Sinking Fund
A sinking fund is a fund required to be setup by the bond issuer to which it must contribute money each period to repurchase a certain portion of the bond issue. It can also be referred to a fund created by a company to accumulate money for replacement of a large asset or any other major expenditure.
In case of bonds, the sinking fund is a credit enhancement because it is a separate custodial account whose funds are earmarked for repurchase of bonds. In an accelerated sinking fund, the issuer is entitled to retire a higher percentage of the bond. An accelerated sinking fund provision has an embedded call option because it allows the bond issuer to retire bonds earlier than their scheduled retirement.
Formula
Let A be the money accumulated and P be the periodic contribution, if the interest rate is r, there are n number of years and m number of payments per year, we can use the future value of annuity formula to find the accumulated amount A:
$$ \text{A}=\text{P}\times\frac{{(\text{1}+\frac{\text{r} _ \text{s}}{\text{m}})}^{\text{n}\times \text{m}}-\text{1}}{\frac{\text{r} _ \text{s}}{\text{m}}} $$
Dividing both sides by the second term on the right hand side in the above equation and flipping it, we get the formula for calculation of periodic contribution needed:
$$ \text{P}=\frac{\text{A}}{\frac{{(\text{1}+\frac{\text{r} _ \text{s}}{\text{m}})}^{\text{n}\times \text{m}}-\text{1}}{\frac{\text{r} _ \text{s}}{\text{m}}}} $$
Example
Goliath Infrastructures (GI) just issued 5 million $100-par bonds payable carrying 8% coupon rate and maturing in 15 years. The bond indenture requires GI to set up a sinking up to pay off the bond at the maturity date. Semi-annual payments are to be made to the fund which is expected to earn 5% per annum.
Find the amount of required periodic contributions.
The future value required to be accumulated equals $500 million (=5,000,000*$100)
Since the payments are semi-annual, the periodic interest rate = 5%/2 = 2.5%
Number of periods = 2*15 = 30
$$ \text{Periodic contribution to sinking fund}=\frac{\text{\$500,000,000}}{\frac{{(\text{1}+\frac{\text{5%}}{\text{2}})}^{\text{15}\times\text{2}}-\text{1}}{\frac{\text{5%}}{\text{2}}}}=\text{\$11,388,820} $$
by Obaidullah Jan, ACA, CFA and last modified on