Sinking Fund Formula

Updated on January 5, 2024
Article byAshish Kumar Srivastav
Reviewed byDheeraj Vaidya, CFA, FRM

What Is The Sinking Fund Formula?

A sinking fundrefers to a fund that is set aside by an economic entity over a period of time to take care of the planned expenses or the debt obligations. An investor, on the contrary, uses it to repurchase a definite portion of the bond issue or for the replenishment of a major asset or any other similar capital expenditureCapital ExpenditureCapex or Capital Expenditure is the expense of the company's total purchases of assets during a given period determined by adding the net increase in factory, property, equipment, and depreciation expense during a fiscal year.read more. This amount saved serves multiple purposes during emergency situations.

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Source: Sinking Fund Formula (wallstreetmojo.com)

When one starts a business, there are lots of planned expenses, which must be fulfilled gradually to record a successful business. The sinking fund calculated using the formula allows businesses to keep aside a fund that would help them bear the planned expenditure for their business.

Sinking Fund Formula Explained

Sinking Fund formula helps calculate the amount to be kept aside from the revenue over a period to bear other planned future expenses. It, in short, becomes a saving for the business, which stores this amount intentionally to bear the expenses that have been already planned.

There are multiple expenses of a business throughout the month, these sinking funds that are simply kept aside help businesses to not touch its incoming profits and deal with those expenses from the savings that it does in the form of sinking fund.

Once the entities know what to save for, they can plan the amount accordingly. For investors, sinking fund is a slightly different concept. Here, the corporate bond issue gets a safety cover in the form of sinking fund. The bond issuer is required to contribute a certain amount of money to the sinking fund each period, and the formula to calculate the sinking fund is as shown below.

Sinking Fund, A= [(1+(r/m))n*m-1] / (r/m) * P

where

  • P = Periodic contribution to the sinking fund,
  • r = Annualized rate of interest,
  • n = No. of years
  • m = No. of payments per year

And the formula for the periodic contribution to the sinking fund can be represented as,

Periodic Contribution, P = (r/m) / [(1+(r/m))n*m-1] * A

The savings calculated using the formula helps investors have funds to pay off bonds at maturity.

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How To Calculate?

Given below are the steps to follow to calculate sinking fund using the formula:

  1. Firstly, determine the required periodic contribution to be made to the sinking fund as per the company strategy. The periodic contribution is denoted by P.

  2. Now, the annualized rate of interest of the fund and the frequency of the periodic payment has to be determined, which are denoted by r and m, respectively. Then the periodic interest rate is computed by dividing the annualized interest rate by the number of pay per year. i.e Periodic interest rate = r / m

  3. Now, the number of years has to be determined, and it is denoted by n. Then the total number of periods is computed by multiplying the number of years and the frequency of payments in a year. i.e Total number of periods = n * m

  4. Finally, the calculation of the sinking fund can be done by using the periodic interest rate (step 2) and the total number of periods (step 3), as shown above.

Sinking Fund Explained in Video

 

Examples

Let us consider the following examples to understand the concept better and check its calculation aspects:

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

Example #1

Let us take an example of a sinking fund with a monthly periodic contribution of $1,500. The fund will be required to retire a newly taken debt (zero-coupon bonds) raised for the ongoing expansion project. Do the calculation of the amount of the sinking fund if the annualized rate of interest is 6%, and the debt will be repaid in 5 years.

Use the following data for the calculation of the Sinking Fund.

sinking fund formula example 1.1

Therefore, the calculation of the amount of the sinking fund is as follows,

sinking fund formula example 1.2
  • Sinking Fund = ((1+6%/12) ^(5-12) – 1)/(6%/12) * $1,500

Sinking Fund will be –

sinking fund formula example 1.3
  • Sinking Fund = $104,655.05 ~ $104,655

Therefore, the company will require a sinking fund of $104,655 to retire the entire debt five years from now.

