# Sinking Fund: Definition & Formula

Instructor: Douglas Stockbridge

DJ Stockbridge is currently pursuing a Masters degree in Accounting.

In this lesson, you will learn about sinking funds. By the end of the lesson, you will be able to recount the definition and give reasons why a company, and its creditors, may insist on having a sinking fund.

Imagine it's the middle of March and you and some friends have decided to fill out brackets (predicting the winners) for the Men's College Basketball Tournament (aka March Madness).

Normally, the person with the closest bracket to the actual result wins a free dinner. They get to choose the place and everyone else pays. You and your friends decide the reward will be the same this year, however, Janet boasts, ''I bet any of you that I will select a perfect bracket. I will get every selection correct.''

You are a finance/accounting major and you remember some of your introductory probability and statistics classes. You know there's a higher likelihood of getting struck by lightning or winning the lottery than picking all correct selections, so you call her out: ''Yeah, I'll make that bet. I will pay you \$10,000 in 5 years if you pick a perfect bracket, but if you do not, you need to pay me \$500.''

''Deal!'' she replies. Over the following weeks, you were horrified to see the impossible happen. She actually did pick a perfect bracket, and now you are responsible to pay her \$10,000 in 5 years.

The problem is that you don't have very much money at all. You have some cash in the bank and you have steady employment, but it will be difficult finding \$10,000 to give to her. From your finance/accounting days, you remember a concept called a sinking fund. This may help relieve some of the pressure of paying \$10,000 all in year 5.

## Sinking Fund

A sinking fund is a way for a borrower to pay down the principal amount that it owes before the principal payment date occurs. For example, if the maturity calls for a principal of \$100M due in 3 years, a sinking fund would allow the issuer to pay a certain amount in this year and the next year to reduce the total liability in year 3. You can kind of think of sinking funds as allowing you to 'pre-pay' the principal.

In terms of its mechanics, the issuer gives money to a trustee who is then responsible for purchasing the bonds in the open market. It may be in the lender's contract that the sinking fund can buy back bonds at face value. If that isn't an option, then the trustee just buys the bonds at the market price. It may be in the contract that the trustee holds the cash in the sinking fund until bonds appear in the open market at attractive prices. In that case, a company may build up a reserve fund as they wait patiently to buy the bonds back.

If they do have the option, the trustee then buys bonds at the lesser of face value or market value. For example, if the bonds trade at a premium (i.e. greater than 100), and the trustee has the option of buying the bonds at face value or market value, they will choose to buy at the face value because the total cost would be lower.

In our March Madness example, a sinking fund could be established to help you pay the \$10,000. For example, you could designate a friend, Steve who would act as the 'trustee.' As you save money each year, you can transfer the money to Steve who would invest it in safe securities in anticipation of the big payment date in year 5.

This way you wouldn't be overwhelmed by the big payment. You could focus yourself on ''taking baby steps'' by saving a certain amount each year and allocating it to the sinking fund. The amount you pay could be \$1,500 in years 1-4, and \$4,000 in year 5.

## A Real-World Example

To show an example of a bond with a sinking fund, let's imagine there is a company looking to use \$212M due in 30 years. Let's assume the bond is exclusively principal-only. This means interest is due each year, and then the final payment is composed the whole principal amount (\$212M) and the interest for that year.

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