nongrowth: TCJA 0.2582 0.2409 $9.922 $10.633 $0.710 7.16% 27.74% Growth (g L =3.12%): TCJA 0.2554 0.2381 $10.030 $10.758 $0.728 7.25% 28.40% Growth (g L =3.90%): TCJA 0.2407 0.2226 $10.644 $11.506 $0.863 8.11% 33.68% Growth (g L =4.50%): TCJA 0.2718 0.2499 $10.807 $11.756 $0.948 8.77% 32.28% Overall Average for PTs 0.2563 0.2377 $10.111 $10.902 $0.791 7.81% 30.48% Panel B: C Corps (CCs) Nongrowth: Pre-TCJA 0.5434 0.4354 $8.038 $10.032 $1.994 24.81% 45.65% Growth (gL=3.12%): Pre-TCJA 0.5501 0.4609 $7.940 $9.476 $1.536 19.35% 35.17% Nongrowth: TCJA 0.5288 0.4537 $9.769 $11.385 $1.616 16.54% 31.28% Growth (g L =3.12%): TCJA 0.5124 0.4526 $10.080 $11.413 $1.333 13.22% 25.81% Growth (g L =3.90%): TCJA 0.4941 0.4337 $10.454 $11.910 $1.455 13.92% 28.18% Growth (g L =4.50%): TCJA 0.4766 0.4132 $10.839 $12.502 $1.663 15.35% 32.20% Overall Average for CCs 0.5176 0.4416 $9.520 $11.120 $1.600 17.20% 33.05% Table 2reports seven optimal outputs for pass-throughs (PTs) and C corps (CCs) for conditions of nongrowth and growth and for two tax rate schemes of pre-TCJA and TCJA as discussed in Section 2.3. The optimal outputs were first defined in Appendix B. Growth tests include an annual growth rate of 3.12% for pre-TCJA tests. A rate of 3.12% is consistent with seventy years of historical compounded growth using annual US real GDP growth data given by the US Bureau of Economic Analysis (2020). Due to TCJA lowering taxes, growth is projected to increase. Thus, besides using a 3.12% historical rate, our TCJA growth tests also included an annual growth rate of 3.90% and an upper bound growth rate of 4.50%. These growth rates were first discussed in Section 1. The outputs in Panel A are for PTs and outputs in Panel B are for CC. Values for outputs in all rows occur at the optimal Pchoices given in the “P Choice” column where a Pchoice stands for the proportion of unlevered firm value (E U ) retired with debt (D). As argued in Section 4.2, the optimal credit rating (OCR) is Moody’s A3 for PTs with an exception being for the 4.50% growth tests where OCR is Baa2. For CCs, OCR is Baa2 for all tests. This OCR is based on the same considerations given in Section 4.2 when identifying an OCR for PTs. All tests have a before-tax cash flow of $1,000,000. All dollar values in this Table 2are given in millions. The last row of each panel provides averages of the preceding six rows. The averages for max % ∆ E U in Panel B are high compared to pre-TCJA research. These higher values can be explained by the fact that outputs can be sensitive to the change in credit spreads over time. Tests using Damodaran’s archived spreads for 2018 at http://pages.stern.nyu.edu/~{}adamodar/New_Home_Page/dataarchived.html provide lower max % ∆ E U values that are consistent with pre-TCJA research. For example, while the average of all max %∆EUvalues for both panels in Table 2is 12.50%, it is 7.33% using 2018 data. 6.1.1. Debt Choice Outputs In terms of the debt choice outputs found in the “P” and “ODV” columns in Panel A, the last row in these two columns reveals that optimal Pchoices and ODVs average 0.2563 and 0.2377, respectively, for the six PT tests that cover nongrowth, growth, pre-TCJA and TCJA situations. These two PT averages are substantially below the corresponding CC averages found in last row of Panel B where Pand ODV average 0.5176 and 0.4416, respectively. Of importance, we find little variation in either optimal Pchoices or ODVs for each panel. The smallest standard deviation of 0.0088 occurs for ODVs for PTs and the largest of 0.0287 occurs for optimal Pchoices for CCs. ODVs are lower than optimal P choice because they take into account the gain in leverage that increases firm value and thus lowers ODVs relative to their corresponding optimal Pchoices. 