On january 1, 2017, culver company issued 10-year, $2,140,000 face value, 6% bonds, at par. each $1,000 bond is convertible into 14 shares of culver common stock. culver’s net income in 2017 was $296,000, and its tax rate was 40%. the company had 91,000 shares of common stock outstanding throughout 2017. none of the bonds were converted in 2017. (a) compute diluted earnings per share for 2017.

a) diluted earnings per share = 0

Explanation:

Diluted earnings per share (DEPS) is a recalculation of the basic EPS. The difference between DEPS and EPS is, EPS represents the current position of earnings per share. No changes in number shares and/or earnings in the future are incorporated in the basic EPS.

Whereas DEPS is a representation of  not only the current position of earnings and shares but also includes the commitments an entity has already made whose occurrence may result in an increase/decrease in the amount of earnings and/or number of shares. For example, in the question Culver Company has issued 10-year convertible bonds which right now have no impact on basic EPS but if in the future these bond holders exercise their right of conversion, this would result in an increase in number of ordinary shares hence decreasing/diluting the basic EPS. The entities use DEPS to show shareholders the impact of such commitments on the basic EPS to improve their decision making.

So in 2017 none of the bonds were converted therefore no diluted earnings per share is calculated in 2017.

If all of the bonds were converted in 2017 the DEPS would have been calculated as follows:

The formula for calculating DEPS is as follows;

DEPS = (Net income + interest savings) ÷ number of ordinary shares + increase in ordinary shares as a result of conversion.

Tax savings as a result of conversion=$128400 ($2140000×6%). Because if bond holders convert into ordinary shares then Culver company will not have to pay them interest and hence the amount of interest is saved.

Increase in ordinary shares upon conversion= 29960 ($2140000÷$1000=2140 bonds. Each bond is convertible into 14 shares therefore, 2140×14=29960).

Now Lets calculate DEPS as follows;

DEPS = ($296000+$128400) ÷ 91000+29960

DEPS =$424400÷120960

DEPS = $3.5

i might look it up later.

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