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In order to calculate DEPS, we need to assume that the bonds had been converted at the beginning of the year and calculate what the EPS Effect would have been if this had happened. If the bonds had been converted, there would have been 20,000 additional shares outstanding during the year. There also would have been more income available to the common shareholders since interest would not have needed to be paid. The interest saved would have been $16,000 (the $200,000 face amount × the 8% bond rate - we do not care about market rate). However, if they had not paid interest, income would have been higher by $16,000, and they would have had to pay taxes on the $16,000. These taxes would have been $5,440 leaving $10,560 as available to common shareholders. Dividing this by the 20,000, we get an EPS Effect of $.528. This is less than the basic EPS so these convertible bonds are dilutive. We add the $10,560 to the net income of $107,000 and the 20,000 shares to the 80,000 outstanding and we get a new calculation of $117,560 divided by 100,000 shares, giving us a DEPS of $1.18.
This answer results from calculating the amount of interest saved from the conversion of the bonds as $16,000 × .34. The amount of interest saved is $16,000 × (1 ? .34).
This answer incorrectly uses the market rate to calculate the interest on the bonds. Because the bonds were issued at par, the company's effective annual interest rate on the bonds is the same as their nominal rate. The current market rate is not relevant, because that is not the rate the company's interest expense is based upon. Note: However, if the bonds had not been issued at par but had a premium or discount that is being amortized, the amount of interest expense would have been different from the cash interest paid. In most circumstances in the U.S., it is the interest expense including any amortization of premium or discount that is a deductible expense on a corporation's taxes, not the cash interest paid.
This answer does not increase income available for common shareholders by the saved interest (net of taxes) from the bonds that are assumed to have been converted.