Bond Valuation final final.doc

58
Bonds and their Valuation Chapter Learning Objectives: To understand the concept of long term debt financing and the types of bonds. To explain some of the basic features of a bond. To compute a bond holder’s expected rate of return. To estimate the value of a bond and different yields. To understand the term structure of interest rates and various hypothesis. To explain the important relationships those exist in bond valuation. To understand the duration of a bond and the sensitivity of a bond. To discuss the factors those affect the bond pricing. To understand the indenture and the callability features in it. Bond is a debt instrument issued for a period of more than one year with the purpose of raising capital by borrowing. So bonds are long-term debt or funded debt, issued by corporations, and governments and their agencies to finance operations or special projects. Corporations pay back interest and principal from earnings, whereas governments pay from taxes, or revenues from special projects. Most individual bonds have five features when they are issued: issue size, issue date, maturity date, maturity value, and coupon. Once they are issued, yield to maturity becomes the most important figure for determining the actual yield an investor will receive. Here yield means return. Issue size – The issue size of a bond offering is the number of bonds issued multiplied by the face value. For example, if an entity issues two million bonds with a 1000 taka face price, the issue size is 2000 million taka or 2 billion taka. The issue size reflects both the borrowing needs of the entity issuing the bonds, as well as the market’s demand for the bond at a yield that’s acceptable to the issuer.

Transcript of Bond Valuation final final.doc

Bonds and their ValuationChapter Learning Objectives:

To understand the concept of long term debt financing and the types of bonds.

To explain some of the basic features of a bond.

To compute a bond holders expected rate of return.

To estimate the value of a bond and different yields.

To understand the term structure of interest rates and various hypothesis.

To explain the important relationships those exist in bond valuation.

To understand the duration of a bond and the sensitivity of a bond. To discuss the factors those affect the bond pricing.

To understand the indenture and the callability features in it.

Bond is a debt instrument issued for a period of more than one year with the purpose of raising capital by borrowing. So bonds are long-term debt orfunded debt, issued by corporations, and governments and their agencies to finance operations or special projects. Corporations pay back interest and principal from earnings, whereas governments pay from taxes, or revenues from special projects.

Most individual bonds have five features when they are issued: issue size, issue date, maturity date, maturity value, and coupon. Once they are issued, yield to maturity becomes the most important figure for determining the actual yield an investor will receive. Here yield means return.

Issue size The issue size of a bond offering is the number of bonds issued multiplied by the face value. For example, if an entity issues two million bonds with a 1000 taka face price, the issue size is 2000 million taka or 2 billion taka. The issue size reflects both the borrowing needs of the entity issuing the bonds, as well as the markets demand for the bond at a yield thats acceptable to the issuer. Issue date The issue date is simply the date on which a bond is issued and begins to accrue interest. For example, if bond is issued on January 1st then the bond issuer will have to pay coupon/interest from that day to the bond holders.

Maturity date The maturity date is the date on which an investor can expect to have his or her principal repaid. It is possible to buy and sell a bond in the open market prior to its maturity date. After the maturity day when the principal is paid bond issuers have no business with the bond holders.

Maturity value the amount of money the issuer will pay the holder of a bond at the maturity date. This can also be referred to as par value or face value. Normally it is either 1000 taka or 100,000 taka which should be paid to the bond holders at the maturity date.

Periodically, the issuer pays interest to the investor, which is calculated by multiplying the par value by the interest rate divided by the number of payments in a year. Example: if the interest rate is 14% and the par value is 1,000 taka, then the interest earned annually is 140 taka. If the company pays interest semi-annually, which most do, then the bondholder will receive 2 payments of 70 taka every year until maturity. When the bond matures, then the current owner gets back the par value of the bond. In other words, the loan is paid off. Because the amount of interest the bond pays is fixed, bonds are a type offixed-income security.Since bonds trade on the open market from their date of issuance until their maturity, their market value will typically be different than their maturity value. However, if we think the risk of default is non-existence; investors can expect to receive the maturity value at the specified maturity date, even if the market value of the bond fluctuates during the course of its life. Coupon The coupon rate is the periodic interest payment that the issuer makes during the life of the bond. For instance, if a bond with a 100,000 taka maturity value offers a coupon of 14%, the investor can expect to receive 14,000 taka each year until the bond matures. The term coupon comes from the days when investors would hold physical bond certificates with actual coupons that they would cut off and present for payment. Yield to Maturity Since corporate bonds trade on the open market, the actual yield an investor receives if they purchase a bond after its issue date (the yield to maturity) is different than the coupon rate. For example, a company issues 10-year bonds with a face value of 100,000 taka each and a coupon of 14%. In the two years following the issuance, the company experiences rising earnings, which adds cash to its balance sheets and provides it with a stronger financial position. All else equal, its bonds would rise in price, say to 101,000 taka, and the yield would fall (since prices and yields move in opposite directions). While the coupon would remain at 14%, meaning that investors would receive the same payment each year (14,000 taka), an investor who purchased the bond after it had already risen in price would receive a lower yield to maturity. In this case 14,000 taka coupon divided by the 101,000 taka, for a yield to maturity of 13.86% instead of 14% coupon. In this way, a bonds coupon and its actual yield are not necessarily the same. Yield to maturity, and not the coupon, is the yield an investor will actually receive after they buy a bond.Types of BondsBonds can be classified on various bases. One classification may be based on the nature of the issuer. It is called government bonds and corporate bonds. There are many types of corporate bonds that can be offered in order to finance corporate activity. Each corporation chooses the particular type of bond that it offers depending on a variety of factors. These include general financial market conditions, the financial strength of the corporation, the length of time during which the funds are needed, and so on. On the other side of the coin, investors choose among available types of bonds depending on their investment goals. Some investors are seeking safety, while others are seeking high current yields and are willing to take more risk.Bangladesh governments Treasury Bills are less than one year maturity, but Treasury Notes mature in 2 to 10 years which is considered as intermediate term bond and the long-term Treasury bond has a maturity over 10 years.

A company can issue bonds just as it can issue stock. Large corporations have a lot of flexibility as to how much debt they can issue: the limit is whatever the market will bear. Corporate bonds are characterized by higher yields because there is a higher risk of a company defaulting than a government. The upside is that they can also be the most rewarding fixed-income investments because of the risk the investor must take on. The company's credit quality is very important: the higher the quality, the lower the interest rate the investor receives. We will discuss the credit ratings of a company later on.

Variations on corporate bonds include Convertible bonds, Callable bonds, Floating rate bonds, Zero coupon bonds, Debentures, and so on.

Convertible bondsConvertible bonds are bonds that are issued by corporations and that can be converted to shares of the issuing company's stock at the bondholder's discretion.Issuing convertible bonds is one way for a company to minimize negative investor interpretation of its corporate actions. For example, if an already public company chooses to issue stock, the market usually interprets this as a sign that the company's share price is somewhat overvalued. To avoid this negative impression, the company may choose to issue convertible bonds, which bondholders will likely convert to equity should the company continue to do well.From the investor's perspective, a convertible bond has a value-added component built into it: it is essentially a bond with a stock option hidden inside. Thus, it tends to offer a lower rate of return in exchange for the value of the option to trade the bond into stock.An example of convertible bond in Bangladesh is ACI 20% convertible bond.

Callable bondsA bond that can be redeemed by the issuer prior to its maturity is known as callable bonds. Usually a premium is paid to the bond owner when the bond is called. It is also known as a "redeemable bond." By issuing this type of bonds, the issuer reserves the right but no obligation to call the bond prior to the prescribed maturity. One of the benefits for corporations to issue this type of bond is to save interest payment when the interest rate is falling or now have a better financing deal. So it can pay off the high coupon payment and reissue it with lower rate. Since it puts the investors at a disadvantaged position, usually a premium is paid to the bond owners when the bond is called.Puttable bondsA puttable bond has the option which allows the bond holder to sell it to the bond issuer at specific dates before maturity where the repurchase price is set at the time of issue. The holder of the puttable bond has the right, but not the obligation, to demand early repayment of the face value or principal.Price of a puttable bond is always higher than the price of a straight bond because the put option adds value to an investor and so the yield on a puttable bond is lower than the yield on a conventional bond.Floating rate bonds

