Measuring investment distortions arising from stockholder-bondholder conflicts

Robert Parrino, Michael S. Weisbach

JFE 1999

There are several different principal-agent relationships that have implications in finance (eg manager/stockholder, bondholder/stockholder), this paper focuses on the BH/SH relationship. Within this relationship, there are several different sources of conflict, among them are dividend payout, claim dilution, asset substitution and underinvestment (Smith and Warner 1979). This paper focus on the under/overinvestment issue, the costs of which will be referred to generally as ‘agency costs’ in this discussion. Perrino and Weisbach consider the situation where managers act to maximize shareholder value instead of firm value resulting in the following two problems:
Underinvestment problem – Safe, positive NPV projects may be foregone if the benefit to bondholders exceeds benefit to shareholders.
Overinvestment problem – Risky, negative NPV projects may be pursued if the benefits to stockholders are positive regardless of the offsetting decrease in value (of larger magnitude) to bondholders.
These problems emanate directly from the limited liability aspect of equity. While many papers have previously documented these issues, among them, Myers (1977) and Jensen and Meckling (1976), they had not previously been quantified in the manner that Perrino and Weisbach used throughout this paper. This main contribution of this paper is the rigorous examination of the magnitudes of these agency costs under various conditions. By quantifying these distortions, we are better able to understand their relative importance to other factors affecting capital structure choices.

Wealth transfer measurements:


Monte Carlo simulation (5000 draws) is used to value both debt and equity separately and derive expected changes to each after the selection of projects with various characteristics.
Value of debt is calculated using a discounted cash flow model.
Value of Equity is calculated using a discounted cash flow analysis with a terminal value.

Assumptions of the base model:

Covariance between project cash flows and firm cash flows is .5
Pre-tax operating cash flow (firm) = $1000
Pre-tax operating cash flow (project) = $100
Cash flows follow a random walk without drift for 30 years after which they remain constant
σ of firm CF is assumed to be median of actual σ of operating firm CF observed from 1981 – 1995, base case = 72.38%
k_(e,U) is found using CAPM
Interest expense after project adoption is based on Table 1, panel B on page 11 which assigns a credit rating based on various debt levels and specifies a corresponding interest rate
Debt to total capital is amount observed for each firm in 1995, base case = 20%
Debt maturity is rolling 15yrs and which point it is renewed at applicable rates
Firm specific marginal tax rates taken from Graham (1996), base case = 34.40%
Firm specific asset betas taken from 1996 Cost of Capital Yearbook, base case = 0.76
Projects are financed entirely by equity

The source of these transfers is the effect of the project on the risk of the overall firm. Zero NPV projects that make the firm less risky benefit BH, projects that make the firm more risky benefit SH.
Vertical-intercept = Minimum NPV necessary to accept project at 0% σ
Horizontal-intercept = project risk level where no wealth transfer occurs
Absolute value of Slope = $ of wealth transfer to stockholders for a 1% increase in σ
Line can be viewed as ‘accept/reject’ boundary. Projects above the line will be accepted by shareholders, projects below the line will be rejected.
Another way of looking at this is to consider points where the accept/reject line is above the Horizontal-axis as points where the stockholders will require a greater return than that predicted by CAPM in order to accept the project. Conversely, points where the line is below the X-axis indicate places where stockholders would accept projects with less than the return predicted by CAPM.

The greater the Vertical-intercept, the greater the underinvestment problem will be for relatively safe projects
As the absolute value of the slope increases, the magnitude of wealth transfers will increase.
The Hoizontal-axis is a measure of risk, where σ is low, the project is relatively safe, where σ is high, the project is comparatively risky.
The Horizontal-intercept signals where the problem shifts from underinvestment to overinvestment. It can also be thought of as the only level of project risk where the correct decision is made. That is, at this project risk level, the discount rate for the levered firm is equal to the discount rate at an unlevered firm.


Base case (see attached graph1):

Vertical-intercept = $13.33
Horizontal-intercept = 139%
|Slope| = .096 (9.6¢ is transferred to SH for every 1% (nominal) increase in σ)
Range of distortion in incremental rates: 0.14% at σ=0% to (2.35%) at σ=600%


Analysis of graphs:

Under the base conditions, projects with 0% σ will be rejected unless the NPV is greater than $13.33. This is an underinvestment problem. Positive NPV projects will continue to be rejected until σ reaches 139%. At σ beyond 139% all positive NPV projects will be accepted, however, negative NPV projects will also begin to be accepted as σ increases, this is an overinvestment problem. To pick one point for illustration, a project with σ = 600% would be accepted with a negative NPV as high as -$50.00, under the base conditions. Note that the distance between the accept/reject line and the Horizontal-axis in graph 1 is exactly equal to the distance between the ‘Equity Investment’ curve and the ‘Change in Equity Value’ curve in graph 2.

