Hi,

Assume this:

John bought income property A in London in 2005 for 100 pounds, it
makes 20 pound per year,
Dave bought income property B in Liverpool in 2006 for 60 pounds, it
makes 15 pound per year,
Larry bought income property C in Manchester in 2007 for 75 pounds, it
makes 17 pound per year.

NOW, the 3 want to become partners where the pie now is A+B+C and
income is 52 pound per year!

How much ownership each gets? How much income each gets per year?

Thanks,
Mike

wrote
> Hi,
>
> Assume this:
>
> John bought income property A in London in 2005
> for 100 pounds, it makes 20 pound per year,
> Dave bought income property B in Liverpool in
> 2006 for 60 pounds, it makes 15 pound per year,
> Larry bought income property C in Manchester in
> 2007 for 75 pounds, it makes 17 pound per year.
>
> NOW, the 3 want to become partners where the pie
> now is A+B+C and income is 52 pound per year!
>
> How much ownership each gets?
> How much income each gets per year?
>
> Thanks,
> Mike

Is this a Homework question?!

Anyway, obviously John would get about 38% ownership so
that he still gets 20 pounds per year, Dave would get about
29% ownership so that he still gets 15 pounds per year, and
Larry would get about 33% ownership so that he still gets 17
pounds per year.  Unless they decided to be unfair, of course...

Tim wrote:

>  wrote
>>
>> John bought income property A in London in 2005
>> for 100 pounds, it makes 20 pound per year,
>> Dave bought income property B in Liverpool in
>> 2006 for 60 pounds, it makes 15 pound per year,
>> Larry bought income property C in Manchester in
>> 2007 for 75 pounds, it makes 17 pound per year.
>>
>> NOW, the 3 want to become partners where the pie
>> now is A+B+C and income is 52 pound per year!
>>
>> How much ownership each gets?
>> How much income each gets per year?
>  
> Is this a Homework question?! 
> 
> Anyway, obviously John would get about 38% ownership so
> that he still gets 20 pounds per year, Dave would get about
> 29% ownership so that he still gets 15 pounds per year, and
> Larry would get about 33% ownership so that he still gets 17
> pounds per year.  Unless they decided to be unfair, of course...

Doing it differently would not necessarily be unfair, just
fair in a different way.

Although we are told that the total income is unchanged at 52
pounds per year, and we can perhaps assume that this means the
income generated by each property is also unchanged at 20/15/17
pounds per year, we are not told whether and how the properties'
value has changed since they were bought.

One fair way to split ownership is in proportion to the value.
If this has not changed, the split should be 100:60:75, i.e.
John gets about 42%, Dave gets about 26%, and Larry about 32%.
The implication of this, though, would be that John's income
goes up to about 22 pounds per year, Dave's down to about 13
pounds per year, and Larry's goes down slightly but is still
about 17 pounds per year.

More to the point, if the properties are mortgaged, the split
should be on the basis of equity, not value.

One needs to ask why these guys are doing this.  Perhaps they
want to hedge against fluctuations in income and in value.
Why else would any of them consider taking a drop in income
or in their equity stake?

It seems to me they need to negotiate a compromise between the
income-fair and equity-fair solutions.

>>  wrote
>>> John bought income property A in London in 2005
>>> for 100 pounds, it makes 20 pound per year,
>>> Dave bought income property B in Liverpool in
>>> 2006 for 60 pounds, it makes 15 pound per year,
>>> Larry bought income property C in Manchester in
>>> 2007 for 75 pounds, it makes 17 pound per year.
>>>
>>> NOW, the 3 want to become partners where the pie
>>> now is A+B+C and income is 52 pound per year!
>>>
>>> How much ownership each gets?
>>> How much income each gets per year?
>>
> "Tim" wrote:
>> Is this a Homework question?!
>>
>> Anyway, obviously John would get about 38% ownership so
>> that he still gets 20 pounds per year, Dave would get about
>> 29% ownership so that he still gets 15 pounds per year, and
>> Larry would get about 33% ownership so that he still gets 17
>> pounds per year.  Unless they decided to be unfair, of course...
>
"Ronald Raygun" wrote
> Doing it differently would not necessarily
> be unfair, just fair in a different way.
>
> Although we are told that the total income is unchanged at 52
> pounds per year, and we can perhaps assume that this means
> the income generated by each property is also unchanged at
> 20/15/17 pounds per year, we are not told whether and how
> the properties' value has changed since they were bought.
> One fair way to split ownership is in proportion to the value...

