Returns Are Able to Be Measured - Report Example

Bond yield measures Your name Name of Assignment 12th December , 2012 Outline Introduction Measures of yield Coupon Rate Current yield Yield to maturity Yield to call The Relationship of Different Yield Influences of Interest Rates References Introduction Investors would like investments that their returns are able to be measured. In most instances present value and internal rate of return are used to measure the ability of an investment to generate cash flows that can reward an investor. However, in the case of investment in bond there is a need to have measures which can guarantee an investor the easiest way to understand the return to be received from his investments. This is done by calculating the yield of the bond at various stages of its existence. This is because a bond can be held up to maturity, can be solved at the current rate in the market, it can be called, it can be put or it can be converted. All these actions require a determination of the yield it would generate before buying them. The methods of determining the yield, at specific bond can generate at any time include current yield, yield to maturity, yield to call, yield to put, promised yield, realized yield and coupon rate. Measures of yield Coupon Rate Coupon rate is a measure of yield if the bond is not trading the market thus the bar value becomes the price that can be obtained if the investor wants to pull out of the investment(Brealey, Myers and Marcus, 2007). It is determined by dividing annual coupon amount and a par value. Assume a bond which has annual cash flows of 80 and a par value of 1000 with a maturity period of 5 years. The coupon rate is determined as follows Coupon rate = = = 8% The yield using the par value is 8 %. It is a times called nominal yield or coupon yield. Current yield Current yield is the yield that can be made if the bond was sold at the market price and generating returns at the annual carbon rate. It is determined by dividing annual coupon rate by bond price and is expressed in form of percentage. To illustrate this, we assume a bond with a coupon rate of 8 percent and a par value of 1000 which will mature in 5-years time and it is selling in the market currently at price of 960. The current yield will be calculated as follows Current yield = = = 8.33% In this case, the current yield is found to be 8.33%. Current yield is inversely related to market price of a bond meaning that if there is a constant change in market price the current yield changes. It will also noted that if the bond is selling at a premium the current yield will be lower than the carbon yield or nominal yield. If the bond is selling at a discount, the current yield will be higher than the coupon yield. Yield to maturity Yield to maturity is a measure which is important to the investor who intends to hold the investments to its maturity period. It is sometimes called yield. It uses the present value of all cash flows that is the internal rate of return of all cash flows. This means it considers all the cash flows received by an investor during the lifetime of the investments. The assumption here is that the investor is not intending to exercise any option before maturity period. To calculate the yield t maturity, for most bonds it is a difficult exercise since trial and error method is employee. Assume a bond which has a 5-year maturity with a par value of 1,000 bearing a coupon rate of 8% trading in the market at 800. The bond interest is paid semi-annually. The present value of the interest-payment stream of $100 per year for 5 years is as follows: V=P+ V=40+ = 961.54 +675.56= $1,637.1 The present value of the bond to maturity is 1637.1, that mean the bond has a present value greater than the par value. However yield to maturity need to be calculated to determine whether it is greater than the coupon rate. This has been calculated using excel file as follows yield to maturity 1 2 3 4 5 6 7 8 9 10 cashflow (800) interest 40 40 40 40 40 40 40 40 40 40 principal 1000 (800) 40 40 40 40 40 40 40 40 40 1040 present value 1/(1+i/2)2n 1 0.96154 0.92456 0.889 0.85480 0.82193 0.79032 0.7599 0.7307 0.7026 0.6756 PV of CF -800 38.4615 36.9823 35.560 34.1922 32.8771 31.6126 30.396 29.228 28.103 702.587 Yield to maturity 2.72% In this case, the yield to maturity has been determined t be 2.72% Yield to call Yield to call is a yield of a bond which can be called before the maturity period and in most instances the bond holders may receive a special called price or a par value. When a bond is called the investor does not receive any coupon amount. Therefore to determine whether he has made a return, the investor needs to calculate the present value as well as the internal rate of return. This is called redemption of a bond before maturity and usually is exercised by most investors since most of the bonds in the market are callable at a specified price(Fischer and Jordan, 2006). The must determine the measure of return when there is likelihood that the issuer may recall the bond at a future term and this is called yield to call. This rate is measured with other rate to see the duration one should hold the bond whether to maturity, redemption or selling in the market. There is always many calls to a bond that creates in the market. We calculate a bond’s yield to call using the straight bond pricing formula we have been using with two changes. First, instead of time maturity, we use time to the first possible call date. Second, instead of face value, we use the call price(Fischer and Jordan, 2006). The resulting formula is thus: where: T Calculating yield to call requires the same trial-and-error procedure as calculating a yield to maturity. Most financial calculators will either handle the calculation directly or can be tricked into it by just changing the face value to the call price and the time to maturity to time to call(Fischer and Jordan, 2006). To illustrate this we assume a bond which has a coupon rate of 12%, a current market price of 900 a maturity period of 5 years, first call on the second year at 1080 and second call on the fourth year at 1050. The coupon amount is paid semi-annually. We have