Malkin corp. has no debt but can borrow at 8.75 percent. the firm’s wacc is currently 16 percent, and there is no corporate tax.

Response:

a.

16%

b.

17.3%

c.

23.25%

d.

16%

Clarification:

WACC represents the average cost of capital for a firm, based on the proportions of debt and equity multiplied by their respective costs.

Having the capital cost, the next step is to compute the equity cost.

Cost of Capital = (Cost of Equity x Proportion of equity) + (Cost of Debt x Proportion of Debt)

a.

No Debt

16% = (Cost of Equity x 1 ) + (8.75% x 0)

16% = Cost of Equity + 0

Cost of Equity = 16%

b.

15% Debt and 85% for Equity (100%-15%)

16% = (Cost of Equity x 85% ) + (8.75% x 15%)

0.16 = (Cost of Equity x 0.85) + 0.013125

0.16 - 0.013125 = Cost of Equity x 0.85

0.146875 = Cost of Equity x 0.85

Cost of Equity = 0.146875 / 0.85 = 0.17279

Cost of Equity = 17.3%

c.

50% Debt and 50% for Equity (100%-50%)

16% = (Cost of Equity x 50% ) + (8.75% x 50%)

0.16 = (Cost of Equity x 0.50) + 0.04375

0.16 - 0.04375 = Cost of Equity x 0.50

0.11625 = Cost of Equity x 0.50

Cost of Equity = 0.11625 / 0.50 = 0.2325

Cost of Equity = 23.25%

d.

WACC in b and c remains at 16%

Response:

A) 16%

B) 17.28%

C) 23.25%

D) with debt at 15%, WACC remains 16%

With debt at 50%, WACC remains 16%

Clarification:

WACC or weighted average cost of capital denotes the rate at which the firm effectively finances its assets.

The formula for WACC is:

WACC = {[total equity/(total debt + equity)] x cost of equity} +  {[total debt/(total debt + equity)] x cost of debt x (1 - tax rate)}

A) equity stands at 100%

WACC = cost of equity = 16%

B) The Modigliani-Miller Proposition II states that the cost of equity adjusts with an increase in debt, applying the following formula

= old cost of equity + [(old cost of equity - cost of debt)x(debt/equity)x(1 - taxes)]

Equity being 85%, debt being 15%

Cost of equity = 16% + [(16% - 8.75)x(0.15/0.85)] = 16% + 1.28% = 17.28%

C) equity being 50%, debt being 50%

Cost of equity = 16% + [(16% - 8.75)x(.5/.5)] = 16% + 7.25% = 23.25%

D) Given the absence of corporate taxes, taking on debt does not lower WACC.

Equity being 85%, debt being 15%

WACC = (0.85 x 17.28%) + (.15 x 8.75%) = 14.69% + 1.31% = 16%

Equity being 85%, debt being 15%

WACC = (0.50 x 23.25%) + (.5 x 8.75%) = 11.625% + 4.375% = 16%