# Nonprofits and Pass-Throughs: Performance Comparison

^{*}

## Abstract

**:**

## 1. Introduction

_{L}) and thus identify the optimal debt-to-firm value ratio (ODV) that, in turn, is aligned with an optimal credit rating (OCR). The key to these computations is the assumption of analogous risk classes. As NPs are subsidized by PTs, their revenue streams are influenced by the same economic factors and thus capable of having similar risk classes. The assumption of parallel risk classes for NPs and PTs implies the same costs of borrowing. For our tests, costs of borrowing are based on credit spreads matched to bond ratings and interest coverage ratios (ICRs). The same borrowing costs for NPs and PTs enable the CSM to compute outcomes so that comparisons can be made and conclusions can be drawn that are based on different tax rates.

_{L}). Second, while we know that NPs have a significant valuation advantage by not paying taxes, we reveal the extent of this advantage by showing that max V

_{L}for NPs is 51.63% higher than PTs. Third, we show that growth helps nongrowth NPs more than nongrowth PTs in increasing max V

_{L}. To illustrate, NPs achieve a 13.83% increase when going from their nongrowth max V

_{L}to their growth max V

_{L}while PTs only attain a 3.42% rise.

_{BT}) that is 26.63% smaller than PTs and an unlevered growth rate (g

_{U}) that is 7.97% lower than PTs. The latter two results occur because PBR

_{BT}and g

_{U}are positively related to retained earnings (RE) and PTs can only use RE after business taxes are paid on it while NPs avoid business taxes. Fifth, while NPs increase their value more than PTs when going from their nongrowth max V

_{L}to their growth max V

_{L}, a different picture emerges when going from their unlevered firm value (E

_{U}) with growth to their max V

_{L}with growth. For example, in terms of the maximum gain to leverage (max G

_{L}), NPs gain 2.25% less in absolute dollars by issuing debt compared to PTs. This can be explained by not having an interest tax shield, which is a key valuation component of mainline capital structure theory. While this finding is supported, on average, by robust tests, these tests indicate a great variability in outcomes. In particular, greater growth rates cause NPs to gain more and not less.

_{U}) from a debt-for-equity transaction, we find that NPs increase 4.57% from their unlevered equity value with growth while PTs increase 7.29% from their unlevered equity value with growth. This finding is supported by robust tests including those with greater growth. Seventh, with regard to the net benefit from leverage (NB), we find that E

_{U}for NPs rises 15.93% for every dollar of debt while E

_{U}for PTs increases 27.96%. Thus, while this indicates that NPs are less efficient in their use of each dollar of debt, it also reflects the fact that NPs not only have greater ODVs but also have higher firm valuations and so must issue more debt to attain the same optimal credit rating (OCR). For both NPs and PTs, OCR is Moody’s rating of A3.

## 2. Background and Literature Review

#### 2.1. Key Features of Nonprofits (NPs) and Pass-Throughs (PTs)

#### 2.2. Equity and Debt Financing for Nonprofits (NPs) and Pass-Throughs (PTs)

#### 2.3. Assignment of Unlevered and Levered Tax Rates for Nonprofits (NPs) and Pass-Throughs (PTs)

_{L}) equations in our methodology section, we present unlevered and levered federal equity tax rates where the subscript “1” indicated an unlevered tax rate and the subscript “2” indicates a levered tax rate. Thus, for what follows T

_{C}

_{1}, T

_{E}

_{1}, and T

_{D}

_{1}are unlevered corporate, personal equity, and personal debt tax rates at the federal level, while T

_{C}

_{2}, T

_{E}

_{2}, and T

_{D}

_{2}are the corresponding levered tax rates that change with leverage as described by Hull (2014). By definition, unlevered refers to no debt. With this in mind, our use of the unlevered debt tax rate of T

_{D}

_{1}is only for practically purposes as we need a starting point for the debt tax rate that rises with leverage. For CSM papers, where T

_{D}

_{1}is not emphasized as a starting point, T

_{D2}is simply called T

_{D}.

_{E2}), the Tax Policy Center (2016) noted that over two-thirds of PTs are taxed at either the maximum federal tax rate of 0.396 or the 0.28 alternative minimum rate. The average of these two rates generates a T

_{E2}of 0.338. The Small Business Administration (SBA Office of Advocacy 2009), the National Federation of Independent Business (2013), and the Tax Policy Center (2018) indicate that most PTs experience a T

_{E}

_{2}below 0.3 indicating a median would fall below 0.3. However, according to the Brookings (2017), almost half of PT income comes from businesses with an T

_{E}

_{2}near the TCJA maximum. Considering all sources and the recent fall in T

_{E2}under TCJA an effective T

_{E}

_{2}between 0.21 and 0.34 is a reasonable ballpark estimate for TCJA tests. As we begin with an unlevered firm and allow tax rates to change when debt increases as described by Hull (2014), our tests use a personal unlevered equity tax rate (T

_{E}

_{1}) that is greater than an effective levered T

_{E}

_{2}achieved at the optimal debt-to-firm value ratio (ODV).

_{E}

_{1}of 0.30 for PTs. This usage enables us to achieve an effective levered T

_{E}

_{2}that is near 0.255 at ODV where T

_{E}

_{2}changes by 0.03 in its predicted direction for each increasing debt-for-equity choice. As described later, each of our fifteen increasing debt-for-equity choices corresponds to a fall in the quality of one of the fifteen credit ratings given by Damodaran (2020).

_{E}

_{1}is 0.36 and the effective levered T

_{E2}is around 0.31 at ODV. An H tax rate gives greater weight to averages whereas an L tax rates provides a greater weight to medians. The above L and H tax rates occur under TCJA tax laws. Thus, tests using these tax rates under TCJA can be referred to simply as TCJA tests. When testing pre-TCJA tax rates, we increase our TCJA unlevered and effective levered T

_{E2}values by 0.02 for both the L and H tax rate tests given that TCJA drops rates for its tax brackets by about 0.02 on average. Tax rates for our L tax rate tests under TCJA are used in the first five tables and first five figures, while tax rates for our robust tests (that include L tax rate tests for a pre-TCJA tax environment and H tax rate tests for both pre-TCJA and TCJA tax environments) are used in the last three tables and the last five figures. In addition, these last tables and figures incorporate a greater growth rate (as discussed later).

_{D2}). If debt is held longer than three years, any capital gains are taxed at the lower capital gains rate with a typical maximum rate of 0.20 for which we expect a T

_{D}

_{2}around 0.16. A marginal T

_{D}

_{2}based on the imputed rate from the highest rated municipal and corporate bond yields varies over times and can be near the maximum statutory rate. However, this imputed tax rate is more of a marginal tax rate than an effective tax rate. Considering all factors, a range from 0.16 to 0.26 is feasible for an average T

_{D2}. For our TCJA tests where T

_{D2}increases with leverage, we set the unlevered T

_{D}

_{1}at 0.18 to get a levered T

_{D}

_{2}around 0.21 at ODV. For our pre-TCJA tests, we increase T

_{D}

_{1}by 0.01 due to expectations of slightly greater rates on debt income. We use the same TCJA and pre-TCJA values for T

_{D}

_{1}and T

_{D}

_{2}for both our L and H tax rate tests as the focus is on the business tax rate that directly impacts (i) internal growth that stems from the use of retained earnings (RE) and (ii) the ITS that results in tax savings at the business tax rate level.

_{D}

_{2}of zero. Bowman (2015) writes that most NP debt is tax-exempt. He also notes that the trend has been to issue even more tax-exempt debt. Given the possibility of zero tax rates, our L tax rate tests for NP use zero values for the unlevered corporate tax rate (T

_{C}

_{1}), T

_{E}

_{1}, and T

_{D}

_{1}. Since zero tax rates cannot change with leverage, the levered tax rates of T

_{C}

_{2}, T

_{E}

_{2}, and T

_{D}

_{2}are also zero. For our H tax rate tests for NPs, we assume tax rates are not zero but small. For these tests, we set both T

_{C}

_{1}and T

_{E}

_{1}at 0.02 where we assume the existence of minor for-profit ventures (such as gift shops). We set T

_{D}

_{1}at 0.04 where we assume some debt is issued that is not tax-exempt. Given that T

_{C}

_{1}and T

_{E}

_{1}are small, they cannot change much and so achieve similar effective levered tax rates for T

_{C}

_{2}and T

_{E}

_{2}. T

_{D}

_{1}is slightly larger and so T

_{D}

_{2}is slightly higher at 0.045 since T

_{D2}increases with leverage. For pre-TCJA tests, we increase these unlevered tax rates by 0.01 and achieve effective levered tax rates that have a similar increase. In addition, we set both T

_{C}

_{1}and T

_{E}

_{1}at 0.03 for pre-TCJA tests and so they both fall so that T

_{C}

_{2}and T

_{E}

_{2}are both about 0.025. Finally, we set T

_{D}

_{1}at 0.05 for pre-TCJA tests and it rises so that T

_{D}

_{2}is about 0.06.

#### 2.4. Capital Structure Models

## 3. Methodology

#### 3.1. Capital Structure Model (CSM)

_{L}) = V

_{L}− V

_{U}where V

_{L}is levered firm value consisting of levered equity (E

_{L}) and debt (D) and V

_{U}is unlevered firm value or, equivalently, unlevered equity value (E

_{U}), Hull (2014) extends the CSM research on C corps (CCs) by incorporating changes in tax rates and shows that the nongrowth CC equation is

_{L}= (1 − α

_{I}r

_{D}/r

_{L})D + (1 − α

_{2}r

_{U}/r

_{L})E

_{U}

_{I}and α

_{2}capture the effects of effective tax rates with α

_{1}= (1 − T

_{E}

_{2})(1 − T

_{C}

_{2})/(1 − T

_{D2}) and α

_{2}= (1 − T

_{E}

_{2})(1 − T

_{C}

_{2})/(1 − T

_{E}

_{1})(1 − T

_{C}

_{1}) where T

_{E}

_{1}and T

_{E}

_{2}are the respective unlevered and levered personal equity tax rates, T

_{C}

_{1}and T

_{C}

_{2}are the respective unlevered and levered corporate equity tax rates, and T

_{D2}is the debt tax rate, which by definition is a levered tax rate;

_{D}, r

_{L}, and r

_{U}, are, respectively, the cost of debt, cost of levered equity, and cost of unlevered equity;

_{U}) with D = (1 − T

_{D2})I/r

_{D}where I is the interest payment; and,

_{U}= (1 − T

_{E}

_{1})(1 − T

_{C}

_{1})C/r

_{U}where C is the before-tax payout with C = (1 − PBR

_{BT})(CF

_{BT}) where PBR

_{BT}is the before-tax plowback ratio with PBR

_{BT}= 0 in (1) due to nongrowth and CF

_{BT}is the perpetual before-tax cash flow where equals CF

_{BT}= C for nongrowth since PBR

_{BT}= 0.

_{BT}refers to cash flows before federal taxes. Since CF

_{BT}is analogous to earnings before interest and taxes (EBIT), this means that the non-federal taxes would have already been recorded as expenses when computing EBIT. Thus, any other applicable non-federal tax (state, payroll, county, municipal, property, and sales) would have been expensed before federal taxes are considered.

_{L}) given by Hull (2010) and providing nongrowth and growth constraints. Since the CSM assumes internal growth through earnings retained from operations, the growth constraint is also called the retained earnings (RE) constraint. The CSM growth CC equation with tax rate changes is

_{L}= (1 − α

_{I}r

_{D}/r

_{Lg})D + (1 − α

_{2}r

_{Ug}/r

_{Lg})E

_{U}

_{I}, α

_{2}, r

_{D}, and D are the same as defined when presenting Equation (1);

_{Lg}, and r

_{Ug}, are, respectively, the growth-adjusted cost of levered equity (which is r

_{L}minus the levered equity growth rate, g

_{L}), and the growth-adjusted cost of unlevered equity (which is r

_{U}minus the unlevered equity growth rate, g

_{U}); and,

_{U}= (1 − T

_{E}

_{1})(1 − T

_{C}

_{1})C/r

_{Ug}where C = (1 − PBR

_{BT})(CF

_{BT}) with PBR

_{BT}= RE/CF

_{BT}> 0 due to using RE for growth.

_{L}for a pass-through (PT) with nongrowth and growth. The Hull (2019) nongrowth PT equation can be expressed in the same manner as the nongrowth CC equation given in (1) but with different definitions for those variables affected by dissimilar tax laws governing CCs and PTs (in particular, T

_{C}

_{1}and T

_{C}

_{2}are zero for PTs and the corporate business tax rate, T

_{C}

_{2}, is replaced by the personal business tax rate, T

_{E}

_{2}). The PT nongrowth equation is

_{L}= (1 − α

_{I}r

_{D}/r

_{L})D + (1 − α

_{2}r

_{U}/r

_{L})E

_{U}

_{I}and α

_{2}capture the effects of effective tax rates with α

_{1}= (1 − T

_{E}

_{2})/(1 − T

_{D2}) as (1 − T

_{C2}) falls out from the earlier CC equation for α

_{1}since T

_{C2}= 0 for PTs and α

_{2}= (1 − T

_{E}

_{2})/(1 − T

_{E}

_{1}) as (1 − T

_{C2}) and (1 − T

_{C1}) both fall out from the earlier CC equation for α

_{2}since T

_{C2}= 0 and T

_{C1}= 0 for PTs;

_{E}

_{1}, T

_{E}

_{2}, T

_{D2}, r

_{D}, r

_{L}, r

_{U}, D, I, and C are the same as just defined when presenting Equation (1); and,

_{U}= (1 − T

_{E}

_{1})C/r

_{U}as (1 − T

_{C1}) falls out of the earlier CC equation for E

_{U}since T

_{C}

_{1}= 0 for PTs.

_{L}= (1 − α

_{I}r

_{D}/r

_{Lg})D + (1 − α

_{2}r

_{Ug}/r

_{Lg})E

_{U}

_{I}and α

_{2}are the same as given in (3);

_{D}and D are the same as prior equations.

_{Lg}and r

_{Ug}are the same as given in (2) except g

_{L}and g

_{U}are adapted to PTs (as described below); and,

_{U}= (1 − T

_{E}

_{1})C/r

_{Ug}where C = (1 − PBR

_{BT})(CF

_{BT}) with PBR

_{BT}= RE/CF

_{BT}> 0 due to using RE for growth.

_{U}. The g

_{U}for CCs given in (2) has its origins in Hull (2010) who argues g

_{U}= r

_{U}(1 − T

_{C}

_{1})RE/C where RE represents retained earnings used for growth with RE determined by the plowback-payout decision. Hull (2019) extends the g

_{U}used for unlevered CCs and applies it to unlevered PTs. In his extension, T

_{C1}is replaced with T

_{E}

_{1}so that g

_{U}= r

_{U}(1 − T

_{E}

_{1})RE/C for PTs. The replacement of T

_{C1}with T

_{E1}reflects the fact that the CC business tax rate of T

_{C1}is at the corporate level, while the PT business tax rate of T

_{E1}is at the personal level. In brief, both T

_{C}

_{1}for CCs and T

_{E}

_{1}for PTs are business level tax rates because they apply to taxes paid on income generated by business operations and before any federal taxes are paid. As discussed in Section 2.3, the PT business tax rate fell from a maximum of 0.396 to 0.37 in 2018 with the enactment of TCJA and the CC business tax rate fell from a maximum corporate tax rate of 0.35 to a flat rate of 0.21 under TCJA.

