# Sinking Fund

A sinking fund is a fund set up to accumulate money for payoff of a bond at some future date. It receives periodic contributions from the issuer that accumulate such that at the time of maturity the balance in the sinking fund equals the par value of the bonds payable.

Sinking fund provision is the legal clause in the bond indenture which requires setup of a sinking fund for payoff of a bond. Accelerated sinking fund provision is the clause that entitles the issuer to pay off the bond before the due date.

## Formula

Where the sinking fund receives uniform periodic contributions, the amount of contributions can be calculated by a modification of the future value of annuity formula.

Periodic Contribution to Sinking Fund = | Par Value of Bonds to be Paid off | ||

(1 + r_{s})^{n} − 1 | |||

r_{s} |

Where *r _{s}* is the rate of return earned by the money deposited in the sinking fund.

## 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.

__Solution__

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

Periodic Contribution to Sinking Fund = | $500,000,000 | = $11,388,820 | ||

(1 + 2.5%)^{30} − 1 | ||||

2.5% |

VC must deposit $11,388,820 at the end of each 6 months for 15 years in order to accumulate enough money to pay off the bonds when they are due.

Written by Obaidullah Jan