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Sinking Fund problem

Berks Corporation is expecting to have EBIT next year of $12 million, with a standard deviation of $6 million. Berks have $30 million in bonds with coupon of 10%, selling at par, which are being retired at the rate of $2 million annually. Berks also have 100,000 shares of preferred stock, which pays annual dividend of $5 per share. The tax rate of Berks is 40%. Calculate the probability that Berks will not be able to pay interest, sinking fund, and favored dividends, out of its current income, next year.

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From the given details,

Sinking fund requirement = $2 million/(1 – 0.4) = $3.33 million
Interest payment requirement = $30*10% = $3 million
Preferred dividend to be paid = 100,000*$5 = $500,000 = $0.5 million
Preferred dividend requirement = $0.5 million/(1 – 0.4) = 0.833 million
Total requirement = $7.167 million

In order to determine the probability,

Z = (7.167 – 12)/6 = -0.8056
P(z) = 78.97%

This is the probability that Berks will be able to make more than its requirements. Hence the probability that Berks will not be able to pay interest, sinking fund and preferred dividends out of its current income next year is 21.03%

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