DBC Support - Sinking Fund Adjustment example
Assumptions:
A term bond:
Dated Date 1/1/1994
Delivery Date 1/1/1994
Maturity Date 1/1/2004
Interest Rate 6.000%
Price 97.000
Yield 6.411%
Insurance 0.5% of total D/S
Sinking Fund Par Amount Total D/S Insurance Cost
1/1/2003 1,000,000 1,540,000 7,700
1/1/2004 1,000,000 1,600,000 8,000
Method for computing PV rate used for sinking fund adjustment calculation:
Apply the entire insurance cost to the entire term bond and compute as though
all sinking funds were left to maturity. Thus the PV rate is calculated using
the cash flow of 2,000,000 maturing on 1/1/2004 with a target of
(2,000,000 - 60,000 - 15,700) = 1,924,300. This results in a PV rate of 6.5211601%.
PROOF OF ARBITRAGE YIELD
Benchmarks
Simulated full term bond with Bond Insurance
Present Value
to 1/01/1994
Date Debt Service @ 6.5211601%
----------------------------------------------------
Jul 1, 1994 60,000.00 58,105.43
Jan 1, 1995 60,000.00 56,270.68
Jul 1, 1995 60,000.00 54,493.86
Jan 1, 1996 60,000.00 52,773.15
Jul 1, 1996 60,000.00 51,106.77
Jan 1, 1997 60,000.00 49,493.01
Jul 1, 1997 60,000.00 47,930.21
Jan 1, 1998 60,000.00 46,416.75
Jul 1, 1998 60,000.00 44,951.09
Jan 1, 1999 60,000.00 43,531.70
Jul 1, 1999 60,000.00 42,157.13
Jan 1, 2000 60,000.00 40,825.97
Jul 1, 2000 60,000.00 39,536.84
Jan 1, 2001 60,000.00 38,288.42
Jul 1, 2001 60,000.00 37,079.41
Jan 1, 2002 60,000.00 35,908.58
Jul 1, 2002 60,000.00 34,774.73
Jan 1, 2003 60,000.00 33,676.67
Jul 1, 2003 60,000.00 32,613.29
Jan 1, 2004 2,060,000.00 1,084,366.30
----------------------------------------------------
3,200,000.00 1,924,300.00
====================================================
Proceeds Summary
Delivery date 1/01/1994
Par Value 2,000,000.00
Premium (Discount) -60,000.00
Arbitrage expenses -15,700.00
------------------
Target for yield calculation 1,924,300.00
Computation of yield of deep discount term bond. The entire term is
assumed to mature on 1/1/2004, but the bond insurance amount remains
at $15,700.
PROOF OF ARBITRAGE YIELD
Benchmarks
Actual Term Bond w/Sinking Fund Adjustment & Bond Insurance
Present Value
Sinking Fund to 1/01/1994
Date Debt Service Adjustments Total @ 6.5211601%
----------------------------------------------------------------------------------
Jul 1, 1994 60,000.00 60,000.00 58,105.43
Jan 1, 1995 60,000.00 60,000.00 56,270.68
Jul 1, 1995 60,000.00 60,000.00 54,493.86
Jan 1, 1996 60,000.00 60,000.00 52,773.15
Jul 1, 1996 60,000.00 60,000.00 51,106.77
Jan 1, 1997 60,000.00 60,000.00 49,493.01
Jul 1, 1997 60,000.00 60,000.00 47,930.21
Jan 1, 1998 60,000.00 60,000.00 46,416.75
Jul 1, 1998 60,000.00 60,000.00 44,951.09
Jan 1, 1999 60,000.00 60,000.00 43,531.70
Jul 1, 1999 60,000.00 60,000.00 42,157.13
Jan 1, 2000 60,000.00 60,000.00 40,825.97
Jul 1, 2000 60,000.00 60,000.00 39,536.84
Jan 1, 2001 60,000.00 60,000.00 38,288.42
Jul 1, 2001 60,000.00 60,000.00 37,079.41
Jan 1, 2002 60,000.00 60,000.00 35,908.58
Jul 1, 2002 60,000.00 60,000.00 34,774.73
Jan 1, 2003 1,060,000.00 -4,967.36 1,055,032.64 592,166.47
Jul 1, 2003 30,000.00 30,000.00 16,306.64
Jan 1, 2004 1,030,000.00 1,030,000.00 542,183.15
----------------------------------------------------------------------------------
3,140,000.00 -4,967.36 3,135,032.64 1,924,300.00
==================================================================================
Proceeds Summary
Delivery date 1/01/1994
Par Value 2,000,000.00
Premium (Discount) -60,000.00
Arbitrage expenses -15,700.00
------------------
Target for yield calculation 1,924,300.00
Yields for Sinking Fund Adjustments
Term Bond
Maturing Yield
-------------------------------
1/01/2004 6.5211601%
-------------------------------
The sinking fund adjustment of -4,967.36 on 1/1/2003 is computed using the
term yield of 6.5211601% computed on the previous page as follows:
Future Debt Service
on 1/1/2003 PV to 1/1/2003
Date Sinking Fund @ 6.5211601%
7/1/2003 30,000 29,052.7130
1/1/2004 1,030,000 965,979.9319
Total PV: 995,032.6449
Less Par Amount: -1,000,000.0000
Sinking Fund Adjustment: -4,967.3551
Rounded adjustment: -4,967.36