Question

Currently, ABC Corp. has as market capitalization of $400 million and a market value of debt of $150 million. The current cost of equity for ABC Corp. is 12% and its current cost of debt is 5%. Assume perfect capital markets (no taxes, no market frictions). You are trying to assess how different transaction would affect the cost of equity.

A) Suppose ABC issues $150 million of new equity and buys back the debt it currently has outstanding. What is ABC’s cost of equity after this transaction?

B) Suppose ABC issues an additional $150 million of new debt and pays its shareholders a dividend (so total debt after this transaction is $300mn). Assuming its cost of debt remains at 5%, what is ABC’s cost of equity after this transaction?

Answer 1

(A)

The repurchase of debts will result in no debts in the company and this will make the company an unlevered company. In this, the cost of equity is equivalent to the weighted average cost of capital (WACC) of the levered firm.

Compute the total capital of the company, using the equation as shown below:

Total capital = Debt capital + Equity capital

                     = $150 million + $400 million

                     = $550 million

Hence, the total capital of the company is $550 million.

Compute the cost of equity after the transaction, using the equation as shown below:

Cost of equity = (Equity capital *Cost of equity before transaction/Total capital) + {(Debt capital/ Total capital)*Cost of debt}

                         = ($400 million*12%/ $550 million) + {($150 million/ $550 million)*5%}

                         = 8.72727% + 1.36364%

                         = 10.09091%

Hence, the cost of equity after transaction is 10.09091%.

(B)

Compute the cost of equity after the transaction, using the equation as shown below:

Cost of equity = Overall cost of capital + {(Overall cost – Cost of debt)*Debt/Equity}

                        = 10.09091% + {(10.09091% - 5%)*$300 million/ $400 million}

                        = 10.09091% + 3.81818%

                        = 13.90909%

Hence, the cost of equity is 13.90909%