Floating rate bonds are so named because the coupon rate is tied to some basic rate such as T-bill rates, Fed Fund rate or London Interbank Offered rate (LIBOR). These provide protection against inflation and interest rate risk and keep bonds selling close to their par values. DebenturesA debenture is a bond that is not secured by any property or collateral. Debentures are backed only by the general creditworthiness and reputation of the issuer. Its safety depends on the assets and earning power of the issuer. Thus, debentures are not as safe as other bonds from the same company, but will usually pay a higher interest rate to compensate for the added risk.Zero Coupon BondsBonds that pay no coupons or interest payments to the bond holders are known as zero coupon bonds. These bonds have a face value that is redeemed at the end of maturity. Instead, investors buy zero coupon bonds at a deep discount from their face value, which is the amount a bond will be worth when it "matures" or comes due. When a zero coupon bond matures, the investor will receive one lump sum equal to the initial investment.Junk BondsA junk bond, also known as a "high-yield bond" or "speculative bond," is a bond rated "BB" or lower because of its high default risk. Since junk bonds have a higher risk of defaults, it typically offers interest rates much higher than safer government bonds or even other corporate bonds.Sovereign BondsA long term debt security issued by a national government for international capital investors and institutional buyers and usually denominated in a foreign currency. The foreign currency used will most likely be a hard currency, and may represent significantly more risk to the bondholder. To finance the Padma Bridge Bangladesh government is considering issuing sovereign bonds.Islamic Bonds

Shariah is the law of Islam which bans usury and interest paymentsconsequently, it also bans conventional bonds. As if Muslim countries can benefit from international investment, and so international investors can invest in projects in Muslim countries, variations of the typical bond have been financially engineered to work somewhat like bonds, but still be compliant with Shariahthus, they are calledIslamic bonds.One such structured product is thelease-back, orijarah, structure. If a company wanted to raise money to build a plant, for instance, using this method, it would set up a special entity specifically for this project that would buy the plant. Investors would lend money to the special entity, in return for lease payments, in lieu of interest, for the term of the deal. At the end of the term, the principal is returned to investors, and the project becomes the property of the company.Another way to avoid paying interest, at least in name, is to form ajoint venturecalled amusharakah. The joint venture partners buy Islamic bonds and receive a percentage of profits over the term of the loan. An example of Islami bond in Bangladesh is Mudaraba savings bond issued by Islami bank.

Main Reasons for Issuing Bonds are as follows:Governments have no choice but to borrow when they are unable to meet their expenses from current revenue. Corporations, on the other hand, have a wider choice in the matter of financing their operations e.g., retained earnings, new equity issues, etc. But they still prefer to go in for borrowing for the following reasons:1. To Reduce the Cost of Capital :

Bonds are the cheapest source of financing. A corporation is willing to incur the risk of borrowing in order to reduce the cost of capital by financing a portion of its assets with securities bearing a fixed rate of return in hope of increasing the ultimate return to the equity holder.2. To Gain the Benefit of Leverage :The presence of debt and/or preference shares in the companys financial structure means that it is using financial leverage. When financial leverage is used, changes in earnings before interest and tax (EBIT) translate into the larger changes in earnings per share.

However, leverage is a two-edged sword as EBIT can rise or fall. If it falls, and financial leverage is used, the equity holders endure negative changes in EPS that are larger than the relative decline in EBIT. For example, if a company can borrow at 10% and put the funds to works to earn more than 10%, the earnings on the equity holders are increased and vice versa.3. To Effect Tax Saving :Unlike dividends on equity, the interest on bonds is deductible in figuring up corporate income for tax purposes. Hence, the EPS increases if the financing is through bonds rather than with preference or equity shares.4. To Widen the Sources of Funds :By issuing bonds, the corporation can attract funds from individual investors and especially from those investing institutions which are reluctant or not permitted to purchase equity shares.5. To Preserve Control :An increase in debt does not diminish the voting power of present owners since bonds ordinarily carry no voting right. However, a manager must be concerned with the effect of fixed cost securities on both EPS and the price earnings ratio.

An increase in risk has a depressing influence on a price- earnings ratio, while an increase in growth will tend to increase the price-earnings ratio.

Fixed cost securities affect both risk and growth. If the risk effect outweighs the growth effect, then the price-earnings ratio will decline. If the growth effect outweighs the risk effect, then the price earnings ratio will increase.

Bond Principles: Terms of Repayment

Interest only - the periodic payments are entirely interest.Sinking fund - periodically, a portion of the debt principal is set aside or a certain number of the bonds are retired. Balloon loan - the debt may be partially amortized with each payment. Income bond- interest is payable only if it is earned.Annuities - most bonds are annuities plus an ultimate repayment of principal.Zero coupon - only the par value is returned at maturity.

Variable (adjustable) rate - the rate fluctuate in accordance with some market index or predetermined schedule.Inflation-indexed Treasury bonds - the principal value is adjusted based on the consumer price index. Why would an investor invest in bond market?There are various reasons for an investor to consider in investing bonds like:

Diversification

Regular income

Potential tax benefits

Preservation of principal.Cash Flows of a BondCash flows of a typical bond consists of two parts- the periodic coupon payments and the final redemption payment.

Consider a bond that pays a 10% coupon, has a par or face value of 1,000 taka and matures in 5 years. Suppose also that the market rate of interest for such a bond (i.e., your required rate of return, kb) is 8%. Thus,

Par = 1,000 takaCoupon Rate = 10%

Maturity = 5 years

Kb = 8%

The cash flows that are promised by the company include interest payments of 100 taka per year for five years and the payment of the face value of 1,000 taka at the end of five years.

0

1

2

3

4

5

100 100 100 100 100

1,000

1,100

PVIFA 8%,4 = 3.3121

331.21

PVIF 8%,5 = .6806

748.661,079.87 takaThe value of the bond is 1,079.87 taka which is selling at a premium relative to the par value of 1,000 taka. (A bond selling at less than par is said to be selling at a discount.) Pricing of BondsThe price or value of a bond is determined by discounting the bond's expected cash flows to the present using the appropriate discount rate. The price of the bond should equal the present value of its expected cash flows. The coupons and principal repayment of 1,000 taka are known and the present value, or price, can be determined by discounting these future payments from the issuer at a appropriate required yield, r, for the issue.

This relationship is expressed for coupon bond by the following formula:PV of a Bond = C. Pmt*{1 (1+ r/n) t*n} + Face Value

nr/n

(1+r/n)t*nWhere, C = the annual coupon payment,

r = the required return on the bond, and

t = the number of years remaining until maturity.n = Number of compounding in a year.

Problem 3.1: If a 1000 taka face value bond paying 15% coupon whereas it is maturing in 10 years and the interest rate is 12%. How much should you pay for this bond? Face ValueCoupon rateMaturing timeInterest rate

100015%10 years12%

PV of a Bond = C. Pmt*{1 (1+ r/n) t*n} + Face Value

n r/n

(1+r/n)t*n

=150*[{1-(1+.12)-10}/.12] + (1000/1.1210)

=150*5.6502230+ 321.973

=847.53345+321.973

=1169.50 taka.

So, an investor should pay maximum 1159.50 taka for this bond.

Problem 3.2: If a 12% semi-annual bond maturing in 10 years is selling in the market for 750 taka when the market interest rate is 16%. Should you buy this bond at 750 taka?

Face ValueCoupon rateMaturingInterest rate

1000Annual 12% or 6% semi-annual10 years or 20 semi-annualAnnual 16% or semi-annual 8%

PV of a Bond = C. Pmt*{1 (1+ r/n) t*n} + Face Value

n r/n

(1+r/n)t*n

=120/2*[{1- (1+.16/2)-10*2}/.16/2] + (1000/(1+.16/2) 10*2) = 803.63 taka.Yes, we should buy the bond because its intrinsic value 803.63 taka is higher than the market price of 750 taka.Discount and premium bonds

A bond whose market price is less than its par value is selling at a discount. It is called discount bond. The price of such bonds rise as maturity approaches. If the market price is more than the par value, the bond is selling at a premium. It is called premium bond. The price of such bonds fall as maturity approaches.Yield on the bond

The return of a bond is largely determined by its interest rate, which, in turn, is determined by the prevailing interest rate and the creditworthiness of the issuer, assessed by credit rating companies, such as Standard & Poors and Moodys. A higher credit rating allows the issuer to sell its bonds for a higher price, i.e. at a lower interest rate.Nominal yield, or thecoupon rate, is the stated interest rate of the bond, which is a percentage of par value, which, in most cases, is 1,000 taka for corporate bonds. The coupon is usually paid semiannually. Thus, a bond that pays 14% interest pays 140 taka per year in 2 semi-annual payments of 70 taka. The return of a bond is the return/investment, or in the example just cited, 140/1,000 = 14%.Bonds trading in the secondary market will usually have prices that are less or more than par value, thus yielding an interest rate that differs from the nominal yield, called thecurrent yield, orcurrent return. So the price of bonds moves in the opposite direction of interest rates.Current Yield:

Because current bond prices fluctuate, an investor can pay more or less than the par value for a bond. If the investor holds the bond until maturity, he will lose money if he paid a premium for the bond, and he will earn money if he paid for it at a discount. Current yield measure looks at the current price of a bond instead of its face value and represents the return an investor would expect if he or she purchased the bond and held it for a year. This measure is not an accurate reflection of the actual return that an investor will receive in all cases because bond prices are constantly changing due to market factors.Current Yield Formula

Current Yield = Annual Interest Payment

Current Market price of Bond

Problem 3.3: If a bond is paying 14% annual coupon which is now selling in the market for 880 taka, what is the current yield of this bond?

