Sinking Fund Formula

Sinking Fund Formula (Table of Contents)

Sinking Fund Formula
Examples of Sinking Fund Formula (With Excel Template)
Sinking Fund Formula Calculator

In a very simple language, Sinking fund is a type of fund which is set up for repayment of debt. The party who sets up this kind of fund usually sets asides a certain amount of money on a regular basis and which is then used to repay the debt amount. The usual way of retiring the debt is by a bond issue. For example, a company, who has issued a bond in the past and raised money; they can deposit money regularly in the fund for the purpose of buying back the bond each quarter before maturity. So instead of paying the whole principal amount at the expiry of the bond, the borrower will pay off his debt in installments.

If we talk from an investor’s point of view, longer the duration of the bond, higher is the risk that the borrower will default. But sinking fund adds a layer of protection because as the time passes by, the principal amount is getting reduced and there are fewer chances that the borrower will default on the lower principal amount. So sinking funds increase the confidence of investor that the other party will not default.

If we want to calculate the accumulated value in the sinking fund, we can use the following formula :

Where

A – Money accumulated
P – Periodic contribution,
r – Interest rate
t – Number of years
n – Number of payments per year

In other words, we can see what is the Periodic Payment needed by :

Examples of Sinking Fund Formula (With Excel Template)

Let’s take an example to understand the calculation of Sinking Fund formula in a better manner.

You can download this Sinking Fund Template here – Sinking Fund Template

Sinking Fund Formula – Example #1

Consider a food retail company A, which is doing well in its business and to expand its business operations, they want to raise money through debt route. So that is why they have issued $50,000 worth of bonds, which mature in 10 years and has a sinking fund provision.

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Solution:

Amount to be deposited in the Sinking Fund is calculated using the formula given below

Amount to be Deposited in Sinking Fund = Amount of Debt / Time

Amount to be Deposited = $50,000 / 10
Amount to be Deposited = $5,000

So by establishing a sinking fund, company A must regularly deposit, say $5000 each year in the fund which will be exclusively used to retire this debt.

A company can also retire the debt early if there exists an opportunity. So if the market price of the goes down, they can use this fund and can buy back the bonds and issue another bond with lower price and with the remaining time. This will help them to eventually reduce the principal amount of the debt.

Sinking Fund Formula – Example #2

Company XYZ issued bonds worth of $5 million, having a 10% coupon rate and maturing in 10 years. The company has set up sinking up to pay off the bond. Coupons are to be paid semiannually and the market interest rate says 6%.

Solution:

Periodic Contribution is calculated using the formula given below

P = A / (((1 + r / n) ^ (t * n) – 1) / (r / n))

Periodic Contribution = $500,000 / (((1 + 6% / 2) ^ (10 * 2) – 1)/(6% / 2))
Periodic Contribution = $18,607.85

Explanation

Basically, in the sinking funds, since there is sufficient money available to pay off the debt, this helps in ensuring that the default will not happen and that is the main reason of setting up sinking fund at the first place. It is always better to reduce the principal amount long before it matures, consequently lowering credit risk.

To establish a sinking fund, the issuer basically sets up a custodial account and makes systematic payments into it. This can happen that payments might not begin until several years have passed. Generally, the amounts to be deposited are fixed but sometimes variable amounts are also allowed. This is based on a number of factors like earnings levels, a reputation of issuer etc.

Sinking funds can either be in cash or in the form of other bonds (discussed above) or preferred stock. In case of cash deposits, the trustee will use those funds and repurchase some or all of the bonds on the open market. If instead of cash, we have another debt into the custodial account, the issuer usually purchases the bonds itself on the open market if the bonds are trading below par value. Sometimes there can also be a doubling option along with a sinking fund. This allows the issuer to redeem twice the amount prescribed at each step in the sinking fund requirement.

Relevance and Uses of Sinking Fund Formula

There are various ways in which Sinking funds benefit the investors. First and the foremost benefit, which we have discussed above is that the by sinking funds, the likelihood of default becomes very negligible due to less principal outstanding, and thus lowering default risk. Second, if there is an increase in interest rates which will reduce the price of the bonds, investors will have downside protection because the issuer has to at least pay at least the par value of the bond. Third, sinking funds provisions helps in creating a liquid secondary market for bonds.

Every good thing comes with some flaws in it. So there are also some disadvantages of sinking funds. The upside of the bond price is limited for the investor. So if the bond is selling at a higher price, an investor has no option to reap that benefit. Also, sometime, investors might have to reinvest their money elsewhere at a lower rate. This is very risky in case of exercising a doubling option.

At last, we can conclude that sinking fund, because of its simplicity, is very easy to start. However, many people fail or reluctant to do that. One simple reason for that is it needs the discipline to keep the specified money aside on a regular basis. People tend to divert from that path which makes sinking fund, from a simple concept, a complex thing.