Distance to Default and Misspecification of Corporate Economic Value Added

Abstract

The objective of this paper is to offer a mathematical formulation of economic value added (EVA) that incorporates distance-to-default (DD) and thus a default-free capital structure. The latter is extended via the weighted average cost of capital (WACC) to introduce a default-free EVA. The data include the nonfinancial firms listed in the DJIA30 and NASDAQ100 covering the period 1992Q2–2023Q3. The results of standard specification tests and the GMM estimator show that (a) DD causes an increase in WACC and thus, EVA decreases; (b) the interest coverage ratio can be used effectively to compensate for default risk, thus adjusting the default-free EVA positively; (c) both EVA and default-free EVA can effectively be managed via common determinants, namely, net working capital ratio, total liabilities to EBITDA, sales growth rate, debt–equity ratio, and earnings per share; (d) the positive impact of the inflation rate on both EVA and default-free EVA justifies the use of default-free EVA as a metric for equity risk premium; and (e) the robustness of the results via stochastic geometric Brownian motion shows that the determinants of default-free EVA are stable. This paper contributes to related studies by incorporating credit risk via the DD into default-free EVA.

1. Introduction

EVA plays a pivotal role in making diverse financial decisions, such as stock valuation, firm performance, and a metric for employees’ incentive compensation and nonfinancial investment decisions (capital budgeting). The shared interest among those applications is a long-term horizon. That is, the right determination of EVA affects financial decisions in the long term, which is usually associated with nonreversable decisions. In this case, it is crucial to estimate EVA in a way that not only serves long-term financial objectives but also takes into consideration stochastic movements in financial data that characterize the inevitable uncertainty. Nevertheless, the current estimation of EVA does not explicitly address two pillars. The first pillar is that the current estimation of the EVA does not address the long-term perspective or its associated uncertainty. The second pillar involves how EVA takes into account the expected changes in a firm’s credit risk. This paper develops a mathematical formulation to show how default risk affects a firm’s EVA. Default risk is measured via distance to default (DD), which can be altered to reflect the default-free weighted average cost of capital (WACC). The core idea behind EVA is that a company truly creates value for its shareholders only when its returns exceed the cost of the capital it employs. The EVA is expressed as follows.

$$\mathrm{EVA}=\mathrm{NOPAT}-\left(\mathrm{EC}\times \mathrm{WACC}\right)$$

(1)

where EVA = economic value added; NOPAT = net operating profit after taxes; EC = employed capital; WACC = weighted average cost of capital

Equation (1) shows that EVA builds upon the residual income framework, which emphasizes that true profitability must exceed capital charges. Rappaport (1986), Johnson (2001), Young and O’Byrne (2000) and Kampouris (2022) discuss EVA as a convenient metric of shareholder value creation. In this sense, EVA includes an empirical link between a firm’s profitability and the cost of capital. However, Peterson and Peterson (1996) cautioned that EVA’s reliance on accounting adjustments and the cost of capital estimates introduces measurement challenges that may limit its reliability.

The relationship between EVA and capital structure decisions has been a particularly fruitful area of research. Ross et al. (2019) highlighted how the tax advantages of debt financing can enhance EVA by lowering the overall cost of capital. Graham and Harvey’s (2001) survey of corporate financial practices revealed that many firms consciously structure their financing to optimize EVA, although they must balance this against increasing financial risk. Chen et al. (2023) conclude that EVA can be used effectively to ensure sustainable firm performance. Therefore, the current state of the relationship between the EVA and default risk can be depicted via the skewness of each metric, as shown in Figure 1. The objective is to show what happens to the management of a respective firm’s EVA in relation to its DD. Skewness is a good representative of trends in variations (Doane & Seward, 2011). The figure is generated via the calculation of the skewness of EVA and DD for every firm. The resulting data for the skewness of the DDs are arranged in ascending order. As shown in Figure 1, for every respective firm, the skewness of EVA does not align with the skewness of DD, which implies that the determination of EVA does not consider the associated DD.

1.1. Objectives

This paper aims to meet the following objectives.

• The distance-to-default cost is incorporated into the weighted average cost of capital.
• The default-free capital structure is incorporated into the computation of a default-free EVA.
• Examine the firm-specific and macroeconomic determinants of default-free EVA.

