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Chapter 3 COMPARATIVE ANALYSIS OF ZERO-COUPON AND COUPON-PRE-FUNDED BONDS A. LINDA BEYER, Alaska Supply Chain Integrators, USA KEN HUNG, National Dong Hwa University, Taiwan SURESH C. SRIVASTAVA, University of Alaska Anchorage, USA Abstract Coupon-prefunded bonds have been developed and sold by investment bankers in place of zero-coupon bonds to raise funds for companies facing cash flow problems. Additional bonds are issued and proceeds are deposited in an escrow account to finance the coupon payment. Our analysis indicates that a coupon-prefunded bond is equivalent to a zero-coupon bond only if the return from the escrow account is the same as the yield to maturity of the prefunded issue. In reality, the escrow return is lower than the bond yield. As a result, the firm provides interest subsidy through issuing additional bonds which leads to higher leverage, greater risk, and loss of value compared to a zero-coupon issue. Keywords: zero-coupon bond; Macaulay duration; escrow account; Treasury STRIPS; junk bonds; coupon collateralization; financial engineering; coupon pre-funded bond; cash flows; and value loss 3.1. Introduction Coupon-prefunded bonds, new to financial markets, were first issued in 1994 (Doherty, 1997).1 They were introduced as a means to raise capital for firms unable to generate cash flow to make coupon payments, while still meeting the needs of investors to receive coupon income. With a prefunded bond structure, additional bonds are issued and an escrow account is established to finance coupon payments over the life of the bond. In this manner, the bond is considered prefunded. The firm is not required to generate cash flow to meet coupon obligations; it is paid out of the escrow account usually collateralized by treasury securities. The risk-free coupon payment allows the firm to set a lower coupon rate on the bond than the yield on a comparable zero-coupon bond. In general, the cost of funding the escrow account is greater than the return of the escrow account. This leads to an interest rate subsidy and the loss of value. In this paper, we compare zero-coupon bonds to prefunded bonds and ascertain conditions under which the two funding options are equivalent. A prefunded issue simultaneously creates an asset and a liability. The net duration of the pre-funded issue is the weighted average of the asset and liability durations. The model of net duration developed in this paper incorporates increased leverage of the pre-funded issue, and appropriately assess its increased risk. In spite of the fact that a prefunded bond is an interesting concept of financial engineering, there is very little academic research on this topic. COMPARATIVE ANALYSIS OF ZERO-COUPON AND COUPON-PRE-FUNDED BONDS The remainder of this paper is made up of four sections. Section 3.2 discusses the options available to a firm interested in issuing debt. In Section 3.3, we derive a mathematical model for Macaulay duration of the prefunded issue to determine the interest rate risk and calculate the loss in value due to interest rate subsidy. A numerical example and its analysis are presented in Section 3.4. Section 3.5 concludes the paper. 3.2. Funding Options A firm wants to raise funds to finance a new project. The pecking-order theory of capital structure suggests that managers prefer internal equity to external financing (Myers, 1984). In case the internal equity (retained earnings) is not available then issuing new debt is preferred over issuing preferred or additional common stock. Further, firms would like to reduce the interest payment burden. Hence, conventional coupon bond or hybrid financing such as convertible bonds or bonds with warrants are ruled out. The available funding options are (1) zero-coupon bonds, (2) step-up bonds – initially coupon payment is set at a low value and later stepped up, (3) deferred interest bonds – initially there is no interest payment, but it is resumed in 3–7 years, (4) paid-in-kind bonds – issuer has right to pay interest in cash or with similar bonds2, and (5) prefunded bonds. The focus of the study is to compare zero-coupon and coupon-prefunded bonds. 