Current Yield = 140/880 = 15.91%.

Recall that if the market price of a bond goes down, the current yield will go up. Using the above example, if the current bond piece goes down to 700 taka instead 880 taka, the current yield would be: 140/700 = 20%.Yield to Maturity:

Theyield-to-maturity, ortrue yield, of a bond that is held to maturity will have to account for the gain or loss that occurs when the par value is repaid. The yield to maturity is the single interest rate that, when applied to the stream of cash flows associated with a bond, causes the present value of those cash flows to equal the bonds market price.Yield to Maturity and Present Value of a BondThe yield to maturity is found in the present value of a bond formula:

nValue of the bond = Price, P0 = Ct+ Face Value 1 ( 1 + YTM)t ( 1 + YTM)nAssuming investment at the current price of the bond, YTM of the bond is the internal rate of return on the investment of the bond. So, the yield to maturity is the interest rate that will make the present value of the cash flows equal to the price of the bond. Example, If a 1000 taka face value with 12% annual coupon with maturity of 6 years is now trading for 900 taka and assuming that the investors buys it for 900 taka and hold it until maturity. The cash flows of the bond can be shown below:

Price of the bond, P0 = 900 = 120 + 120 + 120+ 120 + 120+ 120 + 1000

1+r(1+r)2 (1+r)3 (1+r)4 (1+r)5 (1+r)6 (1+r)6The solution to determine the YTM of the bond can be attempted through trial and error method by taking an approximate value of r and checking if the right hand side of the equation matches with the price of the bond. The Scientific calculator or excel spreadsheet will give us the yield to maturity of 14.62%.

For calculating yield to maturity, the price of the bond, or present value of the bond, is already known. Calculating YTM is working backwards from the present value of a bond formula and trying to determine what r (YTM) is.

The formula foryield to maturityis complicated and difficult to solve, but it generally will yield an interest rate comparable to newly issued bonds with the same credit rating. The following formula provides an approximation:Approximate YTM = Coupon Payment + Face Value Market value

No. of years to maturity

(Face value + Market value)/2Notice that the formula shown above is used to calculate the approximate yield to maturity. To calculate the actual yield to maturity requires trial and error by putting rates into the present value of a bond formula until P, or Price, matches the actual price of the bond. Some financial calculators and computer programs can be used to calculate the yield to maturity.But if we use our approximation equation of YTM on our above example where the actual YTM was given at 14.62% using the scientific calculator but by using our approximation, we get

Approximate YTM = 120 + (1000 +900)/6

(1000 +900)/2

= 120 + 16.666

950

= 14.385% which is close to 14.62%.

Problem 3.4: The price of a bond is 920 taka with a face value of 1000 taka which is the face value of many bonds. Assume that the annual coupons are 100 taka, which is a 10% coupon rate, and that there are 10 years remaining until maturity. What is the YTM of this bond?

Solution: Using the approximate YTM formula:

Approximate YTM = 100 + (1000 920)/10

(1000 + 920)/2

= 11.25%.After solving this equation, the estimated yield to maturity is 11.25%. But if you use the computer generated trial and error software it will give you the exact YTM of 11.38% which is pretty close.

YTM takes into account the capital loss or gain upon maturity as well as the time value of money. Current yield considers neither. If the current price of the bond is less than its face value, YTM shall be greater than the current yield as the investor would have capital gain upon maturity. But if the bond is selling above face value, YTM shall be lower than current yield since upon maturity the investor would incur a capital loss.

Normally when a bond is issued, it is traded at face value and if this is the case then the YTM and the coupon will be the same. Simply speaking if the price of the bond is selling at par (face value) the YTM will remain the same which equals to coupon rate. Only a change in price above or value to face value will change the YTM and there is an inverse relationship between the price and the YTM of the bond which means if the price of a bond rises the YTM falls and vice versa.Assumptions on YTM:The rate of return on bonds most often quoted for investors is the yield to maturity (YTM), a promised rate of return that will occur only under certain assumption. It is the compound rate (not simple) of return an investor will receive only under certain assumption: The bond is held to maturity. The coupons received while the bond is held are reinvested at the calculated yield to maturity.

If a bond pays periodic interest, it is not possible to lock in a prescribed yield to maturity. When a bond is bought at a discount, yield to maturity will be greater than the current yield and if bought at a premium, the yield to maturity will be less. If a bond trades at a discount, an investor will earn a return both from receiving the coupons and from receiving a face value that exceeds the price paid for the bond. On the other hand, if a bond trades at a premium its coupon rate will exceeds its yield to maturity.The yield to maturity formula is used to calculate the yield on a bond based on its current price on the market. The yield to maturity formula looks at the effective yield of a bond based on compounding as opposed to the simple yield which is found using the dividend yield formula.YTM measures three sources of a bonds return:

Coupon return: Return from coupon payments (current yield).Capital gain return: Capital gain / loss when bond matures, or is sold / called at a predictable point in the future.Reinvestment return: Interest income generated from the reinvestment of coupons (interest on interest).Problem 3.5: If a 1000 taka face value bond paying 15% coupon whereas it is maturing in 10 years and the interest rate is 12%. If it is trading for 1150 taka, what is the current yield and YTM?Solution: Current Yield = (Annual Coupons/Current bond price)

= (150/1150)

= 0.1304 Or 13.04%

YTM = (150+{1000-1150)/10)/{(1000+1150)/2)

=135/1075

=0.1256 Or 12.56%.

Problem 3.6: If a 12% annual bond maturing in 10 years is selling in the market for 750 taka when the market interest rate is 16%. What is the current yield and YTM of this bond?Solution: Current Yield

= (Annual Coupons/Current bond price)

= (120/750)

= 0.16

Or 16%. YTM = {120+{1000-750)/10}/{(1000+750)/2}

=145/875

=0.1657

Or 16.57%

Yield to Call

The term Yield to Call is often abbreviated as YTC, defined that the bond is called on the next eligible call date. The yield is calculated from the cash flows from the coupon payments plus the cash flow of the redemption proceeds at the time of the call. When bond issuers include call options in indenture then it becomes their discretion whether they will expire the bonds early after the call date. Since bond may not wait until maturity and may be redeemed prior to the maturity YTM becomes useless to count. In that case, it would be more relevant to compute the yield to the point of earliest call which is known as yield to call (YTC).

Like the yield to maturity, the yield to call usually cannot be solved for directly. It generally must be determined using trial and error or an iterative technique. Fortunately, financial calculators make the task of solving for the yield to maturity quite simple.To calculate the yield to first call, the YTM formula is used, but the number of periods until the first call date substituted for the number of periods until maturity and the call price substituted for the face value. Issuers often pay a call premium for a specific period of time to call a bond, and therefore the call price usually differ either by an extra coupon payment or fixed at the time of issuance. Yield to call can be approximately calculated from the formula given below:

When it comes to estimate the actual return on a callable bond, yield to maturity has a flaw. If the bond is called, the par value will be repaid and interest payments will come to an end, thus reducing its overall yield to the investor. Therefore, for a callable bond, you also need to know what the yield would be if the bond were called at the earliest date possible. That figure is known as its yield to call. The calculation is the same as with yield to maturity, except that the first call date is substituted for the maturity date. YTC is therefore a good measurement gauge for the expected investment return of a bond at a callable timeMany bonds, especially those issued by corporations, are callable. This means that the issuer of the bond can redeem the bond prior to maturity by paying the call price, which is usually greater than the face value of the bond, to the bondholder. Often, callable bonds cannot be called until 5 or 10 years after they were issued. When this is the case, the bonds are said to be call protected. The date when the bonds can be called is referred to as the call date.The yield to call is the rate of return that an investor would earn if he bought a callable bond at its current market price and held it until the call date given that the bond was called on the call date. It represents the discount rate which equates the discounted value of a bond's future cash flows to its current market price given that the bond is called on the call date. Example, if a 12% annual coupon bond with a face value of 1000 taka maturing in 10 years has a call provision which states that the issuer can call the bond after 4 years at a call price of 1050 taka. If the bond is selling at 900 taka in the market then what is the yield to call of this bond?

Value of the bond = 900 = 120/(1+YTC) + 120/(1+YTC)2 + 120/(1+YTC)3 + 120/(1+YTC)4

Approximate,YTC = 120 + (1050 900)/4

(1050+900)/2

= 157.5/975 = 16.15%

Using scientific calculator or excel function we get YTC of 16.59%.

DURATION OF THE BONDAs we know the price of a bond changes with the changes in interest rate. But the question is, if say, interest rate changes 1%, do all bonds change by the same amount or in same ratio? The answer is no and since the value of a bond is sum total of present values of all cash flows attached with the bond. Now we have o find out what proportion each of the cash flows constitutes the price. This price sensitivity of the bond is measured by the term known as Duration.