1.2. Contribution

This paper contributes to the related literature in two ways. First, a mathematical formulation of the default-free EVA is developed. Second, the paper benefits from stochastic geometric Brownian motion to examine the stability of the determinants of EVA.

The paper is organized as follows. Section 1 discusses the associations between the cost of capital, credit risk and economic value added. Section 2 describes the methodology, data and variables. Section 3 discusses the results. Section 4 concludes.

1.3. The Association Between the Cost of Capital, Credit Risk and Economic Value Added

This section discusses the intrinsic link between the cost of capital and credit risk in addition to the consequences of this link for a firm’s EVA. The discussions that follow connect two perspectives. The first perspective discusses the effects of debt financing on EVA. The second perspective discusses the effects of credit risk on the cost of capital.

1.3.1. Effects of Debt Financing on EVA

As the firm’s value can be represented by the capital invested plus the present value of excess returns, the cost of capital plays a crucial role in the determination of EVA. That is, as the cost of capital increases without sufficient compensating for growth in operating income, EVA decreases (Damodaran, 2006; Stewart, 1991). In this case, Horvathova et al. (2018) conclude that firms that used more long-term debt relative to total capital tended to generate higher EVA. This positive effect has been observed particularly during the growth and maturity stages (Tabas et al., 2016). To that end, the authors in the present paper argue that the computation of EVA explicitly considers the underlying credit risk. That is, firms that are associated with higher credit risk pay higher costs of borrowing; thus, the cost of capital increases. This issue raises a fundamental concern in corporate financing, which is to do with the role of the cost of capital in the determination of the optimal capital structure. That is, the latter must take into account the associated credit risk. In this sense, Margaritis and Psillaki (2010) conclude that an optimal capital structure can improve firm performance and align with increased EVA. Nevertheless, the benefits of long-term debt financing diminish as firms maintain an excessive interest coverage ratio (Cheng & Tzeng, 2011). Therefore, the abovementioned findings help develop the testable hypothesis that follows.

H1. 

“Leverage affects economic value added (EVA) positively and significantly”.

1.3.2. Effects of Credit Risk on the Cost of Capital

Brealey et al. (2017) noted that while equity financing avoids bankruptcy risk, it may dilute EVA if returns fail to exceed the higher cost of equity capital. The authors in this present paper argue that this negative outcome might exacerbate when a firm is using debt financing. In this case, credit risk inevitably affects EVA. The authors in this paper extend the benefits of the seminal credit risk model developed by Black and Scholes (1973) and Merton (1974). The aim is to derive the cost of capital that takes into consideration distance-to-default, as shown in Equation (2).

$$d_2={\displaystyle \frac{\ln \left(\frac{V_A}{X}\right)+\left(r-0.5{\sigma }_A^2\right)t}{{\sigma }_A\sqrt{t}}}$$

(2)

where $V_A$ = market value of equity + book value of debt; $X$ = book value of debt; $r$ = risk-free rate of return (one-year treasury bond); ${\sigma }_A$ = volatility of firm assets; and $t$ = time period (quarter). Equation (2) shows that the ratio of a firm’s market value of assets to the book value of debt ${\displaystyle \frac{V_A}{X}}$ is a debt multiplier. The latter is considered a determinant of the probability of default. That is, ceteris paribus, the model assumes a positive association between the debt multiplier and distance-to-default. Koziol (2014) develops a default risk-adjusted WACC that is usually greater than the unadjusted WACC. The difference between the two estimates is a default risk premium, which is essential for value creation (Baule, 2019; Gleißner, 2019; Haag & Koziol, 2023).

2. Data and Variables

2.1. Data

The data used in this study are obtained from the Thomson Reuters Finance Centre for 120 nonfinancial firms listed at DJIA30 and NASDAQ100. The data cover the years 1992Q2–2023Q3.

2.2. Dependent Variable

In this paper, three dependent variables, namely, the observed EVA, default-free EVA and stochastic default-free EVA, are examined. The first dependent variable examines the observed determinants of EVA. The second variable examines a mathematical development of EVA that takes into consideration a firm’s credit risk being measured via DD. Therefore, the second variable is referred to as default-free EVA. The third variable examines stochastic default-free EVA as a test for robustness. In so doing, stock returns are simulated via geometric Brownian motion to generate stochastic DD and thus stochastic default-free EVA. The next section illustrates the mathematical development of the second dependent variable, namely, default-free EVA.