3.2.1. Zero-Coupon Bonds Pure discount bonds are often called zero-coupon bonds. It was first issued by J.C. Penney Company Inc. in 1982 (Brigham and Daves, 2004). In recent years, other firms (e.g. IBM, GMAC, Alcoa and Martin-Marietta) have issued zero-coupon bonds. Municipalities started issuing zero-coupon bonds in 1983. These bonds are sold at a deep discount and increase in value as they approach maturity. Zerocoupon bonds do not provide interest or coupon payments at regular intervals like other types of 315 bonds. Implicit coupons are automatically reinvested by the issuer at yield to maturity. Interest accrues over the life of the bond and a return is earned as the bond appreciates. At maturity its value equals the face value, and the bond holder receives the yield to maturity expected at the time of purchase. If held to maturity, the investor faces no reinvestment risk but high-interest rate risk, as its market price fluctuates considerably with movements in market rates. Corporate and municipal zero-coupon bonds are usually callable and rated as junk bonds.3 The financial condition of the company issuing bonds predicates the use of junk bonds, i.e. the firm is unable to generate cash flows to meet coupon payments. Junk bonds are typically rated BB or lower by Standard and Poor’s, or BA or lower by Moody’s. Junk bonds offer a high-expected return but require investors to take on higher default risk. Covenants on junk bonds are less restrictive, and therefore provide alternatives for firms that may not meet the more restrictive covenants of conventional bonds. 3.2.2. Coupon Pre-Funded Bonds In raising capital with a prefunded bond issue, additional bonds are issued and an escrow account is established. The firm is not required to generate cash flow to meet coupon obligations over the life of the bond. Bond interests are paid out of an escrow account, which is usually collateralized by treasury securities. In this manner, the bond is considered prefunded. A prefunded bond issue simultaneously creates an asset and a liability. The risk characteristics of prefunded bonds’ interest payments are different from that of traditional coupon-bearing bonds because prefunded bonds’ coupon payments are asset based. The default free nature of the coupon payment allows the firm to set a lower coupon rate than the yield on a comparable zero-coupon bond. In general, the cost of funding the escrow account is greater than the return from the escrow account. This spread leads to an interest rate subsidy which necessitates 316 ENCYCLOPEDIA OF FINANCE issuing more bonds, and hence a loss of value. Greater the spread between the cost of funding the escrow account and the return from the escrow account, the larger the total face value of the prefunded issue and the value loss. With a prefunded bond issue, there are additional flotation costs and cost of establishing the escrow account. However, for this analysis, we consider the escrow costs and additional flotation costs to be negligible. Market price of prefunded bonds fluctuates with movements in market rates, but it does not move as dramatically as zero-coupon bond prices. The reason for this difference is that zero-coupon bonds do not provide any cash flow until maturity. Coupon payments reduce the impact of interest rate changes on prefunded bonds. Market conditions where interest rate movements are frequent and highly variable make prefunded bonds more attractive than zero-coupon bonds. The risk profiles of zero-coupon and prefunded bonds can be summarized as follows: A zero-coupon bond has no reinvestment risk, higher price elasticity to interest rate changes, and a default risk consistent with its junk bond rating. The prefunded bond has reinvestment risk but lower price elasticity to interest rate changes. For a