【正文】 AI = $ – = . The bond would be quoted at % (or approximately 86 10/32) of par. j: Explain the deficiency of the traditional approach to valuation in which each cash flow is discounted at the same discount rate. The use of a single discount factor (., YTM) to value all bond cash flows assumes that interest rates do not vary with term to maturity of the cash flow. In practice this is usually not the case—interest rates exhibit a term structure, meaning that they vary according to term to maturity. Consequently, YTM is really an approximation or weighted average of a set of spot rates (an interest rate today used to discount a single cash flow in the future). The use of spot rates to discount bond cash flows results in an arbitragefree valuation. k: Explain the arbitragefree valuation approach and the role of Treasury spot rates in that approach. The use of multiple discount rates (a series of spot rates that reflect the current term structure) will result in more accurate bond pricing and in doing so, eliminate any (meaningful) arbitrage opportunities. That39。 CPT PV = ? N = , I/Y = 6, FV = 30, PMT = 0。 CPT PV = (ignore the sign). The difference between the $ and the par value ($1000) is the amount of interest that will be earned over the 10year life of the issue. i: Compute the dirty price of a bond, accrued interest, and clean price of a bond that is between coupon payments. Assume we are trying to price a 3year, $1,000 par value, 6% semiannual coupon bond, with YTM = 12%, with a maturity of January 15, 2020, and you are valuing the bond for settlement on April 20, 2020. The next coupon is due July 15, 2020. Therefore, there are 85 days between settlement and next coupon, and 180 days in the coupon period. The fractional period (w) = 85/180 = . The value of the bond calculates out to be $. Note that this bond value includes the accrued interest. This is often referred to as the dirty price or the full price. Unfortunately, when using a financial calculator, you can39。 PMT = 60/2。 PMT = 60/2。 PMT = 60/2。 CPT PV = . This value would typically be quoted as , meaning % of par value, or $. Bond value = [60 / ()1] + [60 / ()2] + [60 + 100 / ()3] = $ Example: Semiannual coupons. Suppose that we have a 10year, $1,000 par value, 6% semiannual coupon bond. The cash value of each coupon is: CPN = ($1,000 * )/2 = $30. The value of the bond with a yield to maturity (interest rate) of 8% appears below. On your financial calculator, N = 20, PMT = 30, FV = 1000, I/Y = 4。s cash flow. This LOS is very straightforward. A bond39。十五 Asset Valuation: Debt Investments: Analysis and Valuation : Introduction to the Valuation of Fixed Ine Securities a: Describe the fundamental principles of bond valuation. Bond investors are basically entitled to two distinct types of cash flows: 1) the periodic receipt of coupon ine over the life of the bond, and 2) the recovery of principal (par value) at the end of the bond39。s cash flow is the coupon or principal value. For an optionfree bond (meaning that the bond is not callable, putable, convertible, etc.), the expected cash flow structure is shown on the time line below. Where m = maturity, par, or face value (usually $1,000, ￡ 1,000, et cetera), CPN = (maturity value * stated coupon rate)/ coupons per year, and N= of years to maturity * coupons per year. So, for an arbitrary discount rate i, the bond’s value is: Bond value= CPN1 + CPN2 + ... + CPNn*m + M (l + i/m)1 (1 + i/m)2 (l + i/m)n*m Where: i = interest rate per annum (yield to maturity or YTM), m = number of coupons per year, and n = number of years to maturity. d: Discuss the diffulties of estimating the expected cash flows for some types of bonds and identify the bonds for which estimating the expected cash flows is difficult. Normally, estimating the cash flow stream of a highquality optionfree bond is relatively straight forward, as the amount and timing of the coupons and principal payments are known with a high degree of certainty. Remove that certainty, and difficulties will arise in estimating the cash flow stream of a bond. Aside from normal credit risks, the following three conditions could lead to difficulties in forecasting the future cash flow stream of even highquality issues: ? The presence of embedded options, such as call features and sinking fund provisions in which case, the length of the cash flow stream (life of the bond) cannot be determined with certainty. ? The use of a variable, rather than a fixed, coupon rate in which case, the future annual or semiannual coupon payments cannot be determined with certainty. ? The presence of a conversion or exchange privilege, so you39。 CPT PV = . Note that the coupons constitute an annuity. Bond Value= n*m ? t=1 30 (1 + )t + 1000 (1 + )n*m = f: Explain how the value of a bond changes if the discount rate increases or decreases and pute the change in value that is attributable to the rate change. The required yield to maturity can change dramatically during the life of a bond. These changes can be market wide (., the general level of interest rates in the economy) or specific to the issue (., a change in credit quality). However, for a standard, optionfree bond the cash flows will not change during the life of the bond. Changes in required yield are reflected in the bond’s price. Example: changes in required yield. Using your calculator, pute the value of a $1,000 par value bond, with a three year life, paying 6% semiannual coupons to an investor with a required rate of return of: 3%, 6%, and 12%. At I/Y = 3%/2。 pute PV = 1, At I/Y = 6%/2。 pute PV = 1, At I/Y = 12%/2。 pute PV = g: Explain how the price of a bond changes as the bond approaches its maturity date and pute the change in value that is attributable to the passage of time.