Explanation for 2016.Spring 14a
Link to the statement of the problem: E (2016.Spring #14)
Solution 1
The formula you need is:
ExRatio = (UCAEbeg - Paidall - UCAEend + ii) / UCAEbeg
where ii = ii = investment income
The first solution the examiner's report gives, (4000 - 3500)/2000 = 25%, which I believe is the correct answer. But they took a shortcut so their solution is hard to follow. I broke my solution into several steps. You have to start with a couple of observations:
- For the undiscounted ratio, you don't need to calculate the investment income. (So that term drops out of the formula.)
- You're given ultimates, but you need to know the UCAE (unpaid) amounts to use the standard excess ratio formula.
So, I used the triangle of undiscounted ultimates to calculate the beginning and ending undiscounted UCAE amounts for AY 2012:
- UCAEbeg
- = ultimate – paid (for AY 2012 at 12 months)
- = 4,000 - 2,000
- = 2,000
- UCAEend
- = ultimate – paid (for AY 2012 at 48 months)
- = 3,500 - cumulative paids
- = 3,500 - (2,000 + 1,000 + 500 + 0)
- = 0
Then I calculated the sum of the paids, excluding the first CY for AY2015:
- Paidall
- = 1,000 + 500 + 0
- = 1,500
Now we can apply the standard formula (see above) with ii = 0:
- ExRatioundiscounted
- = (2,000 - 1,500 - 0) / 2,000
- = 500 / 2,000
- = 25%
The examiner's report gets the same answer by doing all the calculations all in 1 step. I really don't know how you would see this without going through all the steps explicitly, as I did above. It was a poorly presented solution IMHO.
Solution 2
Now, the second solution, where they get 100% is a mystery to me. They use the same formula as for the 25% solution but they don't explain what they're doing. I suspect some candidates may have interpreted "as of December 31, 2015" to mean that you only consider what happened in CY2015 and ignore previous CYs? Then the examiner's decided to give credit for that alternate solution. But I'm only guessing. My advice is to ignore this second solution.
