Private Equity Question?

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...

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.

"Ronald Raygun" 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%.

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

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

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 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.

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. 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

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!

"Ronald Raygun" wrote

"Ronald Raygun" wrote

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

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

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

de 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