Bond Problems And Solutions Pdf


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Vocabulary Multiple Choice Cloze. Levels of Difficulty : Elementary Intermediate Advanced.

Yield to Maturity (YTM)

We have provided a quick outline of what a student will need to know to understand bonds and the pricing or valuation of bonds which is the primary focus in the initial corporate finance program. More advanced finance courses will introduce students to advanced bond concepts including duration, managing bond portfolios, understanding and interpreting term structures, etc.

A bond is a debt instrument that provides a periodic stream of interest payments to investors while repaying the principal sum on a specified maturity date. The face value also known as the par value of a bond is the price at which the bond is sold to investors when first issued; it is also the price at which the bond is redeemed at maturity.

In the U. Occasionally a bond is issued with a much longer maturity; for example, the Walt Disney Company issued a year bond in There have also been a few instances of bonds with an infinite maturity; these bonds are known as consols. With a consol, interest is paid forever, but the principal is never repaid. Many bonds contain a provision that enables the issuer to buy the bond back from the bondholder at a pre-specified price prior to maturity.

This price is known as the call price. A bond containing a call provision is said to be callable. This provision enables issuers to reduce their interest costs if rates fall after a bond is issued, since existing bonds can then be replaced with lower yielding bonds. Since a call provision is disadvantageous to the bond holder, the bond will offer a higher yield than an otherwise identical bond with no call provision.

Some bonds contain a provision that enables the buyer to sell the bond back to the issuer at a pre-specified price prior to maturity. This price is known as the put price. A bond containing such a provision is said to be putable. This provision enables bond holders to benefit from rising interest rates since the bond can be sold and the proceeds reinvested at a higher yield than the original bond.

Since a put provision is advantageous to the bond holder, the bond will offer a lower yield than an otherwise identical bond with no put provision. Some bonds are issued with a provision that requires the issuer to repurchase a fixed percentage of the outstanding bonds each year, regardless of the level of interest rates. A sinking fund reduces the possibility of default ; default occurs when a bond issuer is unable to make promised payments in a timely manner. Since a sinking fund reduces credit risk to bond holders, these bonds can be offered with a lower yield than an otherwise identical bond with no sinking fund.

Bonds are issued by borrowers to raise funds for long-term investments; the main issuers of bonds in the U. Treasury securities are issued by the U. These are free of default risk , which is the risk that the investor will not receive all promised payments.

They are not taxed by state and local governments, but are taxed at the federal level. Another key difference between these securities is that Treasury bills are sold at a discount from their face value and redeemed at face value; Treasury notes and bonds are sold and redeemed at face value and pay semi-annual coupons to investors.

Corporations can raise funds by issuing debt in the form of corporate bonds. These bonds offer a higher promised coupon rate than Treasuries, but expose investors to default risk.

The riskiest corporations offer the highest coupon rates to investors as compensation for default risk. A municipal bond is issued by a state or local government; as a result, they carry little or no default risk.

Occasionally, municipalities do default on their debts; in , the city of Detroit filed for bankruptcy as a result of being unable to pay its debts. Municipal bonds offer an extremely favorable tax treatment to investors. They are not taxed by federal, state or local governments as long as the bond holder lives in the municipality in which the bonds were issued.

As a result, municipal bonds can be issued with very low yields. Foreign bonds are issued by foreign governments and corporations and are denominated in dollars. If they are denominated in a foreign currency, they are known as eurobonds. Dollar-denominated bonds issued in the U.

This formula shows that the price of a bond is the present value of its promised cash flows. The bond makes annual coupon payments. These results also demonstrate that there is an inverse relationship between yields and bond prices:.

For a bond that makes semi-annual coupon payments, the following adjustments must be made to the pricing formula:. As an alternative to this pricing formula, a bond may be priced by treating the coupons as an annuity; the price is therefore equal to the present value of an annuity the coupons plus the present value of a sum the face value. This method of valuing bonds will use the formula:. The bond in the previous example can be priced using this alternate bond valuation formula as follows:.

A zero-coupon bond does not make any coupon payments; instead, it is sold to investors at a discount from face value. The difference between the price paid for the bond and the face value, known as a capital gain , is the return to the investor. The pricing formula for a zero coupon bond is:. What is the market price of this bond? In order to be consistent with coupon-bearing bonds, where coupons are typically made on a semi-annual basis, the yield will be divided by 2, and the number of periods will be multiplied by There are different types of yield measures that may be used to represent the approximate return to a bond.

These include:. This equals the rate of return earned by a bond holder known as the holding period return if:. It is impossible to solve for the yield to maturity algebraically; instead, this must be done using a financial calculator or Microsoft Excel.

The variables in brackets fv, type and guess are optional values; the value of type is set to zero if it is not specified. Guess can be used to provide an initial estimate of the rate, which could potentially speed up the calculation time.

Note that either pv or fv must be negative, and the other must be positive. The negative value is considered to be a cash outflow, and the positive value is considered to be a cash inflow.

Also note that entering semi-annual periods and coupon payments will produce a semi-annual yield; in order to convert this into an annual yield on a bond-equivalent basis , the semi-annual yield is doubled.

For a bond that is callable, the yield to call may be used as a measure of return instead of the yield to maturity. The process is similar to computing yield to maturity, except that the maturity date of the bond is replaced with the next call date.

