Chapter 6 DSM
Strong Corporation has issued $1,000 par value, 20 year, 8% bonds paying semi-annual interest. If the market rate of interest for bonds of similar risk is 6%, what is the current market price of the bonds?
$1231 Since the coupon rate of interest is greater than the market rate of interest, the bonds will sell for a premium. The value of the bonds can be calculated using a financial calculator or Excel, using the following inputs: RATE=3% (6% annually, semi-annual payments), NPER=40 (20 years x 2 payments per year), PMT=40 (8% rate x $1,000 par / 2 payments per year), FV=1000 (par value).
Risky Corporation's bonds are currently selling for $650 and bear a 5% coupon rate and $1,000 par value. If the bonds pay annual interest and have 12 years to maturity, what is the yield to maturity?
10.2% The yield to maturity on the bonds is 10.2%. This can be computed using a financial calculator or the RATE function in Excel, where the PV=(650), N=12, FV=1000, PMT=50.
What is the yield to maturity (YTM) for a $1,000 par value bond selling for $1,100 that matures in 5 years and pays a 10% coupon one time a year?
7.5% The yield to maturity (YTM) for a $1,000 par value bond selling for $1,100 that matures in 5 years and pays a 10% annual coupon one time a year is 7.5%. The easiest way to solve for YTM is with a financial calculator using the following inputs, PV = -$1,100; FV = $1,000; N = 5; PMT = $100; CPT I / Y and get 7.52%. Note that you multiply the coupon rate times the face value to get the dollar value of the coupon payment. It is also worth noting that when a bond is selling for a premium, as in this case, the YTM will be lower than the coupon rate. So the YTM had to be below 10%. This same process will be used to compute the internal rate of return (IRR) for capital budgeting projects.
What is the yield to maturity on a zero coupon bond currently selling for $527.32 that has a $1,000 par value and will mature in 8 years?
8.33%. The yield to maturity on a zero coupon bond currently selling for $527.32 that has a $1,000 par value and will mature in 8 years is 8.33%. The easiest way to calculate the yield to maturity (YTM) is to use a financial calculator. The inputs are: PV = -$527.32; FV = $1,000; N = 8; CPT I / Y and you get 8.33%. You can easily check your work by taking the bond's present value and compounding it for 8 years using the YTM as your compound rate to see if you get a future value of $1,000. So, $527.32(1.0833)8 = $1,000.15. As you can see, there is only a very slight rounding error.
A steeply upward-sloping yield curve indicates that:
Interest rates are expected to rise in the future. A steeply upward-sloping yield curve indicates that interest rates are expected to rise in the future. According to expectations theory, the shape of the yield curve is determined by investor expectations about future interest rates. Therefore, a yield curve that sharply rises indicates that future interest rates are expected to be higher for some reason. Since the yield curve is constructed using nominal interest rates, it does not provide information on real interest rates. Therefore, without information on the inflation rates there is not enough information to determine the current real rate of return. There are several other theories that attempt to explain the shape of the yield curve, but the expectations theory is the most widely used by academics. This theory is also known as the unbiased expectations theory or the pure expectations theory.
A long-term debt instrument issued by a business or government to raise capital is known as a:
bond A long-term debt instrument issued by a business or government to raise capital is known as a bond. Bonds are issued to raise money for operations or to acquire or improve assets. A bond typically pays interest every six months based on the coupon rate and then at maturity the bondholder will receive the face value of the bond, typically $1,000. Stocks are a fractional ownership in a company and therefore a part of equity and not debt. Dividends are a periodic distribution of cash to the stockholders of a firm. There are numerous types of bonds and bond features. Bonds may pay interest or simply be sold at a deep discount.
The present value of a bond's __________ determines the value of the bond.
coupon payment and maturity value The present value of a bond's coupon payment and maturity value determines the value of the bond. The value of any asset is the present value of that asset's cash flows. For a coupon bond, the two cash flows are the periodic coupon payments (typically, every 6 months) and the bond's face value the bondholder receives at maturity. Dividend payments are made to stockholders or shareholders and not bondholders.
