OT: Percentage help please

[mike]

A friend phoned today and asked me to explain the following to him. By the time I'd finished, he was more confused than ever. Could someone please spell it out in simple terms?

Smith and Jones buy a property together.

The cost is £288. Smith pays £200 in cash, and he and Jones jointly take out a mortgage for the remaining £88 which they agree to pay off equally, meaning that Jones will end up owning 15%. (£44/£288=15%)

After three years, the property is worth £450 and they decide to sell. £72 remains on the mortgage.

Jones's financial adviser tells him that after paying off the outstanding £72 from the £450 proceeds of sale, Jones will receive 15% of £378, namely £56.7

Jones has done his own calculation: he will receive 15% of £450 (namely £67.5) from which he will have to pay half of the outstanding mortgage (£72/2= £36) leaving him with £31.5

Jones asks why - mathematically and ethically - his financial adviser's calculation is the correct one.

[Clive George]

Oh joy - this probably needs agreeing at the beginning and writing down.

At a guess, the % ownership shouldn't have been set as a fixed number. Otherwise if they'd liquidated at the beginning the 200K would have been split 170/30 Smith/Jones.

==

One option, based on % payout = % paid

Beginning - 288, of which S has paid 200, J 0. Pay off the mortgage, all the remaining 200K goes to S

End - worth = X, no mortgage, S has paid 244, J 44, split is 85/15 as you said.

Midpoint? Outstanding mortgage is 72, so S has paid 208, J 8, so I'd say S should get 208/216 * 378 = 364, J should get 8/216 * 378 = 14. Which is obviously lower than both :-)

==

Another option, based on splitting the profits 85/15

Beginning - 288, pay off mortgage, pay off S, no profit. End - worth X, profit is X-288, pay back 244+85%(X-288) to S, 44 +

15%(X-288) to J, which is 85/15, phew, that's still right

Middle - worth X, profit is X-288 = 162 in this case. Split 137.7/24.3 then add on amounts already paid. S gets 200 + 8 + 137.7, J gets 8 +

24.3 = 32.3. Mortgage company gets 72.

Hmm, that's the same as J's calculation if the 15% is replaced with using 44/244, so I'd go for that.

==

Financial adviser's version is the one which has S receiving 170K of his original 200K if they liquidate at the beginning, so that's a stupid way to do it. Though it may be how its written down, in which case S should get a better lawyer when writing down the original agreement.

Of course if S + J are amicable souls, they could agree a fair split and ignore what the financial adviser or anybody else says.

[tim......]

Smith and Jones buy a property together.

The cost is £288. Smith pays £200 in cash, and he and Jones jointly take out a mortgage for the remaining £88 which they agree to pay off equally, meaning that Jones will end up owning 15%. (£44/£288=15%)

After three years, the property is worth £450 and they decide to sell. £72 remains on the mortgage.

Jones's financial adviser tells him that after paying off the outstanding £72 from the £450 proceeds of sale, Jones will receive 15% of £378, namely £56.7

Jones has done his own calculation: he will receive 15% of £450 (namely £67.5) from which he will have to pay half of the outstanding mortgage (£72/2= £36) leaving him with £31.5

Jones asks why - mathematically and ethically - his financial adviser's calculation is the correct one.

--------------------------------------------------------------

If I were Smith I'd be asking why(?) too, as doing it this way means that Jones would be stealing a big chunk of my original 200 pound investment.

ISTM that it is neither morally, nor mathematically, the correct calculation

tim

[Andy Champ]

Yes, including the case where the value of the property falls...

Andy

[andrew]

I don't think it is. Smith paid £244 for the property, Jones paid £44. The fact that they both borrowed some of this money is irrelevant. Presumab ly if the property had burnt down, Smith would have lost £244, and Jones £44. They should each get the relevant percentage of the sale, and use th at to pay of the outstanding debt. Jones should get £68.75 (15.28%), from which he should repay the £36, leaving him with £32.75 A

[Nightjar]

Sounds like somebody's homework problem.