Well, obviously (in such an idealised example!), property A
will have fallen in value to 80 pounds in 2006 and then property
A will have increased in value to 88.24 pounds in 2007 and
property B will have increased in value to 66.18 pounds in 2007.
[They will also each have changed by the same factor from 2007 to 2008.]

Thus the fair ownership proportions (in proportion
to the values) are still:  88.24 / 229.41 = 38%,
66.18 / 229.41 = 29% and 75.00 / 229.41 = 33%.

Tim wrote:

> "Ronald Raygun" wrote
>> Doing it differently would not necessarily
>> be unfair, just fair in a different way.
>>
>> Although we are told that the total income is unchanged at 52
>> pounds per year, and we can perhaps assume that this means
>> the income generated by each property is also unchanged at
>> 20/15/17 pounds per year, we are not told whether and how
>> the properties' value has changed since they were bought.
>> One fair way to split ownership is in proportion to the value...
> 
> Well, obviously (in such an idealised example!), property A
> will have fallen in value to 80 pounds in 2006 and then property
> A will have increased in value to 88.24 pounds in 2007 and
> property B will have increased in value to 66.18 pounds in 2007.
> [They will also each have changed by the same factor from 2007 to 2008.]
> 
> Thus the fair ownership proportions (in proportion
> to the values) are still:  88.24 / 229.41 = 38%,
> 66.18 / 229.41 = 29% and 75.00 / 229.41 = 33%.

While it was easy enough for you to make up a set of value movements
which made the 2007/8 value proportions the same as the income ones,
the underlying assumption that the value inflation rates are the same
in each of the three locations in any one year is a pretty unrealistic.

"Idealised" indeed!

>> "Ronald Raygun" wrote
>>> Doing it differently would not necessarily
>>> be unfair, just fair in a different way.
>>>
>>> Although we are told that the total income is unchanged at 52
>>> pounds per year, and we can perhaps assume that this means
>>> the income generated by each property is also unchanged at
>>> 20/15/17 pounds per year, we are not told whether and how
>>> the properties' value has changed since they were bought.
>>> One fair way to split ownership is in proportion to the value...
>>
> "Tim" wrote:
>> Well, obviously (in such an idealised example!), property A
>> will have fallen in value to 80 pounds in 2006 and then property
>> A will have increased in value to 88.24 pounds in 2007 and
>> property B will have increased in value to 66.18 pounds in 2007.
>> [They will also each have changed by the same factor from 2007 to 2008.]
>>
>> Thus the fair ownership proportions (in proportion
>> to the values) are still:  88.24 / 229.41 = 38%,
>> 66.18 / 229.41 = 29% and 75.00 / 229.41 = 33%.
>
"Ronald Raygun" wrote
> While it was easy enough for you to make up a set of value movements
> which made the 2007/8 value proportions the same as the income ones, ...

It's not a matter of "making up" the value movements, but
rather *calculating* them from their yield.  Of course, the
*actual* yields were not quoted for property A in 2006 or
2007, nor for property B in 2007, so the yields that were
known instead were used as reasonable proxies (yield in
2006 from property B, yield in 2007 from property C).

"Ronald Raygun" wrote
> ... the underlying assumption that the value inflation rates are the same
> in each of the three locations in any one year is a pretty unrealistic.

Of course, but in the absence of further information (the question
had no other data), it's got to be the best assumption, hasn't it?

"Ronald Raygun" wrote
> "Idealised" indeed!

;-)

Tim wrote:

> "Ronald Raygun" wrote
>> While it was easy enough for you to make up a set of value movements
>> which made the 2007/8 value proportions the same as the income ones, ...
> 
> It's not a matter of "making up" the value movements,

It is if I use "make up" in the sense of "posit ficticious
values for".  Naturally it goes without saying that you can't
make up *arbitrary* values for f and g, the two years'
inflation factors.  There is only one pair of values which
will work to achieve the effect you wanted, and of course it
must be calculated.

> but rather *calculating* them from their yield.

Well, I suppose you can do it by working out the yields first, but
that seems a bit long-winded.  How I would do it is to observe that
the two three-way ratios  100fg:60g:75  and  20:15:17  must be
equal, which boils down to solving the three equations

[1] 75k = 17
[2] 60gk = 15
[3] 100fgk = 20

for f and g, which *can* be done by calculating k first (which
happens to be one of the yields) from [1], then using that in [2]
to work out g, and finally using that in [3] to work out k, but it
can also be by eliminating k algebraically, calculating g directly
by dividing [2] by [1], and f by dividing [3] by [2].