2.3. Derivation of the Default-Free EVA

EVA Equation (1) shows that a firm’s capital structure, thus the cost of capital, creates an empirical link between EVA and distance to default. Therefore, Equation (2) can be extended to a capital structure that incorporates default risk given that the statistical properties of $d_2$ show that when the distance to default = 7, the probability of default equals zero. Therefore, Equation (2) can be rearranged as follows.

$$\ln \left({\displaystyle \frac{{\mathrm{V}}_{\mathrm{A}}}{\mathrm{X}}}\right)+\left(\mathrm{r}-0.5{\mathsf{\sigma }}_{\mathrm{A}}^2\right)\mathrm{t}=7{\mathsf{\sigma }}_{\mathrm{A}}\sqrt{\mathrm{t}}$$

(3)

Equation (3) is rearranged to explicitly express the firm’s market value-based leverage $\ln \left({\displaystyle \frac{{\mathrm{V}}_{\mathrm{A}}}{\mathrm{X}}}\right)$ as follows.

$$\ln \left({\displaystyle \frac{{\mathrm{V}}_{\mathrm{A}}}{\mathrm{X}}}\right)=\left(7{\mathsf{\sigma }}_{\mathrm{A}}\sqrt{\mathrm{t}}\right)-\left(\mathrm{r}-0.5{\mathsf{\sigma }}_{\mathrm{A}}^2\right)\mathrm{t}$$

(4)

In Equation (4), we take the exponent on both sides of Equation (4) to remove the natural log, which produces Equation (5) as follows.

$${\displaystyle \frac{{\mathrm{V}}_{\mathrm{A}}}{\mathrm{X}}}=\exp \left[\left(7{\mathsf{\sigma }}_{\mathrm{A}}\sqrt{\mathrm{t}}\right)-\left(\mathrm{r}-0.5{\mathsf{\sigma }}_{\mathrm{A}}^2\right)\mathrm{t}\right]$$

(5)

The derivation of a debt ratio requires the total value of a firm ${\mathrm{V}}_{\mathrm{A}}$ to be divided into its main two components, namely, the book value of debt $\mathrm{X}$ and the market value of equity ${\mathrm{V}}_{\mathrm{E}}$, as follows.

$${\mathrm{V}}_{\mathrm{A}}{=\mathrm{X}+\mathrm{V}}_{\mathrm{E}}$$

(6)

Therefore, Equation (6) can be e-arranged to reach a capital structure by dividing both sides by $\mathrm{X}$. It follows that

$${\displaystyle \frac{{\mathrm{V}}_{\mathrm{A}}}{\mathrm{X}}}=1+{\displaystyle \frac{{\mathrm{V}}_{\mathrm{E}}}{\mathrm{X}}}$$

(7)

Substituting Equation (7) into Equation (5) generates Equation (8) as follows.

$$1+{\displaystyle \frac{{\mathrm{V}}_{\mathrm{E}}}{\mathrm{X}}}=\exp \left[\left(7{\sigma }_A\sqrt{t}\right)-\left(r-0.5{\sigma }_A^2\right)t\right]$$

(8)

Therefore, solving Equation (8) for ${\displaystyle \frac{{\mathrm{V}}_{\mathrm{E}}}{\mathrm{X}}}$ generates Equation (9) as follows.

$${\displaystyle \frac{{\mathrm{V}}_{\mathrm{E}}}{\mathrm{X}}}=\left\{\exp \left[\left(7{\mathsf{\sigma }}_{\mathrm{A}}\sqrt{\mathrm{t}}\right)-\left(\mathrm{r}-0.5{\mathsf{\sigma }}_{\mathrm{A}}^2\right)\mathrm{t}\right]\right\}-1$$

(9)

Equation (9) can be rearranged to generate the equity ratio and debt ratio by multiplying both sides in Equation (9) by $\mathrm{X}$, which generates Equation (10) as follows.

$${\mathrm{V}}_{\mathrm{E}}=\mathrm{X}〈\left\{\exp \left[\left(7{\mathsf{\sigma }}_{\mathrm{A}}\sqrt{\mathrm{t}}\right)-\left(\mathrm{r}-0.5{\mathsf{\sigma }}_{\mathrm{A}}^2\right)\mathrm{t}\right]\right\}-1〉$$

