Using the Modigliani-Miller (MM) theory in a perfect market, you want to evaluate a project and how to finance it. The project has free cash flows in one year of $90 in a weak economy or $120 in a strong economy. There is 75% chance that the economy is strong. The initial investment required for the project is $80, and the project’s cost of capital is 10%. The risk-free interest rate is 5%. Suppose that to raise the funds for the initial investment, the project is sold to investors as an all-equity firm. The lowest possible realized return of the unlevered equity is closest to:
| A. | The cost of the levered equity is 56.32% and the cost of capital is 15.00%
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| B. | The cost of the levered equity is 27.96% and the cost of capital is 15.00%
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| C. | The cost of the levered equity is 27.96% and the cost of capital is 10.00%
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| D. | The cost of the levered equity is 56.32% and the cost of capital is 10.00%
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The Modigliani-Miller (MM) theory, a fundamental concept in corporate finance, provides insights into how the value of a firm is unaffected by its capital structure under certain idealized conditions. In a perfect market with no taxes, transaction costs, or information asymmetry, the MM theory asserts that the value of a firm is determined solely by its underlying assets and the cash flows they generate. In this context, let’s analyze the evaluation of a project’s financing using the MM theory and determine the lowest possible realized return of the unlevered equity.
We have a project with two possible outcomes in terms of free cash flows: $90 in a weak economy and $120 in a strong economy. The probability of a strong economy is 75%, and the initial investment required for the project is $80. The project’s cost of capital is 10%, and the risk-free interest rate is 5%. The project is financed through an all-equity firm, meaning that it’s sold to investors without any debt.
Option A
The cost of the levered equity is 56.32% and the cost of capital is 15.00% Option B: The cost of the levered equity is 27.96% and the cost of capital is 15.00% Option C: The cost of the levered equity is 27.96% and the cost of capital is 10.00% Option D: The cost of the levered equity is 56.32% and the cost of capital is 10.00%
To determine the lowest possible realized return of the unlevered equity, we need to consider the MM theory and the principles it offers. According to MM theory, the capital structure does not impact the overall value of the firm when certain assumptions are met. Since the project is financed entirely through equity, the cost of capital for the firm should be equal to the cost of equity.
Given that the cost of capital for the project is 10% and the risk-free rate is 5%, we know that the equity risk premium is 10% – 5% = 5%. Now, considering the probabilities of a strong and weak economy, we can calculate the expected return on equity for the project.
Expected Return = (Probability of Strong Economy * Return in Strong Economy) + (Probability of Weak Economy * Return in Weak Economy) Expected Return = (0.75 * 120 / 80) + (0.25 * 90 / 80) Expected Return = 1.125 + 0.28125 Expected Return = 1.40625
The expected return on equity for the project is 1.40625 times the initial investment, or approximately 40.625%.
Based on the calculations and the principles of the Modigliani-Miller theory in a perfect market, the closest option to the lowest possible realized return of the unlevered equity is Option B: The cost of the levered equity is 27.96% and the cost of capital is 15.00%. This conclusion aligns with the notion that in a perfect market, the capital structure doesn’t impact the value of the firm, and thus, the cost of capital should equal the cost of equity for an all-equity financed project.
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