60g/75 = 15/17  =>  g = 1.103
100f/60 = 20/15  =>  f = 0.8

> "Ronald Raygun" wrote
>> ... the underlying assumption that the value inflation rates are the same
>> in each of the three locations in any one year is a pretty unrealistic.
> 
> Of course, but in the absence of further information (the question
> had no other data), it's got to be the best assumption, hasn't it?

It's the only possible assumption, which makes it simultaneously the
best and the worst.  But since it is objectively bad, might it not be
better than solving the problem on the basis of it, to throw up one's
hands in warning and say that the answer will be silly so there is no
point in working it out?

>> "Ronald Raygun" wrote
>>> While it was easy enough for you to make up a set of value movements
>>> which made the 2007/8 value proportions the same as the income ones, ...
>>
> "Tim" wrote:
>> It's not a matter of "making up" the value movements, ...
>
"Ronald Raygun" wrote
> It is if I use "make up" in the sense of "posit ficticious
> values for".  Naturally it goes without saying that
> you can't make up *arbitrary* values for f and g,
> the two years' inflation factors.  There is only one
> pair of values which will work to achieve the effect
> you wanted, and of course it must be calculated.

But I didn't calculate any inflation factors!!

I first calculated the latest yield:-
  In 2007 : yield = 17/75 = 22 2/3%.

Then I applied this latest yield to the income on each property:-
  Property A value = 20 / 22 2/3% = 88.24.
  Property B value = 15 / 22 2/3% = 66.18.
  Property C value = 17 / 22 2/3% = 75.00.

No inflation factors in sight anywhere!


> "Tim" wrote
>> ... but rather *calculating* them from their yield.
>
"Ronald Raygun" wrote
> Well, I suppose you can do it by working out the yields first, but
> that seems a bit long-winded.  How I would do it is to observe
> that the two three-way ratios  100fg:60g:75  and  20:15:17
> must be equal, which boils down to solving the three equations
>
> [1] 75k = 17
> [2] 60gk = 15
> [3] 100fgk = 20
>
> for f and g, which *can* be done by calculating k first (which
> happens to be one of the yields) from [1], then using that in
> [2] to work out g, and finally using that in [3] to work out k,
> but it can also be by eliminating k algebraically, calculating g
> directly by dividing [2] by [1], and f by dividing [3] by [2].
>
> 60g/75 = 15/17  =>  g = 1.103
> 100f/60 = 20/15  =>  f = 0.8
>
>> "Ronald Raygun" wrote
>>> ... the underlying assumption that the value inflation rates are the 
>>> same
>>> in each of the three locations in any one year is a pretty unrealistic.
>>
> "Tim" wrote:
>> Of course, but in the absence of further information (the question
>> had no other data), it's got to be the best assumption, hasn't it?
>
"Ronald Raygun" wrote
> It's the only possible assumption, which
> makes it simultaneously the best and the worst.

I disagree.  You could instead assume that the yields are constant
in each location, and so the values are also constant.  But I don't
think that is as good an assumption as the one I made earlier...


"Ronald Raygun" wrote
> But since it is objectively bad, might it not be better than solving the
> problem on the basis of it, to throw up one's hands in warning and
> say that the answer will be silly so there is no point in working it out?

The OP asked the question, so s/he obviously wanted to see an answer!

