The provisions of this paragraph (b) may be illustrated by the following examples.
1.148-4(b)(6) Example 1. No early call.
(i) Facts.
On January 1, 1994, City A issues an issue consisting of four identical fixed yield bonds. The stated final maturity date of each bond is January 1, 2004, and no bond is subject to redemption before this date. Interest is payable on January 1 of each year at a rate of 6.0000 percent per year on the outstanding principal amount. The total stated principal amount of the bonds is $20 million. The issue price of the bonds $20,060,000.
(ii) Computation.
The yield on the issue is computed by treating the bonds as retired at the stated maturity under the general rule of section 1.148-4(b)(1). The bonds are treated as redeemed for their stated redemption prices. The yield on the issue is 5.8731 percent per year compounded semiannually, computed as follows:
Date Payments PV (5.8731 percent)
111995 $ 1,200,000 $1,132,510
111996 1,200,000 1,068,816
111997 1,200,000 1,008,704
111998 1,200,000 951,973
111999 1,200,000 898,433
112000 1,200,000 847,903
112001 1,200,000 800,216
112002 1,200,000 755,210
112003 1,200,000 712,736
112004 21,200,000 11,883,498
____________
$ 20,060,000
============
1.148-4(b)(6) Example 2. Mandatory calls.
(i) Facts.
The facts are the same as in Example 1. In this case, however, the bonds are subject to mandatory sinking fund redemption on January 1 of each year, beginning January 1, 2001. On each sinking fund redemption date, one of the bonds is chosen by lottery and is required to be redeemed at par plus accrued interest.
(ii) Computation.
Because the bonds are subject to specified redemptions, yield on the issue is computed by treating the bonds as redeemed in accordance with the redemption schedule under section 1.148-4(b)(2)(ii). Because the bonds are not sold at a discount, the bonds are treated as retired at their stated redemption prices. The yield on the issue is 5.8678 percent per year compounded semiannually, computed as follows:
Date Payments PV (5.8678 percent)
____ ________ ___________________
111995 $1,200,000 $1,132,569
111996 1,200,000 1,068,926
111997 1,200,000 1,008,860
111998 1,200,000 952,169
111999 1,200,000 898,664
112000 1,200,000 848,166
112001 6,200,000 4,135,942
112002 5,900,000 3,714,650
112003 5,600,000 3,327,647
112004 5,300,000 2,972,407
____________
$ 20,060,000
============
1.148-4(b)(6) Example 3. Optional early call.
(i) Facts.
On January 1, 1994, City C issues an issue consisting of three bonds. Each bond has a stated principal amount of $10 million dollars and is issued for par. Bond X bears interest at 5 percent per year and matures on January 1, 1999. Bond Y bears interest at 6 percent per year and matures on January 1, 2002. Bond Z bears interest at 7 percent per year and matures on January 1, 2004. Bonds Y and Z are callable by the issuer at par plus accrued interest after December 31, 1998.
(ii) Computation.
(A) The yield on the issue computed as if each bond is outstanding to its maturity is 6.0834 percent per year compounded semiannually, computed as follows:
Date Payments PV (6.0834 percent)
____ _________ ________________
111995 $ 1,800,000 $1,695,299
111996 1,800,000 1,596,689
111997 1,800,000 1,503,814
111998 1,800,000 1,416,342
111999 11,800,000 8,744,830
112000 1,300,000 907,374
112001 1,300,000 854,595
112002 11,300,000 6,996,316
112003 700,000 408,190
112004 10,700,000 5,876,551
_____________
$30,000,000
=============
(B) The yield on the issue computed as if all bonds are called at the earliest date for redemption is 5.9126 percent per year compounded semiannually, computed as follows:
Date Payments PV (5.9126 percent)
____ ________ ____________________
111995 $1,800,000 $1,698,113
111996 1,800,000 1,601,994
111997 1,800,000 1,511,315
111998 1,800,000 1,425,769
111999 31,800,000 23,762,809
_____________
$30,000,000
=============
(C) Because the yield on the issue computed by assuming all bonds in the issue subject to redemption within 5 years of the issue date are redeemed at maturity is more than one-eighth of one percentage point higher than the yield on the issue computed by assuming all bonds subject to optional redemption within 5 years of the issue date are redeemed at the earliest date for their redemption, each bond is treated as redeemed on the date that would produce the lowest yield for the issue. The lowest yield on the issue would result from a redemption of all the bonds on January 1, 1999. Thus, the yield on the issue is 5.9126 percent per year compounded semiannually.