Colin Bignell

[Tim Streater]

The reason is because the asset they have is not worth £450. It's worth £378. The fact that a house is involved with certain values of the

*house* is not relevant.

[John Rumm]

This sounds like a case of leverage...

Allowing for the rise in value, Smith put in the equivalent of £312 of equity (200/288*450). The remaining 137K is the growth in value of the shared mortgage investment.

Hence Smith should get £312 (as a minimum). Then each an equal share of (137 - 72) /2 or £32.50

[Tim Streater]

I think Jones is correct, having thought about it back and forth. Take the example that they sell the house immediately after purchase for the same price and repay the mortgage.

Then by Jones' method, he gets 15% of £288 which is £44. Smith gets 85% of £288, which is £244. Each then pays off their share of the mortgage (£44 each). Jones then ends up with zero, which is what he started with, and Smith with £300, also what he started with.

Thus each ends up where they started, which is what you'd expect in this example.

The adviser's method means that after the mortgage is paid off, the pair would be left with £200. Why should Jones get £30 of that?

[Martin Brown]

I think Smith should get another financial adviser!

I have an even harder line interpretation in favour of Smith based on the actual invested ownership of the property at the time of the sale!

Jones only ends up owning 15% of the property if they run the mortgage to full term completion. Terminating early he only owns a fraction of that 15% (3.846%). It all depends what was defined in the contract.

Mortgage was paid equally so each has paid in £ (88-72)/2 = £8

Smith has paid 200 + 8 and Jones £8

Jones is therefore entitled to only his share of the property value at the time of the sale 8/208 ths of 450 = £17.31 and is contractually obliged to pay off half the mortgage £36 so he *owes* Smith £18.69.

[Andrew May]

No, the asset is worth £450. How it is financed is irrelevant.

[Tim Streater]

Mmm, I thought that originally too. But as long as they pay the mortgage off, it doesn't matter *how* they pay it off. That is, a load of small payments over years (because they own the house a long time) or some number of small payments followed by a big one (because as the OP proposed, they sell after three years).

Once they've paid it off, Jones' share goes to 15%. And if they sell early, they *have* to pay it off so it matters not when they do it. They could pay it off after one year in one payment if they wanted, it still all amounts to the same.

[Tim Streater]

Yes, I concluded that too, eventually.

[Tim Streater]

Oops, £200, not £300, sorry.

[djc]

Another variation.

Smith has 200/288 (~69.5%) share. 'The Mortgage' has the remaining 88/288 (~30.5%) share

When the property is sold Smith has 450/288*200 = 312.50 'The Mortgage' has 450/288*88 = 137.50 'The Mortgage' after redemption nets 137.50 - 72 = 65.50 which is divided equally So Smith gets 345.25 and Jones 32.75

Which is being generous to Jones as Smith has carried the greater burden of risk. If the property were repossessed and realised less than 288 the loss would fall on Smith.

[mike]

Thanks for all the informative replies.

Obviously my problem in trying to explain the financial advisor's interpretation was the wrong-headed assumption that his way was in some way "the way it's done", paying off the mortgage out of the proceeds before divvying up the rest.

As is clear from the responses, there are several ways to work this out depending on interpretation of the original intent and value at a given time, although everyone seems to agree that Jones's method is fairer than the financial advisor's. And if any kind of written contract exists between Smith and Jones, that would clear things up... or muddy the waters further.

[Tim Streater]

ISTM that a contract specifying the calculation method is important, along with it specifying what happens under early sale (a likely circumstance), drop in property value (not unknown), etc.

The big mistake is "We're mates, we don't need a contract".

[Andy Champ]

The result of course being "We were mates, so we thought we didn't need a contract".

Andy

[tim......]

plus the "interest" forgone on that 200 pounds

tim

[tim......]

Yeah, and at the start of the contract he owned 0%. Are you seriously suggesting that he should always get back 15% even if none of the loan had been paid off?

tim