meaningful analysis of the interest rate risk, one must examine the combined interest rate sensitivity of the escrow asset and the bond liability. The default risk of the prefunded issue should be decomposed into two components: the default risk of the coupon payments and the default risk of the maturity payment. The coupon payments are default free but the default risk of the maturity payments is much higher. This is due to the increased leverage of the prefunded issue compared to zero-coupon financing. In spite of the default-free coupon payments, the prefunded bonds are usually rated as junk bonds. In the next section, the combined interest rate sensitivity of the escrow asset and the bond liability is examined. A model for the net Macaulay duration of the prefunded issue is developed, and loss of value due to interest rate subsidy is calculated. 3.3. Macaulay Duration and Value Loss In this section, we calculate the total face value of the prefunded bonds issued, initial balance of the escrow account, interest rate subsidy provided by the firm, effective cost of the prefunded issue, and resulting loss of value. Also, we derive an expression for the net Macaulay duration of the prefunded issue, i.e. the weighted average durations of the coupon bond and the escrow asset The face values of zero-coupon bonds issued, to raise an amount B, is Bz ¼ B(1 þ rz )n (3:1) where rz is the discount rate for the zero-coupon bond with maturity n. The Macaulay duration of zero-coupon bond is its maturity (Fabbozzi, 2000). Let Bpf be the face value of the prefunded bonds issued to raise an amount B. The annual coupon payment is Bpf (rpf ), where rpf is the prefunded bond yield. The initial balance in the escrow annuity account set up to meet the coupon payments is Bpf
B. Hence,

Bpf
B ¼ Bpf rpf PVIFAres ,n (3:2) B
Bpf ¼ 1
rpf PVIFAres ,n where PVIFA indicates present value interest factor of an annuity, n is the maturity, and res is the rate of return on the escrow account. Substituting the algebraic expression for PVIFA we get4 Bpf ¼ res (1 þ res )n B rpf
(rpf
res )(1 þ res )n (3:3) The initial balance in the escrow account is Bpf
B ¼ rpf ½(1 þ res )n
1B rpf
(rpf
res )(1 þ res )n (3:4) Escrow account is funded at a cost of rpf and provides a return of res . Consequently, the firm is providing a pre-tax interest subsidy of (rpf Bpf ) (rpf
res ) per year, which increases the cost of prefunded issue and leads to loss of value. COMPARATIVE ANALYSIS OF ZERO-COUPON AND COUPON-PRE-FUNDED BONDS The loss of value is: Value Loss ¼ (rpf Bpf )(rpf
res ) (1 þ rpf )n
1 (1 þ rpf )n (3:5) and the effective cost of the prefunded issue is given by:  1=n res (1 þ res )n reff ¼
1 (3:6) rpf
(rpf
res )(1 þ res )n The concept of duration was introduced by Macaulay (1938) as a measure of price sensitivity of an asset or liability to a change in interest rates. Working independently, Samuelson (1945) and Redington (1952) developed the same concept about the interest rate risk of bonds. Details of duration computation can be found in any finance text (Fabbozzi, 2000). A prefunded bond issue creates an asset, the escrow account annuity with market value Bpf
B; and a liability, coupon bonds with market value Bpf . The net market value of the prefunded issue is B. Let Des and Dpf represent the duration of escrow annuity and the bond liability respectively. Duration Des is the Macaulay duration of an n-year annuity with yield res and Dpf is the Macaulay duration of an n-year coupon bond with yield to maturity rpf . The net duration of the prefunded issue is the weighted average of the durations of the escrow account and the coupon bond. Hence Dnet ¼ Bpf Bpf
B  Dpf
 Des B B (3:7) 317 where (Bpf =B) and (
(Bpf
