For cars registered after 1/11/2010 the circulation tax is based on emissions. The official emission figure for a Toyota Yaris 1.4 Diesel is 104 g/km. The charge for cars with emissions in the range 101 to 120 g/km is €0.98 /g/km so for the Yaris it would be €101.92.
For cars registered before 1/11/2010 the circulation tax is based on engine size, arranged in bands, and varying with age. The Toyota Yaris has an engine size of 1364 cc which is in the band 1358 to 1548 cc. For cars registered after 1/1/2006 the charge for that band is €255. If your friend's car was registered between 1/1/2006 and 1/11/2010 then it looks like the charge is correct.
Looking at earlier dates, registered before 1/1/2006 back to 1/1/2001 the charge would be €240. Registered before 1/1/2001 it would be €225. There is no band with a charge of €105. Is it possible that your friend bought the car second hand part way through last year and it had been off the road? I always understood that you had to pay the full year's tax even if you only had it for a few days but I think somebody posted recently that they had only been charged a fraction of the full year's charge.
PS Vehicle information taken from Parkers Guide. Circulation Tax information taken from an email sent out by my accountant, George Atsalakis, yesterday.