_{L}. The g

_{L}for levered CCs mentioned in (2) was first given by Hull (2010) but later corrected by Hull (2018) who offers proof that g

_{L}= r

_{L}(1 − T

_{C}

_{2})RE/[C + G − (1 − T

_{C}

_{2})I] for levered CCs where G is the perpetual before-tax cash flow stemming from G

_{L}with G = r

_{Lg}G

_{L}/(1 − T

_{E}

_{2})(1 − T

_{C}

_{2}). The G

_{L}equation given by the CSM for growth applications requires an iterative procedure (such as offered by Excel) because g

_{L}, G

_{L}, and G are interdependent. Hull (2019) extends the g

_{L}for levered CCs by replacing T

_{C}

_{2}with T

_{E}

_{2}so that we now have the levered PT version, which is g

_{L}= r

_{L}(1 − T

_{E}

_{2})RE/[C + G − (1 − T

_{E}

_{2})I] with G = r

_{Lg}G

_{L}/(1 − T

_{E}

_{2}) where (1 − T

_{C}

_{2}) falls out of the earlier CC equation for G since T

_{C}

_{2}= 0 for PTs. In conclusion, when going from a CC to a PT, both growth formulae (g

_{U}and g

_{L}) just replace the unlevered and levered corporate business tax rate on CC income with the corresponding unlevered and levered personal business tax rates on PT income.

_{U}depends on the plowback-payout decision through RE, g

_{L}depends on both the plowback-payout decision through RE and the debt-equity decision through I. Thus, the growth equations, Equations (2) and (4), tie together growth and leverage through g

_{L}. Besides G, another variable instrumental in the derivational process for CSM growth equations is the perpetual levered equity value (E

_{L}). As applied to CCs, E

_{L}= (1 − T

_{E}

_{2})(1 − T

_{C}

_{2})(C − I)/r

_{Lg}. As applied to PTs, E

_{L}= (1 − T

_{E}

_{2})(C − I)/r

_{Lg}where (1 − T

_{C}

_{2}) falls out since T

_{C}

_{2}is zero for PTs. For the corresponding CC and PT nongrowth equations for G and E

_{L}, we substitute r

_{L}for r

_{Lg}. Under historical and current tax laws, I is considered a tax deductible expense. This leads to an interest tax shield (ITS) for PTs of T

_{E}

_{2}(I) that is like the ITS for CCs except that it uses T

_{E}

_{2}instead of T

_{C}

_{2}as the interest deduction comes at the personal business level for PTs instead of the corporate business level. With RE fixed by the company’s plowback-payout decision, the denominator in the g

_{L}equation for CCs points out that the expression of C + G > (1 − T

_{C}

_{2})I must hold to prevent the earmarked amount of RE from relinquishing some of its growth funds to service debt. In addition, this expression must hold to prevent g

_{L}< 0 from occurring. For the g

_{L}equation found in (4) for PTs, C + G > (1 − T

_{E}

_{2})I must hold to maintain its targeted amount of RE and prevent g

_{L}< 0 from happening. Based on the definition of g

_{L}for CCs, Hull (2018) posits that the growth (RE) constraint of C + G − (1 − T

_{C}

_{2})I ≥ RE must hold. For PTs, Hull (2019) points out that the growth constraint of C + G − (1 − T

_{E}

_{2})I ≥ RE must hold. If these growth constraints do not hold, a firm no longer has sufficient RE to achieve growth with internal funds. Since RE is zero for nongrowth, the nongrowth constraint can be expressed as C + G − (1 − T

_{C}

_{2})I ≥ 0 for CCs or, equivalently, C + G ≥ (1 − T

_{C}

_{2})I. For PTs, we have the nongrowth constraint of C + G ≥ (1 − T

_{E}

_{2})I as T

_{E}

_{2}replaces T

_{C}

_{2}.

_{E}

_{1}), (1 − T

_{E}

_{2}) and (1 − T

_{D2}) all reduce to 1 when applied to NPs. If we assume a CC ownership form for an NP, the multiplicands of (1 − T

_{C}

_{1}) and (1 − T

_{C}

_{2}) also reduce to 1 when applied to NPs. With all multiplicands equal to one because tax rates are zero, both α

_{1}and α

_{2}equal 1 since they are composed solely of multiplicands. When applied to NPs, zero values for tax rates also reduce multiplicands to one for CC and PT formulae that involve growth rates and constraints. For NPs, we now have: g

_{U}= r

_{U}RE/C, g

_{L}= r

_{L}RE/[C + G − I], G = r

_{L}G

_{L}; and, the growth and nongrowth constraints are C + G − I ≥ RE and C + G > I, respectively. Finally, zero tax rates reduce ITS to zero. In brief, when tax rates are all zero for NPs, all CMS outputs are invariant to the form of ownership (PT or CC) that is used. This is because all outputs are the same for either ownership from that is used by the CSM.

#### 3.2. Identifying the Optimal P Choice

_{U}) retired with debt (D). Identifying the optimal P choice for nongrowth tests is simple as we just find the largest firm value from all tests for feasible P choices where a feasible P choice refers to a leverage choice where the nongrowth constraint is not violated. While identifying optimal nongrowth outputs is straightforward such is not the case for growth and a general procedure is needed. In applying the CSM with growth, Hull (2019) offers the following general two-step procedure when determining the optimal P choice.

_{BT}(CF

_{BT}) and the CSM g

_{L}(that represents the long-run sustainable growth rate) is defined in terms of RE, we are able to change PBR

_{BT}until our chosen g

_{L}is achieved for each feasible P choice. Second, we identify the P choice that generates the max V

_{L}among all feasible P choices and this P choice is the optimal choice.

_{L}that corresponds to a credit rating that can be called the optimal credit rating (OCR). For our main tests that focus on the years of 2018 and 2019, the nongrowth OCR is Moody’s A3. This OCR is also used for our growth tests as described next.

_{BT}that attains a g

_{L}of 3.12% to use with the CSM perpetuity model equations of (2) and (4). A growth rate of 3.12% is suggested by the growth in the annual U.S. real GDP as supplied by the U.S. Bureau of Economic Analysis (2018) the past seventy years. The usage of a GDP growth rate as a proxy for g

_{L}assumes that GDP is a result of the growth in businesses including the risk-taking residual equity ownership of businesses. The exact correctness of the 3.12% selection is not essential to our major findings and other realistic g

_{L}values consistent with other long-run periods perform similarly. However, we should point out that large deviations from 3.12% can have a significant influence on firm value. For example, growth rates significantly greater than 3.12% can lead to much greater firm value. For some of the results reported in Section 5, we choose a PBR

_{BT}that attains a g

_{L}of 3.90%. The rate of 3.90% is suggested by the Tax Policy Center (2018) for an TCJA tax environment that reports an estimated boost in growth per year of about 0.8% for both 2018–2020 (average of six sources) and for 2018–2027 (average of five sources). Thus, tests using 3.90% are only applicable for a TCJA tax environment. The use of 3.90% for a TCJA environment is used by Hull and Hull (2020) in their examination of business growth, taxpayer wealth and federal tax revenue. Utilization of 3.90% is also one of two larger growth rates tested by Hull (2020b) in their PT and CC study.

#### 3.3. CSM Approach to Growth

_{U}), or equivalently unlevered equity (E

_{U}), is captured by g

_{U}which increases as PBR

_{BT}rises. For example, using the CSM formula of g

_{U}= r

_{U}(1 − T

_{C}

_{1})RE/C from Section 3.1 and noting RE = PBR

_{BT}(CF

_{BT}), we have g

_{U}= r

_{U}(1 − T

_{C}

_{1})PBR

_{BT}(CF

_{BT})/C where we use T

_{C}

_{1}if we classify an NP as a CC (T

_{E}

_{1}if we classify an NP as a PT). When debt (D) enters the picture, g

_{U}becomes g

_{L}with g

_{L}> g

_{U}as can be seen from the definitions given for g

_{U}and g

_{L}in Section 3.1. The issuance of D to retire E

_{U}makes D a de facto partner in growth in terms of increasing the growth rate per equity share. One might even argue that by supplying capital for corporate purposes, D frees up more operational cash flows for growth. Thus, one could argue that the D in conjunction with operating cash flows are now part of the same available cash flows from which a firm could retrieve funds for growth and so debt is a partner in growth.

_{L}models, like the CSM, in that D is issued to retire E

_{U}as opposed to a debt offering that seeks funds for purposes different from equity retirement. The latter does not increase EM as much as a debt-for-equity transaction. Like the DuPont model, the CSM shows magnification but in the form of growth where g

_{U}is magnified by D and becomes g

_{L}. Since this also serves to increase ROE if growth is profitable, the CSM can be viewed as attaining the same outcome as the DuPont model, which is that D increases ROE.

_{U}to g

_{L}. Outside this framework, D can be issued for purposes other than retiring E

_{U}and thus could be part of cash flows available to the firm for its chosen usages for equity payouts (dividends), RE, and I.

#### 3.4. P Choices, Costs of Borrowing, and Betas

_{BT}, we use the following equation to get the interest (I) paid on debt (D) per USD 1,000,000 in CF

_{BT}: I = (1 − T)CF

_{BT}/ICR. For NP tests, we compute I using the CSM’s T

_{C}

_{2}for T where T

_{C}

_{2}is the business tax rate for CCs. For PTs, T is the same as the CSM’s use of T

_{E}

_{2}. The use of both T

_{C}

_{2}and T

_{E}

_{2}were described in Section 2.3. Since there are fifteen ICR values, we compute fifteen I values.

_{D2}values and cost of debt (r

_{D}) values, we calculate fifteen D values where D = (1 − T

_{D2})I/r

_{D}. We then compute fifteen P choices using P = D/E

_{U}. Table 1 reports these P choices in the first column along with their corresponding ICRs, Moody’s ratings and credit spreads in the second, third, and fourth columns, respectively. As NPs and PTs have different T

_{D2}values, their P choices differ slightly.

_{F}) of 2.5% to get fifteen values for the r

_{D}. To illustrate, for the first credit rating of Aaa/AAA where the credit spread (CS) is 0.63%, we have: r

_{D}= r

_{F}+ CS = 2.5% + 0.63% = 3.13%. This value is reported in the first row of the r

_{D}column in Table 1. Using an equity risk premium of stocks over bonds (EPB) of 3.45%, we compute costs of levered equity (r

_{L}). We have r

_{L}= r

_{D}+ EPB = 3.13% + 3.45% = 6.58%. This value is reported in the first row of the r

_{L}column. Finally, we compute debt and equity betas using the CAPM with these values given in the last two columns. These computations reveal two required results. First, the first debt beta (β

_{D}) of 0.126 is greater than the risk-free beta of zero. Second, the first levered equity beta (β

_{L}) of 0.816 is greater than the unlevered beta (β

_{U}) of 0.8 (given later). Of further importance, the β

_{L}at the OCR of A3 is 0.9333 and thus near the market beta (β

_{M}) of 1. This value for β

_{L}is Table 1 is reflective of our tests indicating that our NPs and PTs are representative of a company with an average market risk.

## 4. Results Using Low (L) Tax Rates under TCJA with Historical Growth

#### 4.1. Variables and Computations

_{1}and α

_{2}, using (i) the L tax rates under TCJA as given in the bottom half of Panel A in Exhibit 2 and (ii) the historical growth rate of 3.12% discussed in Section 3.2. As argued by Hull (2014), α

_{1}and α

_{2}can exercise a key valuation function in the first and second components, respectively, of CSM G

_{L}equations. However, for NPs with L tax rates that are all zero, α

_{1}and α

_{2}values do not exercise an influence because α

_{1}=1 and α

_{2}=1 for all P choices where P refers to the proportion of unlevered equity (E

_{U}) retired with debt (D). For an alpha variable to change with leverage, at least one tax rate has to be greater than zero. As computed in Panel A, the first P choice for PTs gives (rounding off to two digits) α

_{1}= 0.87 and α

_{2}= 1.01 while the fifth P choice gives α

_{1}= 0.94 and α

_{2}= 1.06. The latter P choice is also the optimal choice and coincides with optimal outcomes including the optimal credit rating (OCR), which is Moody’s rating of A3.

_{BT}. These six variables are: retained earnings (RE); cost to use RE (CRE); %CRE per USD 1,000,000 of CF

_{BT}; before-tax payout (C); unlevered equity growth rate (g

_{U}); and, E

_{U}. From the E

_{U}values in this panel for the NP and PT, we can see just how much advantage an NP has by not paying taxes. As computed in Panel B, the advantage is USD 6,287,372 as E

_{U}is USD 17,546,149 for an NP but only USD 11,258,777 for a PT. From this panel, we can also discover that CRE is USD 0 for NPs. This compares to USD 90,657 for PTs. CRE per USD 1,000,000 of CF

_{BT}is 0% for NPs and 9.07% for PTs. This difference casts light on the before-tax plowback ratio (PBR

_{BT}) outcomes in Panel B where NPs achieve 3.12% growth with a PBR

_{BT}of 0.2598 at its OCR of A3 compared to 0.3519 for PTs at its OCR of A3. We observe that as the cost of using RE increases, the size of PBR

_{BT}also increases.

_{BT}and thus less RE is needed to achieve the same growth rate of 3.12%. If less RE is needed with lower tax rates, then growth using RE becomes more affordable when tax rates are lowered. This conclusion is consistent with the empirical research (as summarized by McBride 2012) and tax experts at the Tax Foundation (2018) and Tax Policy Center (2020) who argue that higher tax rates inhibit growth. With higher taxes, more before-tax RE is needed to grow and the CRE per USD 1,000,000 of CF

_{BT}becomes too costly. This explains our later results where we find that using a high business tax rate yields a nongrowth firm value greater than its growth value.

#### 4.2. Illustrations of NP and PT Outcomes

_{L}) that coincides with the maximum firm value (max V

_{L}) since max V

_{L}= E

_{U}+ max G

_{L}. The process to identify max V

_{L}was described in Section 3.2. In Panel A, ODV, max V

_{L}, max G

_{L}and other optimal outcomes are in bold print column. Panel B provides computations for these optimal outcomes.

_{L}) that is positive. However, with larger DVs and lower quality credit ratings, G

_{L}will decline reversing the trend where DV is smaller than P choices. Besides changes in the denominator of DV, the differences between P and DV in Table 3 can also be explained by the low sensitivity of ODVs to situations like the change in tax rates and the value of certain variables (such as β

_{U}). For example, there is less deviation between P and ODV for PTs if tax rates are not allowed to change. Furthermore, P and ODVs converge for slightly lower β

_{U}values. Finally, as seen in the last column of Table 3, a violation of the growth constraint does not occur until we reach the last column where P is 0.3579. Due to this violation, there are no values in the last column.