2 According to our records, Damodaran’s ICRs were the same for 2018 and 2019. Thus, whereas spreads changed for these two years, the ratings and ICRs that are matched to the spreads did not change. We do not know to what extent, if any, ICRs were provided prior to 2018 because Damodaran’s archive files do not always contain the same details that were provided during the year when the data was first reported. Regardless, our best guest is that ICRs for 2017 existed and are similar to 2018 and 2019. Prior to 2017, we have no record that Damodaran reported ICRs. Int. J. Financial Stud. 2020,8, 46 23 of 32 When we repeated our debt choice tests for PTs using spreads for 2018, we found that the optimal Pchoices and ODVs are similar to 2019 spreads. However, using 2017 spreads produced averages of 0.3069 for optimal Pchoices and 0.2776 ODVs, indicating higher debt levels for PTs. For CCs, using 2017 spreads cause no real change. However, using 2018 spreads, we found averages of 0.4186 for optimal Pchoices and 0.3752 for ODVs. Like the use of 2019 spreads, we found little variation in either optimal Pchoices or ODVs when using 2017 or 2018 spreads. Based on three years of spread data, we offer the following conclusions. First, PT debt choice values using 2019 spread data may understate what occurs historically. Second, the opposite appears for CCs, as the use of 2019 spread data may overstate what occurs historically. In fact, for the three growth tests under TCJA using 2018 spreads, the average ODV for CCs is 0.3376 (which compares to 0.4331 for the same tests using 2019 spreads). Third, the annual change in credit spreads matched to ICRs can have an impact on debt choice outputs. The latter implies managers can experience difficulty in targeting leverage ratios to achieve maximum firm value as an ODV. Not only is their ODV subject to variation each year but they could experience annual adjustments costs that are great enough to prevent adjustments to maintain an ever changing ODV. In this study, we assume the data by Damodaran (2020) for his small firm classification represents PTs since PTs consist primarily of smaller enterprises. While the latter is true, we should also point out that there are also very small CCs and very large PTs. In fact, most firms are small for all for-profit businesses. To cast light on the accuracy of our ODV findings for PTs, we tried to find PT leverage ratio data to compare to this study. While extant research on DVs for PTs is sparse, our PT outputs for ODV (from what we can decipher) are similar to that reported from extant research. For example, Mohaghegh (2019) finds the average DV (described as the debt-to-asset ratio) of unincorporated non-financial firms (assumedly mostly PTs) has ranged from 0.23 to 0.40 for a period from 1975 though 2007 with larger values in later years. To the extent market value is greater than book assets, this range of 0.23 to 0.40 would be lower. More recently than Mohaghegh, Bowman (2015) compares the leverage of nonprofits with nonfinancial non-corporate businesses (or PTs). He reports the average DV is 0.25 in terms of long-term debt to real estate where the latter assumedly represents capital assets for PTs. Based on short-term and long-run debt data from Damodaran (2020), Bowman’s DV for PTs with short-term debt would be about 0.2659. This lies within our range of 0.2377 to 0.2776 using spreads from the past three years. While DVs can change over time, we conclude that the historical numbers appear to be similar to our PT debt choice outputs. Graham and Harvey (2001) survey 392 CFOs. In terms of a debt ratio (measured by debt to total assets), they note one-third is below 0.2, one-third is between 0.2 and 0.4, and the remaining is greater than 0.4. Viewing their study as primarily a CC study, their numbers show some disagreement with our CC results where we find average ODV of 0.4416 that is achieved with a Baa2 rating. However, Graham and Harvey point out that 32% of their sample contain a Moody’s A2 rating, which would lead to lower DVs. For example, if the OCR for our CC tests was A2 and we set PBR to achieve a 3.12% growth rate under TCJA, the DV would be 0.3656 for CCs. It would be 0.2780 if we used 2018 spreads. The latter is consistent with the empirical research by Hull et al. (2018) who find an average DV of 0.263 for their sample of 1189 seasoned equity offers for firms that are smaller in size and would straddle the small and large firm size classifications given by Damodaran (2020). Finally, the medium ratings of A3 and Baa2 we find for OCRs for all of our PT and CC tests are consistent with that reported by Morningstar (2019), as these ratings are by far the most common ratings. 