Finance Short Response 4
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WE B E X T E N S I O N 5A ACloser Look at Zero Coupon Bonds
Some bonds pay no interest but are offered at a substantial discount below theirpar values and hence provide capital appreciation rather than interest income.These securities are called zero coupon bonds (“zeros”), or original issue discount bonds (OIDs). Some corporations use these bonds to manage their matu- rity structure. In addition, these bonds provide some desirable tax features for cor- porations, as we discuss later in this extension.
Corporations first used zeros in a major way in 1981. IBM, Alcoa, JCPenney, ITT, Cities Service, GMAC, Martin-Marietta, and many other companies have used them to raise billions of dollars. Municipal governments also sell “zero munis.” Shortly after corporations began to issue zeros, investment bankers figured out a way to create zeros from U.S. Treasury bonds, which were issued only in coupon form. In 1983 Salomon Brothers bought $1 billion of 7%, 30-year Treasuries. Each bond had 60 coupons worth $35 each, which represented the interest payments due every 6 months. Salomon then, in effect, clipped the coupons and placed them in 60 piles; the last pile also contained the now “stripped” bond itself, which represented a prom- ise of $1,000 in the year 2013. These 60 piles of U.S. Treasury promises were then 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. A pension fund that, in 1984, expected to need money in 2009 could have bought 25-year certificates backed by the interest the Treasury will pay in 2009.
In 1985, the Treasury Department began allowing investors to strip long-term U.S. Treasury bonds and directly register the newly created zero coupon bonds, called STRIPs, with the Treasury Department. This bypasses the role formerly played by investment banks. Now virtually all U.S. Treasury zeros are held in the form of STRIPs. These STRIPs are, of course, safer than corporate zeros, so they are very popular with pension fund managers.
To understand how zeros are used and analyzed, consider the zeros 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 com- pany does not anticipate major cash flows from the project for about 5 years; how- ever, 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. He has decided on a 5-year zero coupon bond issue, with 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
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firm’s after-tax cost of debt if it uses 6%, 5-year maturity zeros, and he also wants to know what the bond’s cash flows will be. Figure 5A-1 provides an analysis of the sit- uation, and the subsequent numbered list explains the table itself. See the worksheet “Web 5A” in Ch05 Tool Kit.xls for all calculations. Because the table was calculated in Excel, there is no rounding in intermediate steps.
1. The information in the “Input Data” section, except the issue price, was given in the preceding paragraph, and the information in the “Analysis” section was calcu- lated 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 = 6% with 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 = $747.26.1 Note that $747.26, when compounded annually for 5 years at 6%, will grow to $1,000, as shown in Figure 5A-1.
3. The year-end accrued values, as shown on Line 2 in the analysis section, rep- resent the compounded value of the bond at the end of each year.2 The
F IGURE 5A-1 Analysis of a Zero Coupon Bond from Issuer’s Perspective
Input Data
Analysis:
Amount needed = $50,000,000
$747.26
$1,000
6%
40% 0% $0
5
Maturity value = Pre-tax market interest rate, rd =
Maturity (in years) = Corporate tax rate = Coupon rate =
Coupon payment (assuming annual payments) =
Years (1) Remaining years
After-tax-cost of debt = 3.60%
Number of $1,000 zeros the company must issue to raise $50 million Amount needed/Price per bond
66,911.279 bonds. $66,911,279Face amount of bonds = # bonds × $1,000 =
= =
0 5 4 3 2 1 0
$890.00 $943.40 $1,000.00$839.62 $0.00 $0.00 $0.00$0.00
$792.09$747.26
$747.26
$44.84 $17.93 $17.93
$47.53 $19.01 $19.01
$50.38 $20.15 $20.15
$53.40 $21.36 $21.26
$56.60 $22.64
($977.36)
$0.00
1 2 3 4 5
(2) Year-end accrued value
(3) Interest payment (4) Implied interest deduction on discount
(5) Tax savings (6) Cash flow
Issue Price = PV of payments at rd =
1This value is reported to two decimal places, but all significant digits will be used in the subsequent calculations. 2Line 1 is included in the Excel table because it facilitates some calculations.