_{L}is positive and increasing until we go past P = 0.1580, while the second component is positive and increasing except for the downward bump that occurs at P = 0.1929. Together these two components (that represent G

_{L}) are increasing except at the downward bump at P = 0.1929 until we go past P = 0.2921. At the optimal P of 0.2921, we find that max G

_{L}is USD 1.163M (M = million) and max V

_{L}is USD 18.709M. After the optimal P choice is reached, we find growth rates greater than 3.12%. While rates greater than 3.12% are not sustainable, on average, for a perpetuity situation if a long-run historical growth rate is only 3.12%, we have already achieved our optimal and so their unsustainability is a moot point.

_{L}, r

_{Ug}, r

_{Lg}, max G

_{L}, max V

_{L}, E

_{L}, max %∆E

_{U}, NB, and ODV are calculated for the optimal choice of P = 0.2921. For the latter five variables, we use the following definitions: V

_{L}= G

_{L}+ E

_{U}(which only holds when we begin with an unlevered situation and not like the levered situation used by Hull (2012) who derives incremental G

_{L}equations that allow for a wealth transfer); E

_{L}= V

_{L}− D; percent change in E

_{U}(%∆E

_{U}) = G

_{L}/E

_{U}in percentage form; net benefit from leverage (NB) = G

_{L}/D in percentage form; and, debt-to-firm value ratio (DV) = D/V

_{L}. The max %∆E

_{U}of 6.63% found in the bold print column agrees with the for-profit (FP) research (Graham 2000; Korteweg 2010; Van Binsbergen et al. 2010) that collectively suggests that leverage increases firm value between 4% and 10% at ODV. Thus, it appears that NPs, like for-profits (FPs), can attain ODVs similar to those found for FPs despite differences over time such as changes in tax rates and tax laws. If we consider the results of our tests using both our H and L tax rates presented in Exhibit 2, the NP values reported in this paper for max %∆E

_{U}range from 2.46% to 8.83% with a mean of 5.67% and a median of 5.48%. Finally, as seen in the next to last row of Panel B, NB is reported as 22.69%. Thus, every dollar of debt adds 22.69 cents to E

_{U}at the ODV of 0.2739.

_{L}values of 3.49%, 3.97%, and 4.49%. Regardless, V

_{L}values for these higher growth rates are not greater than max V

_{L}that is achieved when g

_{L}= 3.12%. This was also true for NPs in Table 3.

_{L}is positive for the first six P choices for a PT. This is similar to the results in Table 3 for an NP where the first five P choices were also positive. The second component for PTs is increasing. This is similar to NPs where its second components was also increasing except for a downward bump at the P choice corresponding to Moody’s rating of A1. Similar to the generally increasing G

_{L}for NPs in Panel A of Table 3, Panel A of Table 4 reveals that G

_{L}is strictly increasing for PTs until we go past the OCR of A3. At A3, we see that max G

_{L}is USD 1.046M and max V

_{L}is USD 12.305M. These values are less than the corresponding values in Table 4 for NPs where max G

_{L}is USD 1.163M and max V

_{L}is USD 18.709M.

_{U}is 9.29% for a PT and this is greater than 6.63% for an NP while the ODV of 0.2447 for a PT is less than the ODV of 0.2739 for an NP. The smaller %∆E

_{U}for an NP can be at least partially explained by its greater E

_{U}value since it has a larger max G

_{L}value than a PT. Like %∆E

_{U}, the NB of 22.69% for an NP is less than 34.75% reported for a PT. Once again, since the NP value for max G

_{L}is larger than that for a PT, the smaller NB can be explained by the larger E

_{U}for which it takes more debt to retire greater amounts of E

_{U}to achieve the OCR of A3. At ODV, Table 4 shows that that PTs issue only USD 3.011M in debt compared to USD 5.125M in debt for NPs in Table 3. More debt issued for NPs relative to their max G

_{L}translates into a smaller NB so that NPs can be said to be relatively less efficient in its use of debt by getting less value per dollar of debt that is issued.

_{L}, max V

_{L}and ODV where NPs have greater relative values and for %∆E

_{U}and NB where NPs have smaller relative values. Since NPs do not have an interest tax shield (ITS) when the business tax rate is zero, their greater max G

_{L}values indicate other positive leverage-relate effects are operative. These effects are consistent with agency trade-off models discussed in Section 2.4.

#### 4.3. Five Illustrative Figures Using TCJA Tax Rates and Growth of 3.12%

_{L}, V

_{L}, %∆E

_{U}, and g

_{L}and they are plotted along the vertical axis with ratings along the horizontal axis where ratings are decreasing in quality (from the highest quality of Aaa to the lowest quality of Ba2). These outcomes include both NP values (in solid line trajectories) and PT values (in dashed line trajectories). These two trajectories enable us to contrast NP and PT outcomes. These figures only show the feasible points or those points where the growth constraint is not violated. As first shown in Section 4.2, the growth constraint sets in for NPs at a Moody’s credit rating of Ba2 (speculative rating), which is a notch in quality above that for PTs where the growth constraint occurs at B1 (highly speculative rating). For these five figures, like Table 3 and Table 4, we use the low (L) tax rates under TCJA given in the bottom half of Panel A in Exhibit 2. For the L tax rate tests, all NP tax rates are zero and PT unlevered corporate, personal equity, and personal debt tax rates are: T

_{C}

_{1}= 0; T

_{E}

_{1}= 0.30; and, T

_{D}

_{1}= 0.18. The corresponding PT levered tax rates are: T

_{C}

_{2}= 0; T

_{E}

_{2}= 0.2576 (projected was 0.255); and, T

_{D}

_{2}= 0.2087 (projected was 0.21).

_{U}) retired by debt (D) and is computed as D/E

_{U}. The NP trajectory (solid line) undergoes greater increases in P values at Moody’s ratings decrease in quality. This trajectory reaches the Moody’s rating of Ba1 before the growth constraint sets in. At this plot point of Ba1, P is 0.3377. The PT trajectory (dashed line) continues to a rating of Ba2 where P is 0.3322. Thus, even though the PT trajectory has more P choices, it still does not reach the height of 0.3377 achieved by NPs. Figure 1 reveals that, for any rating that might be targeted, NPs must issue relatively more debt to achieve the same target. This holds not only for relative dollars in debt but, as can be seen in Table 3 and Table 4, it also holds for absolute dollars in debt.

_{L}) along the vertical axis against credit ratings along the horizontal axis. As seen in Figure 1, the decrease in quality represents increasing P choices. Thus, Figure 2 also illustrates the concave relation between G

_{L}when plotted against increasing leverage choices. Consistent with trade-off theory that posits an optimal debt-to-firm value ratio (ODV) exists, Figure 2 reveals full (two-sided) concave trajectories except for the NP trajectory (solid line) where there is a downward bump for a Moody’s rating of A1 (upper medium grade rating). This bump is where the G

_{L}differences in the NP trajectory and PT trajectory (dashed line) peak at USD 0.801M − USD 0.643M = USD 0.158M (which is a 24.49% difference in terms of the higher NP value of USD 0.801M). By the time we get to the last credit rating of Ba1 for which both NPs and PTs have feasible plot points, we find a small difference in G

_{L}of USD 0.734M − USD 0.749M = −USD 0.015M between a PT and an NP (which is only a −2.04% difference).

_{L}of USD 1.163M is greater than the PT max G

_{L}of USD 1.046M. The greater NP value appears to be inconsistent with the notion that the advantage from an ITS should be greater for PTs compared to NPs. This is because an ITS is virtually non-existent given the tax-exempt status of NPs compared to PTs where interest lowers taxable income. However, debt still adds value for NPs due to other influences such as those posited by agency models. To illustrate, the percentage increase in unlevered value from issuing debt (%∆E

_{U}) is 6.63% for NPs in Table 3. This compares to 9.29% for PTs in Table 4. Thus, despite having a greater absolute gain (as seen in the max G

_{L}values), NPs gain relatively less from debt and this latter result is consistent with NPs not having an ITS. However, any PT advantage from having an ITS is offset since NP debt owners pay less personal tax on debt compared to PT debt owners. To illustrate the offsetting nature for the tests represented in Figure 2, the difference in business tax of 0.2576 favoring PTs is substantially neutralized by the difference in the personal tax on debt of 0.2087 favoring NPs.

_{L}with V

_{L}. Since our valuations are after all taxes are considered, this figure visually shows the tremendous V

_{L}advantage that an NP (solid line trajectory) has from not paying taxes when everything else is equal (such as same before-tax cash flows, same costs of borrowing, and same growth rate). Thus, Figure 3 serves to depict, from a strictly tax standpoint, the vast differences in V

_{L}that occur when everything is the same except tax rates. In fact, Figure 3 reveals that the NP max V

_{L}of USD 18.709M is USD 6.404M greater than the PT max V

_{L}of USD 12.305M. Only a small portion of this difference of USD 6.404M can be explained by the gain to leverage since the NP max G

_{L}of USD 1.163M in Figure 2 is only USD 0.117M greater than the PT max G

_{L}of USD 1.046M.

_{U}). This figure illustrates the greater relative gain to leverage for PTs (dashed line trajectory) compared to NPs (solid line trajectory) by showing the superiority of PTs over NPs for all feasible leverage choices as represented by credit ratings. The difference in %∆E

_{U}between NPs and PTs of 9.29% − 6.63% = 2.67% peaks at the OCR of A3. The differences in values for %∆E

_{U}increase up to A3 and then slowly decline. The decline is short-lived because the growth constraint is violated after Ba1 for NPs and after Ba2 for PTs. In fact, if we plotted the %∆E

_{U}differences, we would get a full (two-sided) concave relation. Thus, the peak in the %∆E

_{U}differences reveals the OCR for both NPs and PTs. Finally, the two max %∆E

_{U}values of 9.29% for PTs and 6.63% for NPs are consistent with the empirical research (Graham 2000; Korteweg 2010; Van Binsbergen et al. 2010) that indicates a range of 4% to 10%, albeit that research is assumedly geared more toward large FPOs dominated by C corps (CCs).

_{L}) against ratings. This figure reveals that g

_{L}values for PTs are greater until the OCR of A3 is reached, at which point g

_{L}values for NPs are greater. While an NP achieves a growth rate of 4.12% at its last feasible credit rating (which is Ba1), a PT would only attain a growth rate of 3.49% at its last feasible rating (which is Ba2). Of interest (and as seen in Figure 2, Figure 3 and Figure 4), higher growth rates do not lead to greater values for G

_{L}, V

_{L}, and %∆E

_{U}. However, if we had achieved these higher rates at the OCR of A3, then tests (that we have conducted) indicate that greater valuations can often occur.

_{L}) values greater than 3.12% once a firm goes past its ODV. As noted previously, a growth of 3.12% was determined from annual U.S. real GDP growth data given by the U.S. Bureau of Economic Analysis (2018). Thus, based on this data, a growth rate greater than 3.12% is not sustainable at least for an average firm. However, the question of sustainability in Figure 1, Figure 2, Figure 3, Figure 4 and Figure 5 is moot as the enterprise has already achieved its ODV (and its OCR of A3). If we set the before-tax plowback ratio (PBR

_{BT}) so that 3.12% is achieved with the lowest choice of debt corresponding to the highest grade credit rating then we can achieve a max G

_{L}greater than that achieved at a rating of A3. However, it is unlikely that a typical enterprise could simultaneously attain the highest possible investment-grade credit rating while sustaining a long-run historical growth rate. In fact, a typically credit rating is issued with a medium grade rating, which is the classification for A3. The highest quality grade ratings are rare and, as noted by Morningstar (2019), have become even more rare over time.

## 5. Results Incorporating High Tax Rates (H), Pre-TCJA Tax Rates, and Increased Growth

_{U}and max V

_{L}; and, leverage gain outcomes of max G

_{L}, max %∆E

_{U}, and NB. To these outcomes we add three growth-related outcomes of PBR

_{BT}, g

_{U}, and DGN. The eleventh outcome is OCR.

#### 5.1. H and L Results with TCJA Tax Rates and 3.12% Growth

_{C1}) of 0, while the H results use a T

_{C1}of 0.02. The L results for PTs use an unlevered personal business tax rate (T

_{E1}) of 0.30, while the H results use a T

_{E1}of 0.36. In reporting results for years 2014–2017, we use the ICRs given by Damodaran (2019) as associated with his 2018 spreads and ratings that were reported in January 2019. These 2018 ICRs are the same as the 2019 ICRs provided by Damodaran (2020) as tied to his 2019 spreads and ratings that were given in January 2020. These ICRs were provided in Table 1. The purpose of including the years 2014–2017 is not to report the most precise results (since we do not know the ICRs for these four years) but to illustrate how the eleven outcomes change when credit ratings change if ICRs (that determine leverage ratios) are held constant using TCJA tax rates that began in 2018. In essence, we answer the question: “What would result if we used sets of spreads prior to TCJA?”

_{L}with growth minus max V

_{L}with nongrowth. The lower values in this last column occur for the H tax rate tests and reflect the difficulty of growth adding values when the business tax rate is high making the after-tax usage of retained earnings (RE) more expensive. These lower values for DGN are consistent with the proof given by Hull (2010) where the minimum g

_{U}implies that the business tax rate on RE must be less than the before-tax plowback ratio (PBR

_{BT}) to make growth valuable for an unlevered firm. Thus, PBR

_{BT}must rise whenever the business tax rate on RE rises or growth becomes less valuable. Lower values for DGN are also consistent with empirical research, as reviewed by McBride (2012), that shows growth increases when tax rates decrease. While DGN is a new outcome added to Table 5, the outcomes in the other ten columns have the same definitions given previously in Table 2, Table 3 and Table 4.

#### 5.1.1. Credit Spread Results

_{U}of USD 18.949M and max V

_{L}of USD 20.027M both occur for the NP-L test using 2014 spreads while the smallest E

_{U}of USD 9.838M and max V

_{L}of USD 10.576M both occur for the PT-H test using 2018 spreads. Thus, despite lower taxes beginning in 2018, Table 5 reports that this year was PT’s worst performing year. However, this is not the final story, as the next table will consider both the increase in growth that is projected under TCJA and also the higher pre-TCJA tax rates for years prior to 2018. By doing this, the firm values in Table 5 will fall slightly for the years 2014–2017 (due to higher pre-TCJA taxes) but can rise substantially for the years 2018–2019 (from greater growth projected under TCJA due to lower tax rates).

