VALUING BONDS Pertemuan 7 -mupo- VALUING BONDS Pertemuan 7 -mupo- Mata kuliah: F Pengantar Analisis Pendapatan Tetap Dan Ekuitas Tahun: 2010

Bina Nusantara University 3 VALUING BONDS Materi: 1. Bond valuing model and Bond valuing process 2. Valuing a Bond with an Embedded Option 3. Valuation and analysing Callable Bond 4. Valuing a putable bond 5. Analysis of convertible bond

1. Bond valuing model and Bond valuing process The valuation process begins with determining The valuation process begins with determining benchmark interest rates. benchmark interest rates. There are 3 potential markets where benchmark interest rate There are 3 potential markets where benchmark interest rate can be obtined: can be obtined: - the Treasury market - the Treasury market - a sector of bond market - a sector of bond market - the market for the issuer’s securities - the market for the issuer’s securities In building a model to value bonds with embedded option is that the In building a model to value bonds with embedded option is that the future cash flows will depend on what happen to interst rate in the future cash flows will depend on what happen to interst rate in the future. future. For a given interest rate volatility, there are several interest rate For a given interest rate volatility, there are several interest rate models that have been used in practice to construct an interest rate models that have been used in practice to construct an interest rate tree. An interst model is probabilistic description of how interest can tree. An interst model is probabilistic description of how interest can change over life of the bond. An interest rate model does this by change over life of the bond. An interest rate model does this by making an assumption about the relationship between the level of making an assumption about the relationship between the level of short term rates and the interest rate volatility as measured by the short term rates and the interest rate volatility as measured by the standart deviation. standart deviation.

Bond valuing model and Bond valuing process (cont’) The building of a model to value bonds with embedded option is more Complex than building a model to value option free bonds, the basic Principles are the same. In the case of valuing an option free bond, the model that is built is simply a set of spot rates that are used to value cash flows. BOND VALUATION PROCESS BOND VALUATION PROCESS If a bond has an ambedded option, the following can we done: If a bond has an ambedded option, the following can we done: - Given a required yield to maturity, we can compute the value of a - Given a required yield to maturity, we can compute the value of a bond. bond. Exp: If required yield to maturity of a 9 year, 8% coupon bond the pays interest semiannualy is 7%, its price is Exp: If required yield to maturity of a 9 year, 8% coupon bond the pays interest semiannualy is 7%, its price is Given the observed market price of a bond we can calculate its - Given the observed market price of a bond we can calculate its yield to maturity. yield to maturity. exp: if the price of a 5 Year, 6% coupon bond that pays interest semiannualy is 93.84, its yield maturity is 7.5% exp: if the price of a 5 Year, 6% coupon bond that pays interest semiannualy is 93.84, its yield maturity is 7.5% - Given yield to maturity, a yield spread can be computeed. - Given yield to maturity, a yield spread can be computeed. exp: if the yield to maturity for a 5 yer, 6% coupon bond that pays exp: if the yield to maturity for a 5 yer, 6% coupon bond that pays

Bond valuation process (cont’) Bond valuation process (cont’) interest semiannualy is 7.5% and its yield is compared to interest semiannualy is 7.5% and its yield is compared to benchmark yield of 6.5%, then the yield spread is 100 basis points (7.5% minus 6.5%) benchmark yield of 6.5%, then the yield spread is 100 basis points (7.5% minus 6.5%) 2. Valuing a bond with an embedded Option 2. Valuing a bond with an embedded Option There are various models that have been developed to value a There are various models that have been developed to value a bond with embedded options. The one that we usu to illustrate bond with embedded options. The one that we usu to illustrate the issues and assumptions options is the binomial model. The the issues and assumptions options is the binomial model. The interest rates there are used in the valuation process are interest rates there are used in the valuation process are obtained from a binomial interest rate tree. obtained from a binomial interest rate tree. 3. Valuation and analysing Callable bond 3. Valuation and analysing Callable bond The valuation process proceeds in the same fashion as in the The valuation process proceeds in the same fashion as in the case of an option free bond, but with one exception: when the case of an option free bond, but with one exception: when the call option may be exercise by the issuer, the bond value at a call option may be exercise by the issuer, the bond value at a node must be changed to reflect the lesser of its values if it is node must be changed to reflect the lesser of its values if it is not called and the call price. not called and the call price.

