September 2001 Q8 - Initial Estimate

[kika258]

Hi, Can anyone please tell me how to get an initial estimate in finding the Internal Rate of Return?

I manage to get formulae well but fail to get an initial estimate for IRR and hence it will be very time consuming to find it through trial and error.

In the answers given, it seems that he is taking some kind of average of the payments/revenues, is that true?

Thanks a lot

Marika

 

[didster]

Any of the following, it's only a guess. Good actuaries need to know how to guess.

Trusty old actuarial intuition.
Trusty old roll of a die.
"divide and conquer" technique. Try 10%. If higher try 20%, if lower try 5%, then 2.5% 7.5% etc until you get smaller and smaller gaps. You could even try to make it more sophistcated by "judging" the extent to which you missed and close the gap by more than half.

Even more apparently sophisticated approaches.
total income/total outgo averaged over an average time money is held.
comparing to an annuity and flipping through the tables until you find a rate close enough.

Bear in mind that efficiency is the goal. Don't spend ages trying to come up with a guess that is only marginally better than a simple one (eg always start with 10%)

 

[John Lee]

If you're using the Table mode on the Casio calculator then getting a first guess isn't critical as the calculator takes the bulk of the calculation...

 

[kika258]

thanks a lot for your help.

I don't know if you could help me with this one. Actually I just want to verify it. Pastpaper Aprill 2000 Quest 10. In order to find the price paid by the original investor, he first finds the price as at I April 1991 and then accumulates to 1 July 1991. i.e

P = 0.75x7 a_19^(2) + 100 v^19 and then multiplies by (1+i)^(3/12) and gets an answer of 9,385.40

Instead I had tried getting the price as at I july 1991 immediately using
P= 0.75(7) a_18.75 ^ (2) + 100v^(18.75)

and got an answer of 9,255. It seems close but I'm not sure why I did not get the same answer, cos in my opinion both methods have the same reasoning.

 

[John Lee]

thanks a lot for your help.

I don't know if you could help me with this one. Actually I just want to verify it. Pastpaper Aprill 2000 Quest 10. In order to find the price paid by the original investor, he first finds the price as at I April 1991 and then accumulates to 1 July 1991. i.e

P = 0.75x7 a_19^(2) + 100 v^19 and then multiplies by (1+i)^(3/12) and gets an answer of 9,385.40

Instead I had tried getting the price as at I july 1991 immediately using
P= 0.75(7) a_18.75 ^ (2) + 100v^(18.75)

and got an answer of 9,255. It seems close but I'm not sure why I did not get the same answer, cos in my opinion both methods have the same reasoning.

It's your annuity that's wrong. It's should be an annuity-due of 19 years (same as the annuity in arrears as it's the same number of payments). Some of the confusion is that the annuity-due finishes after the last payment - which is why it's easy to underestimate. Hence, better to count the number of payments!

So take this annuity-due and then multiply it by v^0.25