_{L}of USD 1.513M occurs for the NP-L test for 2014, while the highest max %∆E

_{U}of 14.50% and NB of 42.00% both occur for the PT-H test for 2017. The lowest max G

_{L}of USD 0.404M and max %∆E

_{U}of 2.46% both are found for the NP-H test for 2018, while the lowest NB of 9.18% takes place for the NP-L test for 2018. Thus, using 2018 spreads yield the lowest leverage gain outcomes. The average max %∆E

_{U}for all tests in Table 5 is 7.52%. This percentage is consistent with the empirical research (Graham 2000; Korteweg 2010; Van Binsbergen et al. 2010). This research suggests that debt can increase firm value by about 7% on average.

_{BT}of 0.3800 occurs for the PT-H test using spreads for 2015 and the largest g

_{U}of 2.826% occurs for the NP-H test using spreads for 2014. The smallest PBR

_{BT}of 0.2431 and g

_{U}of 2.088% both take place for the NP-L test using 2018 spreads. The highest positive DGN of USD 3.516M occurs for the NP-L test using 2014 spreads while the most negative value of −USD 0.152M takes place for the PT-H test using 2017 spreads. The negative value indicates that nongrowth provide more wealth than growth. According to the CSM, this can be explained in terms of the high business tax rate on earnings retained for growth as these funds are subject to taxes before they can be used for growth.

#### 5.1.2. Results for 2018–2019 Period

_{L}for NPs is 51.63% higher than PTs. While we already know NPs (with lower taxes) will ceteris paribus have a higher valuation than PTs, the 51.63% tells us how high. Of interest, max V

_{L}for NPs is achieved with a PBR

_{BT}that is 26.63% smaller than PTs and an unlevered growth rate (g

_{U}) that is 7.97% lower than PTs. As discussed previously, this is because PTs use internal funds (e.g., RE) for growth after they pay taxes on RE and NPs do not pay taxes on RE. In brief, PTs have to set aside more before-tax RE for growth because it will shrink once taxes are paid on it.

_{L}), NPs gain 2.25% less in absolute dollars by issuing debt compared to PTs. This 2018–2019 result is unlike the earlier result for the year 2019 where NPs had a greater max G

_{L}value compared to PTs where we also used low (L) tax rates. The less gain of 2.25% can be explained by not having an interest tax shield (ITS), which is a key valuation component of mainline capital structure theory. However, as will be seen later, robust tests do not support the lesser gain of 2.25%. For example, if we assume greater growth under TCJA, we find that NPs gain more and not less. In terms of the maximum percent change in unlevered equity value (max %∆E

_{U}) from a debt-for-equity transaction, we find that PTs increase 7.29% while NPs increase 4.57%. Once again, this is consistent with NPs not have an ITS. Unlike max G

_{L}, robust tests support this finding for max %∆E

_{U}. Despite having 12.27% greater ODVs than PTs, debt is less critical for the beneficiaries of NPs services as debt adds less value. Finally, the results for NB, resemble those for max %∆E

_{U}in that PTs have greater values. Thus, the NB results indicate that PTs are more efficient than NPs by adding more value per dollar of debt added.

_{L}values in Table 5 for PTs and NPs, we can show that nongrowth max V

_{L}is USD 15.942M for NPs and USD 11.572M for PTs. Given the corresponding max V

_{L}for growth of USD 18.147M for NPs and USD 11.982M for PTs, we can demonstrate that NPs achieve a 13.83% increase in max V

_{L}when going from nongrowth to growth compared to only 3.42% for PTs. Once again, these achievements occur because NPs, unlike PTs, are not taxed on internally retained funds used for growth.

_{U}and max V

_{L}, and the growth-related outcome of DGN. We find smaller NP values for the growth-related outcomes of PBR

_{BT}and g

_{U}and the gain to leverage outcomes Max G

_{L}, Max %∆E

_{U}, and NB. For both NPs and PTs for 2018–2019, we find that the higher business tax rates are only associated with smaller values for E

_{U}and Max V

_{L}for both L and H tax rate tests. Otherwise, larger values are associated with at least one L or H tax rate test. Regardless of ownership type, both NPs and PTs have an OCR of A3 for both the L and H tax rate tests. From the latter outcome, we deduce that credit ratings are a greater factor than tax rates in determining the OCR for NPs and PTs for the years of 2018–2019. This finding is consistent with the credit rating research (Graham and Harvey 2001; Kisgen 2006) that suggests credit ratings are very instrumental in determining capital structure outcomes. Finally, we can conclude that the tax-exempt nature of NPs not only explain their ability to profit more from growth but also explain their lower gain from debt.

#### 5.2. H and L Results with Pre-TCJA Tax Rates and 3.90% Growth

_{L}and nongrowth max V

_{L}). For example, using the NP-L test for 2018–2019, we find that the DGN value of USD 3.944M in Table 6 (with 3.90% growth) is higher than the DGN value of USD 2.204M in Table 5 (with 3.12% growth). This is an increase of about USD 1.740M. For the NP-H test the differential is similar at USD 1.654M. Thus, if growth does increase from 3.12% to 3.90% as projected, then the differential (between growth max V

_{L}and non-growth max V

_{L}) widens. Compared to the NP differentials for DGN, we find that that the PT differentials are lower at USD 0.988M and USD 0.848M for the respective PT-L and PT-H tests. Less widening for PTs is consistent with the notion that PTs increase less with growth due their greater cost of using RE.

_{L}, max %∆E

_{U}, and NB tests are positive for all NP and PT tests when we compare Table 5 and Table 6 (where the comparisons involve subtracting Table 5 value from Table 6 and dividing this quantity by Table 5 value). The percentage changes for these three outcomes are highly positive for both NP tests for 2018–2019. The only comparison tests for this two-year period that manifest negative percentage changes are those for P and ODV. For example, it can be shown for the period of 2018–2019 that ODV falls 8.73%, 8.69%, 7.62%, and 7.22%, for the respective NP-L, NP-H PT-L, and PT-H tests for 2018–2019. We conclude that if TCJA does increase growth from 3.12% to 3.90% (as predicted by tax experts), the growth-related outcomes (g

_{U}, PBR

_{BT}, and DGN), valuation outcomes (E

_{U}and max V

_{L}), and leverage gain outcomes (max G

_{L}, max %∆E

_{U}, and NB) are positively influenced while debt choice outcomes (P and ODV) decline. Finally, OCR is unchanged.

#### 5.3. Five Illustrative Figures of H and L Results with Pre-TCJA Tax Rates and 3.90% Growth

_{L}, max V

_{L}, PBR

_{BT}, unlevered growth rate (g

_{U}), and change in unlevered firm value (%ΔE

_{U}) are graphically shown in Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10. These outcomes use the values given in Table 6 that are based on (i) pre-TCJA tax rates with a growth rate of 3.12% when individually testing the years of 2014, 2015, 2016 and 2017 and the combined years of 2014–2017 and (ii) TCJA tax rates with a growth rate of 3.90% when testing the individual years of 2018 and 2019 and the combined years of 2018–2019. Like Table 6, these figures also use both low (L) and high (H) tax rates. The five outcomes (max G

_{L}, max V

_{L}, PBR

_{BT}, g

_{U}, and %ΔE

_{U}) are plotted as a function of spreads by years/periods and have the following eight plot points: four pre-TCJA years of 2014, 2015, 2016, 2017; two TCJA years of 2018 and 2019; and, two periods composed of pre-TCJA years of 2014–2017 and TCJA years of 2018–2019. For Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10, the following holds for each figure: NP-L trajectory, solid line; NP-H trajectory, small dashed line; PT-L trajectory, large dashed line; and, PT-H trajectory, dotted line.

_{L}changes when credit spreads change over time while ICRs are constant with changes in tax and growth rates a function pre-TCJA versus TCJA tax legislation. Despite differences in max G

_{L}over time, there are some constants. For example, five of the greatest max G

_{L}values occur for five plot points on the PT-H (dotted line) trajectory. These plot points are 2014, 2015, 2016, 2018, and the combined pre-TCJA years of 2014–2017. As the PT-H tests use the high business personal tax rate, larger max G

_{L}values are consistent with a greater ITS that increases as the business tax rate increases. NP-L tests also stand out as three of the greatest max G

_{L}value occur for three plot points on the NP-L (solid line) trajectory. These plot points are 2017, 2019, and the combined TCJA years of 2018–2019. Since the NP-L test uses zero tax rates, these three largest max G

_{L}values cannot be explained in terms of a larger ITS based on a larger business tax rate. They are consistent with the notion that greater agency benefits can result from debt for NPs as argued by Manne (1999).

_{L}with max V

_{L}. Figure 7 documents the extent that NPs consistently have greater max V

_{L}values. This is seen in the contrast between the two NP trajectories at the top (the solid line trajectory for NP-L and the small dashed line trajectory for NP-H) and the two PT trajectories at the bottom (the large dashed line trajectory for PT-L and the dotted line trajectory for PT-H). Thus, regardless of how spreads change over time, NPs outperform PTs as expected given the great tax advantage of NPs. As also expected, the L tax rate test for each ownership type produces a superior max V

_{L}value compared to the corresponding H tax rate test. For example, the solid line trajectory for NP-L has greater max V

_{L}values compared to the small dashed line trajectory for NP-H, while the large dashed line trajectory for PT-L has greater max V

_{L}values than the dotted line trajectory for PT-H.

_{BT}) over time as credit spreads change. Except for the year 2015 where PBR

_{BT}for the NP-L test is slightly greater than the NP-H test, this figure graphically shows that the greater tax rates as experienced by either the H tax rates (compared to the L tax rates) or by PTs (compared to NPs) are associated with greater PBR

_{BT}values. To illustrate the positive relation between tax rates and PBR

_{BT}, the dotted line trajectory at the top for PT-H tests (that contains the highest tax rates) has the highest PBR

_{BT}values. Since before-tax RE = PBR

_{BT}(CF

_{BT}) and RE is taxed before it can be used for growth, more before-tax RE must be set aside to attain the same growth rate at OCR when taxes are higher. If a firm cannot set aside enough, then the desired growth will not occur. This is consistent with the notion, expressed by empirical research as overviewed by McBride (2012), that greater taxes make growth more difficult and even unaffordable if taxes are too high. It is also consistent with the CSM that argues that PBR

_{BT}must be greater than the business tax rate to help insure that growth adds value. Finally, despite lower tax rates for the TCJA years of 2018 and 2019 that would lower PBR

_{BT}, the higher PBR

_{BT}for these two years occur in Figure 8 because we use a growth rate of 3.90% as opposed to 3.12% for pre-TCJA years. A rate of 3.90% is consistent with what tax experts expect under TCJA where tax rates fall.

_{U}) over time as credit spreads change. Figure 9 resembles Figure 8 in that PT values are typically greater than NP values. The lone exceptions in Figure 9 occur for the year of 2014 where the NP values for g

_{U}are greater than those for PTs. For the period of 2014–2017, NPs and PTs have similar g

_{U}values that (for these tests) are based on the levered equity growth rate (g

_{L}) attaining 3.12% at OCR. The largest g

_{U}values occur for the three TCJA tests (2018, 2019 and 2018–2019) that are associated with a g

_{L}of 3.90%. According to the CSM, for unlevered firm value to increase with growth, the minimum g

_{U}should be greater than the unlevered equity rate of return (r

_{U}) times PBR

_{BT}. The latter relation holds for most of our tests indicating growth is valuable. Exceptions are accompanied by a nongrowth max V

_{L}that is similar to or even greater than its growth max V

_{L}. The greater nongrowth max V

_{L}values can be identified from Table 6 as they occur when DGN is negative.

_{U}over time as credit spreads change. This figure displays how PT values are always superior to NP values. In contrast to NP values that are similar, Figure 10 shows the greater differences in PT values between the H and L tax rate tests. This reflects the greater difference in tax rates between the two H and L tax rate PT tests. The last plot point for the PT-H trajectory (dotted line) is 10.27% and that for the PT-L trajectory (larger dashed line) is 8.32%. Since the value of 8.32% is closer to what the pre-TCJA empirical research finds, the value of 10.27% suggests that lower tax rates under TCJA (where greater growth is generated) will cause a greater increase in unlevered firm value at ODV.

#### 5.4. Key Comparisons

_{L}of USD 18.147M for NP-L in Table 5 and the max V

_{L}of USD 11.968M for PT-L in Table 5. The percentage change is (USD 18.147M−USD 11.968M)/USD 11.968M = 0.5163 or 51.63% as found in the T5-L row of the Max V

_{L}column in Table 7. The last (DGN) column of Table 7 contains only the difference in NP and PT values and thus is not a percentage.

_{L}, max %∆E

_{U}, and NB) show more variation than other outcomes when comparing the first two rows where growth is 3.12% with the last two rows where growth is 3.90% and this is especially true for max G

_{L}where we find drastic differences in terms of the actual sign changing from negative for the two Table 5 values to positive for the two Table 6 values. This observation about greater variation can be confirmed by looking at the last (StDev) row of Table 7 that shows the standard deviation is the greatest for these three leverage gain outcomes with respective standard deviations of 17.29%, 12.31%, and 10.36% for max G

_{L}, max %∆E

_{U}, and NB. In addition, there are greater variations between NP and PT outcomes when we use H tax rates and this is true for either Table 5 or Table 6 comparisons. This can be explained by greater differences in tax rates for PTs compared to NPs. We now comment on some of the more important results in .

_{BT}) drop of 26.63%, which was cited previously, is consistent with other PBR

_{BT}results in Table 7. As seen in the mean row, PBR

_{BT}for the four tests declines, on average by 27.52%, which is very consistent with 26.63%. The pattern for the unlevered equity growth rate (g

_{U}) is similar to that for PBR

_{BT}, e.g., the smaller values for both PBR

_{BT}and g

_{U}occur for the two L tax rate tests. Since retained earnings (RE) is positively related to both outcomes, our conclusion that NPs grow with less need for RE (compared to PTs) still holds.

_{L}for NPs compared to PTs. As seen in Table 7 for the T5-L test, this is the lowest value from the four max V

_{L}tests. As further seen in the mean row, the mean max V

_{L}of 56.69% reveals that 51.63% is generally consistent but may also be a bit of an understatement when we consider all four tests for max V

_{L}in Table 7. The other valuation outcome, unlevered equity value (E

_{U}), shows a pattern similar to max V

_{L}, e.g., the lowest percentage change of 55.57% occurs for the T5-L test. In conclusion, our earlier assertion about much greater after-tax valuations for NPs hold as robust tests confirm this assertion. Of further interest in understanding valuation in terms of nongrowth and growth, the DGN column of Table 7 show the difference between nongrowth max V

_{L}and growth max V

_{L}for NPs after we subtract out that same difference for PTs. The greater values for DGN in the T6-L and T6-H rows (compared to the T5-L and T5-H rows) show that greater growth helps NPs more than PTs in achieving higher growth valuations. Thus, our earlier conclusion holds: if lower taxes leads to greater growth (as tax experts expect) then more value can be added (beyond the nongrowth max V

_{L}) for NPs compared to PTs. This is consistent with the notion that NPs are not taxed on the RE that they use for growth and thus are always in a better position to profit from growth as the economy enters a recovery or expansion. Consistent with what tax experts advocate, growth becomes more affordable when tax rates are lower.