This is because yield to call is based on the assumption that the bond will be called on the next call date. The face value is replaced with the call price since this is the amount that the investor will receive if the bond is called. What is the yield to call? In this case, the bond will mature in eight years, but it can be called in three years.

The yield to call is computed as follows:. The current yield is simpler measure of the rate of return to a bond than the yield to maturity. The current yield is computed as:. This measure has the benefit of simplicity. It suffers from the drawback that it does not account for the time value of money. Excel contains a set of specialized bond functions that can be used to account for several complications that arise in bond pricing, such as day-count conventions. Money market instruments e.

Note that the settlement date and maturity date are represented as numerical values in Excel. The date January 1, is represented as 1; all later dates represent the number of days that have passed since January 1, As an example, suppose that a bond is sold on June 15, with a maturity date of June 15, What is the price of the bond?

Note that the price of the bond is entered as Also note that represents June 15, and represents For example,. This article is one part of a series on fixed income portfolios. Other articles in this series include:. These include: Face Value Coupon Rate Coupon Maturity Call Provisions Put Provisions Sinking Fund Provisions a Face Value The face value also known as the par value of a bond is the price at which the bond is sold to investors when first issued; it is also the price at which the bond is redeemed at maturity.

Treasury Treasury securities are issued by the U. Treasuries can be classified by their maturities as follows: Treasury bills — the maturity is one year or less; the currently available maturities are 4 weeks, 13 weeks, 26 weeks and 52 weeks Treasury notes — the maturity ranges between 1 and 10 years; the currently available maturities are 2, 3, 5, 7 and 10 years Treasury bonds — the maturity ranges between 20 and 30 years; the currently available maturity is 30 years Another key difference between these securities is that Treasury bills are sold at a discount from their face value and redeemed at face value; Treasury notes and bonds are sold and redeemed at face value and pay semi-annual coupons to investors.

In order to be consistent with coupon-bearing bonds, where coupons are typically made on a semi-annual basis, the yield will be divided by 2, and the number of periods will be multiplied by 2: 5 Yield Measures There are different types of yield measures that may be used to represent the approximate return to a bond.

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Problems and Solutions 1 CHAPTER 1—Problems

Question 1. Explain the formation of a chemical bond. This can occur in two ways; by transfer of one or more electrons from one atom to other or by sharing of electrons between two or more atoms. Question 2. Question 3.

Solutions to Practice Questions Bonds 1. Although bond was issued at par, the level of interest rate may change later. The face value, F. If … If its dividends are expected to grow at a rate of 3 percent per year, what is the expected dividend per share for Bulldog five years from today? They are Optional, and are not part of the required material. The yield curve is slightly downward sloping, reflecting lower expected future rates of interest. Basically many assumptions need to be made in order for the Dividend Growth Model to work well.

Problems and Solutions 1 CHAPTER 1—Problems

What is the value of the bond, if the discount rate is 15 percent by factor formula and table? Coupons are paid semi annually, what is the price of this debt by general floating equation? What is the price of this bond?

Only RUB Chapter 18 Section 2 - Types of Bonds. Na 2 O is forms this type of bond: answer choices. Tags: Question

Chapter 18 section 2 reinforcement types of bonds

A financial security refers to an instrument such as a stock or bond that represents a financial claim against assets. For example, as was covered in Chapter One, bonds typically have a fixed cash flow stream over a finite time horizon while stocks typically have a variable cash flow stream over a potentially infinite time horizon. Stocks also tend to be riskier than bonds, which results in investors demanding higher rates of return to compensate for the additional risk. While financial securities may have different characteristics, the concept of valuation is essentially the same regardless of the specific security. While the definition above is more conceptual, we can easily turn it into an applied process to value all stocks, bonds, or other investment opportunities. The process is as follows:. What changes as we deal with different stocks, bonds, and other investment opportunities is not the process, but how we apply the process.

Yield to maturity YTM is the annual return that a bond is expected to generate if it is held till its maturity given its coupon rate, payment frequency and current market price. Yield to maturity is essentially the internal rate of return of a bond i. Yield to maturity of a bond can be worked out by iteration, linear-interpolation, approximation formula or using spreadsheet functions. The iteration method of calculating yield to maturity involves plugging in different discount rate values in the bond price function till the present value of bond cash flows right-hand side of the following equation matches the bond price left-hand side :. Where P is the bond price i. Annual yield to maturity equals periodic yield to maturity multiplied by number of coupon payments per year:. There is an inverse relationship between bond price and bond yield which means that if price is low, yield must be high and vice versa.

We have provided a quick outline of what a student will need to know to understand bonds and the pricing or valuation of bonds which is the primary focus in the initial corporate finance program. More advanced finance courses will introduce students to advanced bond concepts including duration, managing bond portfolios, understanding and interpreting term structures, etc. A bond is a debt instrument that provides a periodic stream of interest payments to investors while repaying the principal sum on a specified maturity date. The face value also known as the par value of a bond is the price at which the bond is sold to investors when first issued; it is also the price at which the bond is redeemed at maturity. In the U. Occasionally a bond is issued with a much longer maturity; for example, the Walt Disney Company issued a year bond in

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