Levered, Inc., and Unlevered, Inc., are identical in every way except their capi

Question

Levered, Inc., and Unlevered, Inc., are identical in every way except their capital structures. Each company expects to earn $28.2 million before interest per year in perpetuity, with each company distributing all its earnings as dividends. Levered’s perpetual debt has a market value of $83 million and costs 8 percent per year. Levered has 1.5 million shares outstanding, currently worth $123 per share. Unlevered has no debt and 3.7 million shares outstanding, currently worth $71 per share. Neither firm pays taxes.

What is the value of each firm?

Explanation / Answer

As the Unlevered is an all-equity firm, its value is equal to the market value of its outstanding shares. It has 3.7 million shares outstanding @ $71 per share.

Hence, the value of Unlevered firm is $262.7 million (3.7 million shares * $71 per share).

According to Modigliani-Miller Proposition I, in the absence of taxes, the value of a levered firm equals the value of an otherwise identical unlevered firm.

As Levered is similar to Unlevered in every way but for its capital structure and both pay no taxes, their values should be equal.

Modigliani-Miller Proposition I (No Taxes):       VL =VU

Therefore, the market value of Levered, Inc. would be $262.7 million.

Since Levered has 1.5 million shares, worth $123 per share, the market value of Levered’s equity is $184.5 million. The market value of its debt is given as $83 million.

Therefore, the current market value of Levered, Inc. is:                          

                            VL     = B + S

                                    = $184.5 million + $83 million = $267.5 million.

As the sum of the market values of equity and debt of the levered firm is $267.5 million as against the value of $262.7 million propounded by MM I proposition, it means that the levered firm is overvalued and unlevered undervalued. Arbitrage would set in as rational investors would buy the unlevered's stock.

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