_{L}drop of 2.25% for NPs compared to PTs, that we reported previously, is somewhat consistent with the mean of 0.62% given in Table 7. However, there is a large variation ranging from a drop of 20.69% for the T5-H tax rate test with a growth of 3.12% to an increase of 21.14% for the T6-L tax rate test with a growth of 3.90%. This variability points out that the max G

_{L}outcome can deviate significantly when comparing NPs and PTs with the deviation a function of both tax rates and growth rates. Regardless, the two positive percentages occur in rows T6-L and T6-H that represent the higher growth rate tests in Table 6. These results point out the greater importance of a higher growth rate for NPs as it creates relatively more value from debt compared to PTs.

_{U}), earlier we stated that NPs gain 37.32% less (as seen in the T5-L row of Table 7). The mean row agrees with this assertion as we find an average drop of 37.68% for max %∆E

_{U}. However, like the max G

_{L}results, we find noteworthy variation as values for max %∆E

_{U}range from −52.72% to −22.58%. Regardless, of this variation, our prior finding holds as NPs gain much less from debt compared to PTs. While these percentages are highly negative the actual differences do not reflect these large percentages. For example, we previously reported that max %∆E

_{U}increased 4.57% for NPs and 7.29% for PTs. These were results for the L tax rate tests as given in Table 5. The corresponding percentages for the H tax rate tests are 4.51% for NPs and 9.55% for PTs and so these results are somewhat similar to what we reported earlier. However, the tests using Table 6 values are marginally higher with respective values of 6.44% and 8.32% for L tax rate tests and 6.36% and 10.27% for H tax rate tests compared to the corresponding values in Table 5 of 4.57% and 7.29% for L tax rate tests and 4.51% and 9.55% for H tax rate tests.

_{U}in that values in the T5-L and T5-H rows are more negative. Negative values indicate that NPs are less efficient in using debt compared to PTs. There is a common theme for our three leverage gain outcomes of max G

_{L}, max %∆E

_{U}, and NB in that they show greater variability than the two debt choice of P and ODV and the two valuation outcomes of E

_{U}and max V

_{L}. Despite the differences that can be highlighted from examining Table 7, we do find one constant as seen in the OCR column. Here we find A3 as the OCR for all tests using the years 2018–2019.

#### 5.5. Limitations and Future Research

## 6. Summary

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Acronym Glossary

Acronym: Term | Definition and/or Meaning for This Study’s Purpose | Main Location |

NP: nonprofit | Ownership form characterized by its tax-exempt status | Exhibit 1 |

PT: pass-through | Ownership form where taxes on paid at the personal level | Exhibit 1 |

FP: for-profit | A business whose earnings are subject to taxes because they fall within either the C corp or pass-through ownership form. | Section 1 |

CC: C corp | Ownership form where taxes on paid at both the corporate and personal levels | Section 1 |

TCJA: Tax Cuts and Jobs Act | US revenue act that favors C corps relative to pass-throughs by reducing corporate tax rates more than personal tax rates. | Section 1 |

CSM: Capital Structure Model | A trade-off model that identifies the maximum firm value from a series of increasing debt issues that retire unlevered equity | Section 3.1 |

CF_{BT}: cash flows before taxes | Cash flows available before federal taxes are paid and before any applicable tax shield lowers business taxes. | Section 3.1 |

PBR_{BT}: before-tax plowback ratio | The amount of retained earnings (RE) divided by cash flows before taxes (CF_{BT}) | Section 3.1 |

OCR: Optimal credit rating | Credit rating that corresponds to max V_{L} and ODV. | Section 3.2 |

RE: retained earnings | Before-tax cash flows from operations used strictly for growth that leads to increased production of goods and/or services. | Section 3.3 |

Costs of borrowing | Cost of debt (r), cost of unlevered equity(_{D}r), cost of levered equity (_{U}r)_{L} | Table 1 |

ICR: interest coverage ratio | Comes in three firm categories of small, large, and financial service and are used to compute leverage choices. | Table 1 |

α_{I} and α_{2}: alphas | Coefficients that capture the effects of tax rates | Table 2 |

E_{U}: unlevered equity value | E_{U} is the same as unlevered firm value (V_{U}) because unlevered means no debt. Thus, value consists only of equity. | Table 2 |

g_{U}: unlevered equity growth rate | The growth rate for an unlevered growth firm. | Table 2 |

g_{L}: levered equity growth rate | The growth rate for a levered growth firm. This rate ties together the plowback-payout and debt-equity choices. | Table 3 |

Max G_{L}: maximum gain to leverage | The greatest gain to leverage among all feasible leverage choices. | Table 3 |

V_{L}: firm value | V_{L} = E_{L} + D where E_{L} is levered equity value and D is debt value. For our application of the CSM, V_{L} is also E_{U} + G_{L}. | Table 3 |

Max V_{L}: maximum firm value | Max V_{L} = E_{U} + max G_{L} where max V_{L} can also be identified by the greatest V_{L} among all feasible V_{L} outputs. | Table 3 |

DV: debt-to-firm value ratio | A leverage ratio computed as D/V_{L} where D is debt value and V_{L} is firm value. | Table 3 |

ODV: optimal DV | The optimal DV associated with the greatest attainable firm value among feasible DV choices, which is max V_{L}. | Table 3 |

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**Figure 1.**P choices are plotted along vertical axis against Moody’s credit ratings along horizontal axis. P is debt divided by unlevered equity value. The nonprofit trajectory is the solid line and the pass-through trajectory is the dashed line. We use credit spreads for 2019, TCJA low (L) tax rates, and 3.12% growth where the growth (RE) constraint sets in after Ba1 for nonprofits (NPs) and after Ba2 for pass-throughs (PTs). The optimal credit rating (OCR) is A3.

**Figure 2.**Gain to leverage (G

_{L}) values are plotted along the vertical axis against Moody’s credit ratings along the horizontal axis. The nonprofit trajectory is the solid line and the pass-through trajectory is the dashed line. We use credit spreads for 2019, TCJA low (L) tax rates, and 3.12% growth where the growth (RE) constraint sets in after Ba1 for nonprofits (NPs) and after Ba2 for pass-throughs (PTs). The optimal credit rating (OCR) is A3.

**Figure 3.**Firm Value (V

_{L}) values are plotted along the vertical axis against Moody’s credit ratings along the horizontal axis. The nonprofit trajectory is the solid line and the pass-through trajectory is the dashed line. We use credit spreads for 2019, TCJA low (L) tax rates, and 3.12% growth where the growth (RE) constraint sets in after Ba1 for nonprofits (NPs) and after Ba2 for pass-throughs (PTs). The optimal credit rating (OCR) is A3.

**Figure 4.**%ΔE

_{U}values are plotted along vertical axis against Moody’s credit ratings along horizontal axis. %ΔE

_{U}is G

_{L}as a percent of unlevered equity (E

_{U}). The nonprofit trajectory is the solid line and the pass-through trajectory is the dashed line. We use credit spreads for 2019, TCJA low (L) tax rates, and 3.12% growth where the growth (RE) constraint sets in after Ba1 for nonprofits (NPs) and after Ba2 for pass-throughs (PTs). The optimal credit rating (OCR) is A3.

**Figure 5.**Levered equity growth rate (g

_{L}) values are plotted along vertical axis against Moody’s credit ratings along horizontal axis. The nonprofit trajectory is the solid line and the pass-through trajectory is the dashed line. We use credit spreads for 2019, TCJA low (L) tax rates, and 3.12% growth where the growth (RE) constraint sets in after Ba1 for nonprofits (NPs) and after Ba2 for pass-throughs (PTs). The optimal credit rating (OCR) is A3.

**Figure 6.**Maximum gain to leverage (max G

_{L}) values are plotted along the vertical axis against six years (where annual credit spreads are different) and two periods (where annual credit spreads are averaged) along the horizontal axis. The four trajectories are NP-L trajectory, solid line; NP-H trajectory, small dashed line; PT-L trajectory, large dashed line; and, PT-H trajectory, dotted line. We use pre-TCJA tax rates for 2014–2017 with 3.12% growth rate and TCJA tax rates for 2018–2019 with 3.90% growth rate. Both the low (L) and high (H) tax rates are used where the growth (RE) constraint sets in after Ba1 for nonprofits (NPs) and after Ba2 for pass-throughs (PTs). As seen in Table 6, the optimal credit rating (OCR) varies over time with an OCR of A3 for the last two years of 2018 and 2019 for both NPs and PTs.

**Figure 7.**Maximum firm value (max V

_{L}) values are plotted along the vertical axis against six years (where annual credit spreads are different) and two periods (where annual credit spreads are averaged) along the horizontal axis. The four trajectories are NP-L trajectory, solid line; NP-H trajectory, small dashed line; PT-L trajectory, large dashed line; and, PT-H trajectory, dotted line. We use pre-TCJA tax rates for 2014–17 with 3.12% growth rate and TCJA tax rates for 2018–2019 with 3.90% growth rate. Both the low (L) and high (H) tax rates are used where the growth (RE) constraint sets in after Ba1 for nonprofits (NPs) and after Ba2 for pass-throughs (PTs). As seen in Table 6, the optimal credit rating (OCR) varies over time with an OCR of A3 for the last two years of 2018 and 2019 for both NPs and PTs.

**Figure 8.**Before-tax plowback ratio (PBR

_{BT}) values are plotted along the vertical axis against six years (where annual credit spreads are different) and two periods (where annual credit spreads are averaged) along the horizontal axis. The four trajectories are NP-L trajectory, solid line; NP-H trajectory, small dashed line; PT-L trajectory, large dashed line; and, PT-H trajectory, dotted line. We use pre-TCJA tax rates for 2014–17 with 3.12% growth rate and TCJA tax rates for 2018–2019 with 3.90% growth rate. Both the low (L) and high (H) tax rates are used where the growth (RE) constraint sets in after Ba1 for nonprofits (NPs) and after Ba2 for pass-throughs (PTs). As seen in Table 6, the optimal credit rating (OCR) varies over time with an OCR of A3 for the last two years of 2018 and 2019 for both NPs and PTs.

**Figure 9.**Unlevered equity growth rate (g

_{U}) values are plotted along the vertical axis against six years (where annual credit spreads are different) and two periods (where annual credit spreads are averaged) along the horizontal axis. The four trajectories are NP-L trajectory, solid line; NP-H trajectory, small dashed line; PT-L trajectory, large dashed line; and, PT-H trajectory, dotted line. We use pre-TCJA tax rates for 2014–17 with 3.12% growth rate and TCJA tax rates for 2018–2019 with 3.90% growth rate. Both the low (L) and high (H) tax rates are used where the growth (RE) constraint sets in after Ba1 for nonprofits (NPs) and after Ba2 for pass-throughs (PTs). As seen in Table 6, the optimal credit rating (OCR) varies over time with an OCR of A3 for the last two years of 2018 and 2019 for both NPs and PTs.

**Figure 10.**Percent change in unlevered equity (%ΔE

_{U}) values are plotted along the vertical axis against six years (where annual credit spreads are different) and two periods (where annual credit spreads are averaged) along the horizontal axis. The four trajectories are NP-L trajectory, solid line; NP-H trajectory, small dashed line; PT-L trajectory, large dashed line; and, PT-H trajectory, dotted line. We use pre-TCJA tax rates for 2014–17 with 3.12% growth rate and TCJA tax rates for 2018–2019 with 3.90% growth rate. Both the low (L) and high (H) tax rates are used where the growth (RE) constraint sets in after Ba1 for nonprofits (NPs) and after Ba2 for pass-throughs (PTs). As seen in Table 6, the optimal credit rating (OCR) varies over time with an OCR of A3 for the last two years of 2018 and 2019 for both NPs and PTs.

P Choice | ICR | Moody’s Rating | Credit Spread | r_{D} | r_{L} | β_{D} | β_{L} |
---|---|---|---|---|---|---|---|

0.0759 | 24.000 | Aaa | 0.6300% | 3.1300% | 6.5800% | 0.1260 | 0.8160 |

0.1580 | 11.000 | Aa2 | 0.7800% | 3.2800% | 6.7300% | 0.1560 | 0.8460 |

0.1929 | 8.500 | A1 | 0.9750% | 3.4750% | 6.9250% | 0.1950 | 0.8850 |

0.2361 | 6.750 | A2 | 1.0764% | 3.5764% | 7.0264% | 0.2153 | 0.9053 |

0.2921 | 5.250 | A3 | 1.2168% | 3.7168% | 7.1668% | 0.2434 | 0.9334 |

0.3303 | 4.250 | Baa2 | 1.5600% | 4.0600% | 7.5100% | 0.3120 | 1.0020 |

0.3370 | 3.750 | Ba1 | 2.0000% | 4.5000% | 7.9500% | 0.4000 | 1.0900 |

0.3579 | 3.250 | Ba2 | 2.4000% | 4.9000% | 8.3500% | 0.4800 | 1.1700 |

0.3448 | 2.750 | B1 | 3.5100% | 6.0100% | 9.4600% | 0.7020 | 1.3920 |

0.3774 | 2.250 | B2 | 4.2120% | 6.7120% | 10.1620% | 0.8424 | 1.5324 |

0.4258 | 1.750 | B3 | 5.1480% | 7.6480% | 11.0980% | 1.0296 | 1.7296 |

0.3874 | 1.375 | Caa | 8.2000% | 10.7000% | 14.1500% | 1.6400 | 2.3300 |

0.4994 | 1.025 | Ca2 | 8.6424% | 11.1424% | 14.5924% | 1.7285 | 2.4185 |

0.6335 | 0.650 | C2 | 11.3412% | 13.8412% | 17.2912% | 2.2682 | 2.9582 |

0.8541 | 0.380 | D2 | 15.1164% | 17.6164% | 21.0664% | 3.0233 | 3.7133 |

_{C}

_{2})CF

_{BT}/ICR where T

_{C}

_{2}is the effective (average) corporate tax rate on business income and CF

_{BT}is the before-tax cash flows that for our tests equals USD 1,000,000 (with CF

_{BT}analogous to EBIT). For PTs, the business tax rate is the levered personal tax rate (T

_{E2}). From the fifteen ICR values, we compute fifteen I values. From these fifteen I values, we use their corresponding levered personal debt rate (T

_{D2}) and cost of debt (r

_{D}) values to calculate fifteen debt (D) values where D = (1 − T

_{D2})I/r

_{D}. We next compute the fifteen P choices where P is the proportion of unlevered equity (E

_{U}) retired by D. In equation form, we have P = D/E

_{U}. This table reports P choices for NPs in the first column along with corresponding Moody’s ratings and credit spreads in the third and fourth columns. As NPs and PTs have different T

_{D2}values, the P choices provided in this table for NPs are not the same as those used for PTs. To get fifteen r

_{D}values (as seen in the r

_{D}column) we add each credit spread (CS) to the risk-free rate (r

_{F}) of 2.5% so that we have: r

_{D}= r

_{F}+ CS. If we factor in the recent downward trend, an r

_{F}of 2.5% is consistent with the 30-year government bonds as given by Federal Reserve Economic Data (2020) for the past fifteen years. To get a cost of levered equity (r

_{L}) matched to each r

_{D}, we add an equity risk premium over a corporate bond portfolio (EPB) to each r

_{D}. Following Hull, we use EPB = 3.45%. By adding 3.45% to our fifteen increasing r

_{D}values, we get fifteen increasing r

_{L}values. In equation form, we have: r

_{L}= r

_{D}+ EPB. From each r

_{D}and r

_{L}we compute respective debt beta (β

_{D}) and levered equity beta (β

_{L}) using the CAPM where β

_{D}= (r

_{D}− r

_{F})/(r

_{M}− r

_{F}) and β

_{L}= (r

_{L}− r

_{F})/(r

_{M}− r

_{F}).

