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We will first carry out a tabular comparison of the two capital structures and then do the commentary:
Debt/ Equity mix
Earnings before interest and tax
Earnings after interest
Earnings after tax (a)
Number of ordinary shares outstanding (b)
7,500,000 (see working 1 below)
Earnings per share a/b
$5 per share
$5.8 per share
Value of debt (c)
Value of equity (d)
$348,000,000(see working 3 below)
Return on equity (a/d)*100
$46.4 (see working 2 below)
Debt to equity ratio (c/d)*100
Number of ordinary share before debt issue = 10,000,000
Value of debt issued= $100,000,000
Number of shares bought back= 1000,000,000/40
So the number of shares left outstanding= 10,000,000-2,500,000
The firm's current price/ earnings ratio is 8 ($40/$5 per share). If this P/E remains the same, then the new price of the share will be 8* the new EPS, that is 8*5.8, which gives us a price of $46.4 per share.
Since we have 7.5 million shares outstanding, and the price of one share is now $46.8, the value of equity is =7,500,000*46.8
from this, it can be seen that issuing debt will certainly increase the value of the firm and improve its return on equity, but it will also increase its debt gearing levels.