Duration is the time weighted average of the cash flows as compared to its total value. It is calculated using the following formula:

Duration of the bond = [ 1x CF1 + 2x CF2 + 3x CF3 + .]

(1+r)1 (1+r)2 (1+r)3

P0The term duration has a special meaning in the context of bonds. It is a measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows. It is an important measure for investors to consider, as bonds with higher durations carry more risk and have higher price volatility than bonds with lower durations.

It is important to note, however, that duration changes as the coupons are paid to the bondholder. As the bondholder receives a coupon payment, the amount of the cash flow is no longer on the time line, which means it is no longer counted as a future cash flow that goes towards repaying the bondholder.

Some aspects of duration To obtain maximum price volatility, investors should choose bonds with the longest duration Duration is additive Portfolio duration is just a marketvalue weighted average of each individual bonds modified duration Duration measures volatility which isnt the only aspect of risk in bonds.

Duration depends on three factors: Maturity of the bond. Coupon payments. Yield to maturity. Duration increases with time to maturity but at a decreasing rate. For coupon paying bonds, duration is always less than maturity

For zero coupon-bonds, duration equals time to maturity Duration increases with lower coupons. Duration increases with lower yield to maturity.Importance of duration Allows comparison of effective lives of bonds that differ in maturity, coupon.

Used in bond management strategies particularly immunization.

Measures bond price sensitivity to interest rate movements, which is very important in any bond analysis.Estimating Price Changes Using DurationProblem 3.7: If a 10 year maturity bond with a face value of 1000 taka paying 12% annual coupon when the market interest rate for this type of security with the same risk is 10%. What is the duration of this bond?Face Value = 1000

Coupon Rate = 12%

Maturity = 10 Years

So the Duration of the bond is

YearCash FlowPV of cashflow(10%)Proportion of total valueTime X Proportion

(PV of cashflow/Total value)

1Tk.120.00Tk.109.099.72%0.10

2Tk.120.00Tk.99.178.83%0.18

3Tk.120.00Tk.90.168.03%0.24

4Tk.120.00Tk.81.967.30%0.29

5Tk.120.00Tk.74.516.64%0.33

6Tk.120.00Tk.67.746.03%0.36

7Tk.120.00Tk.61.585.48%0.38

8Tk.120.00Tk.55.984.99%0.40

9Tk.120.00Tk.50.894.53%0.41

10Tk.1,120.00Tk.431.8138.46%3.85

Tk.1,122.89100.00%6.54

The duration of the bond is 6.54 Years. Approximate, YTM = [{C+(F-P)/n}\] / {(F+P)/2}

= [{120+(1000-1122.89)/10}\] / {(1000+1122.89)/2}

= 107.711/1061.445

= 0.10147

The duration of a bond is primarily affected by its coupon rate, yield, and remaining time to maturity. The duration of a bond will be higher if the coupon is lower, lower its yield, and longer the time left to maturity. The following scenarios of comparing two bonds should help clarify how these three traits affect a bonds duration: If the coupon and yield are the same, duration increases with time left to maturity. If the maturity and yield are the same, duration increases with a lower coupon. If the coupon and maturity are the same, duration increases with a lower yield.Sensitivity of bond pricesDuration of the bond is a measure of the sensitivity of bond price with the change in the yield. The volatility of the bond is approximately given by the following equation:

Volatality of the bond = - Duration

(1+ YTM/m)Where m is the number of times the coupons payments are made in a year. Here duration is measured in years and YTM is expressed as decimal.So the volatility of the bond is

Volatility = (-Duration)/ (1+YTM)

= (-6.54) / (1.1)

= -5.945

So for 1% change in the YTM, the price will change by -5.945%. Three Sources of Earning from bond investment:

Note that a bondholder has three possible sources of dollar returns from a bond investment, which we call the total dollar return: The coupons, which are the semiannual interest payments on a coupon-paying bond. A capital gain or loss- the difference between the purchase price and the price received when the bond is sold, matures or is called.

Interest on interest, resulting from the reinvestment of the coupons. Problem 3.8: If a 10 years 1000 taka face value bond is paying 12% annual coupon where the YTM is 14%, what is the duration of this bond?Solution: Face Value = 1000

Coupon Rate = 12%

Maturity = 10 Years

YTM = 14%

So the Duration of the bond isYearCash FlowPV of cashflow(14%)Proportion of total valueTime X ProportionPV of cashflow(15%)

(PV of cash flow/Total value)

1Tk.120.00Tk.105.2611.75%0.12Tk.104.35

2Tk.120.00Tk.92.3410.31%0.21Tk.90.74

3Tk.120.00Tk.81.009.04%0.27Tk.78.90

4Tk.120.00Tk.71.057.93%0.32Tk.68.61

5Tk.120.00Tk.62.326.96%0.35Tk.59.66

6Tk.120.00Tk.54.676.10%0.37Tk.51.88

7Tk.120.00Tk.47.965.35%0.37Tk.45.11

8Tk.120.00Tk.42.074.70%0.38Tk.39.23

9Tk.120.00Tk.36.904.12%0.37Tk.34.11

10Tk.1,120.00Tk.302.1133.73%3.37Tk.276.85

Tk.895.68100.00%6.12Tk.849.44

The duration of the bond is 6.12 Years.

So the volatility of the bond if YTM changes from 14% to 15% is

Volatility = (-Duration)/ (1+YTM)

= (-6.12) / (1.01)

= -6.059%

So for 1% change in the YTM, the price will change by -6.059%.

And the new price of the bond will be 849.44 taka.Convexity of a bondDuration is the linear measure of how the price of a bond changes in response to changes in interest rates. As interest rates change, the prices of a bond wont change linearly but would change in some curved function form which is convex in shape. The change in a bonds duration for a given change in yields can be measured by its convexity.As the yield on a bond changes so too does its duration, a bonds convexity measures the sensitivity of a bonds duration to changes in yield. Duration is an imperfect way of measuring a bonds price change, as it indicates that this change is linear in nature when in fact it exhibits a sloped or convex shape. A bond is said to have positive convexity if duration rises as the yield declines. A bond with positive convexity will have larger price increases due to a decline in yields than price declines due to an increase in yields. Positive convexity can be thought of as working in the investors favor, since the price becomes less sensitive when yields rise (prices down) than when yields decline (prices up). Bonds can also have negative convexity, which would indicate that duration rises as yields increase and can work against an investors interestMalkiels theorems:

Malkiels theorems are a set of relationships among bond prices, time to maturity, and interest rates.RULE 1: The higher the expected rate of inflation, the higher the required returns on bonds.

RULE 2: The higher a bonds credit rating, the lower its default risk and the lower its yield.

RULE 3: All other things remaining the same, the longer the maturity of a bond, the higher its interest rate (yield) will be (at least most of the time).RULE 4: The higher a bonds liquidity risk, the higher its yield will be.

RULE 5: All other things remaining the same, convertible bonds will have lower yields than nonconvertible bonds. RULE 6: All other things remaining the same, bonds will call provisions will have higher yields than bonds without call provisions. Bond rating

Table 1. Quality Ratings Used by Moodys and Standard & Poor's

Moody's Rating SystemStandard & Poor's Interpretation

Rating System

AaaAAA High-quality debt instruments

AaAA

A A Strong to adequate ability to pay

Baa BBB principal and interest

Ba BB

BB

Caa

Ca CCC Ability to pay principal andCC interest speculative

C C

DDD

DD In default

D

Note: Both rating services use factors to amend the above rating categories to indicate a range within a given rating. Moody's uses a 1, 2, or 3 factor, and Standard & Poor's uses a plus or minus factor. For example, a Moody's rating of Aa2 indicates a firm that is in the midrange of all firms with a double-A rating.

The Bond Indenture The bond indenture is a three-party contract between the bond issuer, the bondholders, and the trustee. The trustee is hired by the issuer to protect the bondholders interests. The indenture includes:

The basic terms of the bond issue. The total amount of bonds issued. A description of the security.

The repayment arrangements. The call provisions. Details of the protective covenants.Factors Affecting Bond Yields The real rate of interest

Expected future inflation

Interest rate risk

Default risk premium

Taxability premium

Liquidity premium Change in inflation risk- A rise in inflation will cause the nominal interest rates to go up since the central bank would be keep to control inflation by raising the cost of borrowings and so does the value of bond would go down.

Default risk or credit risk- It is the possibility that a borrower will be unable to repay principal and interest as agreed upon in the loan document. Usually, it is rated by agencies like Moodyand Standard & Poors. Interest rate risk - the chance of loss due to changing interest rates. If the market interest goes up investors would like to invest in money market which will make investment in bond less attractive and thus lower bond prices. Call risk - the possibility that the company will exercise a bonds call feature. Reinvestment rate risk - the chance that the interest received cannot be reinvested to earn as much as the bonds original yield to maturity. - the higher the coupon on a bond, the higher its reinvestment rate risk.

