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EPS problem

XY Corporation is an all equity firm with a total value of $20 million. It needs an additional capital of $5 million, which may be either equity, or debt at the interest rate of 10%. After the new capitalization, the expected EBIT is $5 million, with standard deviation of $1.5 million. The company pays income tax at 50% rate, and it has 1 million shares outstanding. What is the preferred technique of raising new capital, if the objective is to maximize the EPS? What is the probability that you are correct in your decision?

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From the given details,

Total value of the firm is $20 million which has 1 million shares and hence the share price is $20/share. When the issue of shares is involved, to raise $5 million at $20/share, the outstanding shares will increase by 0.25 million.

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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 $5 million by issuing debt at 10% interest rate.

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

((EBIT - $0.5)(1 – 0.5) – 0)/1 = ((EBIT - $0)(1 – 0.5) – 0)/1.25
1.25*(0.5 EBIT – 0.25) = 1*(0.5 EBIT)
0.625 EBIT – 0.3125 = 0.5 EBIT
0.125 EBIT = 0.3125
EBIT = $2.5 million

Hence the probability that the above decision is right is

Z = ($2.5 – 5)/1.5 = -1.667
P(z) = 95.22%

Thus the debt financing must be recommended and the probability that this is right is 95.22%.

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