2016 Spring Q14c
Given the formula you gave us to calculate the e/d ratio, I am having a hard time making sense of the solution provided on the examiner's report.
Here is my solution:
e/d ratio = [APV(bgn) - APV(end) - sum(paid) + ii]/APV(bgn)
APV(bgn)=2,750
APV(end)=2,800
sum(paid)=1,000
ii=64.125 answered in question b.
plugging these values into the equation above, I get -35.85%
Here is the examiner's report solution:
( Change in Ultimate + Investment Income ) / Prior Outstanding
= (2750-2800+64)/1250 = 1.13%
Why did they not account for the paid amount?
How does the 1250 in the denominator translate to the equation you gave us?
Comments
I'm glad you asked this because it shows how closely you have to pay attention to exactly what you need for the formula and what you're actually given in the problem.
Ok, here's what's going on: The APV provided in the 3rd triangle is the APV of the ultimate. But you need the APV of the unpaid:
Then
We can now substitute into the formula I gave you using your sum(paid) = 1000:
The examiner's report skipped some steps because the paid values are already embedded in the ultimate values that they used in the numerator. They also never pointed out the obvious mistake people would make which is using the given APV as if it were unpaid rather than ultimate. I do think they were trying to trick people. It really doesn't make sense to refer to an ultimate value as APV because the paid portion is not discounted with PfADs. Only the unpaid portion gets the "APV treatment".
Anyway, this is a trick they've used before so now you know! I will link to here from the wiki.