Corporate Tax Shields

EXERCISE 02

Rai and Mediaset are hypothetical firms with identical operating risk and perpetual annual EBIT of €500 million. Rai has no debt. Mediaset has permanent debt of €1,500 million at 3.75%, valued at par. The unlevered cost of capital is 9% and corporate tax is 30%. There are no personal taxes or distress costs; assume full interest deductibility and stationary operations with no net reinvestment. All monetary amounts are in € millions.

A.Find both firm values and Mediaset’s equity value.
B.Find Mediaset’s required equity return.
C.Calculate each firm’s WACC.
D.Reduce corporate tax to 27.5%, holding the other inputs fixed. Recalculate both firm values and explain the changes.

A.

V_U=\frac{EBIT(1-T_c)}{r_U},\qquad V_L=V_U+T_cD

V_{Rai}=\frac{500(0.70)}{0.09}\approx3{,}888.89

V_{Mediaset}=\frac{350}{0.09}+0.30(1{,}500)\approx4{,}338.89

E_{Mediaset}=4{,}338.888889-1{,}500

Mediaset equity = €2,838.89 million.

B.

r_E=r_U+(r_U-r_D)(1-T_c)\frac{D}{E}

r_E=9\%+(9\%-3.75\%)(0.70)\frac{1{,}500}{2{,}838.888889}

Mediaset cost of equity = 10.941781%.

C.

WACC=r_U\left(1-T_c\frac{D}{V_L}\right)

WACC_{Rai}=9\%

WACC_{Mediaset}=9\%\left(1-\frac{450}{4{,}338.888889}\right)

Mediaset’s after-tax WACC is 8.066581%. The debt tax shield lowers WACC; its equity return remains above Rai’s.

D.

V_{Rai}^{\prime}=\frac{500(0.725)}{0.09}\approx4{,}027.78

V_{Mediaset}^{\prime}=\frac{362.5}{0.09}+0.275(1{,}500)\approx4{,}440.28

\Delta V_{Rai}=\frac{500(0.025)}{0.09}\approx138.89

\Delta V_{Mediaset}=\frac{500(0.025)}{0.09}-0.025(1{,}500)\approx101.39

Both firms gain value because operating income is taxed less. Mediaset gains €37.50 million less because its interest tax shield falls from €450.00 million to €412.50 million. Keep EBIT, debt and the unlevered required return unchanged.