Question

company D is currently an unlevered firm. the company expects to generate $200 milllion of operating profits in perpetuity. the firm is considering a capital restructuring to have $500 million of debt. its cost of debt is 6%. unlevered firms in the same industry have cost of equity capital of 12%. the corporate tax rate is 30%. a. what is the value of company D before capital restructuring? b. what will be the value of company D after capital restructuring? c. what will be the WACC of company D after capital restructuring?

Answer 1

Following information is given in the question for company D:

1. Perpetual operating profits is $200,000,000
2. Debt amount is $500,000,000
3. Before tax cost of debt is 6%
4. Cost of equity capital (Ke) of unlevered firms in same industry is 12%
5. Tax rate is 30% or 0.30 in decimal

Value of company D before capital restructuring can be calculated by using cost of equity capital of unlevered firms in same industry as company D is in, since company D is also an unlevered firm before capital restructuring.

Value of company D before capital restructuring can be calculated as below:

Value of company D = Operating profits / Cost of capital

Where –

Operating profits is $200,000,000 annually up to perpetuity

Cost of capital is the cost of equity capital of 12% or 0.12 (as it is the only capital)

Value of company D = Operating profits / cost of capital

Value of company D = $200,000,000 / 0.12

Value of company D = $1,666,666,666.66

Hence the value of company D or value of Equity is $1,666,666,666.66

Value of company D after capital restructuring can be only calculated using the weighted average cost of capital (WACC) since the firm has taken a debt of $500,000,000 to restructure its capital.

Weighted Average Cost of Capital (WACC) = [Cost of Equity (Ke) * Weight of Equity (We)] + [Cost of Debt (Kd) * Weight of Debt (Wd)]

Where –

• Ke is the cost of equity capital in the same industry as considered above of 12% shall also be considered here since equity structure has not changed
• Kd is the after tax cost of debt

Kd = Before tax cost of debt ( 1 – Tax rate )

Kd = 6 (1 – 0.30)

Kd = 6 * 0.70

Kd = 4.2 or 4.2%

• Wd is the weight of debt

Wd = Debt / (Debt + Equity)

Wd = $500,000,000 / ($500,000,000 + $1,666,666,666.66)

Wd = $500,000,000 / $2,166,666,666.66

Wd = 0.23

• We is the weight of equity

We = Equity / (Debt + Equity)

We = $1,666,666,666.66 / ($500,000,000 + $1,666,666,666.66)

We = $1,666,666,666.66 / $2,166,666,666.66

We = 0.77

WACC = (Ke * We) + (Kd * Wd)

WACC = (12 * 0.77) + (4.2 * 0.23)

WACC = 9.24 + 0.97

WACC = 10.21 or 10.21%

Value of company D after capital restructuring can be only calculated as below:

Value of company D = Operating profits / Cost of capital (WACC)

Where –

Operating profits is $200,000,000 annually up to perpetuity

Cost of capital is the weighted average cost of capital of 10.21% or 0.1021 (as calculated above)

Value of company D = Operating profits / WACC

Value of company D = $200,000,000 / 0.1021

Value of company D = $1,958,863,858.96