4. Valuing a Putable bond 4. Valuing a Putable bond A putable bond is one in which the bondholder has right to force A putable bond is one in which the bondholder has right to force the issuer to pay off the bond prior to the maturity date. the issuer to pay off the bond prior to the maturity date. The value of putable bond, is grater thn the value of the The value of putable bond, is grater thn the value of the corresponding option free bond: corresponding option free bond: valuable of putable bond = value of an option+ value of the put valuable of putable bond = value of an option+ value of the put option option Suppose that a bond is both putable and callable. The procedure Suppose that a bond is both putable and callable. The procedure for valuing such a structure is to adjust the value at each node to for valuing such a structure is to adjust the value at each node to refect whether the issue would be put or called. refect whether the issue would be put or called. At each node there are 2 decisions about the exercising of an At each node there are 2 decisions about the exercising of an option that must be made. option that must be made. First, given the valuation from the backward induction method at First, given the valuation from the backward induction method at a node, the call rule is invoked to determine whether the issue a node, the call rule is invoked to determine whether the issue will called. If it is called, the value at the node is replaced by the will called. If it is called, the value at the node is replaced by the call price. The valuation prosedure then continues using the call call price. The valuation prosedure then continues using the call price at the node. price at the node.

Valuing a Putable bond (cont’) Valuing a Putable bond (cont’) Second, if the call option is not exercised at anode, it must be Second, if the call option is not exercised at anode, it must be determined whether or not the put option is exercised. If it is determined whether or not the put option is exercised. If it is exercised, then the value from the backward induction method is exercised, then the value from the backward induction method is overriden and the put price is substituted at that node and is overriden and the put price is substituted at that node and is used in subsequent calculations used in subsequent calculations 5. Analysis of Convertible bonds 5. Analysis of Convertible bonds Convertible bond is a security that can be converted into Convertible bond is a security that can be converted into common stock at the option of investor. It is a bond with an common stock at the option of investor. It is a bond with an embedded option is granted to the investor. Morever, since a embedded option is granted to the investor. Morever, since a convertible bond may be callable and putable, it is a complex convertible bond may be callable and putable, it is a complex bond because the value of the bond will depend on both how bond because the value of the bond will depend on both how interest rates change (which affects the value of the call and any interest rates change (which affects the value of the call and any put option) and how changes in the market price of the stock put option) and how changes in the market price of the stock affects the value of the option to convert to common stock. affects the value of the option to convert to common stock.

Analysis of Convertible bonds (cont’) Analysis of Convertible bonds (cont’) The conversion provision of a convertible security grant the The conversion provision of a convertible security grant the securityholder the right to convert the security into securityholder the right to convert the security into predetermined number of shares of the common stock of the predetermined number of shares of the common stock of the issuer. An exchangeable security grants the securityholder the issuer. An exchangeable security grants the securityholder the right to exchange the security for common stock of a firm other right to exchange the security for common stock of a firm other than the issuer of the security. than the issuer of the security. The number of shares of common stock that the securityholder The number of shares of common stock that the securityholder will receive from exercising the call option of a convertible will receive from exercising the call option of a convertible security is called the conversion ratio. security is called the conversion ratio. Exp: assume the conversion ratio is 20. If investor converts the Exp: assume the conversion ratio is 20. If investor converts the bond for stock the investor will receive 20 shares of common bond for stock the investor will receive 20 shares of common stock. Suppose that the par value for comvertible bond is $ 1000 stock. Suppose that the par value for comvertible bond is $ 1000 at issuance, investors are purchasing the common stock for $ 50 at issuance, investors are purchasing the common stock for $ 50 per share ($ 1000/20 shares). This price is reffered to in the per share ($ 1000/20 shares). This price is reffered to in the prospectus as the conversion price and some investors refer prospectus as the conversion price and some investors refer

