2010 Sept Q4 (NPV)

[Trevor]

Hi, I attempted the 2010 September Question 4, on the calculation of NPV

I couldn't understand the logic used in the solution.
In this question, premiums are received at the start of each period, and outgo at the end
So naturally, we will include one year of investment return on the premium each year before deducting the outgo at the end of period
The question has provided the profit at each period, which did not allow for investment returns at all

Even ignoring investment return, I still don't understand why:

1. If the profit occurs at the end of the year, the first year cashflow (-100) should allow for survivorship, so -100*0.9
   However the solution takes 100 without allowing for survivorship, is this conceptually correct?
   They explicitly mentioned profit cashflow arise at the end of the year and discount the first cashflow by 1.08, so it should really allow for that 1 year of survivorship. Otherwise there is a misalignment in the timeline. (although there is an alternative solution)
2. In addition first point above, the solution seems to be calculating a profit vector. In each period, the profit is discounted all the way to policy inception (t=0), but did not allow for survivorship fully.
   eg: in period 4, profit is 50, the NPV for t=5 is calculated as: 50*1.08^5*0.5. But this didn't allow for the probability of surviving from t=0 to t=4 (start of last period).
   My calculation will be: 50*1.08^5*0.9*0.8*0.7*0.6*0.5. Discounting back to the inception date, we need to live through all the previous 4 years before we can enjoy the final year profit

If I assume no investment returns, and allow survivorship from inception date, I calculate profit signature (instead of profit vector),
this gives me an NPV of -16.
I would be very stressed under an exam condition getting a negative value (as compared to a very positive value in product B of this question), but still convinced all my calculation are correct.

In the CMP, chapter 19 section 1.2, the definition given for NPV is:
Discounting the profit signature at the risk discount rate produces a 'net present value'.

I therefore have high doubts on the solution given.

Can I know why is the solution doing the calculation as such?

Thanks,
Trevor

 

[Mark Willder]

Hi, I attempted the 2010 September Question 4, on the calculation of NPV

I couldn't understand the logic used in the solution.
In this question, premiums are received at the start of each period, and outgo at the end
So naturally, we will include one year of investment return on the premium each year before deducting the outgo at the end of period
The question has provided the profit at each period, which did not allow for investment returns at all

Even ignoring investment return, I still don't understand why:

1. If the profit occurs at the end of the year, the first year cashflow (-100) should allow for survivorship, so -100*0.9
   However the solution takes 100 without allowing for survivorship, is this conceptually correct?
   They explicitly mentioned profit cashflow arise at the end of the year and discount the first cashflow by 1.08, so it should really allow for that 1 year of survivorship. Otherwise there is a misalignment in the timeline. (although there is an alternative solution)
2. In addition first point above, the solution seems to be calculating a profit vector. In each period, the profit is discounted all the way to policy inception (t=0), but did not allow for survivorship fully.
   eg: in period 4, profit is 50, the NPV for t=5 is calculated as: 50*1.08^5*0.5. But this didn't allow for the probability of surviving from t=0 to t=4 (start of last period).
   My calculation will be: 50*1.08^5*0.9*0.8*0.7*0.6*0.5. Discounting back to the inception date, we need to live through all the previous 4 years before we can enjoy the final year profit

If I assume no investment returns, and allow survivorship from inception date, I calculate profit signature (instead of profit vector),
this gives me an NPV of -16.
I would be very stressed under an exam condition getting a negative value (as compared to a very positive value in product B of this question), but still convinced all my calculation are correct.

In the CMP, chapter 19 section 1.2, the definition given for NPV is:
Discounting the profit signature at the risk discount rate produces a 'net present value'.

I therefore have high doubts on the solution given.

Can I know why is the solution doing the calculation as such?

Thanks,
Trevor

Hi Trevor

The examiners report says "A number of different calculation approaches were deemed by the Examiners to be acceptable for this question part, each of which was given full credit" and then says later "Any ratio of NPV/PVP using a combination of the above results was given full credit". So the examiners clearly thought that with the benefit of hindsight that the question was ambiguous. I agree that the information given in the question doesn't really make sense, eg you're right that the profit should allow for interest.

So I wouldn't worry about why the solution uses any particular approach. The examiners were just trying to be generous given that the question was ambiguous.

I would agree with the approach that you have taken and I think the examiners would have accepted it too.

The key in the exam, particularly with numerical questions, is not to panic or get distracted if the question doesn't work out. Even if your answer was wrong, you can still get lots of method marks. It's important not to spend too long on these questions and move on to the next opportunity to score more marks.

Best wishes

Mark