Example #2

Let us take an example of a company ABC Ltd which has raised funds in the form of 1,000 zero-coupon bonds worth $1,000 each. The company wants to set up a sinking fund for repayment of the bonds, which will be after 10 years. Determine the amount of the periodic contribution if the annualized rate of interest is 5%, and the contribution will be done half-yearly.

First, do the calculation of the Sinking Fund Required for the calculation of Periodic Contribution.

example 2.1 - Periodic contribution data
  • Given, Sinking fund, A = Par value of bond * No. of bonds
  • = $1,000 * 1,000 = $1,000,000

Use the following data for the calculation of Periodic Contribution.

example 2.2 - Periodic contribution calculate

Therefore, the amount of the periodic contribution can be calculated using the above formula as,

example 2.3 - Periodic contribution calculation
  • Periodic contribution = (5%/2)/((1+5%/2)^(10*2) -1) * $1,000,000

The periodic contribution will be –

example 2.4 - Periodic contribution result
  • Periodic contribution = $39,147.13 ~ $39,147

Therefore, the company will be required to contribute a sum of $39,147 half-yearly in order to build the sinking fund to retire the zero-coupon bondsZero-coupon BondsIn contrast to a typical coupon-bearing bond, a zero-coupon bond (also known as a Pure Discount Bond or Accrual Bond) is a bond that is issued at a discount to its par value and does not pay periodic interest. In other words, the annual implied interest payment is included into the face value of the bond, which is paid at maturity. As a result, this bond has only one return: the payment of the nominal value at maturity.read more after 10 years.

Relevance and Uses

From the point of view of an investor, a sinking fund can be beneficial in three major ways-

  1. The interim retirement of debt results in lower principal outstanding that makes the final repayment much more comfortable and likely. This lowers the risk of default.
  2. In case the rate of interest increases, which lowers the bond prices, an investor gets some downside riskDownside RiskDownside Risk is a statistical measure to calculate the loss in a security’s value due to variations in the market conditions. Also, it refers to the uncertainty level of realized returns being much lesser than the anticipated ones. read more protection because the issuer is required to redeem a certain portion of these bonds. The redemption is executed at the sinking fund call price, which is usually fixed at the par value.
  3. A sinking fund is required to maintain liquidity of the bonds in the secondary marketSecondary MarketA secondary market is a platform where investors can easily buy or sell securities once issued by the original issuer, be it a bank, corporation, or government entity. Also referred to as an aftermarket, it allows investors to trade securities freely without interference from those who issue them.read more by acting as a buyer. When the interest rates increase, leading to a lower value for the bonds, this provision benefits the investors because the issuers have to buy the bonds even if the prices fall.

Limitations

The demerits of using the formula for calculating the sinking fund are as follows:

  1. If the bond prices increase due to a decrease in interest rate, the investor’s upside may end up limited because of the compulsory redemption mandated for the sinking fund of the bondSinking Fund Of The BondA bond sinking fund refers to the sum a company sets aside for repurchasing its bonds or meeting the related future obligations. Thus, the company saves money with an independent trustee at frequent intervals until the bonds' maturity.read more. This means that the investors would receive the fixed sinking-fund price for their bonds despite the fact that the bonds are priced higher in the open market.
  2. Further, the investors might end up reinvesting their money elsewhere at a lower rate due to the sinking fund provisions in a market with a declining interest rate.

For issuers, the sinking fund acts as credit enhancementCredit EnhancementCredit enhancement is a strategy used by businesses to increase their creditworthiness through a variety of internal and external measures. The fundamental goal is to obtain better debt repaying terms, hence lowering investors' risk of specific structured products in the financial market.read more and, as such, enables companies to borrow cheaply. Consequently, bonds with sinking funds often offer lower yields than similar bonds without sinking funds because of lower default risk and downside protection.

Recommended Articles

This has been a guide to what is the Sinking Fund Formula. We explain the concept with examples, how to calculate it, its relevance & uses, and limitations. You can learn more about accounting from the following articles –

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Comments

  1. Hawa Bolay says

    I want to say thank you so much for the step-by-step calculation on the sinking fund problems above, it helps me a lot on how to calculate problems like these ones.

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