Marketability risk or liquidity risk - the difficulty of selling a bond in the secondary market.Perpetuities

There is a type of bond that never matures called perpetuity, or a consol. (The term consol comes from the fact that the first perpetuities were issued by the British government following the Napoleonic Wars to consolidate their war debts.) If long-term bonds are more sensitive to changes in interest rates than short-term bonds, then consol is more sensitive to changes in interest rates.When N is infinity, the value of a perpetual bond reduces to

Value of a Consol = Coupon payment/ market interest rateProblem 3.9: if a consol (perpetuity bond) is paying 140 taka per year forever what should be the value of that bond given the market interest rate is 12%?

Value of that Consol = 140/0.12 = 1166.67 taka.

Problem 3.10: A perpetual bond has a 10% coupon. The bond yields 8% and the par value is 1000. What is the price of the bond?The price of this bond = 100/0.08 = 1250 taka.

The dirty (or full) price is the amount that the buyer agrees to pay the seller, which is the agreed-upon price plus accrued interest. The price of a bond without accrued interest is called the clean price. The exceptions are bonds that are in default. Such bonds are said to be quoted flat, that is, without accrued interest.Term Structure of Interest RatesA plot of interest rates against time to maturity is known as a yield curve. The term structure of interest rates is a schedule showing the yields of securities that are alike in all respects except for their term to maturity (number of years until the bonds mature). As mentioned above, the longer the time to maturity, the riskier the bond and (usually) the higher the yield. The term structure of interest rates is usually demonstrated using U.S. Treasury securities as shown below:

Term Structure for U.S. Treasury Debt

Time to Maturity Yield 1 month .01%

3 months .20%

6 months .50%

1 year 1.00%

5 years 1.50%

10 years 2.00%

20 years 3.00%

30 years 3.80%

Notice that the required return on U.S. Treasury bonds rises as the time to maturity of the bonds rises. This is the normal state of things. However, on rare occasions, the returns on long-term bonds are lower than those on short-term bonds.

The data in the table can be graphed with the time to maturity on the X axis and the required return or yield on the Y axis as shown below.

U.S. Treasury Securities Yield Curve

The graph shows the longer the time to maturity the higher the yield on Treasury bonds. This is called a normal (because this is normally the shape of the yield curve) or positively sloped yield curve. Investors interpret a normal yield curve as indicating rising inflation in the future (because the inflation is expected to rise in the future) or as indicating an expanding economy (meaning the real rate of interest is expected to rise).

The graph shown below portrays a declining or negatively-sloped yield curve. Notice the rates on longer-term bonds are lower than those of shorter-term bonds. This shape of yield curve is rare, but when it occurs it is usually interpreted to mean a recession is about to occur.

Finally, a flat yield curve is shown on the following page. The required return is the same regardless of maturity. Again, this is rare and indicates an economy in transition from expanding to contracting or contracting to expanding.

Theories of the Term Structure of Interest Rates

(or Why the Yield Curve Has A Particular Shape)There are three theories which try to explain the shape of the yield curve. They are:

1. Expectations Hypothesis

2. Liquidity Hypothesis

3. Market Segmentations Hypothesis

Expectations Hypothesis

The expectations hypothesis says the shape of the yield curve reflects the average annual rate of inflation investors expect for any given maturity. If investors expect inflation rates to rise in the future, then longer term bonds should have higher yields to compensate investors for the higher expected rates of inflation. This would result in a normal (positively-sloped) yield curve. Conversely, if investors expect inflation rates to fall in the future, longer term bonds should have lower yields than shorter term bonds. This would result in a declining (negatively sloped) yield curve. The expectations hypothesis can therefore explain any shape of yield curve (normal, declining or flat).

Liquidity Preference Hypothesis

The liquidity preference hypothesis states that investors prefer to hold short-term bonds (because its easier to predict the short-term prospects for a firm than it is to predict its long-term prospects) and bond issuers would prefer to issue long-term bonds (to lock in access to funds over a long time period in case, in fact, the firms prospects do deteriorate). The result of these assumptions, if true, is that issuers will issue lots of long-term bonds (and few short-term bonds) and investors will want to buy lots of short-term bonds (and few long-term bonds). Together, this means:

1. Short-term bonds will be scarce but demand for them will be high

2. Long-term bonds will be plentiful but demand for them will be low.

To illustrate how the liquidity preference hypothesis might work in action, assume we start out a flat yield curve. Now assume the finance fairy flutters down and decrees that the liquidity preference hypothesis is true. Suddenly bond issuers will issue more long-term bonds at the same time investors sell off those that they already own. As we shall learn shortly, the effect of this is to lower the price of the long-term bonds which causes their yield to rise (trust me on this for now). While all of this is going on, bond issuers are issuing fewer short-term bonds precisely at the moment bond investors are buying all of them they can. Again, as we shall learn, this will cause the prices of the short-term bonds to rise and their yields to fall. The yield curve shown below illustrates how all this might play out:

Yield Curve Under Liquidity Preference Hypothesis

The liquidity preference hypothesis results in a normal or positively sloped yield curve. The liquidity preference hypothesis can only explain this yield curve shape. It cannot explain flat or declining yield curves.

Market Segmentations Hypothesis

The market segmentations hypothesis states that borrowers and lenders have preferred maturity habitats and that they rarely depart from those habitats. For example, most people borrowing money to finance the purchase of a new car do so using 4-year car loans. Similarly, banks feel most comfortable making car loans over 4 years. As another example, most people borrowing money to finance the purchase of a house do so using 30-year home loans. Banks feel most comfortable making home loans over 30 years. Most of us would never consider financing a car over 30 years (even if we could find a bank to make such a loan) because cars typically do not last that long. A 30-year car loan would force us to pay interest toward the purchase of a car long past its useful life. Similarly, most of us would not be interested in financing the purchase of a house using a 4-year loan.

The market segmentations hypothesis predicts the interest rate on 4-year car loans is entirely determined by the supply and demand for funds available for 4-year car loans. Similarly, the interest rate on 30-year home loans is entirely determined by the supply and demand for funds available for 30-year home loans. Car loan interest rates have nothing to do with (do not affect) home loan interest rates and vice versa.

The market segmentations hypothesis can explain any shape of yield curve (normal, declining and flat).Pricing of zero-coupon bonds

An investor normally receive return from bond investment from two way- one is the periodic coupon payments, and the second one is capital gains from the difference between selling value and buying value. But not all bonds will give you return in this way. We may have zero-coupon bonds which do not pay any interest and instead provide all the returns in the form of capital gains by issuing the bond at a price substantially lower than the par value and redeeming them on maturity at par value. This is why it is sometimes called deep discount bond. Some features of Zero-Coupon Bond (Zero) Does not make coupon payments.

Always (almost always) sells at a discount (a price lower than face value), so they are also called pure discount bonds.

Example: Suppose that a one-year, risk-free, zero-coupon bond with a 100,000 taka face value has an initial price of 97,323.60 taka. The cash flows would be:Although the bond pays no coupon, your compensation is the difference between the initial price and the face value. Example: If F = 100,000 taka; T = 8 years; and the annual discount rate is 9%, the bond should sell for = 50,186.63 taka

Exercises: What is the price of a Tk.1000 face value bond paying 6% semi-annual coupon if the required yield is 15%?Solution: We have a 10-year 6% coupon bond with a par value of Tk.1,000 and a required yield of 15%. Given C = 0.06(Tk.1,000) / 2 = Tk.30, n = 2(10) = 20 and r = 0.15 / 2 = 0.075, the present value of the coupon payments is:

= = = =

Tk.30[10.1944913] = Tk.305.835.

The present value of the par or maturity value of Tk.1,000 is: = = =

Tk.235.413. Thus, the price of the bond (P) = Tk.305.835 + Tk.235.413 = Tk.541.25.(b) What is the price of this bond if the required yield increases from 15% to 16%, and by what percentage did the price of this bond change?

If the required yield increases from 15% to 16%, then we have:

== = Tk.294.544.

The present value of the par or maturity value of Tk.1,000 is: = = Tk.214.548.

Thus, the price of the bond (P) = Tk.294.544 + Tk.214.548= Tk.509.09.The bond price falls with percentage fall is equivalent to = (0.059409 or about (5.94%.(c) What is the price of this bond if the required yield is 5%?

If the required yield is 5%, then we have:

= = = Tk.467.675.

The present value of the par or maturity value of Tk.1,000 is: = = Tk.610.271.

Thus, the price of the bond (P) = Tk.467.675 + Tk.610.271 = Tk.1,077.95.

(d) What is the price of this bond if the required yield increases from 5% to 6%, and by what percentage did the price of this bond change?

If the required yield increases from 5% to 6%, then we have:

== = Tk.446.324.

The present value of the par or maturity value of Tk.1,000 is: = = Tk.553.676.