Panel A. Alpha Computations |

Nonprofit (NP) Alpha Computations: |

For our L tax rate tests for NPs, α_{1} = α_{2} = 1 for all P choices because these tests assume NP tax rates are all zero. To illustrate with T_{E}_{1} = T_{E}_{2} = 0; T_{C1} = T_{C2} = 0; T_{D1} = T_{D2} = 0, we have:α _{1} = (1 − T_{E}_{2})/(1 − T_{D2}) = (1 − 0)(1 − 0)/(1 − 0) = 1.00.α _{2} = (1 − T_{E}_{1})/(1 − T_{E}_{2}) = (1 − 0)/(1 − 0) = 1.00. |

Pass-Through (PT) Alpha Computations: |

The unlevered personal debt tax rate (T_{D}_{1}) only exist hypothetically for an unlevered situation, which is a way of saying we assign a beginning value to achieved an effective levered personal tax rate on debt (T_{D}_{2}) at the optimal P choice. For an unlevered situation, the unlevered personal equity tax rate (T_{E}_{1}) is 0.3, T_{D1} = 0.18, and the unlevered corporate tax rate (T_{C1}) = 0. The latter is zero because PTs do not pay corporate taxes. For a levered situation, levered personal equity tax rate (T_{E}_{2}) is less than T_{E}_{1} since T_{E}_{2} decreases by 0.03 with each increasing P choice. T_{D}_{2} is greater than T_{D1} since T_{D}_{2} increases by 0.03 with each increasing P choice.For the first debt-for-equity choice using T _{E}_{1} = 0.3, T_{D2} = T_{D1}(1 + ΔT_{D}_{1}) = 0.18(1 + 0.03) = 0.1854, and T_{E}_{2} = T_{E}_{2}(1 − ΔT_{E}_{2}) = 0.3(1 − 0.03) = 0.291, we have (to ten digits so later computations can minimize rounding off errors):α _{1} = (1 − T_{E}_{2})/(1 − T_{D2}) = (1 − 0.291)/(1 − 0.1854) = 0.8703658237.α _{2} = (1 − T_{E}_{2})/(1 − T_{E}_{1}) = (1 − 0.291) (1 − 0.3) = 1.0128571429.For the fifth debt-for-equity choice using T _{D2} = T_{D1}(1 + 0.03)^{5} = 0.18(1.1592740743) = 0.2086693 and T_{E}_{2} = T_{E}_{1}(1 − 0.03)^{5} = 0.3(0.8587340257) = 0.25762021, we have:α _{1} = (1 − T_{E}_{2})/(1 − T_{D2}) = (1 − 0.25762021)/(1 − 0.2086693) = 0.9381410624.α _{2} = (1 − T_{E}_{2})/(1 − T_{E}_{1}) = (1 − 0.25762021)/(1 − 0.3) = 1.0605425604. |

Panel B. Unlevered Firm Value (E_{U}) Computations |

NP example using CC definitions given in Section 3.1: PBR _{BT} = 0.2598; CF_{BT} = USD 1,000,000; RE = PBR_{BT}(CF_{BT}) = 0.2598(USD 1,000,000) = USD 259,800.Cost to use RE (CRE) = T _{C}_{2}(RE) = 0(USD 259,800) = USD 0.%CRE per USD 1,000,000 of CF _{BT} = USD 0/USD 1,000,000 = 0.00 or 0%.C = (1 − PBR _{BT})(CF_{BT}) = (1 − 0.2598)(USD 1,000,000) = USD 740,200.g _{U} = r_{U}(1 − T_{C}_{1})RE/C = 0.065(1 − 0)USD 259,800/USD 740,200 = 2.28141043%.E _{U} = (1 − PBR_{BT})(1 − T_{E}_{1})(1 − T_{C}_{1})CF_{BT}/(r_{U} − g_{U}) = (1 − 0.2598)(1 − 0)(1 − 0)USD 1,000,000/(0.065 − 0.0228141043) = USD 17,546,149. |

PT example using PT definitions given in Section 3.1: PBR _{BT} = 0.3519; CF_{BT} = USD 1,000,000; RE = PBR_{BT}(CF_{BT}) = 0.3519(USD 1,000,000) = USD 351,900.Cost to use RE (CRE) = T _{E}_{2}(RE) = 0.25762021(USD 259,800) = USD 90,657.%CRE per USD 1,000,000 of CF _{BT} = USD 90,657/USD 1,000,000 = 0.090657 or about 9.07%.C = (1 − PBR _{BT})(CF_{BT}) = (1 − 0.3519)(USD 1,000,000) = USD 648,100.g _{U} = r_{U}(1 − T_{E}_{1})RE/C = 0.065(1 − 0.3)USD 351,900/USD 648,100 = 0.0247052152 or 2.47052152%.E _{U} = (1 − PBR_{BT})(1 − T_{E}_{1})CF_{BT}/(r_{U} − g_{U}) = (1 − 0.3519)(1 − 0.3)USD 1,000,000/(0.065 − 0.0247052152) = USD 11,258,777. |

_{1}and α

_{2}) presented in Section 3.1. These coefficients capture the impact of tax rates in G

_{L}equations. This panel provides sample computations for α

_{1}and α

_{2}for the two ownership categories of nonprofits (NPs) and pass-throughs (PTs). For the illustration in this table, we use the low (L) tax rates under TCJA from the bottom half of Panel A in Exhibit 2. The values for α

_{1}and α

_{2}rise for increasing P choices as long as at least one tax rate is positive. For our tests, positive tax rates change by 0.03 for each subsequent P in the directions discussed by Hull (2014) as described in Section 2.3. For NPs, α

_{1}and α

_{2}do not change for L tax rate tests because all tax rates are zero. The latter is seen below. Panel B provides NP and PT examples for computing the unlevered firm value (E

_{U}). E

_{U}is important since each debt choice retires a fraction of E

_{U}. Consistent with Damodaran (2020), we use 7.5% for the market return (r

_{M}) and 0.8000 for the unlevered equity beta (β

_{U}). Given these values and r

_{F}= 2.50 from Table 1, the unlevered equity rate of return (r

_{U}) given by the CAPM is r

_{U}= r

_{F}+ β

_{U}(r

_{M}− r

_{F}) = 2.5% + 0.8000(7.5% − 2.5%) = 6.50%. When applying the CSM with growth, the before-tax plowback ratio (PBR

_{BT}) is set by trial and error until g

_{L}= 3.12% is achieved at the optimal credit rating (OCR) where the latter is determined by the nongrowth test as described in Section 3.2.

Panel A. Key Outcomes for P Choices (Optimal Outcomes in Bold Print) | |||||||||

P Choice = Proportion of Unlevered Firm Value (E_{U}) Retired by Debt (D) | |||||||||

Outcomes | 0.0000 | 0.0759 | 0.1580 | 0.1929 | 0.2361 | 0.2921 | 0.3303 | 0.3377 | 0.3579 |

Moody’s Rating | n.a. | Aaa | Aa2 | A1 | A2 | A3 | Baa2 | Ba1 | Ba2 |

Debt (D) | 0.000 | 1.331 | 2.772 | 3.386 | 4.42 | 5.125 | 5.795 | 5.926 | n.a. |

Equity growth rate: g_{L} | 2.28% | 2.38% | 2.56% | 2.75% | 2.90% | 3.12% | 3.57% | 4.12% | n.a. |

1st component of G_{L} | 0.000 | 0.338 | 0.591 | 0.567 | 0.556 | 0.418 | −0.175 | −1.031 | n.a. |

2nd component of G_{L} | 0.000 | 0.098 | 0.210 | 0.187 | 0.373 | 0.745 | 1.235 | 1.765 | n.a. |

Gain to leverage: G_{L} | 0.000 | 0.436 | 0.801 | 0.754 | 0.929 | 1.163 | 1.060 | 0.734 | n.a. |

Firm value: V_{L} | 17.546 | 17.982 | 18.347 | 18.300 | 18.475 | 18.709 | 18.607 | 18.280 | n.a. |

Equity value: E_{L} | 17.546 | 16.651 | 15.575 | 14.914 | 14.333 | 13.584 | 12.811 | 12.354 | n.a. |

%∆E_{U} | 0.00% | 2.48% | 4.56% | 4.30% | 5.29% | 6.63% | 6.04% | 4.18% | n.a. |

NB | 0.00% | 32.74% | 28.88% | 22.27% | 22.42% | 22.69% | 18.30% | 12.39% | n.a. |

DV | 0.0000 | 0.0740 | 0.1511 | 0.1850 | 0.2242 | 0.2739 | 0.3115 | 0.3242 | n.a. |

Panel B. Computations for Optimal Outcomes at P = 0.2921 | |||||||||

D = P = 0.2921(USD 17,546,148.72) = USD 5,124,736.08 or D = (1 − T_{D2})I/r_{D} = (1 − 0)USD 190,476.19/0.037168 = USD 5,124,736.08.g _{L} = r_{L}(1 − T_{C}_{2})RE/[C + G − (1 − T_{C}_{2})I] = 0.71668(1 − 0)USD 259,800/[USD 740,200 + USD 47,052.52 − (1 − 0)USD 190,476.19] = 0.0311998742 or about 3.12%.Max G _{L} = (1 − α_{I}r_{D}/r_{Lg})D + (1 − α_{2}r_{U}_{g}/r_{Lg})E_{U} = [1 − 1.00000(0.037168)/0.0404681258]USD 5,124,736.08 + [1 − 1.00(0.0421858957)/0.0404681258]USD 17,546,148.72 = USD 417,915.91 − USD 744,789.77 = USD 1,162,706.Max V _{L} = E_{U} + Max G_{L} = USD 17,546,149 + USD 1,162,706 = USD 18,708,854.E _{L} = V_{L} − D = USD 18,708,854 − USD 5,124,736.08 = USD 13,584,118.Max %∆E _{U} = Max G_{L}/E_{U} = USD 1,162,706/USD 17,546,149 = 0.0663 or 6.63%.NB = Max G _{L}/D = USD 1,162,706/USD 5,124,736.08 = 0.2269 or 22.69%.ODV = D/Max V _{L} = USD 5,124,736.08/USD 18,708,854 = 0.2739. |

_{U}) retired by debt (D). This table uses 2019 data (including spreads) from Damodaran (2020). In the last column, n.a. stands for not applicable as the growth (RE) constraint is violated once P reaches 0.3579. Violations of the growth constraint are described in Section 3.1. When using equation (2), we follow Hull (2014) and allow positive tax rates to change as described in Section 2.3. However, this table uses NP low (L) tax rates for TCJA tests that are all zero and so cannot change as the P choice changes. These zero tax rates are given in the nonprofit column of the bottom half of Panel A in Exhibit 2. As tax rates are all zero, α

_{1}and α

_{2}equal one as described in Table 2. Outcomes are based on before-tax cash flows (CF

_{BT}) of USD 1,000,000 with a historical growth rate of 3.12% that is achieved when a Moody’s A3 is the optimal credit rating (OCR). OCR is determined by the nongrowth test described in Section 3.2. Dollar values for key outcomes are in millions and are after-tax values. Firm value (V

_{L}) = E

_{U}+ gain to leverage (G

_{L}). Levered equity (E

_{L}) = V

_{L}− D. %∆E

_{U}is G

_{L}as a percent of E

_{U}. Net benefit from leverage (NB) is G

_{L}as a percent of D. DV is the debt-to-firm value ratio. The optimal DV is ODV and is identified from the maximum gain to leverage (max G

_{L}) that coincides with the maximum firm value (max V

_{L}) since max V

_{L}= E

_{U}+ max G

_{L}. Optimal outcomes are designated by the bold print column where the optimal P = 0.2921. Panel B provides computation for the optimal outcomes. Panel B computes outcomes at ODV as designated in the bold print column. To minimize rounding off errors, we use values up to eleven decimal points. From Table 1, we have ICR = 5.25, r

_{D}= 3.7168% and r

_{L}= 7.1668% when Moody’s rating is A3, which is the OCR. From Table 2, we have T

_{E}

_{1}= T

_{E}

_{2}= T

_{D1}= T

_{D2}= T

_{C1}= T

_{C2}= 0, g

_{U}= 2.28141043%, r

_{U}= 6.5%, CF

_{BT}= USD 1,000,000, RE = USD 259,800, C = USD 740,200, E

_{U}(or V

_{U}) = USD 17,546,149 and the before-tax plowback ratio (PBR

_{BT}) = 0.2598. For the optimal choice of P = 0.2921 where debt retires 0.2921 of E

_{U}, and I = (1 − T

_{C}

_{2})CF

_{BT}/ICR = (1−0)USD 1,000,000/5.25 = USD 190,476.19, we compute D. Given G (as determined by iterative process due G’s interdependence with G

_{L}and g

_{L}) = r

_{L}

_{g}G

_{L}

**/**(1 − T

_{E}

_{2})(1 − T

_{C}

_{2}) = 0.0404681258(USD 1,162,705.69)

**/**(1 − 0)(1 − 0) = USD 47,052.52, we compute g

_{L}. Using Equation (2) with α

_{1}= 1.00 α

_{2}= 1.00, r

_{Ug}= r

_{U}− g

_{U}= 6.5% − 2.28141043% = 4.21858957%, r

_{Lg}= r

_{L}− g

_{L}= 7.1668% − 3.11998742% = 4.04681258%, and above values for E

_{U}, r

_{D}, and D, we compute Max G

_{L}.