(10)

Therefore, an equity ratio can be developed by dividing both sides of Equation (10) by ${\mathrm{V}}_{\mathrm{A}}$, which generates Equation (11) as follows.

$${\displaystyle \frac{{\mathrm{V}}_{\mathrm{E}}}{{\mathrm{V}}_{\mathrm{A}}}}={\displaystyle \frac{\mathrm{X}〈\left\{\exp \left[\left(7{\mathsf{\sigma }}_{\mathrm{A}}\sqrt{\mathrm{t}}\right)-\left(\mathrm{r}-0.5{\mathsf{\sigma }}_{\mathrm{A}}^2\right)\mathrm{t}\right]\right\}-1〉}{{\mathrm{V}}_{\mathrm{A}}}}$$

(11)

where ${\displaystyle \frac{{\mathrm{V}}_{\mathrm{E}}}{{\mathrm{V}}_{\mathrm{A}}}}$ = ${\mathrm{ER}}_{\mathrm{PD}=0}$ = equity ratio associated with the probability of default (PD) = zero. Therefore, the default-free debt ratio (${\mathrm{DR}}_{\mathrm{PD}=0}$) is $=1-{\displaystyle \frac{{\mathrm{V}}_{\mathrm{E}}}{{\mathrm{V}}_{\mathrm{A}}}}$ $=1-{\displaystyle \frac{\mathrm{X}〈\left\{\exp \left[\left(7{\mathsf{\sigma }}_{\mathrm{A}}\sqrt{\mathrm{t}}\right)-\left(\mathrm{r}-0.5{\mathsf{\sigma }}_{\mathrm{A}}^2\right)\mathrm{t}\right]\right\}-1〉}{{\mathrm{V}}_{\mathrm{A}}}}$.

The inclusion of ${\mathrm{ER}}_{\mathrm{PD}=0}$ and ${\mathrm{DR}}_{\mathrm{PD}=0}$ in the WACC equation generates a weighted average cost of capital associated with a probability of default = 0 (${\mathrm{WACC}}_{\mathrm{PD}=0}$) as follows.

$${\mathrm{WACC}}_{\mathrm{PD}=0}=\left({\mathrm{ER}}_{\mathrm{PD}=0}{\mathrm{R}}_{\mathrm{E}}\right)+\left[{\mathrm{DR}}_{\mathrm{PD}=0}{\mathrm{R}}_{\mathrm{D}}\left({1-\mathrm{T}}_{\mathrm{c}}\right)\right]$$

(12)

Therefore, the incorporation of default-free WACC into EVA, as shown in Equation (1), generates default-free EVA (${\mathrm{EVA}}_{\mathrm{PD}=0}$) as follows.

$${\mathrm{EVA}}_{\mathrm{PD}=0}=\mathrm{NOPAT}-\left\{\left[\left(\mathrm{E}+\mathrm{L}\right)-\left(\mathrm{h}+\mathrm{CL}\right)\right]{\mathrm{WACC}}_{\mathrm{PD}=0}\right\}$$

(13)

where capital employed (C) = total equity + total liability − (cash + current liabilities).

Assuming that E = total equity; L = total liability; h = cash; CL = current liabilities.

The descriptive statistics in Appendix A offer two initial and empirical indications. The first indication is that the average default-free WACC (9.83%) is greater than the observed average WACC (3.30%), where the difference is referred to as the risk premium given that the WACC is considered the minimum required rate of return. The second indication is that the average default-free EVA (126.43) is less than the observed EVA (384.55). This is a plausible consequence that follows from the first indication.

2.4. Independent Variables

These variables are documented in the literature as determinants of economic value added. Gill et al. (2010), Lazaridis and Tryfonidis (2006), Deloof (2003), and Enqvist et al. (2014) reported that companies with effective working capital management, especially those that tightly control receivables and inventory, can improve their profitability and financial performance.

Aktas et al. (2015) and Shin and Soenen (1998) reported that companies that manage short-term financing effectively, particularly through improvements in working capital components, can increase their economic value added (EVA). The study emphasized that firms with shorter cash conversion cycles experienced higher EVA.

H2. 

“Short-term financing is positively and significantly related to economic value added (EVA).”

Tudose et al. (2022) revealed that while liquidity measured by the current ratio enhances ROA, it adversely affects ROE and EVA, indicating that excess liquidity may undermine value creation.

