The MM Theorem: Does Capital Structure Change Value?

Suppose a firm earns 150 every year. It could be funded entirely with equity, or with a mix of debt and equity.

Without tax, the two firms are worth the same. More debt does not move the value. The formula below is that claim. With tax, debt interest lowers the tax bill. Value rises by exactly that benefit. Move debt and watch the two lines pull apart.

For example, imagine two friends opening identical snack bars. One funds it with her own money, the other borrows from a bank. Without tax, the two shops are worth the same: borrowed money does not make a shop more valuable. With tax, the borrower pays less tax thanks to interest, and the shop is worth more by that amount.

Source: Modigliani, F., and Miller, M. H. (1958). The Cost of Capital, Corporation Finance and the Theory of Investment. American Economic Review, 48(3), 261-297. The with-tax formula is from Modigliani, F., and Miller, M. H. (1963). Corporate Income Taxes and the Cost of Capital: A Correction. American Economic Review, 53(3), 433-443.

VL=VUV_L = V_U
VL=VU+TcDV_L = V_U + T_c D

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Examples & Exercises

Compute

A firm earns EBIT=150EBIT = 150 every year forever. The required return is 10%10\% and the corporate tax rate is 25%25\%. With debt of 300300, find firm value in the world with tax.

A firm with EBIT 150150, tax rate 25%25\%, debt 300300
Show proof

  1. Unlevered value is after-tax earnings over the required return: VU=150×(1−0.25)/0.10=1125V_U = 150 \times (1 - 0.25) / 0.10 = 1125.

  2. The tax shield is TcD=0.25×300=75T_c D = 0.25 \times 300 = 75.

  3. Therefore VL=1125+75=1200V_L = 1125 + 75 = 1200.

Answer

12001200

2. Corporate Theories