Ngai Tahu Settlement

Doug Graham Treaty of Waitangi Negotiations

d) Calculations Performed Around 30 September 1999 (T=1999)

Following the above pattern the result of the Present Value
calculation performed around 30 September 1999 is shown in the last column of
Table A, i.e.:

Following clause 18.3, we again refer to equation (4)
(except that CFY 96 becomes CFY 99). Now, for the first time, the condition is
satisfied. So a claim for further redress can be made in accordance with
clause 18.4. The prospective payment, deemed to be made on 31 December
1998, will be denoted $X.

Following clause 18.4, we must now calculate the Real
Value as at 31 December 1994 of the Total Redress Amount up to and including CFY
99. From paragraph (c) of the definition of "Real Value" in clause 18.1.1
this is

= $1,068.749m

As noted above, the prospective payment of an Additional Ngai
Tahu Redress Amount by the Crown, deemed to be made on 31 December 1998, is
designated $X. Following clause 18.4, its Real Value as at 31 December
1994 must be calculated. Following paragraph (d) of the definition of Real Value
in clause 18.1.1, this is

Following clause 18.4, this $X must then be such that
the $180m (the illustrative Real Value of the Ngai Tahu Redress Amount) plus the
real value above of the $X equals 18.2% (the illustrative Agreed Relativity
Percentage) of the $1,068.749m above. So

Thus $X = 15.708m. This payment, deemed to have been made on 31
December 1998, would then be increased to reflect inflation over the period from
31 December 1998 to the end of the quarter immediately before the payment was
made. So, if the payment was made on 15 October 1999, the $X would be increased
to reflect inflation from 31 December 1998 to 30 September 1999.

(e) Calculations Performed Around 30 September
2004

Following clause 18.5, the next possible claim is 5
years later, i.e. around 30 September 2004 (T=2004). We return then to clause
18.3
. Since the condition there for a claim was satisfied earlier with
T=1999, then it will also be satisfied for T=2004. Thus we can proceed directly
to clause 18.4 and calculate the Additional Ngai Tahu Redress Amount,
deemed to be paid on 31 December 2003, and designated $Y. Firstly, we calculate
the Real Value as at 31 December 1994 of the Total Redress Amount up to and
including CFY 2004. Referring to paragraph (c) of the definition of Real Value
in clause 18.1.1 this is

= $1,730.547m

Next we determine the Real Value as at 31 December 1994 of any
Additional Ngai Tahu Redress Amounts up to and including CFY 2004, being the
$15.708m deemed paid earlier and the $Y deemed to be paid on 31 December 2003.
Following paragraph (d) of the definition of Real Value in clause 18.1.1,
this is

Following clause 18.4, this $Y must then be such that
the $180m referred to previously, plus the real value amount in the last
equation above, equals 18.2% of the $1,730.547m above, i.e.:

So, $Y = $143.945m. This payment, deemed to have been made on
31 December 2003, would then be increased to reflect inflation over the period
from 31 December 2003 to the end of the quarter immediately preceding the actual
payment date.

Further claims would then arise every 5 years up to 2044, with
a claim in 2044 even if it was less than 5 years since its
predecessor.

It should finally be noted that, in equation (5), the $15.708m
used is the $X calculated earlier rather than the actual amount paid (the latter
being $X raised to reflect inflation from the deemed payment date to the end of
the quarter preceding the actual payment date). This is because the discounting
performed in equation (5) on the $15.708m presumes payment on 31 December 1998
and this presumption then requires use of the $15.708m.

TABLE A

CFY(n) TARn

$m
PV(TARn)

$m
Present Value
as at
31.12.94 of

Total Redress Amount
$m
1996 100 94.551 449.869
1997 300 268.199 718.069
1998 200 169.057 887.126
1999 150 119.884 1,007.011
1900 250 187.586 1,194.598
2001 200 140.890 1,335.489
2002 150 99.204 1,434.694
2003 100 62.091 1,496.785
2004 50 28.899 1,525.685
2005 100 53.804 1,579.489
2006 50 25.042 1,604.532

TABLE B

Calendar Year (k) Rk tk CPI (beginning of calendar year
k)
rk (1 - tk x
0.75)
1995 .07 .33 1000 .0368872
1996 .07 .33 1020 .0368872
1997 .07 .33 1040.4 .0368872
1998 .07 .33 1061.208 .0368872
1999 .08 .33 1082.4322 .0442647
2000 .08 .33 1104.0808 .0442647
2001 .08 .33 1126.1624 .0442647
2002 .08 .33 1148.6857 .0442647
2003 .09 .30 1171.6594 .0531862
2004 .09 .30 1195.0926 .0531862
2005 .09 .30 1218.9944 .0531862
2006     1243.3743  

FIGURE 1

TIME SPAN OR POINT IN TIME FOR VARIOUS RELATIVITY MECHANISM
ELEMENTS