2.5. Control Variables

Sharma and Kumar (2011), Damodaran (2001a, 2001b) and Kruk (2021) conclude that EVA is positively influenced by inflation when firms effectively manage the tradeoff between prices and costs. Blazenko (2002) develops the concept of inflation adjusted EVA (IEVA), demonstrating how inflation can add to economic profit when firms with current assets adjust prices to match rising costs.

Mursalim and Kusuma (2017) explored how macroeconomic variables, including gross domestic product (GDP) and inflation, influence capital structure among firms in Indonesia, Malaysia, and Thailand. Their regression analysis revealed that GDP significantly affects leverage decisions.

H3. 

“Inflation rates and GDP growth rates positively and significantly affect economic value added”.

The descriptive statistics of the variables are reported in Appendix A.

3. Results and Discussion

This section discusses two sets of results. The first set compares the determinants of the observed and zero-default EVA. The objective is to provide guidance regarding the management of a firm’s operating income and cost of capital such that both generate zero-default EVA. The second set compares the determinants of zero-default and stochastic EVA. The objective is to provide guidance regarding the management of a firm’s zero-default EVA in the case of stochastic movements in stock prices.

Table 1. Determinants of EVA, default-free EVA and stochastic EVA.

Variable	Model 1: Determinants of Observed EVA	Model 2: Determinants of Zero-Default EVA	Model 3: Determinants of Stochastic Zero-Default EVA
Constant	10.47572 (3.027) ***	8.056842 (1.798) *	7.99796 (1.792) *
Net Working capital ratio	51.78647 (3.370) ***	168.6697 (5.694) ***	168.9547 (5.708) ***
Short-term Debt Ratio	−75.9448 (−1.918) **	14.07871 (0.248)	13.3739 (0.236)
Firm size (ln Total Assets)	−22.7933 (−1.677) *	−40.0511 (−2.190) **	−40.0768 (−2.194) **
Interest Coverage Ratio	0.003833 (0.698)	0.017539 (2.014) **	0.017616 (2.026) **
Total Liabilities to EBITDA ratio	0.022004 (5.486) ***	0.034709 (8.270) ***	0.034658 (8.266) ***
Sales Growth Rate	49.99391 (9.721) ***	56.73516 (8.165) ***	56.54164 (8.146) ***
Earnings Per Share	0.261856 (14.517) ***	0.310334 (13.728) ***	0.309417 (13.686) ***
Inflation Rate	704.5796 (4.039) ***	532.7791 (2.258) **	514.1045 (2.182) **
Industry Dummy	Yes	Yes	Yes
Adjusted R-squared	0.4255	0.3257	0.3256
S.E. of regression	3553.902	8015.698	8015.766
Durbin–Watson stat	2.888	2.835	2.836
Mean dependent var	64.22	130.43	130.42
S.D. dependent var	3582.746	8081.638	8081.3
Sum squared residuals	1.88 × 1011	9.54 × 1011	9.54 × 1011
J-statistic	3.44 × 1000	2.142933	2.134608
Prob(J-statistic)	1	1	1

t statistics are reported in parentheses; * significant at the 10% level, ** significant at the 5% level, and *** significant at the 1% level. NOTE that Table 1 reports the significant variables only. Current asset turnover, fixed assets turnover, the long-term debt ratio, the cash conversion cycle, the debt-to-equity ratio, the dividend per share, GDP growth, and the economic cycle are not significantly different.

reports the results of the two sets as follows.

Standard specification tests are carried out. The results of the Hausman test show that the three models fit the fixed effects. The results of linearity versus nonlinearity (RESET) show that a linear form fits the data. The results of the Durbin—Watson test reveal autocorrelation; therefore, all the variables are measured as first differences. The results of the Breusch–Pagan/Cook–Weisberg test reveal that the data are characterized by heteroskedasticity. Therefore, the GMM is a convenient estimation method. As DD (Equation (2)) is sensitive to equity volatility, the stochastic default-free EVA is estimated via the simulation of stock returns (Şamiloğlu, 2005). The stochastic stock returns (SRs) are simulated via geometric Brownian motion (GBM) (Feynman, 2013; Ibe, 2013; Reddy & Clinton, 2016; Kumar et al., 2024; Sinha, 2024) as follows:

$${\Delta \mathrm{SR}}_{\mathrm{t}+\Delta \mathrm{t}}{=\mathrm{SR}}_{\mathrm{t}}\mathsf{\mu }\Delta \mathrm{t}+{\mathrm{SR}}_{\mathrm{t}}\mathsf{\sigma }\mathsf{\epsilon }\sqrt{\Delta \mathrm{t}}$$

