The ﬁrst instrument is a middle dated annuity. This is a class of
security which pays out a constant stream of income. Each payment
can be thought of as being comprised of both interest and principal; to
begin with most of the payment will be interest but as the time to matur-
ity increases then more will be comprised of nominal. There is a for-
mula to calculate its value; this is displayed in the equation below:
where P is the principal amount and r is the annuity rate lasting for n
For example if we consider the ﬁrst tranche, which has a common
annual payment of $115 000 000 lasting for 15 years, r 4%:
This value is very approximate, and considerably overvalues, for reason
we postpone to a later discussion.
Annuities comprise two tranches of the structure. If we examine the
loan proﬁle we can infer why this was the case. The shape can be
approximately described by two distinct patterns. The ﬁrst part com-
prises payouts up to a maturity of about 2018; this is almost a hori-
zontal line. The second shape starts from 2018 and extends to 2023.
This is a downward sloping line and is caused by a heavy loan redemp-
tion schedule over this period.
As annuities produce a horizontal proﬁle they are a natural candidate
for the securitization of the payments until 2018. The question then
arises as to whether there will be sufﬁcient investor appetite for these
long dated instruments. The demand for the various tranches comes
from different sources of the investment community. Generally the prin-
cipal aim is to securitize as much as possible as high-investment grade.
This would then appeal to the large institutional investors who are usu-
ally only allowed through regulatory authorities to deal in such paper.
Further appeal would be anticipated from the retail marketplace.
The long dated annuities would be structured as investment grade
assets, and would ﬁnd a natural home within the pension funds that
P $1278 614 560.
P $115 000 000
(1 0.04) 1
0.04 (1 0.04)
(1 ) 1