Panel A. Key Outcomes for P Choices (Optimal Outcomes in Bold Print) | |||||||||

P Choice = Proportion of Unlevered Firm Value (E_{U}) Retired by Debt (D) | |||||||||

Outcomes | 0.0000 | 0.0683 | 0.1429 | 0.1754 | 0.2155 | 0.2674 | 0.3031 | 0.3131 | 0.3322 |

Moody’s Rating | n.a. | Aaa | Aa2 | A1 | A2 | A3 | Baa2 | Ba1 | Ba2 |

Debt (D) | 0.000 | 0.769 | 1.609 | 1.975 | 2.426 | 3.011 | 3.413 | 3.525 | 3.740 |

Equity growth rate: g_{L} | 2.47% | 2.54% | 2.67% | 2.83% | 2.94% | 3.12% | 3.49% | 3.97% | 4.49% |

1st component of G_{L} | 0.000 | 0.251 | 0.457 | 0.460 | 0.468 | 0.417 | 0.116 | −0.317 | −0.919 |

2nd component of G_{L} | 0.000 | 0.104 | 0.186 | 0.235 | 0.403 | 0.629 | 0.848 | 1.066 | 1.570 |

Gain to leverage: G_{L} | 0.000 | 0.354 | 0.643 | 0.695 | 0.871 | 1.046 | 0.964 | 0.749 | 0.651 |

Firm value: V_{L} | 11.259 | 11.613 | 11.902 | 11.954 | 12.130 | 12.305 | 12.222 | 12.007 | 11.910 |

Equity value: E_{L} | 11.259 | 10.844 | 10.292 | 9.979 | 9.704 | 9.294 | 8.810 | 8.483 | 8.170 |

%∆E_{U} | 0.00% | 3.15% | 5.71% | 6.17% | 7.74% | 9.29% | 8.56% | 6.65% | 5.79% |

NB | 0.00% | 46.11% | 39.96% | 35.20% | 35.91% | 34.75% | 28.23% | 21.24% | 17.42% |

DV | 0.0000 | 0.0662 | 0.1352 | 0.1652 | 0.2000 | 0.2447 | 0.2792 | 0.2935 | 0.3140 |

Panel B. Computations for Optimal Outcomes at P = 0.2674 | |||||||||

D = P(E_{U}) = 0.2674(USD 11,258,777.1) = USD 3,010,617.92 or D = (1 − T_{D2})I/r_{D} = (1 − 0.208669333)USD 141,405.67/0.037168 = USD 3,010,617.92.g _{L} = r_{L}(1 − T_{C}_{2})RE/[C + G − (1 − T_{C}_{2})I] = 0.071668(1 − 0.25762021)USD 351,900/[USD 648,100 + USD 57,036.74 − (1 − 0.25762021)USD 141,405.67] = 0.0311963388 or about 3.12%.Max G _{L} = (1 − α_{I}r_{D}/r_{Lg})D + (1 − α_{2}r_{U}_{g}/r_{Lg})E_{U} = [1 − 0.9381410624(0.037168)/0.04029478476]USD 3,010,617.92 + [1 − 1.0605425604(0.04029478476)/0.0404716612]USD 11,258,777.1 = USD 416,785 − USD 629,451 = USD 1,046,236.Max V _{L} = E_{U} + Max G_{L} = USD 11,258,777 + USD 1,046,236 = USD 12,305,013.E _{L} = V_{L} − D = USD 12,305,013 − USD 3,010,617.92 = USD 9,294,396.Max %∆E _{U} = Max G_{L}/E_{U} = USD 1,046,236/USD 11,258,777 = 0.0929 or 9.29%.NB = Max G _{L}/D = USD 1,046,236/USD 3,010,617.92 = 0.3475 or 34.75%.ODV = D/Max V _{L} = USD 3,010,617.92/USD 12,305,013 = 0.2447. |

_{U}) retired by debt (D). This table uses 2019 data (including spreads) from Damodaran (2020). Violations of the growth (RE) constraint, described in Section 3.1, do not hold for this table as the first violation does not occur until the ninth levered P choice. When using Equation (4), we follow Hull (2014) and allow tax rates to be a function of debt causing α

_{1}and α

_{2}to increase as debt rises as described in Section 2.3. This table uses the low (L) tax rates under TCJA in the PT column in the bottom half of Panel A in Exhibit 2. Outcomes are based on before-tax cash flows (CF

_{BT}) of USD 1,000,000 with a historical growth rate of 3.12% that is achieved when a Moody’s A3 is the optimal credit rating (OCR). OCR is determined by the nongrowth test described in Section 3.2. Dollar values are in millions and are after-tax values. Firm value (V

_{L}) = E

_{U}+ gain to leverage (G

_{L}). Levered equity (E

_{L}) = V

_{L}− D. %∆E

_{U}is G

_{L}as a percent of E

_{U}. Net benefit from leverage (NB) is G

_{L}as a percent of D. DV is the debt-to-firm value ratio. The optimal DV is ODV and is identified from the maximum gain to leverage (max G

_{L}) that coincides with the maximum firm value (max V

_{L}) since max V

_{L}= E

_{U}+ max G

_{L}. Optimal outcomes are designated by the bold print column where the optimal P = 0.2674. Panel B computes outcomes at ODV as designated in the bold print column. To minimize rounding off errors, we use values up to eleven decimal points. From Table 1, we have ICR = 5.25, r

_{D}= 3.7168% and r

_{L}= 7.1668% when Moody’s rating is A3, which is the OCR. From Table 2, we have T

_{E}

_{1}= 0.30, T

_{E}

_{2}= 0.25762021, T

_{D2}= 0.208669333, g

_{U}= 2.47052152%, r

_{U}= 6.5%, CF

_{BT}= USD 1,000,000, RE = USD 351,900, C = USD 648,100, E

_{U}(or V

_{U}) = USD 11,258,777 and the before-tax plowback ratio (PBR

_{BT}) = 0.3519. For the optimal choice of P = 0.2674 where debt retires 0.2674 of E

_{U}, and I = (1 − T

_{E}

_{2})CF

_{BT}/ICR = (1 − 0.25762021) USD 1,000,000/5.25 = USD 141,405.67, we compute D. Given G (as determined by iterative process due G’s interdependence with G

_{L}and g

_{L}) = r

_{L}

_{g}G

_{L}

**/**(1 − T

_{E}

_{2}) = 0.040471661199 (USD 1,046,236.37)

**/**(1 − 0.2576202077) = USD 57,036.74, we compute g

_{L}. Using Equation (4) with α

_{1}= 0.9381410624, α

_{2}= 1.0605425604, r

_{Ug}= r

_{U}− g

_{U}= 6.5% − 2.47052152% = 4.029478476%, r

_{Lg}= r

_{L}− g

_{L}= 7.1668% − 3.11963388% = 4.0471661199%, and above values for E

_{U}, r

_{D}, and D, we compute Max G

_{L}.

P | PBR_{BT} | g_{U} | E_{U} | Max V_{L} | Max G_{L} | Max %∆E_{U} | NB | ODV | OCR | DGN | |
---|---|---|---|---|---|---|---|---|---|---|---|

2014: NP-L | 0.1499 | 0.3025 | 2.819% | USD 18.949 | USD 20.027 | USD 1.078 | 5.69% | 37.96% | 0.1419 | Aa2 | USD 3.516 |

2014: NP-H | 0.1474 | 0.3073 | 2.826% | USD 18.107 | USD 19.129 | USD 1.022 | 5.64% | 38.27% | 0.1395 | Aa2 | USD 3.274 |

2014: PT-L | 0.2683 | 0.3528 | 2.480% | USD 11.270 | USD 12.340 | USD 1.070 | 9.49% | 35.38% | 0.2451 | A3 | USD 0.401 |

2014: PT- H | 0.2806 | 0.3786 | 2.535% | USD 10.029 | USD 11.211 | USD 1.182 | 11.78% | 41.99% | 0.2510 | A3 | USD 0.006 |

2015: NP-L | 0.1810 | 0.2778 | 2.500% | USD 18.056 | USD 18.649 | USD 0.592 | 3.28% | 18.18% | 0.1752 | A1 | USD 2.865 |

2015: NP-H | 0.1777 | 0.2826 | 2.509% | USD 17.265 | USD 17.828 | USD 0.563 | 3.26% | 18.36% | 0.1721 | A1 | USD 2.668 |

2015: PT-L | 0.2047 | 0.3551 | 2.505% | USD 11.301 | USD 11.964 | USD 0.663 | 5.86% | 28.65% | 0.1934 | A2 | USD 0.560 |

2015: PT- H | 0.2137 | 0.3800 | 2.550% | USD 10.045 | USD 10.815 | USD 0.770 | 7.67% | 35.88% | 0.1985 | A2 | USD 0.161 |

2016: NP-L | 0.2902 | 0.2582 | 2.262% | USD 17.505 | USD 18.594 | USD 1.089 | 6.22% | 21.43% | 0.2732 | A3 | USD 2.271 |

2016: NP-H | 0.2843 | 0.2630 | 2.273% | USD 16.746 | USD 17.776 | USD 1.031 | 6.15% | 21.65% | 0.2678 | A3 | USD 2.111 |

2016: PT-L | 0.2656 | 0.3501 | 2.451% | USD 11.236 | USD 12.235 | USD 1.000 | 8.90% | 33.50% | 0.2439 | A3 | USD 0.399 |

2016: PT- H | 0.2777 | 0.3759 | 2.506% | USD 10.000 | USD 11.117 | USD 1.118 | 11.18% | 40.25% | 0.2498 | A3 | USD 0.008 |

2017: NP-L | 0.3608 | 0.2495 | 2.161% | USD 17.296 | USD 18.809 | USD 1.513 | 8.75% | 24.25% | 0.3318 | Baa2 | USD 1.977 |

2017: NP-H | 0.3531 | 0.2543 | 2.172% | USD 16.549 | USD 17.975 | USD 1.426 | 8.62% | 24.40% | 0.3251 | Baa2 | USD 1.836 |

2017: PT-L | 0.3295 | 0.3433 | 2.379% | USD 11.154 | USD 12.462 | USD 1.308 | 11.73% | 35.60% | 0.2949 | Baa2 | USD 0.231 |

2017: PT- H | 0.3452 | 0.3698 | 2.441% | USD 9.937 | USD 11.378 | USD 1.441 | 14.50% | 42.00% | 0.3015 | Baa2 | −USD 0.152 |

2018: NP-L | 0.2733 | 0.2431 | 2.088% | USD 17.154 | USD 17.584 | USD 0.430 | 2.51% | 9.18% | 0.2666 | A3 | USD 2.120 |

2018: NP-H | 0.2677 | 0.2479 | 2.100% | USD 16.415 | USD 16.819 | USD 0.404 | 2.46% | 9.20% | 0.2613 | A3 | USD 1.974 |

2018: PT-L | 0.2493 | 0.3335 | 2.277% | USD 11.047 | USD 11.630 | USD 0.583 | 5.28% | 21.18% | 0.2368 | A3 | USD 0.391 |

2018: PT- H | 0.2606 | 0.3590 | 2.330% | USD 9.838 | USD 10.576 | USD 0.739 | 7.51% | 28.83% | 0.2424 | A3 | USD 0.027 |

2019: NP-L | 0.2921 | 0.2598 | 2.281% | USD 17.546 | USD 18.709 | USD 1.163 | 6.63% | 22.69% | 0.2739 | A3 | USD 2.289 |

2019: NP-H | 0.2861 | 0.2647 | 2.293% | USD 16.786 | USD 17.888 | USD 1.102 | 6.56% | 22.94% | 0.2685 | A3 | USD 2.130 |

2019: PT-L | 0.2674 | 0.3519 | 2.471% | USD 11.259 | USD 12.305 | USD 1.046 | 9.29% | 34.75% | 0.2447 | A3 | USD 0.401 |

2019: PT-H | 0.2796 | 0.3777 | 2.525% | USD 10.019 | USD 11.179 | USD 1.160 | 11.58% | 41.41% | 0.2506 | A3 | USD 0.006 |

2014-17: NP-L | 0.2455 | 0.2720 | 2.44% | USD 17.952 | USD 19.020 | USD 1.068 | 5.99% | 25.44% | 0.2305 | A2 | USD 2.657 |

2014-17: NP-H | 0.2406 | 0.2768 | 2.45% | USD 17.167 | USD 18.177 | USD 1.010 | 5.92% | 25.67% | 0.2261 | A2 | USD 2.472 |

2014-17: PT-L | 0.2670 | 0.3503 | 2.45% | USD 11.240 | USD 12.250 | USD 1.010 | 9.00% | 33.28% | 0.2443 | A3 | USD 0.398 |

2014-17: PT-H | 0.2793 | 0.3761 | 2.51% | USD 10.003 | USD 11.130 | USD 1.128 | 11.28% | 40.03% | 0.2502 | A3 | USD 0.006 |

2018-19: NP-L | 0.2827 | 0.2515 | 2.185% | USD 17.350 | USD 18.147 | USD 0.796 | 4.57% | 15.93% | 0.2703 | A3 | USD 2.204 |

2018-19: NP-H | 0.2769 | 0.2563 | 2.196% | USD 16.601 | USD 17.354 | USD 0.753 | 4.51% | 16.07% | 0.2649 | A3 | USD 2.052 |

2018-19: PT-L | 0.2584 | 0.3427 | 2.374% | USD 11.153 | USD 11.968 | USD 0.815 | 7.29% | 27.96% | 0.2407 | A3 | USD 0.396 |

2018-19: PT-H | 0.2701 | 0.3684 | 2.427% | USD 9.928 | USD 10.878 | USD 0.950 | 9.55% | 35.12% | 0.2465 | A3 | USD 0.017 |

_{L}with growth minus max V

_{L}with nongrowth. All dollar values are in millions. In order to report outcomes for years 2014–2017, we have to assume the same ICRs for these four years as given by Damodaran (2019, 2020) for 2018 and 2019 where these two years have ICRs that are the same. ICRs enable us to compute leverage ratios. The purpose of including the years 2014–2017 is not to report the most precise results (since we do not know the ICRs for these four years) but to illustrate how the eleven outcomes change when credit ratings change if ICRs are held constant using TCJA tax rates that began in 2018.

