Question

The common stock and debt of Northern Sludge are valued at $64 million and $51 million, respectively. Investors currently require a 13% return on the common stock and an 5% return on the debt. If Northern Sludge issues an additional $10 million of common stock and uses this money to retire debt, what is the new expected return on the stock? Assume that the change in capital structure does not affect the risk of the debt and that there are no taxes. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Expected stock return

Answer 1

Solution

• Due to issuance of additional $10 million of common stock, the common stock will increase and the issuance will help in retire the debts of $ 10 million, thereby reducing the debts to $41 million ( $ 51 million minus $ 10 Million).
• The required return shall be the cost of the common stock and debts.

The Determination of New expected return of stock can be computed as follows:

Step 1: Computation of Existing Weighted Average Cost of Capital ( WACC)

Source of Finance (a)	Amount ( In $ million ) (b)	Weights (c) (Note 1)	Cost (d) ( Note 2)	Weighted Cost (e) = (c) * (d)
Common Stock	64	0.5565	13%	7.2345
Debts	51	0.4435	5%	2.2175
Total Capital	115	1		9.452

WACC = 9.45%

Note:

1) Weights in (C) = Amount of each sources of finance / total amount of finance

Common Stock Weights = 64/115 = 0.5565

Debts = 51/115= 0.4435

2) Common Stock Cost can be denoted as K_c and Debt Cost can be denoted as K_d

Now, according to question K_{c =} 13% and K_d =5%

Step 2

From the above table we can say or derive the formula , WACC = Weight of Common Stock * Cost of Common Stock + Weight of Debts * Cost of Debts.

In The given sources of finance, the net effect on changes in capital is nil, as issuance of common stock, money is utilised for retiring debts of that amount. The only thing which changes is the proportion of capital compostion,

Now, Common Stock is 74/115 = 0.6434 and the Debts is 41/115 = 0.3566

Therfore change in capital structure does not effect the risk of debts, so the cost of debts will remain 5% , WACC will remain same which is 9.45 %,

Based on the above datas, we can easily interpolate the cost of equity / rate of return.

Hence, we can say by the formula of WACC in Step 2, will be used,

9.45% = 0.6434* K_e +0.3566 * 5%

$\equiv$ 9.45 % = 0.6434K_e + 1.783 %

$\equiv$ 9.45% - 1.783% = 0.6434 K_e

$\equiv$ 7.67 % = 0.6434K_e

$\equiv$7.67% / 0.6434 = K_e

$\equiv$ 11.92 % = K_e

Hence, we can say cost of equity is 11.92 %

Therfore the New expected Return is 11.92 %