Analysis of Convertible bonds (cont’) Analysis of Convertible bonds (cont’) to it as the stated conversion price. to it as the stated conversion price. 5.1 Traditional analysis 5.1 Traditional analysis Traditinal analysis of convertible bonds relies on measures Traditinal analysis of convertible bonds relies on measures that do not directly value the embedded cal, put, or that do not directly value the embedded cal, put, or common stock option common stock option Minimum value of a Convertible security Minimum value of a Convertible security The conversion value or parity value of a convertible The conversion value or parity value of a convertible security is the value of secrity if it is converted security is the value of secrity if it is converted immidiately: immidiately: Conversion value = market price of common stock x conversion ratio Conversion value = market price of common stock x conversion ratio Exp: The ADC convertible issue, the straight values, of Exp: The ADC convertible issue, the straight values, of the bond is $ per $ 100 of par value. Since the the bond is $ per $ 100 of par value. Since the market price per share of common stock is $ 33, market price per share of common stock is $ 33, conversion ratio 25.32; theconversion value $ 1,000 of conversion ratio 25.32; theconversion value $ 1,000 of par value is: par value is: conversion value = $ 33 x = $ conversion value = $ 33 x = $

Analysis of Convertible bonds (cont’) The conversion value is % of par value. Per The conversion value is % of par value. Per $ 100 of par value the conversion value is $ $ 100 of par value the conversion value is $ Market conversion price Market conversion price The price that an investor effektifly pays for the The price that an investor effektifly pays for the common stock if the convertible is purchased and common stock if the convertible is purchased and then converted into the common stock is called then converted into the common stock is called the market conversion price or conversion the market conversion price or conversion parity price : parity price : market conversion price = market price of convertible security market conversion price = market price of convertible security conversion ratio conversion ratio An investor who purchases a convertible bond An investor who purchases a convertible bond rather than the underlying stock, effectively pays rather than the underlying stock, effectively pays a premium over the current market price of stock. a premium over the current market price of stock. This premium per share is equal to the different This premium per share is equal to the different between the market conversion price and between the market conversion price and

Analysis of Convertible bonds (cont’) Analysis of Convertible bonds (cont’) the current market price of common stock : the current market price of common stock : market conversion premium per share = market conversion premium per share = market conversion price – current market price market conversion price – current market price The market conversion premium per share is ussualy The market conversion premium per share is ussualy expressed as a precentage of the current market expressed as a precentage of the current market price as follows: price as follows: market conversion premium ratio = market conversion premium ratio = market conversion premium per share market conversion premium per share market price of common stock market price of common stock 5.2 Investment characteristics of Convertible bond 5.2 Investment characteristics of Convertible bond depend on the comman stock price. If the price low, depend on the comman stock price. If the price low, The straight value is considerably higher than the The straight value is considerably higher than the conversion value the security will trade much like conversion value the security will trade much like a straight security, is reffed to as a fixed income a straight security, is reffed to as a fixed income equivalent or busted convertible. equivalent or busted convertible.

Analysis of Convertible bonds (cont’) Analysis of Convertible bonds (cont’) When the conversion value is considerably higher than When the conversion value is considerably higher than straight value, it said to be a comman stock equivalen. straight value, it said to be a comman stock equivalen. The market conversion premium per share will be small. The market conversion premium per share will be small. Between these two cases, fixed income equivalent and Between these two cases, fixed income equivalent and comman stock equivalent, the covertible security trade comman stock equivalent, the covertible security trade as a hybrid security,having the characteristic of both as a hybrid security,having the characteristic of both a fixed income security and comman stock instrument. a fixed income security and comman stock instrument. 5.3 An option based valuation approach 5.3 An option based valuation approach Approximation to the value of a convertible bond, Approximation to the value of a convertible bond, the formula : the formula : convertible security value = convertible security value = straight value + value of the option on the stock straight value + value of the option on the stock The value of a convertible bond that is callable is The value of a convertible bond that is callable is equal to: equal to: convertible bond value = convertible bond value = straight value + value of the call option on stock – value of straight value + value of the call option on stock – value of the call option on the bond the call option on the bond

Analysis of Convertible bonds (cont’) Analysis of Convertible bonds (cont’) The callable convertible bond is also putable, the The callable convertible bond is also putable, the value of such a convertible would be equal to: value of such a convertible would be equal to: convertible bond value = convertible bond value = straight value + value of the call option on the stock straight value + value of the call option on the stock - value of the call option on the bond - value of the call option on the bond + value of the putoption on the bond + value of the putoption on the bond