B)=B) are the weights of the coupon bond and the escrow annuity respectively. This definition of net duration, Dnet , captures the increased risk due to additional leverage caused by prefunding of coupon payments and interest subsidy provided by the firm. 3.4. Numerical Example and Analysis A firm wants to raise $10 million by issuing either zero-coupon bonds or prefunded bonds with five or ten year maturity. We assume that transaction costs are identical for both issues and negligible.5 Further, we assume that financial market views the zero-coupon and prefunded bonds to be equivalent securities, and prices them with identical yields. Four different yields, 8 percent, 7 percent, 6 percent, and 5 percent,.on zero-coupon and prefunded bonds are considered for this analysis. Later, we modify this assumption and consider the situation where market views prefunded bond to be safer and erroneously prices them with yields lower than the comparable zero-coupon yields by 25, 50, and 75 basis points. In doing so, market overlooks the added default risk associated with increased leverage. Table 3.1 presents the face value of zero-coupon bonds issued to meet the $10 million funding need. For 5-year maturity with discount rates of 8 percent, 7 percent, 6 percent, and 5 percent, the firm issues zero-coupon bonds with total face values of Table 3.1. Zero-coupon bond Bz ¼ B(1 þ rz )n and Dz ¼ n Discount rate, rz Maturity, n 5 years Maturity, n 10 years Funds needed, B Face value of bonds issued, Bz Market value of bonds issued Duration, Dz Funds needed, B Face value of bonds issued, Bz Market value of bonds issued Duration, Dz 8% 7% 6% 5% $10,000,000 $14,693,281 $10,000,000 5 years $10,000,000 $21,589,250 $10,000,000 10 years $10,000,000 $14,025,517 $10,000,000 5 years $10,000,000 $19,671,514 $10,000,000 10 years $10,000,000 $13,382,256 $10,000,000 5 years $10,000,000 $17,908,477 $10,000,000 10 years $10,000,000 $12,762,816 $10,000,000 5 years $10,000,000 $16,288,946 $10,000,000 10 years 318 ENCYCLOPEDIA OF FINANCE $14,693,281, $14,025,517, $13,382,256, and $12,762,816 respectively. These values are calculated using Equation (3.1). The Macaulay duration of the 5-year zero-coupon bond is 5 years. For 10-year zero-coupon bonds, an 8 percent, 7 percent, 6 percent, and 5 percent discount rate leads to total face values of $21,589,250, $19,671,514, $17,908,477, and $16,288,946 respectively. The Macaulay duration of the 10-year zero-coupon bond is 10 years. In Table 3.2, we present the total face value of the prefunded issue, amount of annual coupon payment disbursed from escrow account, and the effective cost of prefunded issue. It provides the following important inferences. First, when the prefunded bond yield, rpf , is the same as the escrow account return, res , then (i) the total face value of the pre-funded issued is the same as the total face value of the zero-coupon bonds and (ii) the effective cost of prefunded issue, reff , is Total face value and effective cost of prefunded issue  1=n res (1 þ res )n B res (1 þ res )n ¼ and r ¼
1 eff rpf
(rpf
res )(1 þ res )n rpf
(rpf
res )(1 þ res )n Table 3.2. Bpf Prefunded bond yield, rpf n res 8% 7% 6% 8% Face value, Bpf Escrow payment Effective cost, reff $14,693,281 $1,175,462 8.000% 7% Face value, Bpf Escrow payment Effective cost, reff $14,881,302 $1,190,504 8.275% $14,025,517 $981,786 7.000% 6% Face value, Bpf Escrow payment Effective cost, reff $15,082,708 $1,206,617 8.567% $14,181,691 $992,718 7.237% $13,382,256 $802,935 6.000% 5% Face value, Bpf Escrow payment Effective cost, reff $15,298,893 $1,223,912 8.876% $14,368,507 $1,004,395 7.518% $13,509,289 $810,557 6.201% 8% Face value, Bpf Escrow payment Effective cost, reff $21,589,250 $1,727,140 8.000% 7% Face value, Bpf Escrow payment Effective cost, reff $22,825,137 $1,826,011 8.603% $19,671,514 $1,377,006 7.000% 6% Face value, Bpf Escrow payment Effective cost, reff $24,319,478 $1,945,558 9.294% $20,627,322 $1,443,913 7.509% $17,098,477 $1,074,509 6.000% 5% Face value, Bpf Escrow payment Effective cost, reff $26,160,123 $2,092,810 10.094% $21,763,801 $1,523,466 8.087% $18,632,525 $1,117,952 6.421% 5 10 res ¼ escrow return. Maturity ¼ n years. Empty cell represents the improbable case of rpf < rz . 