Chapter 7 Web Appendix 7A

Chapter 7 Web Appendix 7A - WEB APPENDIX 7A Zero Coupon...

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Unformatted text preview: WEB APPENDIX 7A Zero Coupon Bonds 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 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 5 years. However, Pieter Vandenberg, the president, plans to sell the center once it is fully developed and rented, which should take about 5 years. Therefore, Vandenberg wants to use a financing vehicle that will not require cash outflows for 5 years; and he has decided on a 5-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 5-year maturities yield 6% at this time (5-year coupon bonds also yield 6%). The company is in the 40% federal-plus-state tax bracket. Pieter Vandenberg wants to know the firm’s after-tax cost of debt if it uses 6%, 5-year maturity zeros; and he 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. 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 5 years at the rate rd ¼ 6%, annual compounding. Using a financial calculator, we input N ¼ 5, I/YR ¼ 6, PMT ¼ 0, and FV ¼ 1000, then press the PV key to find PV ¼ $747.26. Note that $747.26 compounded annually for 5 years at 6% will grow to $1,000 as shown in Table 7A-1’s time line on Line 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) ¼ Table 7A-1 Basic Data Maturity value rd M a tu r i ty C o r p o r a te ta x r a te I s s ue p ric e Analysis of a Zero Coupon Bond from Issuer’s Perspective $1, 000 6.00%, annual compounding 5 y e a rs 40. 00% $747. 26 Analysis 0 6% 1 2 3 4 5 Years (1) Year-end accrued value $747.26 $792.10 $839.62 $890.00 $943.40 $1,000.00 (2) Interest deduction 44.84 47.52 50.38 53.40 56.60 (3) Tax savings (40%) 17.94 19.01 20.15 21.36 22.64 (4) Cash flow to Vandenberg 747.26 17.94 19.01 20.15 21.36 977.36 After-tax cost of debt 3.60% Face value of bonds the company must issue to raise $50 million = Amount needed/Issue price as % of par = $50,000,000/0.74726 ≈ $66,911,000 7A-1 7A-2 Web Appendix 7A $792.10; the accrued value at the end of Year 2 is $747.26(1.06)2 ¼ $839.62; and in general, the value at the end of any Year N is as follows: 7A-1 4. Accrued value at the end of year N ¼ Issue price  ð1 þ rd ÞN The interest deduction as shown on Line 2 represents the increase in accrued value during the year. Thus, interest in Year 1 ¼ $792.10 À $747.26 ¼ $44.84. The general equation is as follows: Interest in Year N ¼ Accrued valueN À Accrued valueNÀ1 7A-2 5. This method of calculating taxable interest is specified in the Tax Code. 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 tax savings: Tax savings ¼ ðInterest deductionÞðTÞ ¼ $44:84ð0:4Þ 7A-3 ¼ $17:94 in Year 1 6. 7. Line 4 represents cash flows on a time line; it shows the cash flow at the end of Years 0 through 5. At Year 0, the company receives the $747.26 issue price. The company also has positive cash inflows equal to the tax savings during Years 1 through 4. Finally, in Year 5, it must pay the $1,000 maturity value; but it receives one more year of interest tax savings. Therefore, the net cash flow in Year 5 is –$1,000 þ $22.64 ¼ À$977.36. Next, we can determine the after-tax cost (or after-tax yield to maturity) of issuing the bonds. Since the cash flow stream is uneven, the after-tax yield to maturity is found by entering the after-tax cash flows, shown on Line 4 of Table 7A-1, into the cash flow register and pressing the IRR key on the financial calculator. The IRR is the after-tax cost of zero coupon debt to the company. Conceptually, here is the situation: N X $747:26 ð1 þ rdðATÞ Þ0 8. þ $17:94 ð1 þ rdðATÞ Þ1 þ CFN t¼ 1 7A-4 ð1 þ rdðATÞ ÞN $19:01 ð1 þ rdðATÞ Þ2 þ ¼0 $20:15 ð1 þ rdðATÞ Þ3 þ $21:36 ð1 þ rdðATÞ Þ4 þ À $977:36 ð1 þ rdðATÞ Þ5 ¼0 The value of rd(AT) ¼ 0.036 ¼ 3.6%, found with a financial calculator, produces the equality; and it is the cost of this debt. (Input in the cash flow register CF0 ¼ 747.26, CF1 ¼ 17.94, and so forth, out to CF5 ¼ –977.36. Then press the IRR key to find rd(AT) ¼ 3.6%.) Note that rd(1 À T) ¼ 6%(0.6) ¼ 3.6%. As we will see in Chapter 10, the cost of capital for regular coupon debt is found using the formula rd(1 – T). Thus, there is symmetrical treatment for tax purposes for zero coupon and regular coupon debt; that is, both types of debt use the same after-tax cost formula. This was Congress’s intent, which is why the Tax Code specifies the treatment set forth in Table 7A-1.1 The purchaser of a zero coupon bond must calculate interest income on the bond in the same manner as the issuer calculates the interest deduction. Table 7A-2 shows the resulting tax payments for an investor in the 28% tax bracket who purchases the Vandenberg bond. Given this tax treatment, investors pay 1 Note too that we have analyzed the bond as if the cash flows accrued annually. Generally, to facilitate comparisons with semiannual payment coupon bonds, the analysis is conducted on a semiannual basis. Web Appendix 7A Table 7A-2 Basic Data M a tu r i ty va l u e rd M a tu r i ty P e r s o na l ta x r a te I s s ue p ric e Analysis of a Zero Coupon Bond from an Investor’s Perspective $1, 000 6.00%, annual compounding 5 y e a rs 28. 00% $747. 