As market interest rates increase, the value of a bond will __________ all other things equal.
decrease As market interest rates increase, the value of a bond will decrease all other things equal. There is an inverse relationship between the values of outstanding bonds and market rates of interest. When interest rates go up, it decreases the present value of the cash flows associated with an outstanding bond and pushes price (value) lower. When interest rates go down, it increases the present value of the cash flows associated with an outstanding bond and bond prices will move higher.
The risk-free rate of interest is used in a number of financial models. The best approximation for the risk-free rate is:
short-term U.S. Treasuries The risk-free rate of interest is used in a number of financial models. The best approximation for the risk-free rate is short-term U.S. Treasuries. T-bill rates are commonly used as a proxy for the risk-free rate. This rate is useful to determine risk premiums and help calculate required returns for risky assets. The prime rate is the rate that lenders charge their best customers. While this rate is low, it does have a risk premium to compensate lenders for some minimal level of risk. The AAA corporate bond rate is the highest or best debt rating a company could receive but it still carries some minimal risk premium and will carry a higher rate than short-term U.S. Treasuries.
Which of the following is one of the top two bond rating firms?
Standard and Poor's Standard and Poor's is one of the top twobond rating firms. The other large bond rating firm are Moody's. Both of these firms rate debt issues with regard to default risk. The highest rated bonds are the ones that are less likely to default. The other two answer options are fictitious firms. Corporations pay these firms to rate their debt prior to issue. Without an external bond rating it is almost impossible to sell debt, so it is a necessary part of the bond issue process to subject the firm to this external scrutiny. And, the better the rating the lower the coupon payment the firm will need to offer investors.
A bond will sell at __________ if the required return is greater than the coupon rate.
a discount A bond will sell at a discount if the required return is greater than the coupon rate. If investors demand a higher return than can be earned on the coupon rate, the value of the bond will fall until investors can buy the bond and earn a return consistent with the return they could earn on other similar risk bonds. If they buy at a discount, they will receive the coupon payments and also earn some return on the increase in value the bond will experience as it approaches maturity. If the bond is selling at a premium, the reverse will occur. The investor will still receive the coupon payment, but will now lose money on the bond's value as it moves toward maturity and par value.
In the event a firm goes bankrupt, an investment grade senior debenture bond is more likely to receive liquidation proceeds than:
a subordinated debenture In the event a firm goes bankrupt, an investment grade senior debenture bond is more likely to receive liquidation proceeds than a subordinated debenture. Debenture bonds are bonds that do not have assets pledged as collateral that are specifically tied to that bond. And, a subordinated debenture bond means that its claim on liquidation proceeds in the event of bankruptcy is lower than other senior debentures. Mortgage bonds and collateralized bonds have assets specifically attached to them as collateral that can be sold upon bankruptcy and the proceeds exhausted to satisfy the bond debt. Only if that debt is fully satisfied, will any proceeds from the sale of these pledged assets go toward satisfying other creditors.
Default risk is the risk that:
bond interest payments or the principal payment will not be made. Default risk is the risk that bond interest payments or the principal payment will not be made. No investor can know for certain whether a corporation will be able to service its debt. This possibility of non-payment is known as credit risk or default risk and higher credit risk bonds must pay higher interest rates to compensate investors for assuming this level of risk. Coupon rates remain fixed for the life of a bond and the risk associated with changing market rates of interest is known as interest rate risk.
A zero-coupon bond pays no interest payments to the bondholder. It has a $1,000 par value and matures in 5 years. What is the value of this bond if the market rate of interest on similar risk bonds is 10%?
$620.92 A zero-coupon bond pays no interest payments to the bondholder. It has a $1,000 par value and matures in 5 years. The value of this bond when the market rate of interest on similar risk bonds is 10% is $620.92. The value of a zero-coupon bond is easy to calculate. Any bond value is simply the present value of the bond's cash flows and a zero-coupon bond only has one cash flow; the face value received at maturity. So, the value of this bond is equal to, PV = $1,000 / (1.10)^5 = $620.92. To value a zero-coupon bond you always use a discount rate that is equivalent to the current market rates on similar risk bonds. You can identify similar risk bonds by looking at bond ratings. The major bond rating firms, like Standard and Poor's and Fitch, will rate bonds prior to issue and track them throughout their life. So, all you have to do is look up the current market rate of interest for bonds that have the same debt rating.