5% $12,762,816 $638,141 5.000% $16,288,946 $814,447 5.000% COMPARATIVE ANALYSIS OF ZERO-COUPON AND COUPON-PRE-FUNDED BONDS the same as the yield to maturity of the zerocoupon bond, rz . Second, increase in the spread between rpf and res increases the total face value of the bonds issued and its effective cost. Finally, for a given spread the total face value of the bonds issued and its effective cost increases with maturity. For example, consider the case when both rpf and res are equal to 8 percent and the firm wants to issue 5-year maturity bonds to raise $10 million. It can issue either zero-coupon bonds or prefundedcoupon bonds with $14,693,281 face value and 8 percent effective costs. For 10-year maturity, it will have to issue $21,589,250 zero-coupon or prefunded bonds. However, with a 3 percent spread, i.e. rpf ¼ 8 percent and res ¼ 5 percent, the firm will have to issue $15,298,893 coupon bonds with maTable 3.3. 319 turity 5 years or $26,160,132 coupon bonds with maturity 10 years. The effective cost of 5-year and 10-year prefunded issues will rise to 8.876 percent and 10.094 percent respectively. Examples of net duration of pre-funded issue, i.e. the weighted average durations of the escrow asset and coupon bond liability are presented in Tables 3.3 and 3.4. In Table 3.3, we present a 5-year bond issue without spread, i.e. both rpf and res are equal to 8 percent. Firm issues $14,693,281 bonds with annual coupon payment of $1,175,462. Coupon payments are disbursed out of an escrow account with $4,693,281 initial balance. Panel A of Table 3.3 shows that duration of the coupon bond, Dpf , is 4.3121 years. Panel B of Table 3.3 shows that the duration of the escrow annuity, Des , is 2.8465 years. Net duration of the prefunded issue without spread Dnet ¼ Bpf Bpf
B  Des  Dpf
B B Panel A: Bonds issued Time, t Cash outflow, CF PVIF8%,5 CF PVIF t CF PVIF Duration, Dpf 1 2 3 4 5 $1,175,462 1,175,462 1,175,462 1,175,462 15,868,743 0.9259 0.8573 0.7938 0.7350 0.6806 $ 1,088,391 1,007,769 933,120 864,000 10,800,000 $14,693,280 $1,088,391 2,015,538 2,799,359 3,455,999 53,999,999 $63,359,286 4.3121 Panel B: Escrow annuity Time, t Cash inflow, CF PVIF8%,5 CF PVIF t CF PVIF Duration, Des 1 2 3 4 5 $1,175,462 1,175,462 1,175,462 1,175,462 1,175,462 0.9259 0.8573 0.7938 0.7350 0.6806 $1,088,391 1,007,769 933,120 864,000 800,000 $4,693,280 $1,088,391 2,015,538 2,799,359 3,455,999 3,999,998 $13,359,282 2.8465 Panel C: Net durations Fund raised, B Face value of bond, Bpf Bond yield, rpf Bond weight, Bpf =B Bond duration, Dpf $10,000,000 $14,693,281 8.00% 1.469 4.312 Escrow amount, Bpf
B Escrow return, res Escrow weight, (B
Bpf )=B Escrow duration, Des Net duration, Dnet If escrow return equals the bond yield, i.e. res ¼ rpf , then the net duration equals the maturity. $4,693,281 8%
0.469 2.847 5.000 320 ENCYCLOPEDIA OF FINANCE Panel C of Table 3.3 shows that the weights of bond liability and escrow asset are 1.469 and
:0:469 respectively. Hence, the net duration, Dnet , of the prefunded issue is 5 years, which is identical to the duration of a zero-coupon bond. The result is understandable because the firm has no net cash outflow for years one to four, the only cash outflow of $14,693,281 is in year five. In Table 3.4, we present an example of a 5-year prefunded bond issue with 3 percent spread, i.e. rpf ¼ 8 percent and res ¼ 5 percent. Firm issues $15,298,250 bonds with annual coupon payment of $1,223,912. Coupon payments are disbursed out of an escrow account with $5,298,250 initial balance. Firm provides the interest subsidy by issuing additional bonds compared to the example in Table 3.3. Panel A of Table 3.4 shows that the Table 3.4. duration of the coupon bond, Dpf , is 4.3121 years, same as the example in Table 3.3. But the duration of the escrow annuity, Des , increases to 2.9025 years. The weights of bond liability and escrow asset, reported in Panel C of Table 3.4, are 1.530 and
