Commutation example
Under 4 commutation practice problem,
Where does the column 5 - pmt rem @ begining yr come from? Is this given values?
Thanks!
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Under 4 commutation practice problem,
Where does the column 5 - pmt rem @ begining yr come from? Is this given values?
Thanks!
Comments
Hi,
You would take the undiscounted liabilities to be commuted multiplied by the remaining % of payments remaining. Ex:
2016: 3M(100%) = 3M <- You still have to pay the full amount
2017: 3M(1 - 20%) = 2.4M <- You already paid 20% in 2016 and have 80% left to pay
2018: 3M*(1-30%) = 2.1M <- You have already paid 30% in 2016 and 2017 and have 70% left to pay
And so on....
Hi, why is the number of year to discount for risk margin at 2016 1 instead of 0? Isnt the pmt remaining @ beginning of 2016 is at current point of time?
The payment is made in the middle of 2016 so you would have to discount for half a year
Sorry, are you referring to the column 3? To clarify, I am asking column 7 and why does it start with 1 instead of 0?
Yeah I was referring to column 3 whoops. For column 7, you only release the capital at the end of the year because you need to hold capital for each period -> Starting at 0 would mean you'd be releasing capital for 2016 before 2016 has even started!
Thanks! I have a follow-up question. To calculate (6) -cost of capital, why we are multiplying to the payment remaining@beginning of the year instead of to payment remaining@end of the year?
Taking 2016 as an example. We would like to calculate the cost of capital for that year. Thus we need to calculate the amount of capital required for 2016 (derived from the payment remaining at the beginning of the year). If we multiply by payment remaining at the end of the year, we would be looking at the cost of capital for 2017.
To further reiterate this point, if you were to multiply to the payment remaining at the end of the year, there would be no cost of capital for 2019. That wouldn't make sense as we would still have unpaid at the beginning of 2019
I had the same question that was asked and answered above regarding the discount years starting at 1 for column 7. I'll provide an example (Odo practice problem #2a in the commutation random problems) to show where I am getting confused...
If we start with 3M in undiscounted liabilities to be commuted and then pay out 10% of that so 300k halfway through the first year, why do we still discount the original 3M for 1 year in the margin calculation if we paid out 300k of that 6 months prior? I also would have discounted for 0 years and then gone up from there and I see that is wrong just having a hard time understanding why.
Thanks!
I think the confusion here lies in the different information given. The first table (columns 1-4) discount the losses to time 0, using half-years for discounting since the question explicitly states "all pmts are made in the middle of the year". Note that this assumption usually arises for the situation where pmts are made throughout the entire year in a uniform manner. The average of a uniform distribution is the middle.
The second table discounts the risk margin to time 0. This risk margin calculated by multiplying the TMF by outstanding claim liabilities for that. This is the cost of holding the capital that is used to pay the liabilities.
For that first year, we have to hold that 3m in a bank account (which 300k is then siphoned off throughout the year, or at the midpoint). 3m x 1.54% = 45,294. This represents the cost of holding the capital for the whole year. We then discount it back to time 0 (1 year).
Similarly for the second year, we have to hold 2.7m in a bank account (which another 300k is removed from during the year). 2.7m x 1.54% = 41,580. This represents the cost of holding the capital for that whole year. We then discount it back to time 0 (2 years).