The cumulative expense recognized on 31 December 2018 would be based on the increase in the fair value of the SARs from the grant date to the end of the first year of the service period. Since the SARs have a two-year service period, the expense would be recognized over this period, not upfront at the grant date like with stock options. The expense at the end of the first year would reflect the increase in fair value from the grant date to 31 December 2018.

Given the values provided, the SARs had a fair value of 800 units at the grant date and 900 units at the end of the first year (31 December 2018). The cumulative expense would be the difference in the fair value of the SARs from the grant date to 31 December 2018, which is the increase from 800 to 900.

To calculate the cumulative expense, you would multiply the number of SARs granted (500) by the increase in fair value per SAR (900 - 800 = 100) and then multiply that result by the number of executives (5) to get the total cumulative expense:

5 executives * (900 - 800) SARs * 500 SARs = 250,000 units

However, the options given do not match this calculation exactly. It seems there might be a mistake in the provided options, as none of them align with the calculated cumulative expense of 250,000. Please verify the provided answers, as the correct cumulative expense based on the information given would be 250,000.