0:530 respectively. The net duration, Dnet , of the prefunded issue increases to 5.059 years. The interest subsidy creates the additional leverage, and which stretches the duration beyond its maturity.6 Because interest subsidy is a realistic condition, the prefunded bond issue has greater interest rate risk than the comparable zero-coupon bond. Table 3.5 presents net duration, interest subsidy and loss of value associated with a prefunded bond issue for different bond yields and escrow returns. When rpf ¼ res , then there is no interest subsidy or loss of value and the net duration of the pre-funded Net duration of the prefunded issue with spread Dnet ¼ Bpf Bpf
B  Des  Dpf
B B Panel A: Bonds issued Time, t Cash outflow, CF PVIF8%,5 CF PVIF t CF PVIF Duration, Dpf 1 2 3 4 5 $1,223,912 1,223,912 1,223,912 1,223,912 16,522,162 0.9259 0.8573 0.7938 0.7350 0.6806 $1,133,252 1,049,307 971,581 899,612 11,244,706 $15,298,458 $1,133,252 2,098,615 2,914,742 3,598,447 56,223,529 $65,968,585 4.3121 Panel B: Escrow annuity Time, t Cash inflow, CF PVIF5%,5 CF PVIF t CF PVIF Duration, Des 1 2 3 4 5 $1,223,912 1,223,912 1,223,912 1,223,912 1,223,912 0.9524 0.9070 0.8638 0.8227 0.7835 $1,165,630 1,110,124 1,057,261 1,006,915 958,967 $ 5,298,897 $1,165,630 2,220,249 3,171,784 4,027,662 4,794,835 $15,380,160 2.9025 Panel C: Net durations Fund raised, B Face value of bond, Bpf Bond yield, rpf Bond weight, Bpf =B Bond duration, Dpf $10,000,000 $15,298,250 8.00% 1.530 4.312 Escrow amount, Bpf
B Escrow return, res Escrow weight, (B
Bpf )=B Escrow duration, Des Net duration, Dnet If escrow return is less than the bond yield, i.e. res < rpf , then the net duration exceeds maturity. $5,298,250 5%
0.530 2.903 5.059 COMPARATIVE ANALYSIS OF ZERO-COUPON AND COUPON-PRE-FUNDED BONDS Table 3.5. Net duration, interest subsidy, and value loss of prefunded bonds Pre-tax Interest Subsidy ¼ (rpf Bpf )(rpf
res ) per year Value loss ¼ (rpf Bpf )(rpf
res ) Escrow return, res Maturity, n 5 years 8% 7% 6% 5% Maturity, n 10 years 321 8% 7% 6% 5% (1 þ rpf )n
1 (1 þ rpf )n Prefunded bond yield, rpf 8% 7% 7% 7% Net duration, yrs Interest subsidy Value loss Net duration, yrs Interest subsidy Value loss Net duration, yrs Interest subsidy Value loss Net duration, yrs Interest subsidy Value loss 5 0 0 5.019 $11,905 ($47,533) 5.038 $24,132 ($96,353) 5.059 $36,717 ($146,602) 5 0 0 5.016 $9,927 ($40,703) 5.037 $20,088 ($82,364) 5 0 0 5.013 $8,106 ($34,144) 5 0 0 Net duration, yrs Interest subsidy Value loss Net duration, yrs Interest subsidy Value loss Net duration, yrs Interest subsidy Value loss Net duration, yrs Interest subsidy Value loss 10 0 0 10.198 $18,260 ($122,527) 10.433 $38,911 ($261,097) 10.715 $62,784 ($421,288) 10 0 0 10.165 $14,439 ($101,414) 10.358 $30,469 ($214,004) 10 0 0 10.135 $11,180 ($82,282) 10 0 0 Empty cell represents the improbable case of rpf < rz . Zero-coupon and prefunded bonds are priced by market as equivalent securities. issue is equal to bond maturity. The net duration, interest subsidy, and loss of value increases with the increase in the spread, rpf ¼ res . Table 3.6 presents the case when prefunded bonds are priced to yield lower than the zero-coupons. The asset-based coupon payments of the prefunded issue are default free, thus market lowers the yield by 25, 50, or 75 basis points from the comparable zerocoupon yield. We recalculate the total face value, net duration, interest subsidy, and loss of value under these conditions. Results in Table 3.6 indicate that the impact of the spread, rpf
res is still dominant. The total face value and net duration of the prefunded issue is greater than corresponding values for the zero-coupon bond. 3.5. Conclusion Coupon-prefunded bonds have been developed and sold by investment bankers in place of zerocoupon bonds to raise funds for companies facing cash flow problems. Additional bonds are issued and proceeds are deposited in an escrow account to finance the coupon payment. Our analysis indicates that when the prefunded bond yield is the same as the escrow return then total face value of 322 ENCYCLOPEDIA OF FINANCE Table 3.6. Face value, net duration, interest subsidy, and value loss of prefunded bonds Prefunded bond yield, Bpf rz Bz 8% $21,589,250 7% $19,671,514 6% $13,382,256 Face value of pre-funded, Bpf Duration, Dnet Interest subsidy Value loss Face value of pre-funded, Bpf Duration, Dnet Interest subsidy Value loss Face value of pre-funded, Bpf Duration, Dnet Interest subsidy Value loss rz rz
