Interest is paid annually 31 december the net

• Interest is paid annually 31 December.
• The net proceeds from the bond issue amounted to $41 million. The present value of the liability cash flow at the date
of issue was $32.3 million; the remaining $8.7 million was allocated to the conversion option. At the date of issuance,
the market rate of interest for nonconvertible bonds of similar risk was 9%.
• On 30 June 20X1, one-quarter of the bonds are converted.
• The corporation’s income tax rate is 25%.
Based on the convertible bond amortization schedule below, the interest expense (using an effective interest rate of 9%)
in year 6 on the bonds is $3,179,918.
Date Interest Paid Interest Expense Amortization Principal
32,298,811
Year 1 2,400,000 2,906,893 506,893 32,805,704
Year 2 2,400,000 2,952,513 552,513 33,358,217

Date Interest Paid Interest Expense Amortization Principal
Year 3 2,400,000 3,002,240 602,240 33,960,457
Year 4 2,400,000 3,056,441 656,441 34,616,898
Year 5 2,400,000 3,115,521 715,521 35,332,419
Year 6 2,400,000 3,179,918 779,918 36,112,337
Year 7 2,400,000 3,250,110 850,110 36,962,447
Year 8 2,400,000 3,326,620 926,620 37,889,067
Year 9 2,400,000 3,410,016 1,010,016 38,899,083
Year 10 2,400,000 3,500,917 1,100,917 40,000,000
The conversion of $10,000,000 principal amount of bonds results in an additional 20,000 shares issued. In the basic EPS
calculation, the additional shares are outstanding for the second half of the year and are weighted proportionately in the
denominator. On conversion, the amount of interest for year 6 would have been (based on the above schedule):
1 January to 30 June: $3,179,918 × 6/12 × 40/40 = $1,589,959
1 July to 31 December: $3,179,918 × 6/12 × 30/40 = $1,192,469
Total interest expense $2,782,428
The EPS numerator already includes, in earnings, a deduction for (pretax) interest of $1,589,959 on $40,000,000 for the
first half of the year. After the conversion, the interest for the second half of the year will be an interest expense of
$1,192,469 ($1,589,959 × 30/40) on the remaining $30,000,000 for the second half of the year following conversion. The
calculation of basic EPS is shown at the top of Exhibit 20-6.
EXHIBIT 20-­‐6
BASIC AND DILUTED EPS CALCULATIONS

To calculate diluted EPS, the conversion must be backdated to the beginning of the year (step 6). The effect of the
remaining unconverted bonds must be included (step 9). Both of these adjustments are made only if dilutive .
For backdating, the EPS numerator must be reduced by the six months’ interest actually expensed on the $10,000,000
principal amount of converted bonds. At a 25% income tax rate, the first six-months’ interest on the converted bonds was:
Interest expense after-tax = 1,589,959 × 10/40 × (1.00 − .25) = 298,117
In general, the formula for computing the interest savings from conversion is:
Interest expense for the period × fraction of year before conversion × (1 – tax rate)
For example, if the bonds had been retired after four months of the fiscal year, four months of interest would be added
back.
The highlighted section of Exhibit 20-6 shows the add-back of $298,117 after-tax interest expense, and the weighted-
average number of shares is increased to reflect the full amount of shares issued on conversion. Shares are calculated as
20,000 shares × 6/12. The EPS individual effect is $29.81 (i.e., $298,117 ÷ 10,000), which is dilutive, relative to basic EPS
of $50.