From: c.oneill@trl.oz.au (Chris O'Neill)
Subject: Re: Negative Gearing
Organization: Telecom Australia Research Laboratories
Date: Thu, 19 Nov 1992 07:05:58 GMT

Observant readers will have noticed in my article
<1992Nov19.034509.11169@trl.oz.au>:

>Suppose we have 8% inflation, 18% (nominal) interest rate, 6% rate of return
on
>investment, 48.25% tax rate and an interest only loan.  Under these conditions
>the proportion of negative gearing decreases as time goes by and eventually
the
>return exceeds the interest.  For the sake of clarity suppose the original
>amount borrowed and invested is $100,000.  Interest is fixed at $18,000 per
>year.  Rental return is $6,000 the first year and increases with inflation
>after that so we have:
>
>year  rent       loss or gain  loss or gain absorbed   present value of A
>                                   by tax office(A)
>1     $6000      $12000          $5790                 $5790
>2     $6480      $11520          $5558.40              $4710.51
>3     $6998.40   $11001.60       $5308.27              $3812.32
>4     $7558.27   $10441.73       $5038.13              $3066.36
>
>16   $19033.01    $1033.01(gain)  $498.43(gain)          $41.63(gain)
>
>You can do this on a spread sheet if you like but I just wanted to calculate
>the total present value loss absorbed by the tax office if this situation
>continues forever.  This gives the least loss absorbed by the tax office
>because it makes a gain every year after year 15.  I used the geometric series
>summation formula to get the result.
>
>The total present value loss absorbed by the tax office is
>
>[$18000/(1-1/1.18) - $6000/(1-1.08/1.18)] 0.4825   (*)
>
> = $22774
>
>The derivation of (*) is left as an exercise to the reader :-).

that I calculated the total present value of the loss absorbed by the tax
office.  This assumed a discount rate equivalent to a nominal interest rate of
18% which is the interest rate paid by the hypothetical investor.  Now 18% is
reasonable (perhaps a bit high) to assume for the tax office which is an agent
of the Government which is a net borrower.  Being a borrower, the interest rate
appropriate to the Government is the interest rate that a borrower would pay.

Now the interesting point is that since the tax office makes a present value
loss of $22774, does not the investor also make a loss if he hangs on to the
investment forever?

Well, the factor that affects whether a profit or loss is made is the discount
rate (or interest rate) and we know that the interest rate appropriate to the
tax office is 18% (or close to it) in this example.  But the question is what
interest rate is appropriate to the investor?

What the investor is doing is making up the negative gearing losses from his
salary and then getting a return on these contributions in the future.  In fact
you can work out the interest rate that he is effectively getting on the
contributions when the investment eventually makes a profit.

According to my spreadsheet, the investor is getting a rate of return of just
under 12% (nominal) net of tax which was pretty good in the days when inflation
was 8% and borrowing rates were 18%.  Of course, this means that if the tax
office could have borrowed at less than 12% then it would have made a profit
too, but this was not the case.

The above has a great deal of detail involved so I wanted to find a simpler
example that matches reality as closely as possible but is also simple.  I have
chosen the following:

Suppose you borrow $100,000 and invest it all under the conditions of the above
example (18% interest, 8% inflation, 6% rate of return on investment, 48.25%
tax rate).  Suppose you sell if after 1 year for $108,000, i.e. you get a
capital gain equal to inflation.  Now the rental return was $6,000, the
interest was $18,000, so the tax deductable loss was $12,000.  The reduction in
tax reduces this loss to $12,000 (1-0.4825) = $6210.  The net gain is the
capital gain minus the loss resulting from rent, interest, and tax reduction,
i.e. $8000 - $6210 = $1790.

So, you make $1790 and the tax office loses $5790.

Chris O'Neill
Telecom Research
Newsgroups: aus.politics