The price of the bond (P) = Tk.446.324 + Tk.553.676 = Tk.1,000.00. [NOTE. We already knew the answer would be Tk.1,000 because the coupon rate equals the yield to maturity.]

The bond price falls with the percentage fall equal to (Tk.1,000.00 Tk.1,077.95) / Tk.1,077.95 = (0.072310 or about (7.23%.

(e) From your answers to Question 9, parts b and d, what can you say about the relative price volatility of a bond in a high-interest-rate environment compared to a low-interest-rate environment?

We can say that there is more volatility in a low-interest-rate environment because there was a greater fall ((7.23% versus (5.94%).Exercise: A 10-year, 1000 taka corporate bond with a 10 percent annual coupon rate is currently selling for 850 taka:(a)Calculate its current yield.

(b)Calculate its yield to maturity

Solution: (a)current yield= coupon______

current market price

= 100/850 = 11.76 percent

b) Approx. YTM = 100 + (1000 + 850)/10

(1000 + 850)/2

= 115/925 = 12.43% (Approximately)

Exercise: Two 10 percent coupon bonds are selling at par. Bond A has a 15 year maturity and Bond B has a 25 year maturity. If the appropriate required rate of return for these two bonds drops to 8 percent, calculate the percentage change in the price of each bond, using a financial calculator. Assume interest is paid semi-annually.

Solution: Bond A = original price = Tk.1,000; new price = 1000 FV, 8 interest rate, 50 pmt, 30 N, solve for PV = Tk.1,172.92

Percentage change in price = 1172.92 - 1000

1000 = .1179 = 11.79%

Bond B = original price = Tk.1,000; new price = 1000 FV, 8 interest rate, 50 pmt, 50 N, solve for PV = Tk.1,214.82

Percentage change = 1214.82 - 1000

1000 = .2148 = 21.48%

Exercise: Calculate the duration of a bond with a 7 percent coupon and a 3-year maturity currently priced at Tk.1,000. Interest is paid annually.

Solution:

YearCashflowPresent Value PV of CF PV/ Price Year X PV/Price

1Tk.70

.9346

Tk.65.42

.065

.065

2Tk.70

.8734

Tk.61.14

.061

.122

3Tk.1070

.8163

Tk.873.44.873 2.619

Tk.1000

2.806 yearsExercise:

Face Value = 1000

Coupon Rate = 15%

Maturity = 10 Years

Interest rate = 12%

So the price of the bond is

PV = C.Pmt * [{1-(1+r/n)^-t*n} / (r/n)] + {Face Value / (1+r/n)^t*n}

PV = 150 * [{1-(1+.12)^-10} / (.12)] + {1000 / (1+.12)^10}

PV = 850+321.97

PV = 1172

So the present value of the bond is 1172.

The current Yield is

Current Yield = (Annual coupons / Current Bond Price)

= 150 / 1150

= 0.1304

The YTM is

Appx. YTM = [{C+(F-P)/n}\] / {(F+P)/2}

= [{150+(1000-1150)/10}\] / {(1000+1150)/2}

= 135/1075

= 0.1255

So the YTM is 12.56%Case Study 1: Dissecting the numbers and trying to make some sense in bond valuation.Mr. Akram is confused about the corporate bond market in Bangladesh. He finds the coupon rate is quite handsome compare to the fixed deposit rate or even with the government Treasury bond. He is wondering if it is too good to be true. He is evaluating these three options and trying to work out some numbers. He is asking for your help!Offer 1: Fixed deposit on one lac taka is paying 1,000 taka per month forever.Offer 2: Bangladesh governments Treasury bond is paying 12.50% annual coupon which matures in 10 years.

Offer 3: ABC Company issued a corporate bond of 1000 taka face value. It is paying 15% annual coupon which is a medium sized company who are involved in textile sector. This bond has a maturity of 15 years but callable after 5 years. The market price of this bond today is 925 taka.

Mr. Akram wants to know where he should invest his one lac taka. The market expectation is that interest rate will fall in coming months since the inflation has fallen back to single digit and it seems to continue the trend in the next 3-4 years. He is asking for your financial management knowledge which will help him in making the right decision.

Question 1: What is the Current Yield, YTM, and YTC of ABC Company?

Question 2: How does it differ investing in Treasury instrument compare to corporate bond?

Question 3: What are some of the risk involved in corporate bond?Question 4: How fallen inflation will affect the return from bond investment?Case Study 2: Bond investing risks: So you think bonds are totally safe and predictable?

Many people believe they can't lose money in bonds. Wrong! Although the interest payments you'll get from owning a bond are "fixed," your return is anything but. Here are the major risks that can affect your bond's return:Inflation risk

Since bond interest payments are fixed, their value can be eroded by inflation. The longer the term of the bond, the higher the inflation risk. On the other hand, bonds are a classic deflation hedge; deflation increases the value of the takas that bond investors get paid.Interest rate risk

Bond prices move in the opposite direction of interest rates. When rates rise, bond prices fall because new bonds are issued that pay higher coupons, making the older, lower-yielding bonds less attractive. Conversely, bond prices rise when interest rates fall because the higher payouts on the old bonds look more attractive relative to the lower rates offered on newer ones.The longer the term of the bond, the greater the price fluctuation - or volatility - that results from any change in interest rates. There is a close connection between inflation risk and interest rate risk since interest rates tend to rise along with inflation. Interest rate shifts are also a concern for mortgage-backed bondholders, but for a different reason: If interest rates fall, home owners may decide to prepay their existing mortgages and take out new ones at the lower rates. That doesn't mean you'll lose your principal if you hold such a bond. But it does mean you get your principal back much sooner than expected, forcing you to reinvest it at the newly lower rates. For that reason, the prices of mortgage-backed securities don't get as big a boost from falling rates as other kinds of bonds.Note that price fluctuations only matter if you intend to sell a bond before maturity, or you invest in a bond fund whose manager trades regularly. If you hold a bond to its maturity, you will be repaid the bond's full face value. But what if interest rates fall and the issuer of your bond wants to lower its interest costs? Call risk

Many corporate bond issuers reserve the right to redeem, or "call," their bonds before they mature, at which point the issuer is required to pay bondholders only par value. Typically, this happens if interest rates fall and the issuer sees it can lower its costs by selling new bonds with lower yields.

If you happen to own one of the called bonds, not only do you get less than the market price of the bond, but you also have to find a place to reinvest the money. Because of the risk that you won't get the income you expect, callable bonds usually pay a higher rate of interest than comparable, non-callable bonds. So, when you buy bonds, make sure to ask not only about the time to maturity, but also about the time to a likely call.Credit riskThis is the risk that your bond issuer will be unable to make its payments on time - or at all - and it depends on the type of bond you own and the borrower's financial health. Bangladesh governments Treasuries are considered to have virtually no credit risk and junk bonds having the highest default risk.

Bond rating agencies such as Standard & Poor's and Moody's evaluate corporations and municipalities for their credit worthiness. Bonds from the strongest issuers are rated triple-A. Junk bonds are rated Ba and lower from Moody's, or BB and lower from S&P. The highest-quality municipal bonds are backed by bond insurance companies, but there is a trade-off: Insured munis typically yield up to 0.3% points less than comparable uninsured munis. Further, the insurance only guarantees your interest and principal; it won't shield you against interest rate or market risk.

Some higher-coupon munis are also "pre-refunded," meaning that, for esoteric reasons, they are effectively backed by U.S. Treasuries. When a muni is pre-refunded by an issuer, its credit quality and price rise.Liquidity risk

In general, bonds aren't nearly as liquid as stocks because investors tend to buy and hold bonds rather than trade them. While there is always a ready market for super-safe Treasuries, the markets for other bonds, especially junk bonds, can be highly illiquid. If you are forced to unload a thinly-traded bond, you will probably get a low price.Market risk

As with most other investments, bonds follow the laws of supply and demand. The more popular or less plentiful a bond, the higher the price it commands in the market. During economic meltdowns in Asia and Russia, for example, the price of safe-haven U.S. Treasuries rose dramatically.

Question 1: Is it true that the governments Treasuries are totally risk free?Question 2: How changes in inflation would impact the return from bond investment?Question 3: Why should an investor read the indenture to make sure the bond has a call provision? How does it impact the return from bond investment?Question 4: How does it help the bond issuer to add the callability clause in indenture?Case Study 3: ACI to raise Tk 130cr in bondsSarwar A Choudhury, The dailystarAdvanced Chemical Industries (ACI) Limited has decided to borrow Tk 130 crore through issuing convertible zero coupon bonds for loan repayment and fresh investment. The decision came at the company's Board of Directors meeting on Thursday.

A zero coupon bond is a bond bought at a price lower than its face value, but at the time of maturity the repayment will be an amount that the face value actually means. And convertible zero coupon bond means that it is convertible into a company's common stock or share.

The issuance of the bond 'ACI 20% Convertible Zero Coupon Bond', first of its kind, is however subject to the approval of Securities and Exchange Commission, the company officials said.