(14)

where ${\Delta \mathrm{SR}}_{\mathrm{t}+\Delta \mathrm{t}}$ is the change in stock returns; $\mathsf{\mu }$ and $\mathsf{\sigma }$ are the mean and volatility in the percentage change in the SR, respectively; and $\mathsf{\epsilon }$ is the Weiner process that follows the normal distribution with a mean = 0 and standard deviation = 1. The number of iterations for each company = 125, which equals the number of quarters under examination.

The results in Table 1 reflect insightful implications regarding the effects of credit risk (via DD) on firms’ cost of capital and EVA. The common determinants of EVA in the literature remain significant, with the expected sign. The positive effect of the net working capital ratio indicates the contribution of efficient working capital management to firm profitability (Gill et al., 2010; Lazaridis & Tryfonidis, 2006; Deloof, 2003; Enqvist et al., 2014). This contribution is reflected positively on the macro level, as efficient working capital offers firms with opportunities to grow, recover from business crises and improve stock prices (Aktas et al., 2015; Roy et al., 2025; Tron et al., 2018).

Nevertheless, the interest coverage ratio plays a positive role in the determination of the zero-default EVA. This positive effect confirms the impact of default risk on a firm’s profitability. That is, the higher the interest coverage is, the higher the zero-default EVA (Cheng & Tzeng, 2011; Eldomiaty et al., 2025). In addition, Bräuning et al. (2023) conclude that the interest coverage ratio helps firms avoid distress. The latter reflects positively on the economy at large (Greenwald, 2019).

Note that short-term debt has a negative effect on observed EVA only, while the effects are insignificant on default-free EVA and stochastic default-free EVA. This is an indication that both default-free and stochastic default-free EVA cannot be managed via short-term debt effectively enough. Therefore, the second hypothesis is not supported.

The positive effect of total liabilities to EBITDA ratio indicates that firms can extend debt financing proportionately to EBITDA, which reflects a firm’s creditworthiness. The latter has significant and positive economic consequences, as the relevant determination of debt capacity enables firms to extend their respective investments, thus promoting economic growth at large (Bernanke & Gertler, 1989, 1990; Gan, 2007; Kiyotaki & Moore, 1997). Therefore, the first hypothesis is supported.

The positive effects of earning per share on both observed and default-free EVA extend the argument of using EVA as a profitability metric (Okuyan, 2023). The positive effects of inflation rates on EVA and default-free EVA extend the argument that equity returns can be used effectively for hedging against inflation (Aktürk, 2016; Alqaralleh, 2020; Bodie, 1976; Al-Nassar & Bhatti, 2019). This result updates the argument that inflation causes a distortion to EVA and asset economic life (de Villiers, 1997; Howe & Lapan, 1987; Chiang & Chen, 2023). Therefore, the third hypothesis is supported.

4. Conclusions

In this paper, an EVA metric that takes into consideration a firm’s credit risk is developed. The latter is measured via the DD. Therefore, this paper examines the determinants of two new performance metrics, namely, default-free EVA and stochastic default-free EVA. The results for the nonfinancial firms listed in DJIA30 and NASDAQ100 show that the default-fee WACC is consistently greater than the observed WACC for every respective firm. This is an indication that firms’ estimation of WACC does not consider credit risk (via DD) to lower WACC and thus increase observed EVA. Nevertheless, should credit risk be incorporated, default-free EVA can effectively be managed via the net working capital ratio, total liabilities to EBITDA, sales growth rate, debt–equity ratio, and earnings per share. In terms of debt financing, the positive effect of total liabilities to EBITDA ratio has positive economic consequences, as the relevant determination of debt capacity enables firms to extend investments, thus promoting economic growth. In addition, the positive impacts of inflation provide significant evidence that EVA and default-free EVA can be used effectively for hedging against inflation. The results of the uncertainty analysis via stochastic geometric Brownian motion show that the determinants of default-free EVA are stable.