# Valuation of a Sinking Bond Fund

What would the schedule of payments be for a bond with a sinking fund? I know how to price a bond but how does the sinking fund play into it?

Semi-Annual Pay Bonds
Maturity    12/31/2033
Original Par    10,000,000
Coupon Rate 4%
First interest payment date 6/30/2014

Principal Sinking Fund payments of \$1 million per year
(in December) for last 10 years starting in 12/31/2024
(through 12/31/2033)

Bond Interest Payment    Bond Principal Payment   Total Bond Payment
6/30/2014
12/31/2014
6/30/2015
12/31/2015
6/30/2016
12/31/2016
6/30/2017
12/31/2017
6/30/2018
12/31/2018
6/30/2019

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I assume the sinking fund is optional and non-cumulative. In effect the issuer of the bond holds 10 European call options on 1 million at 4% each. These are valued using a binomial tree and are interest rate dependent. To value the bond price the bond as if there were no options embedded (I.e. it's single bullet, plain vanilla bond) and then add (really subtract) the value of the options.

I assume that every year the issuer can call a maximum of 1 million. If they are cumulative (e.g. if in year 2 the issuer can call 2 million if a million was not called the year before) then you're best left off with a monte-carlo simulation.

Fixed Income Securities and Derivatives Handbook - Choudry. Binomial trees starting point: http://en.wikipedia.org/wiki/Binomial_options_pricing_model

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