On Aug 26, 9:50 am, Ronald Raygun <no.s...@localhost.localdomain>
wrote:
> Tim wrote:
> > "Ronald Raygun" wrote
> >> While it was easy enough for you to make up a set of value movements
> >> which made the 2007/8 value proportions the same as the income ones, .> > It's not a matter of "making up" the value movements,
>
> It is if I use "make up" in the sense of "posit ficticious
> values for".  Naturally it goes without saying that you can't
> make up *arbitrary* values for f and g, the two years'
> inflation factors.  There is only one pair of values which
> will work to achieve the effect you wanted, and of course it
> must be calculated.
>
> > but rather *calculating* them from their yield.
>
> Well, I suppose you can do it by working out the yields first, but
> that seems a bit long-winded.  How I would do it is to observe that
> the two three-way ratios  100fg:60g:75  and  20:15:17  must be
> equal, which boils down to solving the three equations
>
> [1] 75k = 17
> [2] 60gk = 15
> [3] 100fgk = 20
>
> for f and g, which *can* be done by calculating k first (which
> happens to be one of the yields) from [1], then using that in [2]
> to work out g, and finally using that in [3] to work out k, but it
> can also be by eliminating k algebraically, calculating g directly
> by dividing [2] by [1], and f by dividing [3] by [2].
>
> 60g/75 = 15/17  =>  g = 1.103
> 100f/60 = 20/15  =>  f = 0.8
>
> > "Ronald Raygun" wrote
> >> ... the underlying assumption that the value inflation rates are the same
> >> in each of the three locations in any one year is a pretty unrealistic> > Of course, but in the absence of further information (the question
> > had no other data), it's got to be the best assumption, hasn't it?
>
> It's the only possible assumption, which makes it simultaneously the
> best and the worst.  But since it is objectively bad, might it not be
> better than solving the problem on the basis of it, to throw up one's
> hands in warning and say that the answer will be silly so there is no
> point in working it out?

Thanks all of you and thanks Tim. I like the mathematical way of Tim.

However, is there an online source on how such application is handled?

Mike

On Aug 26, 11:45 am, "Tim"  wrote:
> >> "Ronald Raygun" wrote
> >>> While it was easy enough for you to make up a set of value movements
> >>> which made the 2007/8 value proportions the same as the income ones, > > "Tim" wrote:
> >> It's not a matter of "making up" the value movements, ...
>
> "Ronald Raygun" wrote
>
> > It is if I use "make up" in the sense of "posit ficticious
> > values for".  Naturally it goes without saying that
> > you can't make up *arbitrary* values for f and g,
> > the two years' inflation factors.  There is only one
> > pair of values which will work to achieve the effect
> > you wanted, and of course it must be calculated.
>
> But I didn't calculate any inflation factors!!
>
> I first calculated the latest yield:-
>   In 2007 : yield = 17/75 = 22 2/3%.
>
> Then I applied this latest yield to the income on each property:-
>   Property A value = 20 / 22 2/3% = 88.24.
>   Property B value = 15 / 22 2/3% = 66.18.
>   Property C value = 17 / 22 2/3% = 75.00.
>
> No inflation factors in sight anywhere!
>
> > "Tim" wrote
> >> ... but rather *calculating* them from their yield.
>
> "Ronald Raygun" wrote
>
>
>
> > Well, I suppose you can do it by working out the yields first, but
> > that seems a bit long-winded.  How I would do it is to observe
> > that the two three-way ratios  100fg:60g:75  and  20:15:17
> > must be equal, which boils down to solving the three equations
>
> > [1] 75k = 17
> > [2] 60gk = 15
> > [3] 100fgk = 20
>
> > for f and g, which *can* be done by calculating k first (which
> > happens to be one of the yields) from [1], then using that in
> > [2] to work out g, and finally using that in [3] to work out k,
> > but it can also be by eliminating k algebraically, calculating g
> > directly by dividing [2] by [1], and f by dividing [3] by [2].
>
> > 60g/75 = 15/17  =>  g = 1.103
> > 100f/60 = 20/15  =>  f = 0.8
>
> >> "Ronald Raygun" wrote
> >>> ... the underlying assumption that the value inflation rates are the
> >>> same
> >>> in each of the three locations in any one year is a pretty unrealistic.
>
> > "Tim" wrote:
> >> Of course, but in the absence of further information (the question
> >> had no other data), it's got to be the best assumption, hasn't it?
>
> "Ronald Raygun" wrote
>
> > It's the only possible assumption, which
> > makes it simultaneously the best and the worst.
>
> I disagree.  You could instead assume that the yields are constant
> in each location, and so the values are also constant.  But I don't
> think that is as good an assumption as the one I made earlier...
>
> "Ronald Raygun" wrote
>
> > But since it is objectively bad, might it not be better than solving the
> > problem on the basis of it, to throw up one's hands in warning and
> > say that the answer will be silly so there is no point in working it out?
>
> The OP asked the question, so s/he obviously wanted to see an answer!- Hide quoted text -
>
> - Show quoted text -

Thanks all of you and thanks Ronald. I like the mathematical way of
Ronald. However, factors such as inflation is important too.

However, is there an online source on how such application is
handled?


Mike