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Old 11-04-2018, 06:10 PM
Sullinator Sullinator is offline
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Default Fm question

A perpetuity has payments of 1, 2, 1, 3, 1, 4, 1, 5,Ö Payments are made at the end of each year. You may assume an annual effective interest rate of 5%. Determine the present value I this perpetuity.
I know this problem was discussed before but Iím stuck. How do I do this? I set up my time line at time 1 payment is 1, time 2 payment is 2, time 3 payment is 1, time of 4 payment is 3, and so on. What do I do now?
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Old 11-04-2018, 06:36 PM
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I have the solution from infinite actuary where they split up the time lines but I don’t get why they did it that way because they didn’t explain it.
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Old 11-04-2018, 06:59 PM
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You have to split it up in ways you can evaluate. Here are two possibilities:

Payments of 1 every year, and payments of 1 at time 2, 2 at time 4, 3 at time 6, etc.

Or

Payments ok 1 at times 1, 3, 5, ..., and payments of 2 at time 2, 3 at time 4, 4 at time 6, etc

You ought to know how to evaluate any of those 4 patterns, and should be able to convince yourself that either way of splitting gives the same answer.
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Old 11-04-2018, 07:15 PM
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Quote:
Originally Posted by Gandalf View Post
You have to split it up in ways you can evaluate. Here are two possibilities:

Payments of 1 every year, and payments of 1 at time 2, 2 at time 4, 3 at time 6, etc.

Or

Payments ok 1 at times 1, 3, 5, ..., and payments of 2 at time 2, 3 at time 4, 4 at time 6, etc

You ought to know how to evaluate any of those 4 patterns, and should be able to convince yourself that either way of splitting gives the same answer.
So for the first option the reason you did that is because payments of 1 every year represents payments if we pretend there is no increase at all correct? And payments of 1 at time 2, 2 at time 4, 3 at time 6 represents the amount you increase by correct?
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Old 11-04-2018, 07:39 PM
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Both splits are of one series with no increase at all, and a second series with increases every other year.

It is often helpful to break into a level series and an increasing series.
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Old 11-04-2018, 07:42 PM
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Quote:
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Both splits are of one series with no increase at all, and a second series with increases every other year.

It is often helpful to break into a level series and an increasing series.
Oh I see thanks.
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Old 11-04-2018, 07:42 PM
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For each option, you can decompose the ugly looking payment streams into simple, closed form solutions.

Option 1: Yes, you get 1 forever assuming no increases. The extra bit is an increasing perpetuity that bumps up every 2 years instead of every 1 year.

Option 2: This has similarities to option 1. You get 1 every 2 years forever and in the "off" years, you get an increasing perpetuity every 2 years.

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Last edited by Breadmaker; 11-04-2018 at 07:43 PM.. Reason: Ninja'd by Gandalf
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Old 11-04-2018, 08:16 PM
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Quote:
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For each option, you can decompose the ugly looking payment streams into simple, closed form solutions.

Option 1: Yes, you get 1 forever assuming no increases. The extra bit is an increasing perpetuity that bumps up every 2 years instead of every 1 year.

Option 2: This has similarities to option 1. You get 1 every 2 years forever and in the "off" years, you get an increasing perpetuity every 2 years.

Ninja'd.
Thanks.
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Old 11-04-2018, 08:27 PM
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Quote:
Originally Posted by Breadmaker View Post
For each option, you can decompose the ugly looking payment streams into simple, closed form solutions.

Option 1: Yes, you get 1 forever assuming no increases. The extra bit is an increasing perpetuity that bumps up every 2 years instead of every 1 year.

Option 2: This has similarities to option 1. You get 1 every 2 years forever and in the "off" years, you get an increasing perpetuity every 2 years.

Ninja'd.
You explained it better than the lecture video.
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Old 11-04-2018, 08:36 PM
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