164 Chapter 4 Annuities
Sinking Funds with Loans
Knowing that her company had a large expense ahead on the horizon, it was prudent of
Shauna to set up a fund to be able to meet it, rather than just wait and then get hit with
a major expense all at once. However, Example 4.3.2 didn’t say that she was under any
obligation to do this. Shauna could just as well have chosen to not worry about the obliga-
tion until the end of the 2 years, hoping that she would be able to come up with the money
when needed. Of course, this risks the unpleasant possibility of being unable to come up
with the required amount to meet the obligation, or being able to come up with it but finan-
cially jeopardizing her company’s finances if its financial position is not strong enough to
comfortably weather a $10,000 payment all at once. Shauna was smart to not want to take
that chance.
But it is not only Shauna who should be concerned about this. Elena must realize that if
Shauna can’t come up with the $10,000 when it is due, she may not get paid. If funds have
not been set aside along the way, and if Shauna’s business isn’t flush enough with cash to
pay the $10,000 all at once, Elena may find that trying to collect her money is trying to
get blood from a stone. Elena may have legal contracts to show that Shauna must pay, and
Shauna might be a decent and honest person with no intention of cheating her friend—but
if the money isn’t there, the money isn’t there. Elena might have to wait longer than she
agreed to before she can collect, she might have to hound Shauna or even sue her to get the
funds, or she may not even be able to collect at all.
Given these possibilities, Elena has good reason to want Shauna to be building up that
balance along the way. To help ensure that she will in fact be able to pay her when the
time comes, it is possible that Elena might insist that as part of their agreement Shauna be
required to set up and pay into a sinking fund. This would not be an unusual provision to
include in their deal.
Loans provide another situation where one party might require another to have a sinking
fund. The following example will illustrate.Example 4.3.3 The Shelbyville Water and Sewer District has borrowed $1.5 million
from a group of investors. The note carries an interest rate of 5.52% compounded
annually, and matures in 7 years. No payments will be made to the investors during
the term of the loan, but the deal requires the district to establish a sinking fund, and
make semiannual deposits into this fund in order to accumulate the full maturity value.
As required, the district sets up an account at a local bank, which offers an interest
rate of 3.8%. How much should each of the deposits be?Before determining the sinking fund payment, we must fi rst determine the future value
to be accumulated. The future value will be the $1.5 million borrowed, together with the
interest that it accumulates. This is not an annuity, but rather is a case of regular com-
pound interest:FV PV(1 i)n
FV $1,500,000(1.0552)^7
FV $2,184,915.96On an amount this large, anything less than a dollar is insignifi cant, so we can reasonably
round this future value to $2,184,916.Now that we know the desired future value, we can readily fi nd the sinking fund payment.FV PMT s _n (^) | (^) i
$2,184,916 PMT s __ 14 | (^) .019
$2,184,916 PMT(15.86753836)
PMT $137,697.23
While we have generally tried to avoid having to write down and retype long decimals, in
these cases trying to combine everything into a single calculator entry is impractical.