## Diluted EPS — Hidden Adjustment Technique
When the exam question gives you the interest expense for the year (not the coupon rate applied to face value for the full year), you may need to back-calculate the period for which the debentures were outstanding.
### The Hidden Adjustment
Why this arises: A company may have issued convertible debentures mid-year. The income statement shows only the actual interest charged — not the full-year figure.
How to detect it:
1. Calculate what the full-year interest would be: Face Value × Coupon Rate × 12/12
2. Compare with the interest expense actually given in the question.
3. The ratio gives you the number of months the debs were outstanding.
$$\text{Months outstanding} = \frac{\text{Actual interest expense given}}{\text{Full-year interest}} \times 12$$
### Applying the Time Weight
Once you know the debentures were outstanding for n months:
| Adjustment | Formula |
|---|---|
| Numerator (savings net of tax) | Actual interest expense × (1 − Tax Rate) |
| Denominator (potential shares) | Total conversion shares × n/12 |
> Shortcut: You can directly use the actual interest expense × (1 − tax rate) for the numerator — no need to recalculate the months separately for the numerator, because the given interest expense already reflects the partial period.