Question

tax rate is 40%

1. Firm X is solely financed by $1 million equity at cost of 10% X wants to raise $0.6 million debt at cost of 4% and use all of it to buy back outstanding equity. a) In a perfect capital market, what will be its new firm value V, WACC and cost of levered equity ry after the buyback? b) In a capital market with corporate taxes, what will be its new firm value V.. WACC and cost of levered equity Tg after the buyback?

Answer 1

1a) Since we're operating in perfect capital markets, value of an unlevered firm shall be the same as the value of a levered firm. The value of the new firm shall become:
V_L = Value of debt + Value of equity = $1million - $0.6million + $0.6million = $1million.

R_E shall be given by:
R_E = R₀ + D/E * (R₀ - R_D),
where R_E is the cost of levered equity,
R₀ is the cost of unlevered equity,
R_D is the cost of debt,
D = Amount of debt
E = Amount of equity

Hence, R_E = 10% + (0.6/0.4)*(10% - 4%)
= 19%

WACC = W_D * R_D + W_E + R_E,

where W_D = Weight of debt = Total debt/Firm value,
W_E = Weight of equity = Total equity/firm value

WACC = 0.6*4% + 0.4*19% = 10%

b) When taxes are introduced, V_L = Value of unlevered firm + Tax rate * Value of debt,
This is because of the tax savings accrued because debts receive tax exemptions.

Since the tax rate has not been given, let us assume that it is 40%

V_L = $1million + 40%*$0.6million = $1.24million

R_E shall be given by:
R_E = R₀ + D/E * (R₀ - R_D) * (1-Tax rate)

where R_E is the cost of levered equity,
R₀ is the cost of unlevered equity,
R_D is the cost of debt,
D = Amount of debt
E = Amount of equity

Since the tax rate has not been given, let us assume that it is 40%

Hence, R_E = 10% + (0.6/0.4)*(10% - 4%) * (1-0.4) = 15.4%

WACC = W_D * R_D + W_E + R_E,

where W_D = Weight of debt = Total debt/Firm value,
W_E = Weight of equity = Total equity/firm value
R_D = After tax cost of debt

WACC = 0.6*4%*(1-0.4) + 0.4*15.4% = 7.6%