What is the value of a $1,000 par value 6% coupon bond with 7 years remaining to maturity assuming annual coupon payments and a market rate of 9% on similar risk bonds?
$849.01 The value of a $1,000 par value 6% coupon bond with 7 years remaining to maturity assuming annual coupon payments and a market rate of 9% on similar risk bonds is $849.01. The easiest way to calculate the bond's value is to use a financial calculator with the following inputs, FV = $1,000; PMT = $60; N = 7; I/Y = 9%; CPT PV and you get $849.01. Note that some financial calculators will generate a negative number for PV, but you simply take the absolute value. It is worth noting that the answer will always be less than the par value when the market rate or discount rate is greater than the coupon rate. If the discount rate is lower than the coupon rate, the bond will sell at a premium.
Investors, analysts and managers often use the yield curve to:
forecast interest rates Investors, analysts and managers often use the yield curve to forecast interest rates. According to expectations theory, the shape of the yield curve depends on the overall market expectation of what interest rates will be in the future. An upward sloping yield curve indicates higher interest rates are expected. Conversely, a downward sloping yield curve indicates lower interest rates are expected in the future. Yield curves are also used to provide some indication of the direction of the overall economy and are thought to be a leading indicator of economic activity. While economic activity may be used to make other financial decisions, the shape of the yield curve is not often used, if at all, to speculate on currency movements, forecast stock prices, or time the purchase of common stock.
All other things equal, a corporation will pay a __________ coupon rate on __________ bonds.
higher, higher risk All other things equal, a corporation will pay a higher coupon rate on higher risk bonds. As the risk of a bond increases, corporations will have to offer a higher rate to compensate investors enough to hold higher risk bonds. Conversely, lower risk bonds will carry lower coupon rates because they have a lower chance of default. One of the basic premises of finance is that there is a risk-return tradeoff for all investments. Higher risk investments of any type have to offer higher returns to investors to be able to attract funds.
Interest rate risk ______ as the time to maturity for a bond increases.
increases Interest rate risk increases with the time to maturity for a bond. Interest rate risk is the risk that the value of a bond will change due to a change in market interest rates. Bond values do move inversely with a change in market interest rates and the longer maturity bonds will move by a larger amount. In other words, longer maturity bonds have higher levels of interest rate risk. So, the risk increases as bond maturity increases, or conversely, as maturity falls risk declines as well. Therefore, it is a direct relationship. As a bond approaches its maturity date the price will grow closer and closer to par value until the two are equivalent on the day the bond matures.
The term structure of interest rates refers to the different:
interest rates of securities with the same risk but different maturity dates The term structure of interest rates refers to the different interest rates of securities with the same risk but different maturity dates. The graphical representation of the term structure of interest rates is called the yield curve. The yield curve is constructed using U.S. Treasury securities in order to hold the risk associated with the issuer constant. This method allows you to see the exact relationship between interest rates and maturity dates without interference from other factors. The interest rates of securities with the same maturity date will vary based on the risk of the issuer, which is not the term structure of interest rates. The terms of agreement associated with a bond's issue are included in a document known as the indenture. These provisions provide details on all bond features and also often restrict the firm's ability to issue new debt. The typical or "normal" yield curve is upward sloping and to the right indicating that the market rates of interest are higher for longer term securities, holding all else constant. There are several theories that attempt to explain the term structure of interest rates that will be reviewed later.
The top four categories of bond ratings are collectively known as __________.
investment grade bonds The top four categories of bond ratings are collectively known as investment grade bonds. Investment grade bonds have a much lower risk of default than the lower rated bonds. The bottom five categories, which includes any bonds rated below Baa and BBB by Moody's and Standard and Poor's respectively, are known as speculative bonds or junk bonds. Junk bonds have to offer a higher return in order to compensate investors to assume a higher level of risk so they are also known as high-yield bonds. A bond can be upgraded or downgraded during its life. Even if a bond is originally issued as an investment-grade bond, the firm's financial condition could deteriorate to the point where the bond was downgraded to junk status. The price of the bond would fall accordingly, which pushes up the yield to investors who opt to purchase the bond from other investors at this time.