2 Web Extension 5A: A Closer Look at Zero Coupon Bonds
accrued value for Year 0 is the issue price; the accrued value for Year 1 is found as $747.26(1.06) = $792.09; and the accrued value at the end of Year 2 is $747.26(1.06)2 = $839.62. In general, the value at the end of any Year N is calculated as follows:
Accrued value at the end of Year N ¼ ðIssue priceÞð1 þ rdÞN (5A-1)
4. The interest deduction as shown on Line 4 represents the increase in accrued value during the year.3 Thus, interest in Year 1 = $792.09 − $747.26 = $44.84.4
The general equation is
Interest in Year N ¼ ðAccrued valueÞN − ðAccrued valueÞN – 1 (5A-2)
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 tax savings:
Tax savings ¼ ðInterest deductionÞðTÞ (5A-3)
For example, in Year 1, the tax savings are
Tax savings ¼ $44:84ð0:4Þ ¼ $17:93 in Year 1
6. Line 5 reports the tax savings as just calculated, and Line 6 reports the cash flows; 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 + $22.64 = −$977.36.
7. 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 6 of Figure 5A-1, into the cash flow register and then 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
t¼1 CFN
ð1þ rdðATÞÞN ¼ 0 (5A-4)
3Line 3 is included for the case of an original issue discount bond with a coupon rate greater than zero but not as high as the going rate in the market. Line 3 is not required for the analysis of a zero coupon bond, such as the one in this example, but the spreadsheet can be used for any OID bond. 4The reported numbers have been rounded, but all significant digits are used in the actual calculations.
Web Extension 5A: A Closer Look at Zero Coupon Bonds 3
For the bond in this example, we have
$747:26
ð1þrdðATÞÞ0 þ $17:93ð1þrdðATÞÞ1
þ $19:01ð1þrdðATÞÞ2 þ $20:15ð1þrdðATÞÞ3
þ $21:36ð1þrdðATÞÞ4 þ −$977:36ð1þrdðATÞÞ5
¼0
The value of rd(AT) = 0.036 = 3.6%, found with a financial calculator, produces the equality, and it is the after-tax cost of this debt. (Input in the cash flow regis- ter CF0 = 747.26, CF1 = 17.94, and so forth, out to CF5 = −977.36; then press the IRR key to find rd(AT) = 3.6%.) The IRR function was used in the Excel model.
8. Note that rd(1 – T) = 6%(0.6) = 3.6%. As we will see in Chapter 9, the cost of capital for regular coupon debt is found using the formula rd(1 − T). Thus, for tax purposes there is symmetrical treatment for zero coupon and regular coupon debt; that is, both types of debt use the same after-tax cost formula. This was the intent of Congress, and it is why the Tax Code specifies the treatment set forth in Figure 5A-1.5
Not all original issue discount bonds (OIDs) have zero coupons. For example, Vandenberg might have sold an issue of 5-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
t¼1 $50
ð1:06Þt þ $1; 000
ð1:06Þ5 ¼ $957:88
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 = $42.12 would have been amortized over the bond’s 5-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 pur- poses) as an OID bond.
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. Given this tax treatment, investors pay 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 unattrac- tive. Consequently, pension funds and other tax-exempt entities buy most zero cou- pon bonds. Individuals do, however, buy taxable zeros for their Individual Retirement Accounts (IRAs). Also, state and local governments issue “tax-exempt muni zeros” that are purchased by individuals in high tax brackets.
Questions (5A–1) Do all original issue discount (OID) bonds have zero coupon payments? Explain.
(5A–2) What are Treasury STRIPs? Are they callable? Explain.
(5A–3) Do Treasury zeros face any interest rate (price) or reinvestment rate risk? Explain.
5Note, 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.
4 Web Extension 5A: A Closer Look at Zero Coupon Bonds
Problems
(5A–1) 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?
(5A–2) Zero Coupon Bonds
An investor in the 35% tax bracket purchases the bond discussed in Problem 5A-1. What is the investor’s after-tax return?
(5A–3) Stripped U.S. Treasury
Bond
McGwire Company’s pension fund projected that a significant number of its employ- ees 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 million. What is their total cost (price) to McGwire today?
(5A–4) 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 is the total tax that you will have to pay on the bond during the first year?
(5A–5) 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?
(5A–6) 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% with semi- annual compounding. The bonds are now callable at a premium of 10% over the ac- crued value. If they were called today, what effective annual rate of return would be earned by an investor who bought the bonds when they were issued and who still owns them today?
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