Game Theory In The Costs of Financial Distress

Game Theory In The Costs of Financial Distress

Companies generate maximum shareholder value for their investors when their investment, financing, and dividend policies are optimal. In this article, i discuss the financing strategies which determine the firm’s optimal capital structure. As interest expenses on debt are tax-deductible, cash flows to equity increase when firms finance a part of their capital with debt. However, as debt is contractual and lenders can seize control of a firm in the event of default interest payments, a firm needs to have a trade-off between financial distress and tax savings. When firms experience financial distress, the equity and debt holders resort to weird behaviors, which i define as the Game theory in the costs of financial distress.

Game theory in the cost of financial distress – Effect of Financial Distress

When a firm’s cash flows go below the interest expenses needed to pay the lenders, the firm is in bankruptcy. There are many reasons firms get into this situation – macroeconomic risks, high-interest rates, COVID, and high leverage.

I categorize the cost of financial distress into direct and indirect costs. The direct costs are legal and administrative costs of bankruptcy and are pretty straightforward to understand. For a large firm like Boeing or United Airlines, the direct cost of bankruptcy does not exceed 5% of its firm value and is always below the size of debt restructuring. When you factor in the probability of bankruptcy which usually is ~10%, the expected cost of direct bankruptcy is 5%/10% = 0.5%. 

However, the indirect cost decimates the firm and prevents it from bouncing back. These costs include customers’ actions to stop doing business, suppliers demanding advance amounts, and key employees changing jobs. If a firm caters to a supplier’s demand, it needs to pay an amount upfront, for which it again has to go to lenders to raise this capital. The lenders will decline to extend the firm’s request because the firm is facing issues repaying its existing loans. Given the current distress, the firm’s WACC will increase because investors demand a higher return for the higher risk.

Due to the higher agency costs, managers will make decisions that will destroy firm value. For instance, managers will delay liquidating the firm because they want to continue getting salaries. Furthermore, since the firm’s odds of returning to normalcy are low, managers will indulge in excessive risk-taking. If they fail, the status quo will not change; however, if their risks succeed, the firm will become healthy, so there is nothing to lose for the managers to gamble.

Conflicts between Equity holders and Debt holders

Let us take an example of a firm to substantiate how the conflicts between equity and debt holders increase during financial distress.

Value of a firm = $100 million

Debt = $90 million

A firm has an opportunity to acquire a start-up for $50 million. The future value of cash flows for the start-up is zero for 66.66% of the time, and there is a 33.33% probability the start-up will generate $120 million.

Expected value of Start-up = (66.66%0+33.33%120) = $40 million

This investment’s NPV is negative for the firm because it invests $50 million and, in return, receives just $40 million. Thus, managers should reject this deal.

However, in my experience, managers will proceed forward with this deal. Let us see why.

If the deal succeeds, then value of firm = $100+$120-$50 = $170 million.

If it happens, the debt holders will get their $90 million, and equity holders will get $80 million. 

If the deal fails, then the value of firm = $100-$50= $50. The debt holders will receive $50, way less than $90 million. However, if this deal does not happen, the lenders will liquidate the firm and take the $90 million proceeds.

When we calculate the expected value of this deal for lenders and equity holders,

Expected value of Debt holders = 1/390+2/350 = $63.33

Expected value of Equity holders = 1/380+2/30 = $26.33

From lenders’ perspective, there is a high risk of not recovering their debt payments as their value of debt reduces from $90 to $63.33. However, from the equity holder’s perspective, the expected value increases from $10 to $26.33.

Thus, equity investors will incline to invest in this negative NPV investment, while debt holders will restrict the equity investors by putting covenants in their contracts. 

In the above example, the equity holders are willing to invest in negative NPV investments because they are gambling on the lender’s money. Now, let us take another example.

A firm has a value of $100 million at 50% probability, while the firm’s value declines to $10 million at 50% probability—the expected value of the firm = $55 million. Therefore, a firm has an opportunity to invest in a project with the following details:

Investment = $15 million

Discount rate = 10%

Cash flows in year1 = $22 million

NPV = -15+(22/1.1) = $5 million

As the above project is NPV positive, managers should invest in this project.

Let us assume the value of debt at the above firm = is $40 million.

For 50% time, the debt holder should recover their liabilities, while for the remaining 50%, the debt holder will recover $10 million and lose $40 million.

At Status Quo

The expected value for debt holders = $40 million

The expected value for equity investors = $10 million

After Investment

The expected value for debt holders = 50%40+50%30 = $35 million

The expected value for equity holders = 50%80 + 50%0 = $40 million

The equity investors would gamble and invest in this project if the financing for this project comes from debt. However, they will not issue new equity to fund this project. The equity investor will think that if they invest and the project succeeds, they gain $30 million, but the debt holders get their $40 million without investing any amount. However, in 50% time, the expected value for equity is 0, but the debt holders will receive $35 million and lose only $5 million.

Thus, the debt holders will agree to this project if the investment gets funded with equity, and they stand to lose a little. This failure to invest in a positive NPV project by equity and debt investors is the indirect cost of financial distress. Shareholders of a highly levered firm facing financial distress will refuse to fund positive NPV investments with equity because most investment benefits will go to lenders. However, if the financing for the investment comes from lenders, they are willing to gamble because they stand to lose nothing.

Solution To This Conflict

The optimum solution to address this issue is to determine the optimal funding structure for this investment which is the outcome of negotiations between lenders and the firm’s management. Firms hire legal counsels and investment bankers to help in restructuring their debt. If the debt for the new investment has higher seniority than existing debt, the firm has a higher chance to refinance the debt as it will find new borrowers. However, existing lenders will object by drafting covenants that prohibit firms from going to a lender to issue debt with higher seniority. 

The firm will often restructure its existing debt by guaranteeing existing debt holders $1 of $5 NPV investment. The shareholders will receive the remaining $4. Thus, after restructuring, the debt holders will get 50%40+50%10+1=$26, and equity holders will get 50%64+50%4 = $34.

However, we need to account for the cost of restructuring, i.e., the payment to lawyers for arriving at restructuring.

My Final Insights

Equity/debt holders resort to game theory in the costs of financial distress at high financial distress. Thus, a firm needs to get proactive by reducing leverage or actively managing leverage by having its debt to equity ratio at a level where tax shields from debt equal the increase in expected costs of financial distress. In my view, this level is the firm’s optimal capital structure. 

Firms with volatile cash flows having high business risk should not go for high leverage to allow for financial flexibility. Thus, software and pharma companies have low leverage compared with regulated monopolies like the utility industry.


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