Zero Coupon Bonds

To understand hoe zeros are used and analyzed, consider the zeros that are going to be issued by Vandenberg Corporation, a shopping center developer. Vandenberg is developing a new shopping center in San Diego. California, and it needs $50 million. The company 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 financing vehicle that will not require cash outflows for five years, and he has decided on a five year zero coupon bond, with 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 k_d=6%, annual compounding. Using the tables, we find PV=$1,000(0.7473) =$747.30. Using a financial calculator, we input N=5,1=6, PMT=0, and FV=1000, the press the PV key to find PV=$747.26. Note that $747.26. Compounded 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 compounded value of the bond at the end of each year. The accrued value for Year 0 is the issue price; the accrued value for Year 1 is found as $747.26(1.06)=$792.10; the accrued value at the end of year 2 is $747.26(1.06)²=$839.62; and in general the value at the end of any year in is

Accrued value at the end of Year n=issue price × (1+k₃)ⁿ.

4. The interest deduction as shown on Line 2 represents the increase in accrued value during the year. Thus, interest in Year 1=$792.10 - $747.26=$44.84. in general,

Interest in year n=Accrued value_n – Accrued value_n-1.

This method of calculating taxable interest is specified in the Tax Code.

5. The company can deduct interest each year, even though the payment is not made in cash. This deduction lowers the taxes that would otherwise be paid, producing the following savings:

Tax savings     = (Interest deduction) (T).

                        = $44.84 (0.4)

                        = $17.94 in year 1.