Parrino and Weisbach use the preceding methodology to measure changes in distortion in response to changes in each of the following seven variables: firm leverage, CF correlations, CF volatilities, project sizes, debt maturity structures, tax rates, firm leverage with risk neutral investors.

A note on table 3:

Amounts in parenthesis are CAPM rates, aka rates of return for an unlevered firm. The figure above this is the difference between the CAPM rate and the project rate of return required by stockholders when leverage is introduced to compensate for the wealth transfer at various levels of risk. It is difficult to compare the nominal value wealth transfers so it is necessary to convert these effects into the incremental rates of return for direct comparison between various scenarios.

Firm leverage:

As leverage is increased from the base case of 20%, the Vertical-intercept, the Horizontal-intercept and the |Slope| all increase. This means higher leverage strictly increases the magnitude of agency costs of debt. This is not a surprise. Incremental rates are monotonically decreasing as project risk increases. With the exception of the points around equilibrium, the scale of the incremental rates is magnified as leverage increases.

Correlations between firm and project cash flows from operations:

All scenarios have the same Vertical-intercept, but |Slope| increases as correlation increases. This means that as the CF from the project begin to match the overall firm’s CF, underinvestment problems will be mitigated while overinvestment will occur for relatively safer projects as compared to the base case. As correlation decreases, the opposite will transpire - the model predicts the underinvestment problem would persist beyond the 400% σ mark at 0.00 correlation. The authors attribute this result to the diversification benefit that results from CF that has a low correlation with the existing assets.

Volatility of the firm’s cash flows:

Firms that have low CF volatility from assets in place do not have a large underinvestment problem but will have a much larger overinvestment problem than firms with high CF volatility. This is essentially a reflection of relative risk - if the overall firm is considered ‘safe’, then the project σ required to meet the risk threshold required by stockholders is comparatively lower. In other words, the point where wealth transfers switch direction occurs at a lower project risk level. Conversely, if the firms existing assets are high risk (high volatility) then it would require a much riskier project before the project would increase the overall risk of the firm and overinvestment would occur.

Project size:

Magnitude of wealth transfer increases as project size increases, but when converted to required rates of return, the distortion is not strictly moving with project size. Generally, smaller projects require a slightly higher return, although that relationship begins to reverse around the 200% mark.

Debt maturity structures:

As predicted by Myers, among others, short term debt essentially eliminates the agency costs examined in this paper. At 3yr maturity, the incremental returns are close to zero across all levels of project risk. As duration increases, wealth transfers increase in magnitude.

Tax rates:

Required rates of return are virtually identical across various tax rates, however, high tax rates do mitigate the overall wealth transfer (smaller |slope|).

Firm leverage (with risk neutral investors):

This is similar to the previous analysis of firm leverage but in this example, the risk neutral investors discount all cash flows at the risk free rate. The relationship between the various debt levels is similar to the previous example although a bit more magnified. Essentially, it is included primarily to demonstrate that altering discount rates does not change the conclusions.

Cross sectional analysis:

The authors take the methodology used to evaluate a ‘typical’ firm in the preceding section and apply it to a cross section of firms in 23 different industries. They match firm CF, cost of debt, maturity of debt, project size, tax rate and asset betas to observed firm values. The results generally confirm the findings from the previous section, here are a few particular observations:


Illustrates the underinvestment problem related to high firm leverage.

Ethyl Corp:

Illustrates how low duration of debt mitigates wealth transfers.


Illustrates how high incremental costs of debt magnify wealth transfers.

The big picture:

The paper demonstrates that there are a variety of different factors that can influence the magnitude of these wealth transfers and that the magnitudes vary considerably across different industries. However, while all of the comparative statics in this paper are interesting, we must not lose sight of the underlying analysis of required rates of return relative to the big picture. With a few extreme exceptions, most of the incremental rates of return are under |3%| in the first section. This is despite the fact that the authors made various assumptions that would lead to the highest possible distortions. When actual firms are analyzed, the most extreme incremental rates do not even surpass |2%|. In the real world, it is so hard to accurately measure cost of capital that these distortions essentially fall within the margin of error. Further, it is unlikely they weigh very heavily against the potential tax benefit of debt. In sum, while the evidence indicates that these agency costs exist, it is unlikely that they are affecting capital structure decisions.

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