6.1.2. Valuation Outputs In regard to the PT valuation outputs based on $1,000,000 in before-tax cash flows, the averages for E U and maximum firm value (max V L ) are $10.111 M and $10.902 M, respectively, in the last row of Panel A. These averages compare to those for CCs in the last row of Panel B where E U and max V L average $9.520 M and $11.120 M, respectively. While the PT average for E U is 6.21% higher than the CC average, the PT average for max V L is 1.95% lower than corresponding CC average. This same Int. J. Financial Stud. 2020,8, 46 24 of 32 pattern is observed when replacing 2019 spreads with either 2017 spreads or 2018 spreads. Panel B of Table 2reveals larger CC valuations occur for the TCJA tests where CCs receive more favorable tax treatment than PTs. While these larger CC valuations are predictable given the huge drop-offin the effective corporate tax rate under TCJA, what Table 2offers is a detailed look at the numbers that reveal precisely how TCJA can increase pre-TCJA firm valuation and how increasing growth consistently increases firm value. Thus, the valuation outputs in Table 2confirm the notion advanced by tax experts, such as those at the Tax Policy Center (2018), that lower taxes are necessary to prevent economic harm and increase business wealth. If we compare max V L values for our two pre-TCJA tests for PTs with those for CCs, we find CCs, on average, have a valuation disadvantage of 6.037%. For the eight TCJA tests (four for PTs and four for CCs), the valuation advantage now favors CCs as its average max V L is 5.727% greater than PTs. The net percentage gain for an average CC over an average PT caused by TCJA is 6.037% + 5.727% =11.764%. This reveals that TCJA can put an average PT in a better position to increase its value by switching its ownership form to a CC. This conclusion is not a product of using spreads for 2019, as 11.764% increases to 13.525% and 13.716% if we use the respective spreads for 2017 and 2018. Together these results indicate that, ceteris paribus, the future will find more businesses claiming the CC ownership form. 6.1.3. Leverage Gain Outputs With respect to the leverage gain outputs for PTs in the last row of Panel A, the averages for max G L ,max % ∆ E U and NB are $0.791 M, 7.81% and 30.48%, respectively. The PT averages for G L and max % ∆ E U are substantially less than those for CCs in Panel B where the values are $1.600 M for max G L and 17.20% for max % ∆ E U . This reveals that CCs get greater gains from leverage both in dollars and percentages. In terms of NB, PTs are now more similar to CCs by having an average of 30.48% compared to 33.05% for CCs. This indicates that PTs are only slightly less efficient than CCs by getting a bit smaller gain for every dollar of debt added. The average PT output of 7.81% for max % ∆ E U is like the prior empirical research (Graham 2000;Korteweg 2010;Van Binsbergen et al. 2010) where max % ∆ E U values range from 4% to 10%. However, the average CC output of 17.20% for max % ∆ E U is greater than prior research. For both ownership forms, we find an overall average of 12.50%, which is still high historically. As was just argued for our ODV results, we can also explain this difference in terms of the recent data from Damodaran (2020) with spreads for 2019. For example, using spreads for 2018, we found the overall average of 12.50% changes to 7.33%, which is consistent with the empirical research where the midpoint is 7%. We concluded that leverage gain outputs, like debt choice outputs, can be sensitive to the annual changes in the spreads used by Damodaran. 6.2. Outputs With Lower Tax Rates While we used effective tax rates consistent with the resources we cite, there is another school of thought that favors lower effective tax rates (as mentioned in Section 2.3.3). Thus, we conduct tests with lower business level tax rates. For these tests, we did the following. First, we lowered the personal equity tax rate for PTs by 0.05 for both pre-TCJA and TCJA tests. Second, we lowered the pre-TCJA corporate tax rate by 0.07 and the TCJA corporate tax rate by 0.03. For these tests with lower business tax rates, we discover that OCRs remained unchanged. For example, Moody’s A3 was optimal for the same PT tests and, as before, Moody’s Baa2 was optimal for the 4.50% growth rate tests. For CC tests, Moody’s Baa2 remained optimal for all tests. In terms of debt choice outputs, we found virtually the same results. For example, the average ODV for PTs only fell from 0.2377 to 0.2352. For CCs, the average ODV fell even less by going from 0.4416 to 0.4409. 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