The common stock and debt of Northern Sludge are valued at $56 million and $44 million, respectively

First, We calculate WACC:

WACC = (Weight of Equity*Cost of Equity)+(Weight of Debt*Cost of Debt)

Here,

Weight of Equity = $56 millions / ($56 millions + $44 millions) = $56 millions / $100 millions = 0.56

Cost of Equity = 16.8%

Weight of Debt = $44 millions / ($56 millions + $44 millions) = $44 millions / $100 millions = 0.44

Cost of Debt = 6.9%

WACC = (0.56*16.8%)+(0.44*6.9%)

= 0.09408 + 0.12444

WACC = 0.12444 or 12.44%

Change in capital structure do not change risk of debt.

So, firm value will not change and cost of capital shall remain same after change in capital structure.

New Equity = $20 million

So, Equity in Total = $56 million+ $20 million = $76 million

Debt retired for $20 million. So debt remaining = $44 million-$20 million = $24 million

so, Weight of debt = 24/(76+24)= 0.24

and weight of Equity is 76/(24+76)= 0.76

Assume Expected Return in Equity is x

WACC = (Weight of Equity*Cost of Equity)+(Weight of Debt*Cost of Debt)

0.12444 = (0.76*x)+(0.24*0.069)

0.12444 -(0.24*0.069) = 0.76x

0.12444 - 0.01656 = 0.76x

0.10788 = 0.76x

x = 0.10788/0.76

x = 0.14195

So, New Expected Return on Equity is 0.14195 or 14.19%