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April 2018 CP2 Paper 2

D

Darragh Kelly

Ton up Member
Hi,

Regarding the solution to the 2018 April Paper 2 Summary Doc IFoA sol, could a tutor please explain the calculation highlted in red please below:

Donation target
For the deficit to be zero by the end of 15 years, donations need to start at $12.6k in year 1, all else being equal to the campaign scenario. It follows that the donations need to be higher than the $10k anticipated by the campaign which resulted in a deficit of $56k after 15 years.
Yields are roughly 2.5% per annum and inflation is 2.5% per annum. The average donation is received in 7.5 years’ time. There are 15 donations so in 15 years’ time the additional $2.6k annual donation roughly has a total value of 2.6 x 1.057.5 x 15 = $56k.

Many thanks,

Darragh
 
Hi Darragh

As ever, the exact details of this check are not the more important thing, focus on doing something to give confidence that the results are reasonable, and it may not have been exactly the same check in the model solution.

But, here, they are trying to justify that the extra donations will cover the deficit. The starting amount is 2.6k higher under the revised donation schedule (12.6 - 10). This is paid for 15 years, and they are assuming this grows at 5% a year (2.5% from investment growth and 2.5% from inflation). So, that 2.6k will be paid 15 times and grow at 5% (which is applied over the half the period as an average). This gives 56k which confirms that this would cover the deficit and therefore the increase to the starting amount is reasonable.

You could have done something similar by taking the 2.6k and multiplying by the 15 years it will be paid for, and then allowing for 2.5% inflation and the 2.4% average return on investments separately (over the 7.5 yr average period) and this would also give 56k.

Sarah
 
Hi Sarah,

Thanks a mill for detailed reply, and noted on not getting bogged down in the detail.

The bit I find hard to follow is the 7.5 yr average peroid and why that's used instead of 15? Could you provide a bit more detail if possible? I remember vaguley for CM2 calculating expected accumulated values at the average interest rate I'm wondering is that where I get the theory on why it's 7.5 years?

Thanks,

Darragh
 
If we assume the interest/inflation happens mid way through each year, it happens at times 0.5, 1.5, 2.5 etc. The average of these is 7.5, so we just use that in this check.
 
Yeah I get you...makes sense

I did some quick revision of CM2 notes...would it be acceptable to approx the mean accumulated value of 2.6k per annum using an annuity factor for an accumulated value at a rate of 5%?

For example the mean accumulated value of 2.6k at time 15 = 2600*(1.05^15-1)/(0.05/1.05), assuming the mean rate of return is 5% (sum of 2.5% for inflation and 2.5% for the mean NBI returns)? I Get about 58.9k vs 56k but I guess its an approximation...

Thanks,

Darragh
 
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