Nobel Prize Ideas: Capital Structure With State Prices Fal

Nobel Prize Ideas †Capital Structure with State Prices Fall 2020 Stuffit

Stuffit Corp. is a company with net present value (NPV) in good, medium, and bad states of $500 million, $250 million, and $50 million, respectively. The firm has $60 million (face value) of perpetual debt issued many years ago. The debt pays a 2.625% annual coupon rate and currently has a market value of $53.10 million. The long-term risk-free rate is 2.5% per year. The firm has 1 million shares outstanding at a current stock price of $164.72 per share. The corporate tax rate is 20%, and bankruptcy costs equal to 40% of the pre-tax asset NPVs in bankruptcy states.

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In analyzing Stuffit Corp., we explore its capital structure using state prices, assess the impact of proposed leverage recapitalizations, evaluate the creation of shareholder value, and examine strategic projects from a financial perspective. This comprehensive approach considers the firm's existing obligations, market valuations, debt covenants, and the potential for value creation through leverage and strategic reorganization.

Determining State Prices Consistent with Market Valuations

To identify the state prices, we need to relate the current market valuation of the firm to its possible future states in a no-arbitrage framework. The current value of the firm is the sum of the values of its equity and debt, which can be expressed as weighted averages of the payoffs in the good, medium, and bad states, discounted appropriately. The state prices are the prices of each state that satisfy these valuations.

Based on the provided data, the firm's total enterprise value (EV) comprises the value of its debt and equity, amounting to roughly the sum of debt market value and equity market value. The debt's market value of $53.10 million and the stock's total value of 1 million shares at $164.72 per share, totaling approximately $164.72 million, gives an enterprise value around $217.82 million.

Using the optional payoffs (NPV in each state) and current valuations, the state prices can be calculated by solving a system of equations matching the discounted expected payoffs to observed market prices, considering the risk-free rate and bankruptcy costs. These state prices are crucial for further valuation and analysis of leverage impacts.

Impact of Leveraged Recapitalization

Required Credit Spread on New Debt

The firm considers issuing an additional $105 million debt to buy back stock. Since the existing debt's market value is $53.10 million with a coupon rate of 2.625%, the new debt must reflect a higher risk premium to compensate for increased leverage. By comparing the yields and credit spreads on existing debt, and considering market conditions, the required credit spread is derived to ensure the firm's debt remains attractive to investors. This spread accounts for the expected default risk given the new leverage level and subordinated status of the new debt.

Number of Shares Repurchased and Pricing

The firm aims to buy back shares using the $105 million raised. At the current market price of $164.72 per share, the number of shares repurchased is approximately 638,.5 shares, calculated as $105 million divided by the share price. Alternatively, if the firm targets a specific buyback size, it may adjust the repurchase price accordingly, considering market impacts and potential price effects of large buybacks.

Shareholder Value Creation from Leverage

The valuation impact of leverage depends on the change in the firm's equity value after recapitalization. By decomposing the firm's total value into components attributable to the existing assets, debt structure, and tax benefits, we can quantify the value added for shareholders. Specifically, debt provides a tax shield, increasing firm value, but also introduces default risk, which must be considered in net valuation changes. The potential increase in shareholder value via leverage is essentially the present value of the tax shield minus the costs of increased bankruptcy risk.

Alternative Recapitalization with Debt Buyout

Maria Sardelli finds that large leverage recapitalizations are blocked by covenants unless existing bonds are retired. The firm considers buying back all existing debt at a premium of 5% (i.e., $63 million payable to bondholders), then raising $168 million to retire this debt and repurchase shares. This scenario involves assessing the new debt's credit spread, valuation effects, and incremental value creation.

Assuming the firm issues new debt of $168 million to retire $63 million of existing bonds at $66.15 million (face value plus 5% premium), the new credit spread is again estimated based on market conditions, default probabilities, and the firm's risk profile post-recapitalization.

Evaluating the shareholder value now considers the net effect of retiring debt at a premium, the reduction in bankruptcy risk, and the impact of share repurchases. The value added to shareholders reflects the tax shield benefits and potential adjustments for issuance costs and call premiums. If the net effect is positive and outweighs costs, the recapitalization can be considered value-creating.

Inclusion of Issuance Costs and Further Analysis

Factoring in the $7 million fee for structuring the new recapitalization alters the cost-benefit analysis. The incremental costs reduce the net benefit from the recapitalization, possibly rendering it neutral or negative in terms of value creation, depending on the magnitude of benefits versus costs.

Assessment of New Business Project

Finally, considering a transformative project with NPVs across states of (350, â€240, â€40), the firm evaluates whether the project adds value. Even after accounting for bankruptcy costs (40% in distress states), the NPV calculation shows whether the project is worthwhile. The project's positive NPVs in good and medium states suggest it would create value, assuming the adjusted NPVs reflect realistic risk considerations.

In sum, the firm's strategic financial decisions revolve around balancing leverage, debt structure, transaction costs, and strategic projects to optimize shareholder value. Careful valuation through state prices, risk assessment, and cost-benefit analyses underpin these complex financial maneuvers.

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