:25% rz
:50% rz
:75% $26,160,123 10.718 yrs $62,784 ($421,288) $21,763,801 10.358 yrs $30,469 ($214,004) $18,632,525 10.135 yrs $11,180 ($82,282) $24,902,535 10.611 yrs $53,074 ($360,179) $20,886,293 10.291 yrs $24,672 ($175,306) $17,985,604 10.094 yrs $7,756 ($57,769) $23,760,313 10.516 yrs $44,551 ($305,799) $20,076,805 10.266 yrs $19,575 ($140,721) $17,382,097 10.058 yrs $4,780 ($36,030) $22,718,277 10.432 yrs $37,059 ($257,307) $19,327,721 10.181 yrs $15,100 ($109,831) $16,817,777 10.027 yrs $2,207 ($16,839) rz ¼ discount rate on zero-coupon bonds, Bz ¼ face value of zero-coupon bonds with 10-year maturity. Escrow account yield ¼ 5%. Prefunded bonds are priced to yield lower than comparable zero-coupon bonds. the prefunded issued is the same as the total face value of the zero-coupon bonds and the effective cost of prefunded issue is the same as the yield to maturity of the zero-coupon bond. Also, increase in the spread between prefunded bond yield and zero-coupon yield increases the total face value of the bonds issued and its effective cost. The interest subsidy creates additional leverage, which stretches the net duration of the prefunded issue beyond its maturity. Further, an increase in the yield spread between prefunded bonds and zerocoupon bonds increases net duration, interest subsidy, and loss of value. Even when prefunded bonds are priced to yield lower than the zerocoupons, impact of the spread is dominant – total face value and net duration of the prefunded issue is still greater than corresponding values for the zero-coupon bond. NOTES 1. For the remainder of this paper we will adopt popular finance nomenclature and refer it as prefunded bonds. However, one must keep in mind that only coupon payments are prefunded. 2. See Goodman and Cohen (1989) for detailed discussion of paid-in-kind bonds. 3. U.S. Treasury sells risk-free zero-coupon bonds in the form of STRIPs. 4. See Ross, Westerfield, and Jaffe (2005) for algebraic expression of PVIFA. 5. Alternately, we can assume that all yields are net of transaction costs. 6. This is analogous to a situation in portfolio construction. Consider two assets with standard deviations 10 percent and 20 percent. For an investor who is long on both assets, the portfolio standard deviation will be between 10 percent and 20 percent. However, if the investor is short on the first asset and long on the second asset then portfolio standard deviation will exceed 20 percent. REFERENCES Brigham, E.F. and Phillip, R.D. (2004). Intermediate Financial Management. Mason, OH: Thomson Southwestern Publishing. Doherty, J. (1997). ‘‘For junk borrowers, pre-funded bonds pick up steam, but they may pose greater risk than zeros.’’ Barrons, MW15. Fabbozzi, F.J. (2000). Bond Markets, Analysis and Strategies. Englewood Cliffs, NJ: Prentice-Hall. Goodman, L.S. and. Cohen,A.H. ( 1989). ‘‘Payment-inkind debentures: an innovation.’’ Journal of Portfolio Management, 15: 9–19. Myers, S.C. (1984). ‘‘The capital structure puzzle.’’ Journal of Finance, 39: 575–592. COMPARATIVE ANALYSIS OF ZERO-COUPON AND COUPON-PRE-FUNDED BONDS Macaulay, F. (1938). Some Theoretical Problems Suggested by the Movement of Interest Rates, Bond Yields, and Stock Prices in the US since 1856. New York: National Bureau of Economic Research. Redington, F.M. (1952). ‘‘Review of the principles of life office valuation.’’ Journal of the Institute of Actuaries, 78: 286–340. 323 Ross, S.A., Westerfield, R.W., and Jaffe, J. (2005). Corporate Finance. Homewood, IL: Irwin McGraw-Hill. Samuelson, P.A. (1945). ‘‘The effect of interest rate increases on the banking system.’’ American Economic Review, 35: 16–27.