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Problem on raising new capital

AB Corporation has 3 million shares of common stock selling at $19 each. It also contains $25 million in bonds with coupon rate of 8%, selling at par. AB requires $10 million in new capital that it can raise by selling stock at $18, or bonds at 9% interest. The expected EBIT subsequent to the new capitalization is $6 million, with a standard deviation of $3 million. Determine the preferred method of raising new capital? What is the probability that you are correct?

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From the given details,

When the issue of shares is involved, to raise $10 million at $18/share, the outstanding shares will increase by 0.56 million.

As a result, the earnings available to common shareholders are higher under common stock alternative than they are under the debt alternative. Hence the financing method must be to raise $10 million by selling shares at $18 per share.

In order to determine the probability that this decision is right, we need the indifference point between the two alternatives.

((EBIT - $2900)(1 – 0.4) – 0)/3000 = ((EBIT - $2000)(1 – 0.4) – 0)/3555.56
3555.56*(0.6 EBIT – 1740) = 3000*(0.6 EBIT – 1200)
2133.33 EBIT – 6,186,667 = 1800 EBIT – 3,600,000
333.333 EBIT = 2,586,667
EBIT = $7,760 (in thousands)

Hence the probability that the above decision is right is

Z = ($7760 – 6000)/3000 = 0.5867
P(z) = 72.13%

Thus the equity financing must be recommended and the probability that this is right is 72.13%.

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