Private Equity Question?

M

maasultan

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

T

Tim

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...

R

Ronald Raygun

Tim said:
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.
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

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.

T

Tim

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%.

R

Ronald Raygun

Tim said:
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!

T

Tim

Tim said:
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).

... 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?

"Idealised" indeed!
;-)

R

Ronald Raygun

Tim said:
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
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?

T

Tim

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!

... 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
Tim said:
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...

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!

M

maasultan

Tim said:
"Ronald Raygun" wrote
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
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

M

maasultan

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

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
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...

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