26 Analysis 0 (1) Year-end accrued value (2) Interest income (3) Tax payment (28%) (4) Cash flow to investor After-tax return $747.26 747.26 4.32% 1 2 3 4 5 $792.10 44.84 12.56 12.56 6% $839.62 47.52 13.31 13.31 $890.00 50.38 14.11 14.11 $943.40 53.40 14.95 14.95 $1,000.00 56.60 15.85 984.15 taxes in each year even though they don’t receive any cash flows until the bond is sold or matures, a situation that many investors find unattractive. Consequently, because of the tax situation, pension funds and other tax-exempt entities buy most zero coupon bonds. Individuals do, however, buy taxable zeros for their individual retirement accounts (IRAs). Also, state and local governments issue “taxexempt muni zeros” that are purchased by individuals in high tax brackets. Not all original issue discount bonds (OIDs) have zero coupons. For example, Vandenberg might have sold an issue of five-year bonds with a 5% coupon at a time when other bonds with similar ratings and maturities were yielding 6%. Such bonds would have had a value of $957.88: Bond value ¼ 5 X $50 $1,000 ¼ $957:88 tþ ð1:06Þ5 t¼ 1 ð1:06Þ If an investor had purchased these bonds at a price of $957.88, the yield to maturity would have been 6%. The discount of $1,000 – $957.88 ¼ $42.12 would have been amortized over the bond’s five-year life, and it would have been handled by both Vandenberg and the bondholders exactly as the discount on the zeros was handled. Thus, zero coupon bonds are just one type of original issue discount bond. Any nonconvertible bond whose coupon rate is set below the going market rate at the time of its issue will sell at a discount, and it will be classified (for tax and other purposes) as an OID bond. Shortly after corporations began to issue zeros, investment bankers figured out a way to create zeros from U.S. Treasury bonds, which at the time were issued only in coupon form. In 1982, Salomon Brothers bought $1 billion of 12%, 30-year Treasuries. Each bond had 60 coupons worth $60 each, which represented the interest payments due every six months. Salomon then in effect clipped the coupons and placed them in 60 piles. The last pile also contained the now “stripped” bond, which represented a promise of $1,000 in the year 2012. These 60 piles of U.S. Treasury promises were placed with the trust department of a bank and used as collateral for “zero coupon U.S. Treasury Trust Certificates,” which are, in essence, zero coupon Treasury bonds. Treasury zeros are, of course, safer than corporate zeros; so they are very popular with pension fund managers. In response to this demand, the Treasury has also created its own “Strips” program, which allows investors to purchase zeros electronically. Corporate (and municipal) zeros are generally callable at the option of the issuer, just like coupon bonds, after some stated call protection period. The call price is set at a premium over the accrued value at the time of the call. Stripped Years 7A-3 7A-4 Web Appendix 7A U.S. Treasury bonds (Treasury zeros) generally are not callable because the Treasury normally sells noncallable bonds. Thus, Treasury zeros are completely protected against reinvestment risk (the risk of having to invest cash flows from a bond at a lower rate because of a decline in interest rates). QUESTIONS 7A-1 7A-2 7A-3 Do all original issue discount (OID) bonds have zero coupon payments? Explain. What is a Treasury strip? Are they callable? Explain. Do Treasury zeros face any interest rate (price) or reinvestment rate risk? Explain. PROBLEMS 7A-1 7A-2 7A-3 7A-4 7A-5 7A-6 ZERO COUPON BONDS A company has just issued 4-year zero coupon bonds with a maturity value of $1,000 and a yield to maturity of 9%. Its tax rate is 40%. What is its after-tax cost of debt? ZERO COUPON BONDS An investor in the 35% tax bracket purchases the bond discussed in Problem 7A-1. What is the investor’s after-tax return? STRIPPED U.S. TREASURY BOND McGwire Company’s pension fund projected that a significant number of its employees would take advantage of an early retirement program the company plans to offer in 5 years. Anticipating the need to fund these pensions, the firm bought zero coupon U.S. Treasury Trust Certificates maturing in 5 years. When these instruments were originally issued, they were 12% coupon, 30-year U.S. Treasury bonds. The stripped Treasuries are currently priced to yield 10%. Their total maturity value is $6,000,000. What is their total cost (price) to McGwire today? ZERO COUPON BOND At the beginning of the year, you purchased a 7-year, zero coupon bond with a yield to maturity of 6.8%. The bond has a face value of $1,000. Your tax rate is 25%. What total tax will you have to pay on the bond during the first year? ZEROS AND EXPECTATIONS THEORY A 2-year, zero coupon Treasury bond with a maturity value of $1,000 has a price of $873.4387. A 1-year, zero coupon Treasury bond with a maturity value of $1,000 has a price of $938.9671. If the pure expectations theory is correct, for what price should 1-year, zero coupon Treasury bonds sell 1 year from now? ZERO COUPON BONDS AND EAR Assume that the city of Tampa sold tax-exempt (muni) zero coupon bonds 5 years ago. The bonds had a 25-year maturity and a maturity value of $1,000 when they were issued; and the interest rate built into the issue was a nominal 10%, but with semiannual compounding. The bonds are now callable at a premium of 10% over the accrued value. What effective annual rate of return would an investor who bought the bonds when they were issued and who still owns them earn if they are called today? ...
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