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The common stock and debt of Northern Sludge are valued at $62 million and $38 million, respectively. Investors currently require a 16.8% return on the common stock and a/an 7.2% return on the debt. If Northern Sludge issues an additional $21 million of common stock and uses this money to retire debt, what happens to the expected return on the stock? Assume that the change in capital structure does not affect the interest rate on Northern’s debt and that there are no taxes.

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jepessoa

Answer:

the expected return on the stock will decrease

Explanation:

total firm's value $100 million

  • equity $68 million
  • debt $32 million

required rate of return:

  • cost of equity 16.8%
  • cost of debt 7.2%

if the firm issues new stock and retires debt:

  • equity $89 million
  • debt $11 million

The return on equity (ROE) measures how much money a company earns per dollar invested, ROE formula = net income / total equity

now let's suppose that the firm's net income is $10 million:

under the old capital structure ROE = $10 / $68 = 14.7%

now under the new capital structure net income will increase by the amount of interests saved = $21 x 7.2% = 1.512

new net income = $11.512

new ROE = $11.512 / $89 = 12.9%

following this example, the new ROE will be 12.2% lower than before because the cost of debt was much lower than the cost of equity.

as the weight of equity increases, the company's WACC will increase also:

  • old WACC = (68/100 x 16.8%) + (32/100 x 7.2%) = 11.424 + 2.304 = 13.728%
  • old WACC = (89/100 x 16.8%) + (11/100 x 7.2%) = 14.952 + 0.792 = 15.744%

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