The theory that postulates the shape of the yield curve is determined by the fact that investors require an interest premium to compensate them for the risks of holding longer term debt is known as:
liquidity preference theory The theory that postulates the shape of the yield curve is determined by the fact that investors require an interest premium to compensate them for the risks of holding longer term debt is known as liquidity preference theory. Longer term debt has a greater price swing when interest rates change so it is riskier in that regard. And, an investor faces some risk of loss of return if rates go up in the future and their money is tied up long-term. Liquidity preference theory maintains that investors will require higher interest rates for longer term debt to compensate them for this risk. This theory works well in explaining a normal yield curve. Market segmentation theory postulates that the shape of the yield curve is determined by the supply and demand for different maturities of debt. The premise of the market segmentation theory is that different investors prefer different maturities of debt (market segments) and that interest rates in each segment are determined by the interaction of supply and demand for that specific maturity range or segment. The pure expectations theory maintains that interest rates are based on expectations of what yields will be in the future. For example, a normal yield curve would suggest that the market expects interest rates to increase. An inverted yield curve would suggest the opposite. This theory makes intuitive sense. Before I tie up my money for a longer term, I want you to pay me more for the opportunity cost of that investment.
The theory that postulates the shape of the yield curve is determined by the supply and demand for different maturities of debt is known as:
market segmentation theory The theory that postulates the shape of the yield curve is determined by the supply and demand for different maturities of debt is known as market segmentation theory. The premise of the market segmentation theory is that different investors prefer different maturities of debt (market segments) and that interest rates in each segment are determined by the interaction of supply and demand for that specific maturity range or segment. The pure expectations theory maintains that interest rates are based on expectations of what yields will be in the future. For example, a normal yield curve would suggest that the market expects interest rates to increase. An inverted yield curve would suggest the opposite. Liquidity preference theory maintains the shape of the yield curve is due to the fact that investors require an additional interest rate premium to entice them to tie up money for longer terms. This theory works well in explaining a normal yield curve. If significant differences exist in yields then investors may opt to alter their preferences and jump between market segments. This activity will effectively smooth the yield curve. This theory does a good job of explaining the yield curve when it is humped or has times when it is rising over certain maturity ranges, and then falling over other maturity ranges.
A yield curve can be constructed using similar risk corporate bonds. The yield curves constructed with corporate bonds will __________ the U.S. Treasury yield curve.
plot above A yield curve can be constructed using similar risk corporate bonds. The yield curves constructed with corporate bonds will plot above the U.S Treasury yield curve. This is because corporate bonds will have a higher risk of default than the comparable Treasury bond, so the corporate bonds will have a higher yield. However, the yield curves will tend to run in a parallel fashion and should not cross at any point. The distance between the U.S. Treasury yield curve and the corporate bond yield curve represents the default risk premium since U.S. Treasuries are considered risk free. This default risk premium is also known as the default spread.
Subordinated debentures are:
unsecured bonds with a junior claim on assets Subordinated debentures are unsecured bonds with a junior claim on assets. A debenture bond is one that does not have any collateral pledged that would revert to the bondholders in case of default. Any bond that is subordinate is a bond that ranks behind senior debt in the event the company goes bankrupt and the firm is liquidated to satisfy its obligations. Bonds that do have assets pledged as collateral are known as mortgage bonds and bonds that do not pay interest during their life, but instead are sold at a deep discount, are known as zero coupon bonds or zeroes. Most bonds are debenture bonds that pay interest based on the bond's coupon rate. These coupon payments are typically semiannual or annual. In addition to the coupon payments the bondholder will receive the face value of the bond at maturity. Many investors buy bonds for the consistent income stream generated by the coupon payments.
The __________ is a graphical representation of the term structure of interest rates.
yield curve The yield curve is a graphical representation of the term structure of interest rates. A yield curve is constructed from U.S. Treasury securities of differing maturities and plots yield on the y-axis and time to maturity on the x-axis. The resulting line that shows this relationship is known as the yield curve and it is typically upward sloping and to the right (normal yield curve). A time line is a tool used in finance that plots the amount and timing of a project's cash flows. Opportunity costs and real interest rates are not often graphed. The yield curve can take on other shapes. For example, an inverted yield curve is a curve that is downward sloping and to the right that indicates short-term interest rates are higher than long-term interest rates. A segmented yield curve has sections of the yield curve increasing and sections of the yield curve decreasing.