P | PBR_{BT} | g_{U} | E_{U} | Max V_{L} | Max G_{L} | Max %∆E_{U} | NB | ODV | OCR | DGN | |
---|---|---|---|---|---|---|---|---|---|---|---|

2014: NP-L | 0.1499 | 0.3025 | 2.819% | USD 18.949 | USD 20.027 | USD 1.078 | 5.69% | 37.96% | 0.1419 | Aa2 | USD 3.516 |

2014: NP-H | 0.1477 | 0.3099 | 2.831% | USD 17.699 | USD 18.709 | USD 1.010 | 5.71% | 38.64% | 0.1397 | Aa2 | USD 3.149 |

2014: PT-L | 0.2683 | 0.3606 | 2.493% | USD 10.850 | USD 11.931 | USD 1.081 | 9.96% | 37.14% | 0.2440 | A3 | USD 0.279 |

2014: PT- H | 0.2814 | 0.3872 | 2.546% | USD 9.610 | USD 10.803 | USD 1.194 | 12.42% | 44.14% | 0.2503 | A3 | −USD 0.114 |

2015: NP-L | 0.1810 | 0.2778 | 2.500% | USD 18.056 | USD 18.649 | USD 0.592 | 3.28% | 18.13% | 0.1752 | A1 | USD 2.865 |

2015: NP-H | 0.2193 | 0.2729 | 2.366% | USD 16.551 | USD 17.165 | USD 0.614 | 3.71% | 16.92% | 0.2114 | A2 | USD 2.273 |

2015: PT-L | 0.2047 | 0.3627 | 2.516% | USD 10.876 | USD 11.556 | USD 0.680 | 6.25% | 30.53% | 0.1926 | A2 | USD 0.433 |

2015: PT- H | 0.2142 | 0.3884 | 2.559% | USD 9.622 | USD 10.410 | USD 0.787 | 8.18% | 38.19% | 0.1980 | A2 | USD 0.038 |

2016: NP-L | 0.2902 | 0.2582 | 2.262% | USD 17.505 | USD 18.594 | USD 1.089 | 6.22% | 21.43% | 0.2732 | A3 | USD 2.271 |

2016: NP-H | 0.2846 | 0.2659 | 2.284% | USD 16.382 | USD 17.420 | USD 1.038 | 6.34% | 22.27% | 0.2676 | A3 | USD 2.022 |

2016: PT-L | 0.2655 | 0.3579 | 2.464% | USD 10.817 | USD 11.831 | USD 1.013 | 9.37% | 35.27% | 0.2428 | A3 | USD 0.277 |

2016: PT- H | 0.2785 | 0.3844 | 2.516% | USD 9.581 | USD 10.713 | USD 1.132 | 11.81% | 42.42% | 0.2491 | A3 | −USD 0.111 |

2017: NP-L | 0.3608 | 0.2495 | 2.161% | USD 17.296 | USD 18.809 | USD 1.513 | 8.75% | 24.25% | 0.3318 | Baa2 | USD 1.977 |

2017: NP-H | 0.3534 | 0.2573 | 2.184% | USD 16.192 | USD 17.621 | USD 1.429 | 8.83% | 24.98% | 0.3247 | Baa2 | USD 1.753 |

2017: PT-L | 0.3295 | 0.3511 | 2.392% | USD 10.740 | USD 12.059 | USD 1.319 | 12.28% | 37.26% | 0.2935 | Baa2 | USD 0.144 |

2017: PT- H | 0.3463 | 0.3785 | 2.454% | USD 9.524 | USD 10.977 | USD 1.452 | 15.25% | 44.04% | 0.3004 | Baa2 | −USD 0.265 |

2018: NP-L | 0.2555 | 0.2867 | 2.613% | USD 18.349 | USD 19.163 | USD 0.814 | 4.43% | 17.36% | 0.2447 | A3 | USD 3.698 |

2018: NP-H | 0.2503 | 0.2919 | 2.626% | USD 17.554 | USD 18.320 | USD 0.765 | 4.36% | 17.42% | 0.2399 | A3 | USD 3.474 |

2018: PT-L | 0.2342 | 0.3835 | 2.830% | USD 11.760 | USD 12.518 | USD 0.758 | 6.45% | 27.52% | 0.2200 | A3 | USD 1.279 |

2018: PT- H | 0.2451 | 0.4097 | 2.887% | USD 10.457 | USD 11.335 | USD 0.877 | 8.39% | 34.23% | 0.2261 | A3 | USD 0.785 |

2019: NP-L | 0.2697 | 0.3038 | 2.836% | USD 19.003 | USD 20.609 | USD 1.606 | 8.45% | 31.33% | 0.2487 | A3 | USD 4.189 |

2019: NP-H | 0.2642 | 0.3091 | 2.850% | USD 18.178 | USD 19.697 | USD 1.518 | 8.35% | 31.61% | 0.2439 | A3 | USD 3.939 |

2019: PT-L | 0.2477 | 0.4016 | 3.054% | USD 12.154 | USD 13.394 | USD 1.239 | 10.20% | 41.17% | 0.2248 | A3 | USD 1.489 |

2019: PT-H | 0.2593 | 0.4279 | 3.111% | USD 10.805 | USD 12.118 | USD 1.312 | 12.14% | 46.83% | 0.2312 | A3 | USD 0.945 |

2014-17: NP-L | 0.2259 | 0.2778 | 2.52% | USD 18.232 | USD 19.268 | USD 1.035 | 5.74% | 32.43% | 0.2121 | A2 | USD 2.657 |

2014-17: NP-H | 0.2320 | 0.2823 | 2.50% | USD 16.962 | USD 17.953 | USD 0.992 | 5.90% | 32.77% | 0.2178 | A2 | USD 2.299 |

2014-17: PT-L | 0.2670 | 0.3581 | 2.47% | USD 10.821 | USD 11.844 | USD 1.023 | 9.46% | 35.05% | 0.2432 | A3 | USD 0.276 |

2014-17: PT-H | 0.2801 | 0.3846 | 2.52% | USD 9.584 | USD 10.726 | USD 1.141 | 11.92% | 42.20% | 0.2495 | A3 | −USD 0.113 |

2018-19: NP-L | 0.2626 | 0.2953 | 2.724% | USD 18.676 | USD 19.886 | USD 1.210 | 6.44% | 24.34% | 0.2467 | A3 | USD 3.944 |

2018-19: NP-H | 0.2573 | 0.3005 | 2.738% | USD 17.866 | USD 19.008 | USD 1.142 | 6.36% | 24.52% | 0.2419 | A3 | USD 3.707 |

2018-19: PT-L | 0.2410 | 0.3926 | 2.942% | USD 11.957 | USD 12.956 | USD 0.999 | 8.32% | 34.34% | 0.2224 | A3 | USD 1.384 |

2018-19: PT-H | 0.2522 | 0.4188 | 2.999% | USD 10.631 | USD 11.726 | USD 1.095 | 10.27% | 40.53% | 0.2287 | A3 | USD 0.865 |

P | PBR_{BT} | g_{U} | E_{U} | Max V_{L} | Max G_{L} | Max %∆E_{U} | NB | ODV | OCR | DGN | |
---|---|---|---|---|---|---|---|---|---|---|---|

T5-L | 9.42% | −26.63% | −7.97% | 55.57% | 51.63% | −2.25% | −37.32% | −43.03% | 12.27% | A3 | USD 1.808 |

T5-H | 2.53% | −30.42% | −9.52% | 67.20% | 59.53% | −20.69% | −52.72% | −54.24 | 7.47% | A3 | USD 2.035 |

T6-L | 8.98% | −24.79% | −7.39% | 56.19% | 53.49% | 21.14% | −22.58% | −29.11% | 10.91% | A3 | USD 2.841 |

T6-H | 2.01% | −28.25% | −8.72% | 68.05% | 62.10% | 4.30% | −38.09% | −39.52% | 5.77% | A3 | USD 2.841 |

Mean | 5.73% | −27.52% | −8.40% | 61.75% | 56.69% | 0.62% | −37.68% | −41.48% | 9.10% | A3 | USD 2.311 |

StDev | 4.01% | 2.39% | 0.92% | 6.80% | 4.94% | 17.29% | 12.31% | 10.36% | 3.00% | n.a. | USD 0.445 |

Nonprofit | Pass-Through |
---|---|

Owned By: No one | Owned By: Investors |

Ownership types: Corporation (501c3), association, trust | Ownership types: Sole proprietorship, partnership, LLC, S corp |

Board Members: Nominated | Board Members: Elected by owners (if applicable) |

Official obligations: Fulfill duties related to goals involving service, education, and research | Official obligations: Increase ownership wealth by providing profitable services and products |

Major Goal: Maximize value in terms of service distributions | Major Goal: Maximize value in terms of monetary distributions |

Mission: Described largely in terms of service, education, research, and growth | Mission: Described largely in terms of profit, efficiency, service, growth |

Decision-making and implementation: Cautiously proceeds to satisfy mission and constituencies | Decision-making and implementation: Quickly responds to profitable opportunities |

Sources of Revenues: Services, contributions, grants, and investments (including endowment income) | Sources of Revenues: Business activities (sales and services) and investments in other businesses |

Equity Distributions: Non-monetary distributions in form of services rendered to those in need | Equity Distributions: Monetary distributions to owners in form of cash payouts and capital gains |

Sources of Equity Financing: Internal equity (eligible revenues, investment/endowment income); External equity (contributions, grants, government) | Sources of Equity Financing: Internal equity (retained earnings); External equity (new partners, new issuances, venture capital) |

Sources of Debt Financing: Personal tax-exempt debt, nonfinancial debt (mortgages), short-term debt (trade credit, bank borrowings avoided) | Sources of Debt Financing: Bond issues, mezzanine debt, Small Business Administration loans, short-term debt (trade credit, bank borrowings) |

Corporate Taxes: Zero or very little taxes resulting from minor taxable profitable ventures | Corporate Taxes: None as PTs do not pay corporate taxes |

Personal Equity Taxes: Zero or very little taxes from minor taxable for-profit ventures | Personal Equity Taxes: Personal taxes paid on business income (even if undistributed) |

Personal Debt Taxes: Zero or minor due to issuing mostly tax-exempt debt | Personal Debt Taxes: Personal taxes paid on interest from debt |

Interest Tax Shield: Zero or very little business tax shield (typically at corporate tax level) | Interest Tax Shield: Full business tax shield (at personal tax level) |

Nonprofit (Unlevered and Levered Tax Rates) | Pass-Through (Unlevered and Levered Tax Rates) |
---|---|

Panel A: Low (L) Tax Rates | |

Pre-TCJA | Pre-TCJA |

T_{C}_{1} = 0 and T_{C}_{2} = 0 | T_{C}_{1} = 0 and T_{C}_{2} = 0 |

T_{E}_{1} = 0 and T_{E}_{2} = 0 | T_{E}_{1} = 0.320 and T_{E}_{2} = 0.275 |

T_{D}_{1} = 0 and T_{D}_{2} = 0 | T_{D}_{1} = 0.190 and T_{D}_{2} = 0.220 |

TCJA | TCJA |

T_{C}_{1} = 0 and T_{C}_{2} = 0 | T_{C}_{1} = 0 and T_{C}_{2} = 0 |

T_{E}_{1} = 0 and T_{E}_{2} = 0 | T_{E}_{1} = 0.300 and T_{E}_{2} = 0.255 |

T_{D}_{1} = 0 and T_{D}_{2} = 0 | T_{D}_{1} = 0.180 and T_{D}_{2} = 0.210 |

Panel B: High (H) Tax Rates | |

Pre-TCJA | Pre-TCJA |

T_{C}_{1} = 0.030 and T_{C}_{2} = 0.025 | T_{C}_{1} = 0 and T_{C}_{2} = 0 |

T_{E}_{1} = 0.030 and T_{E}_{2} = 0.025 | T_{E}_{1} = 0.380 and T_{E}_{2} = 0.330 |

T_{D}_{1} = 0.050 and T_{D}_{2} = 0.060 | T_{D}_{1} = 0.190 and T_{D}_{2} = 0.220 |

TCJA | TCJA |

T_{C}_{1} = 0.020 and T_{C}_{2} = 0.020 | T_{C}_{1} = 0 and T_{C}_{2} = 0 |

T_{E}_{1} = 0.020 and T_{E}_{2} = 0.020 | T_{E}_{1} = 0.360 and T_{E}_{2} = 0.310 |

T_{D}_{1} = 0.040 and T_{D}_{2} = 0.045 | T_{D}_{1} = 0.180 and T_{D}_{2} = 0.210 |

Credit Ratings Moody’s/S&P | Credit Spreads by Years/Periods (Means for the Two Periods in the Last Two Columns) | |||||||
---|---|---|---|---|---|---|---|---|

2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2014–2017 | 2018–2019 | |

Aaa/AAA | 0.4000% | 0.7500% | 0.6000% | 0.5400% | 0.7500% | 0.6300% | 0.5725% | 0.6900% |

Aa2/AA | 0.7000% | 1.0000% | 0.8000% | 0.7200% | 1.0000% | 0.7800% | 0.8050% | 0.8900% |

A1/A+ | 0.9000% | 1.1000% | 1.0000% | 0.9000% | 1.2500% | 0.9750% | 0.9750% | 1.1125% |

A2/A | 1.0000% | 1.2500% | 1.1000% | 0.9900% | 1.3750% | 1.0764% | 1.0850% | 1.2257% |

A3/A- | 1.2000% | 1.7500% | 1.2500% | 1.1300% | 1.5625% | 1.2168% | 1.3325% | 1.3897% |

Baa2/BBB | 1.7500% | 2.2500% | 1.6000% | 1.2700% | 2.0000% | 1.5600% | 1.7175% | 1.7800% |

Ba1/BB+ | 2.7500% | 3.2500% | 2.5000% | 1.9800% | 3.0000% | 2.0000% | 2.6200% | 2.5000% |

Ba2/BB | 3.2500% | 4.2500% | 3.0000% | 2.3800% | 3.6000% | 2.4000% | 3.2200% | 3.0000% |

B1/B+ | 4.0000% | 5.5000% | 3.7500% | 2.9800% | 4.5000% | 3.5100% | 4.0575% | 4.0050% |

B2/B | 5 0000% | 6.5000% | 4.5000% | 3.5700% | 5.4000% | 4.2120% | 4.8925% | 4.8060% |

B3/B- | 6.0000% | 7.5000% | 5.5000% | 4.3700% | 6.6000% | 5.1480% | 5.8425% | 5.8740% |

Caa/CCC | 7.0000% | 9.0000% | 6.5000% | 8.6400% | 9.0000% | 8.2000% | 7.7850% | 8.6000% |

Ca2/CC | 8.0000% | 12.0000% | 8.0000% | 10.6300% | 11.0800% | 8.6424% | 9.6575% | 9.8612% |

C2/C | 10.0000% | 16.0000% | 10.5000% | 13.9500% | 14.5400% | 11.3412% | 12.6125% | 12.9406% |

D2/D | 12.0000% | 20.0000% | 14.0000% | 18.6000% | 19.3800% | 15.1164% | 16.1500% | 17.2482% |

Mean | 4.2633% | 6.1400% | 4.3067% | 4.8433% | 5.6692% | 4.4539% | 4.8883% | 5.0615% |

StDev | 3.6493% | 5.8879% | 3.9770% | 5.5558% | 5.5745% | 4.4309% | 4.7429% | 4.9991% |

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## Share and Cite

**MDPI and ACS Style**

Hull, R.; Van Dalsem, S.
Nonprofits and Pass-Throughs: Performance Comparison. *Int. J. Financial Stud.* **2021**, *9*, 13.
https://doi.org/10.3390/ijfs9010013

**AMA Style**

Hull R, Van Dalsem S.
Nonprofits and Pass-Throughs: Performance Comparison. *International Journal of Financial Studies*. 2021; 9(1):13.
https://doi.org/10.3390/ijfs9010013

**Chicago/Turabian Style**

Hull, Robert, and Shane Van Dalsem.
2021. "Nonprofits and Pass-Throughs: Performance Comparison" *International Journal of Financial Studies* 9, no. 1: 13.
https://doi.org/10.3390/ijfs9010013