to determine the yield to call for the bond at the second year and the fourth year. This has been done using the same formula employed when calculating yield to maturity. We will began by the first call and go to the second call. The following is the excel calculation for the first and second call. Yield to first call 1 2 3 4 cashflow (900) interest 60 60 60 60 principal 1080 (900) 60 60 60 1140 present value 1/(1+i/2)2n 1 0.943396 0.889996 0.839619 0.792094 PV of CF -900 56.60377 53.39979 50.37716 902.9868 Yield to call 4.64% The second call Yield to second call 1 2 3 4 5 6 7 8 cash flow (900) interest 60 60 60 60 60 60 60 60 principal 1050 (900) 60 60 60 60 60 60 60 1110 present value 1/(1+i/2)2n 1 0.952381 0.907029 0.863838 0.822702 0.783526 0.746215 0.710681 0.676839 PV of CF -900 57.14286 54.42177 51.83026 49.36215 47.01157 44.77292 42.64088 751.2917 Yield to call 3.07% The yields to the second call are 3.07% as shown in the diagram above. Yield to put Yield to put is the expected internal rate of return on a bond it is putable that is when a bond holder can sell a bond at a specified price. Like yield to maturity trial and error is employed in determining the value of the yield to the time the put is exercised. Let us assume a bond putable at three years with a put price of 1150. The par value is 1,000 with a coupon rate of 7% and current market price of 950 Yield to put 1 2 3 4 5 6 cash flow (950) interest 35 35 35 35 35 35 principal 1150 (950) 35 35 35 35 35 1185 present value 1/(1+i/2)2n 1 0.952381 0.907029 0.863838 0.822702 0.783526 0.746215 PV of CF -950 33.33333 31.74603 30.23432 28.79459 27.42342 884.2652 Yield to call 1.57% The Relationship of Different Yield From the above calculations, one can note that bonds have the following characteristics. Premium bonds: Coupon rate > Current yield > Yield to maturity Discount bonds: Coupon rate < Current yield < Yield to maturity Par value bonds: Coupon rate = Current yield = Yield to maturity Influences of Interest Rates In determining the interest rate, the customer will accept various factors; play a role, this includes purchasing power, reinvestment, risk liquidity preference and availability of funds in the market. Purchasing power—people will intend to purchase bonds if they have extra income for investment. If they do not have income then they are not likely to purchase anything. This means when the prices of the bond go up, the interest in the market will also go up in order to protect the depreciating power of debt payments. This in turn affects the investors(Fischer and Jordan, 2006). Reinvestment risk—if after you purchase a bond, interest rates decline (rises), it will not be possible to reinvest interest payments at the proposed yield to maturity, but they will be reinvested at lower rates and the ending sum would be below (above) what you expected. Note that the price risk and the reinvestment risk resulting from a change in interest rates have opposite effects on an investor’s ending wealth position. Specifically, an increase in the level of interest rates will cause an ending price that is below expectations, but the reinvestment of interim cash flow (coupons) will be at a rate above expectations. The reserve is true for declining interest rates(Fischer and Jordan, 2006). Liquidity preference—this theory derives the equilibrium basic interest rate from the demand for and supply of money at any given time. Spending units are postulated to demand money balances to be held for liquidity to spend later. The demand for money balances is directly related to the income or wealth of the holder; the greater the income, the greater the demand for money. However, to the extent that money promises no or little return, holding money balances incurs an opportunity cost. The higher the interest rate, the higher the opportunity cost and the smaller the demand for money balances. Thus, the quantity of money demanded is related inversely to the interest rate(Fischer and Jordan, 2006). If prices are not expected to change, the nominal interest rate is equal to the real interest. The real rate is assumed to be affected only by changes in aggregate income and in aggregate money supply by government, not by changes in the rate of inflation. The demand for money balances for given levels of income and price expectations is shown as schedule L0. The demand varies inversely with market interest rates, so the schedule slopes downward to the right because at first approximation, the supply of money may be assumed to be determined completely by the Fed without regard to the level of interest rates. If income and/or price expectations increase, the demand for money increases and the L schedule shifts out the right, say to L1. Interest rates rise to i1. If the Fed increases the money stock, the M schedule shifts to the right, and interest rates decline. The initial change in interest rates brought about by a change in the money supply is likely to be only temporary(Crescenzi, 2010). References Besley, S., & Brigham, E. (2008). Principles of Finance (4th ed.). Mason: Cengage Learning. Bomfim, A.N. (2001). Measuring equilibrium real interest rates: What can we learn from yields on indexed bonds? Retrieved on July 31, 2012 from http://www.federalreserve.gov/pubs/feds/2001/200153/200153pap.pdf Brealey, R, Myers S. & Marcus, A. (2007). Fundamentals of corporate Finance. Boston: McGraw-Hill Irwin. Brigham, E. F., & Ehrhardt, M. C. (2010). Financial Management Theory and Practice. New York: Cengage Learnings. Coombs, H. M., Hobbs, D., & Jenkins, D. E. (2005). Management accounting: principles and applications. New York: Sage Publications. Correia, C., Flynn, D., Uliana, E., & Wormald, M. (2007). Financial Management. Juta and Company Ltd. Crescenzi, A. (2010). The Strategic Bond Investor: Strategies and Tools to Unlock the Power of the Bond Market. Sidney: McGraw-Hill Companies. Fischer, D. & Jordan, R. (2006). Security Analysis and Portfolio Management. New York: Prentice Hall Ross, S., Westerfield, R., & Jaffe, J. (2005). Corporate finance. New York: McGraw Hill Company Shim, J. K., & Siegel, J. G. (2008). Financial Management. New York: Barron's Educational Series. Read More