Question

ONLY NEED QUESTION F!!!

The Ex Nihilo Corporation has a debt-equity ratio of 0.5. Details of the balance sheet are given in Table 3.

Table 3: Ex Nihilo Co’s balance sheet (market values, numbers in millions)

Assets Liabilities

Fixed Investments £18,000

Debt ? Equity ?

The beta of Ex Nihilo Co’s fixed investments is 1.5. The risk-free rate is 3% and the average return on the market index is 7%.

a. What is Ex Nihilo Co’s weighted average cost of capital (WACC)?

b. What are the values of Ex Nihilo Co’s debt and equity?

c. Ex Nihilo Co’s cost of borrowing is 3.5%. What is Ex Nihilo Co’s cost of equity capital?

d. Assuming that Modigliani-Miller irrelevance of borrowing policy holds, what would the cost of Ex Nihilo Co’s equity be if the debt-equity ratio increases to 1.0? You should assume that the increase in borrowing increases the cost of borrowing to 3.6%.

e. Explain the trade-off theory of borrowing.

f. Assume that the debt-equity ratio of Ex Nihilo Co has been raised to 1.0. Modigliani-Miller irrelevance of borrowing does not hold, so the increase in borrowing will increase both the PV of the corporate tax shield of borrowing and the PV of the expected bankruptcy costs. The PV of the tax shield is £0.6bn and the PV of the bankruptcy costs is £0.1bn. The cost of debt capital is 3.6%. Assuming that both the PV of the tax shield and the PV of the bankruptcy costs have a beta of 1.5, what is the new WACC and the new cost of equity capital?

Answer 1

f. Modigliani-Miller irrelevance of borrowing does not hold and hence the increase in borrowing increases both the PV of the corporate tax shield of borrowing and the PV of the expected bankruptcy costs.

PV of the tax shield = £0.6bn or £600 Million

PV of the bankruptcy costs = £0.1bn or £100 Million

Cost of debt capital is 3.6%.

PV of the tax shield and the PV of the bankruptcy costs beta = 1.5

a. Cost of equity:

Beta of fixed investments = 1.5

Beta of fixed investments (unlevered beta) = Equity beta/(1+(1-tax rate)(debt/equity)

Thus, Equity Beta = Unlevered beta*(1+(1-tax rate)(debt/equity)

=1.5*(1+(1-0%)*1) (tax rate not given, hence taken as zero %)

=3

Thus, cost of equity = Risk free rate + (beta of equity (market rate - risk free rate))

= 3%+(3*(7%-3%) = 3%+(3*4%) = 15%

b. Weighted average cost of capital

Fixed Investment (Total Assets) = £18,000 Million

Revised Fixed Investment = £18,000 + £600 - £100 = £18,500 (PV of Interest tax - PV of bankrupty costs)

Thus, Equity + Debt = £18,500

Let Equity be X

Debt/Equity = 1 or 1X

Thus, equity = X+1X = £18,500

2X=£18,500

X=£18,500/2=£9,250

Debt = £9,250

Computation of Weighted Average cost of capital:

Weighted Average Cost of Capital (WACC) = (Cost of Equity * Equity/Total Capital) + (Cost of Debt * Debt/Total Capital)

= (15%*£9,250/£18,500)+(3.6%*£9,250/£18,500) = 7.5%+1.8% = 9.3%