"The prime object of issuing the zero coupon bond is to repay the loan provided by the existing financiers," said Muallem A Choudhury, executive director (finance and planning) of ACI.

"The rest of the borrowed money, if there is any, will be injected to the company's business as fresh investment," he added.

Maturity period of the bond is five years with yearly redemption. It means 20 percent value of the bond will be repaid to the investors in each year with a 10.5 percent discount rate.

Of the yearly repaying amount, 20 percent will be converted into ACI shares.

Along with the discount or interest, the investors, excluding banks and insurance companies, will also get tax exemption on the income from the zero coupon bond.

The bond will be traded in Dhaka and Chittagong stock exchanges, which is also subject to the approval of the authorities.

The trading of the debt instrument will help the capital market in activating the bond market, as the existing one is almost inactive.

The bond will be issued through both private placement and initial public offering. Alliance Financial Services Ltd is the issue manager of the bond, while Industrial and Infrastructure Development Finance Co Ltd is the facility manager.

ACI, which has investments in pharmaceuticals, consumer brands and commodity products, agribusinesses, crop care and public health, livestock and fisheries, fertiliser and seeds business, posted net profits of Tk 36.25 crore in 2007. The company posted net profits of Tk 17.18 crore as of June 30.

The ACI subsidiaries include ACI Formulations Limited, Apex Leathercrafts Limited, ACI Salt Limited, ACI Pure Flour Limited, ACI Foods Limited, Consolidated Chemicals Limited, Premiaflex Plastics Limited, Creative Communications Limited, ACI Motors Limited and ACI Logistics Limited.Question 1: What is a zero coupon bond?Question 2: What is convertible bond? How would ACI convert this ACI 20% convertible bond?Question 3: How would ACI use the money raised from the issuance of bond?Question 4: What factors should an investor keep an eye once he/she bought this ACI bond?Case Study 4: Bond market in Bangladesh- problems and prospects.Bond is a long term debt instrument which is mostly backed up by either assets or goodwill. This long-term debt market plays a complementary role in developing economy through allocation of funds to the different deficit sectors. The debt market consists of money market, mortgage market, bond market and derivative market. Unfortunately, the corporate bond market of Bangladesh is quite small. Bond market in Bangladesh is dominated by treasury debt securities which is almost risk free and used by the government of Bangladesh to finance the budget deficit. Like in any other country, a well-developed tradable private bond market is critical to ensuring stability and efficiency of the financial market in Bangladesh. An efficient bond market is also important for managing public debt and bank liquidity and for efficient conduct of the monetary policy.The bond market in Bangladesh is characterized by low base market, very few market participants, non-diversified products, lack of tailor-made financial instruments etc. There is a lack of quality bond issuers, very little interest for individual investors to buy corporate bonds and almost non-existence of intermediaries who could be a market player.

Bond markets in most countries have been built on the same basic elements: a number of issuers with long term financing needs, investors with a need to place savings or other liquid funds in interest bearing securities, and intermediaries that bring together investors and issuers, and an infrastructure that provide a conducive environment for transaction of securities, ensures legal title to securities and settlement of transactions and provides price discovery information. The regulatory regime provides the basic framework for bond market. Developing bond market can be more complicated than developing equity market. This need supporting pricing infrastructure and more sophisticated market participants. Bond Market acts as buffer of equity market. This enables issuers and investors to convert the limitations of equity market into the opportunities. Financial system to be sound and effective has to have an efficient bond market. Otherwise, Capital Market especially cannot play its due role for developing economy through allocation of capital; and generating employment opportunities through industrialization of economy of the country.Developing bond market can be attributed to the following reasons (IOSC, 2002):

a) An alternative source of domestic debt finance;

b) Lower cost of capital;

c) Reduced risks associated with maturity and currency mismatch;

d) Broadening of capital markets;

e) Efficient pricing of credit risk; and

f) Ensuring financial stability.

Following policies have been put forwarded for the development of bond market in Bangladesh:1. Bangladesh Securities and Exchange Commission (BSEC) can deregulate the existing laws and promulgate new laws for creating congenial regulatory environment for the development of bond market in the country.

2. Establishment of Dhaka Inter-bank Offered Rate (DIBOR) like London Inter-bank Offered Rate (LIBOR) is one step ahead for the developing of bond market. This has to give a fair opportunity for establishment of long term yield curve which is pre-condition for that.

3. BSEC (Bangladesh Stock Exchange Commission) can undertake both education and training program for the market participants which will create awareness among the market participants.

4. The Government has to offer some fiscal benefits like it does for FDIs for the development of bond market in Bangladesh.

5. The government should stop issuing securities offering interest rate higher than market yield rate.

6. Government should encourage state owned enterprises for raising funds by issuing corporate bond from the market.

Question 1: How does issuing bonds benefit the bond issuers?Question 2: What are some of the problems exists in bond market of Bangladesh?

Question 3: What could be done for the development of bond market in Bangladesh?

Question 4: How would a vibrant corporate bond market help the Bangladesh economy?True/False1. A bond's payment at the maturity is referred to as its face value.2. When the market interest rate exceeds the coupon rate, bonds sell for less than face value to provide enough compensation to investors.3. Current yield overstates the return of premium bonds since investors who buy a bond at a premium face a capital loss over the life of the bond.4. A bond's rate of return is equal to its coupon payment divided by the price paid for the bond.5. Bonds selling at a premium price offer a higher current yield (which overstates the true return) than bonds selling at par value.6. The current yield measures the bond's total rate of return.7. Zero-coupon bonds are issued at prices considerably below face value, and the investor's return comes from the difference between the purchase price and the payment of face value at maturity.8. If the appropriate rate of interest on a bond is greater than its coupon rate, the market value of that bond will be above par value.9. There is a direct relationship between bond ratings and the required rate of return on bonds; that is, the higher the rating, the higher is the required rate of return.10. A bond holder is the owner of the company.

11. A legal document that has all the terms and conditions of a bond is called indenture.

12. A zero coupon bond always sells at discount and will be redeemed at face value.

13. Bond ratings measure the bond's credit risk.14. If the current yield is above the coupon rate, the bond is selling at a premium.15. In bond valuation, the appropriate discount rate is the required yield.16. The higher the discount rate used in bond valuation, the higher the bonds intrinsic value.17. When interest rates go up, the price of bonds go up as well.MULTIPLE CHOICE QUESTIONS:

1. The coupon rate of a bond equals:A) its yield to maturity.B) a percentage of its face value.C) the maturity value.D) a percentage of its price.2. Periodic receipts of interest by the bondholder are known as:A) the coupon rate

C) the default premiumB) a zero-coupon

D) coupon payments3. Which of the following presents the correct relationship? As the coupon rate of a bond increases, the bond's:A) face value increases.

C) current price decreases.B) interest payments increase.

D) maturity date is extended4. What happens when a bond's expected cash flows are discounted at a rate lower than the bond's coupon rate?A) The price of the bond increases.B) The coupon rate of the bond increases.C) The par value of the bond decreases.D) The coupon payments will be adjusted to the new discount rate.5. A __________ bond is a bond where the bondholder has the right to cash in the bond before maturity at a specific price after a specific date.A)callable

B)coupon

C)puttable

D) treasury6. Everything else equal the __________ the maturity of a bond and the __________ the coupon the greater the sensitivity of the bond's price to interest rate changes.A)longer; higher

C)shorter; higherB)longer; lower

D)shorter; lower7. A coupon bond which pays interest of 60 taka annually, has a par value of 1,000 taka, matures in 5 years, and is selling today at a 75.25 taka discount from par value. The current yield on this bond is _________.A) 6.00%

B) 6.49%

C) 6.73%

D) 7.00%8. A coupon bond which pays interest of 4% annually, has a par value of 1,000 taka, matures in 5 years, and is selling today at 785 taka. The approximate yield to maturity on this bond is _________.A) 7.2%

B) 8.8%

C) 9.1%

D) 9.6%

9. A callable bond pays annual interest of 60 taka, has a par value of 1,000 taka, matures in 20 years but is callable in 10 years at a price of 1,100 taka, and has a value today of 1055.84 taka. The approximate yield to call on this bond is _________.

A) 6.00%

B) 6.58%

C) 8.00%

D) 7.20%

10. Consider a 7-year bond with a 9% coupon and a yield to maturity of 12%. If interest rates remain constant, one year from now the price of this bond will be _________.

A)higher

B)lower

C)the same

D)indeterminate11. The ___________ is the document defining the contract between the bond issuer and the bondholder.

