【正文】 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 life. Thus, in valuing a bond, you39。re dealing with an annuity of coupon payments, plus a large single cash flow, as represented by the recovery of principal at maturity, or when the bond is retired. These cash flows, along with the required rate of return on the investment, are then used in a present value based bond model to find the dollar price of a bond. b: Explain the three steps in the valuation process. The value of any financial asset can be determined as the sum of the asset’s discounted cash flows. There are three steps: ? Estimate the cash flows. ? Determine the appropriate discount rate. ? Calculate the sum of present values of the estimated cash flows. c: Explain what is meant by a bond39。s cash flow. This LOS is very straightforward. A 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。re dealing with a convertible (or exchangeable) bond, rather than a straight bond in which case, it39。s difficult to know how long it will be before the bond is converted into stock. e: Compute the value of a bond, given the expected cash flows and the appropriate discount rates. Example: Annual coupons. Suppose that we have a 10year, $1,000 par value, 6% annual coupon bond. The cash value of each coupon is: CPN= ($1,000 * )/1 = $60. The value of the bond with a yield to maturity (interest rate) of 8% appears below. On your financial calculator, N = 10, PMT = 60, FV = 1000, I/Y = 8。 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。 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。 n = 3*2。 FV = 1000。 PMT = 60/2。 pute PV = 1, At I/Y = 6%/2。 n = 3*2。 FV = 1000。 PMT = 60/2。 pute PV = 1, At I/Y = 12%/2。 n = 3*2。 FV = 1000。 PMT = 60/2。 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. A bond’s value can differ substantially from its maturity value prior to maturity. However, regardless of its required yield, the price will converge toward maturity value as maturity approaches. Returning to our $1,000 par value bond, with a threeyear life, paying 6% semiannual coupons. Here we calculate the bond values using required yields of 3, 6, and 12% as the bond approaches maturity. Time to Maturity YTM = 3% YTM = 6% YTM = 12% years 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, h: Compute the value of a zerocoupon bond. You find the price or market value of a zero coupon bond just like you