07 Chapter model

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07 Chapter model 4/2/2016 1:31 2/14/2006 Chapter 7. Bonds and Their Valuation INPUT DATA Years to Maturity 15 Coupon rate 10% Annual Payment \$100 Par value \$1,000 10% Value of bond = \$1,000.00 Thus, this bond sells at its par value. That situation always exists if the going rate is equal to the coupon rate. Bond Going rate Value (r) \$1,000 Refer to the Excel Tutorial for Data Table Instructions. 0% \$2,500.00 5% \$1,518.98 10% \$1,000.00 15% \$707.63 20% \$532.45 The value of any financial asset is the present value of the asset's expected future cash flows. The key inputs are (1) the expected cash flows and (2) the appropriate discount rate, given the bond's risk, maturity, and other characteristics. The model developed here analyzes bonds in various ways. Bond valuation requires keen judgment with regard to assessing the riskiness of the bond, i.e., what is the likelihood that the promised coupon and maturity payments will actually be made at the scheduled times? Also, investing in bonds requires one to make implicit forecasts of future interest rates--you don't want to buy long-term bonds just before a sharp increase in interest rates. We do not deal with these important but subjective issues in this spreadsheet. Rather, we concentrate on the actual calculations used, given the inputs. BOND VALUATION (Section 7.3) A bond has a 15-year maturity, a 10% annual coupon, and a \$1,000 par value. The required rate of return (or the yield to maturity) on the bond is 10%, given its risk, maturity, liquidity, and other rates in the economy. What is a fair value for the bond, i.e., its market price? Going rate, r d Suppose the going interest rate changed from 10%, falling to 5% or rising to 15%. How would those changes affect the value of the bond? We could go to the input data section above and change the value for r d from 10% to 5% and then 15%, and observe the change in value. Alternatively, we can set up a data table to show the bond's value at a range of rates, i.e. to show the bond's sensitivity to changes in interest rates. A B C D E F G H I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

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EXAMPLE Use the Rate function to solve the problem. Years to Maturity 14 Coupon rate 10% Annual Payment \$100.00 5.00% Current price \$1,494.93 Par value = FV \$1,000.00 We can use the data table to construct a graph that shows the value of standard 10% annual coupon, \$1,000 face value bonds at a variety of interest rates. YIELD TO MATURITY (YTM) (Section 7.4) The YTM is the rate of return that a bond earns if the issuer makes all scheduled payments and the bond is held to maturity. The YTM is the same as the total rate of return discussed in the chapter, and it can also be interpreted as the "promised rate of return," or the return to investors if all promised payments are made. The YTM for a bond that sells at par consists entirely of an interest yield. However, if the bond sells at any price other than its par value, the YTM consists of the interest yield together with a positive or negative capital gains yield.
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