A)indenture

B)covenant

C)trustee

D)collateral

12. If you are holding a premium bond you must expect a _______ each year until maturity. If you are holding a discount bond you must expect a _______ each year until maturity.A)capital gain; capital loss

C)capital loss; capital gainB)capital gain; capital gain

D)capital loss; capital loss13. Which of the following statements is correct for a 10% coupon bond that has a current yield of 7%?A) The face value of the bond has decreased.B) The bond's maturity value exceeds the bond's price.C) The bond's internal rate of return is 7%.D) The bond's maturity value is lower than the bond's price.14. A bond's yield to maturity takes into consideration:A) current yield but not price changes of a bond.B) price changes but not current yield of a bond.C) both current yield and price changes of a bond.D) neither current yield nor price changes of a bond.15. A debenture is _________.A)secured by other securities held by the firmB)secured by equipment owned by the firmC)secured by property owned by the firmD)unsecured.

16. The discount rate that makes the present value of a bond's payments equal to its price is termed the:A) rate of return.

C) yield to maturity.B) current yield.

D) coupon rate.17. What is the coupon rate for a bond with three years until maturity, a price of 1,053.46 taka, and a yield to maturity of 6%?A) 6%

B) 8%

C) 10%

D) 11%

18. What is the yield to maturity for a bond paying 100 taka annually that has six years until maturity and sells for 1,000 taka?A) 6%

B) 8%

C) 10%

D)11%

19. Which of the following factors will change when interest rates change?A) The expected cash flows from a bondB) The present value of a bond's paymentsC) The coupon payment of a bondD) The maturity value of a bond.20. What happens to the coupon rate of a bond that pays 80 taka annually in interest if interest rates change from 9% to 10%?A) The coupon rate increases to 10%.B) The coupon rate remains at 9%.C) The coupon rate remains at 8%.D) The coupon rate decreases to 8%.21. Which of the following is fixed (e.g., cannot change) for the life of a given bond?A) Current price.

B) Current yieldC) Yield to maturity.D) Coupon rate22. What is the rate of return for an investor who pays 1,054.47 taka for a three-year bond with a 7% coupon and sells the bond one year later for 1,037.19 taka?A) 5%

B) 5.33%

C) 6.46%

D) 7%23. The __________ of a bond is computed as the ratio of coupon payments to market price.A)nominal yield

B) current yieldC) yield to maturityD) yield to call24. A bond has a par value of Tk.1,000, a time to maturity of 10 years, and a coupon rate of 8% with interest paid annually. If the current market price is Tk.750, what is the approximate capital gain yield of this bond over the next year?A) 0.7%

B) 1.8%

C) 2.5%

D) 3.4%25. A bond is selling at a discount if the:A) yield-to-maturity is greater than the coupon rate.

B) yield-to-maturity is less than the coupon rate.

C) market price is greater than the par value.

D) yield-to-call is less than the coupon rate.

26. All other factors constant, the -------------- of a bond, the shorter the duration.A) longer the term

C) higher the riskB) higher the coupon rate

D) higher the rating27. Duration can be used to:A) minimize default riskB) minimize reinvestment risk.C) minimize interest rate risk.D) maximize return.28. The YTM calculation assumes:A) reinvestment of interest is at the coupon rate.B) no reinvestment of interest.C) reinvestment of interest is at YTM rate.D) reinvestment of interest is at the risk-free rate.

29. Convexity is important in bond analysis becauseA) the price-yield relationship is imprecise.

B) the relationship between bond maturity and interest rate changes is convex.

C) the relationship between bond price changes and duration is an approximation.

D) bonds have a convex relationship with duration.

SHORT QUESTIONS:1. What is a bond? How it is different from equity? What are the four types of bonds?

2. Why isnt Bangladesh governments treasure bonds not necessarily risk-free?

3. Define consol and zero coupon bonds.

4. Why there is a interest rate risk in bond investment, when coupon amounts are fixed?

5. Why do bond prices and yield to maturity vary inversely?6. If there are two bonds which matures in 10 years. One has 12% coupon and the other has 8% coupon but both has the same yield to maturity. Which bond should you buy and why?

7. How do you think the value of a bond would change witha) Increasing face value

b) Increasing coupon rate

c) Increasing the periodicity of coupon

d) Increasing the term to maturity.8. What is the difference between yield to maturity and yield to call?9. Define convertable bonds like ACI 20% convertable bonds, putable bonds, income bonds, indexed bonds, Brac epl bonds, and mudaraba islamic bond.10. Describe how the annual bond valuation formula is changed to evaluate semi-annual coupon bonds. Then write out the revised formula.

11. Why does the coupon rate affect the volatility of bond price?12. To which type of risk are holders of long-term bonds? 13. How does value of a bond change as it nears its maturity?14. What factors may aafect the bond ratings?

15. Why are bond ratings important both to firms and to investors?16. What is duration of a bond?BROAD QUESTIONS:1. A 6 year bond with par value 1000 taka has a current yield 7.5 percent and a coupon rate of 8 percent. What is the bonds price? 2. A 6 year bond with 1000 taka par value pays 80 taka interest annually and sells for 950 taka. What is the coupon rate, current yield and yield to maturity? 3. A firm sells bonds with a par value of 1000 taka, carry a 8% coupon rate, with a maturity period of 9 years. The bond sells at a yield to maturity of 9%.

a. What is the interest payment you should receive each year?

b. What is the selling price of the bond? c. What will happen to the bond price, if the yield to maturity falls to 7%? 4. What is the duration of a bond? What is the convexity of a bond?5. Contrast the current yield calculation and the calculation of yield to maturity in terms of their usefulness to investors in decision-making.

6. Bangladesh bank issues a 10 year treasury bond at 12% coupon with the par value of 1000 taka. If the market yield increases shortly afterwards, what happens to the following parameters:

a) coupon rate b) price c) current yield d) yield to maturity.7. Why is a call provision advantages to a bond issuer? When will the issuer initiate a refunding call? Why?

8. ABC corporation has issued 12 percent annual coupon 1000 taka par value bonds maturing in 10 years. What should be the current price of this bond if the interest rate is 15 percent?

9. ABC corporation has issued 14% coupon bond with a par value of 1000 taka which matures in 20 years. The bond is callable in 5 years at 1140 taka. This bond currently sells for 1050 taka.

a. What is the current yield?

b. Yield to call

c. Yield to maturity

10. Vermex bonds currently sell for 975 taka which has got 7 years maturity with a 12 percent annual coupon and have a per value of 1000 taka. What is their YTM? What is their current yield.11. Why is the yield to call a more appropriate measure to use for callable bonds with high coupons rather than the yield to maturity?12. Calculate the present value of 6 year bond with a par value of 1000 taka and having 9% coupon rate if the current interest rate is 12%? 13. The interest rate increases from 10% to 12% suddenly. Find the present values of the two bonds given below both before and after the change.

a) Both the bonds have same coupon rate of 11%.

b) Bond 1 has a maturity of 5 years and bond 2 has a maturity of 15 years.

(Note: 5 year bond sells at 1012 taka before the increase in interest rate. Now after the rise in interest rate it is trading at 940 taka. Decrease is 7.11%. On the other hand, the 15 year bond sells at 1060 before the rise in inters rate and now after the change in interest rate it is trading at 720 taka. There is a fall of almost 32% decrease in price.

14. Terreta corporation 1000 taka par value bonds currently sell for 1250 taka. These bonds can be called five years at a call price of 1120 taka and pay an annual coupon of 120 taka. What is their yield to call?15. Identify one way to minimize both interest rate and reinvestment rate risk for an investor with a fixed investment horizon.16. What is bond rating? Why is it so important for both bond issuers and bond investors? What factors are looked upon by the credit rating agencies in grading a bond?Maturity

1 mo 6 mo 1 yr 5 yrs 10 yrs 20 yrs 30 yrs

Kd (Yield)

4.0%

3.0%

2.0%

1.0%

0

Normal (positively sloped) yield curve

Kd (Yield)

4.0%

3.0%

2.0%

1.0%

0

Declining (negatively -sloped) yield curve

1 mo 6 mo 1 yr 5 yrs 10 yrs 20 yrs 30 yrs

Kd (Yield)

4.0%

3.0%

2.0%

1.0%

0

Flat yield curve

1 mo 6 mo 1 years 5 years 10 years 20 years 30 years

Kd (Yield)

18.0%

16.0%

12.0%

10.0%

8.0%

0

Start: Flat yield curve

1 mo 6 mo 1 yr 5 yrs 10 yrs 20 yrs 30 yrs

Bond issuers issue more long-term bonds as investors sell them. Long-term bond prices fall and their yields rise.

Bond issuers issue fewer short-term bonds as investors buy all they can. Short-term bond prices rise and their yields fall.

_1441720360.unknown

_1441720368.unknown

_1441720372.unknown

_1441720374.unknown

_1441720373.unknown

_1441720371.unknown

_1441720369.unknown

_1441720366.unknown

_1441720367.unknown

_1441720362.unknown

_1441720363.unknown

_1441720361.unknown

_1441720356.unknown

_1441720359.unknown

_1441720357.unknown

_1441720354.unknown

_1441720355.unknown

_1441720353.unknown