Question

1. A firm is solely financed by equity with market value of $50,000 and cost of equity of 10%. It wishes to raise another $50,000 via corporate bonds with cost of debt of 5% and keep it as cash. Hold investment policies fixed.
   1. In a MM world without taxes,
      1. What would the firm value be after debt issuance in a? Firm Value = Equity Value + Debt Value – Cash.
      2. What would be the cost of equity after debt is raised?
      3. What would be the WACC after debt is raised?
   2. In a MM world with taxes of 40%,
      1. What would be the cost of equity after debt is raised?
      2. What would be the additional value created by debt?
      3. What would be the WACC after debt is raised?

Answer 1

a. In a MM world without taxes
i
Firm Value = Equity Value + Debt Value – Cash.
Firm Value = 50,000+50,000-50000 = 50,000
ii
As there is no debt initially, the cost of equity and WACC is same i.e. 10%
To calculate new cost of equity
ke = WACC + (WACC − kd) × D /E
10%+(10%-5%)*(50000/50000) = 15%
ke = 15%
iii
WACC = kd × D/V + ke × E/V
(5%*(50000/100000))+(15%*(50000/100000)) = 10%
WACC = 10%
b. In a MM world with taxes of 40%
i
As there is no debt initially, the cost of equity and WACC is same i.e. 10%
ke = WACC + (WACC − kd) × (1 − t) × D/E
10%+(10%-5%)*(1-40%)*(50000/50000) = 13%
ke = 13%
ii
Value of levered firm = Value of unlevered firm + (tax rate × Debt value)
50,000+(40%*50,000) = 70,000
Additional value = Value of firm with taxes - Value of firm without taxes
70,000 - 50,000 = 20,000
So the additional value created by debt is 20,000
iii
WACC = ke × E/V + kd × (1 - t) × D/V
(13%*(50000/100000))+(5%*(1-40%)*(50000/100000)) = 8.00%
WACC = 8%
ke = cost of equity
kd = cost of debt
E = Equity value
D = Debt value
V = Debt + Equity