Web Appendix 7A

# Web Appendix 7A - 19819_07Aw_p1-5.qxd 10:31 AM Page 7A-1...

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7A-1 To understand how zeros are used and analyzed, consider the zeros that are going to be issued by Vandenberg Corporation, a shopping center developer. Vandenberg is develop- ing a new shopping center in San Diego, California, and it needs \$50 million. The com- pany does not anticipate major cash flows from the project for about five years. However, Pieter Vandenberg, the president, plans to sell the center once it is fully developed and rented, which should take about five years. Therefore, Vandenberg wants to use a financ- ing vehicle that will not require cash outflows for five years, and he has decided on a five- year zero coupon bond issue, each bond having a maturity value of \$1,000. Vandenberg Corporation is an A-rated company, and A-rated zeros with five-year maturities yield 6 percent at this time (five-year coupon bonds also yield 6 percent). The company is in the 40 percent federal-plus-state tax bracket. Pieter Vandenberg wants to know the firm’s after-tax cost of debt if it uses 6 percent, five-year maturity zeros, and he also wants to know what the bond’s cash flows will be. Table 7A-1 provides an analysis of the situation, and the following numbered paragraphs explain the table itself. 1. The information in the “Basic Data” section, except the issue price, was given in the preceding paragraph, and the information in the “Analysis” section was calculated using the known data. The maturity value of the bond is always set at \$1,000 or some multiple thereof. 2. The issue price is the PV of \$1,000, discounted back five years at the rate r d ± 6%, annual compounding. Using a financial calculator, we input N ± 5, I/YR ± 6, PMT ± 0, and FV ± 1000, then press the PV key to find PV ± \$747.26. Note that \$747.26, com- pounded annually for five years at 6 percent, will grow to \$1,000 as shown by the time line on Line 1 in Table 7A-1. 3. The accrued values as shown on Line 1 in the analysis section represent the com- pounded value of the bond at the end of each year. The accrued value for Year 0 is the WEB APPENDIX WEB APPENDIX 7A Zero Coupon Bonds Basic Data Maturity value \$1,000 r d 6.00%, annual compounding Maturity 5 years Corporate tax rate 40.00% Issue price \$747.26 Analysis 02 3 \$1,000.00 56.60 22.64 ² 977.36 \$943.40 53.40 21.36 ³ 21.36 \$890.00 50.38 20.15 ³ 20.15 \$839.62 47.52 19.01 ³ 19.01 \$792.10 44.84 17.94 ³ 17.94 \$747.26 ³ 747.26 3.60% (1) Year-end accrued value (2) Interest deduction (3) Tax savings (40%) (4) Cash flow to Vandenberg After-tax cost of debt Face value of bonds the company must issue to raise \$50 million = Amount needed/issue price as % of par 45 1 = \$50,000,000/0.74726 ± \$66,911,000 6% Years TABLE 7A-1 Analysis of a Zero Coupon Bond from Issuer’s Perspective

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issue price; the accrued value for Year 1 is found as \$747.26(1.06) 5 \$792.10; the accrued value at the end of Year 2 is \$747.26(1.06) 2 5 \$839.62; and, in gen- eral, the value at the end of any Year N is (7A-1) 4. The interest deduction as shown on Line 2 represents the increase in accrued value during the year. Thus, interest in Year 1
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Web Appendix 7A - 19819_07Aw_p1-5.qxd 10:31 AM Page 7A-1...

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