# If you recall there are several ways to estimate r d

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If you recall, there are several ways to estimate Rd. The takeaway slide from that class is reproduced below: 1.USING THE COMPANY’S OWN BONDSNO COMPARABLE BOND The first method is to find the existing YTM on the firm’s own bonds of similar time to maturity. There are no Metro Power bonds that are close to a 10 year maturity. The closest that we have is a Metro Power Bond that matures on April 1st, 2012 thus it has 5½ years remaining. Recall that bond pricing is nonlinear so using a 5 ½ year bond to estimate a 10 year bond is probably a poor choice. 5.23%
9 2.USING BONDS OF SIMILAR RISK (DOMINION POWER) 5.23% A second option is to use similar bonds. Those in the same industry, with the same bond rating and time to maturity. There are 2 electric utility bonds that have 10 years to maturity: Dominion Power and PEPCO. However, the PEPCO bond is rated BBB+ and the Dominion Power bond is rated AA. Since the Metro bond is rated AA, the Dominion Power bond is a better choice since it is “more similar” in terms of risk. We only need to calculate the YTM on the Dominion Power bond. Recall that bond pricing is an application of time value of money. The current bond price is the present value of the coupon payments plus the present value of the face value. Because the series of coupon payments is a series of constant payments, we can use the present value annuity formula to calculate the present value of the coupon payments. For the Dominion Bond, we know that it has 10 years remaining to maturity and pays semiannual coupons. We know that because the coupon rate is 6.75%, the bond pays semi-annual coupons of \$3.375 per \$100 face value. Remember that the coupon rate is the (total annual coupons / face value of the bond). In this case, the bond pays \$6.75 per year (assuming \$100 face value), so each semi-annual payment will be 6.75/2 = 3.375. We also need to remember that C, r, and t must match. Because we have semiannual payments, we need a semiannual rate and number of semiannual periods. With 10 years remaining to maturity, this means that we have t=20 (10 years x 2 periods per year). We also know that the price is \$111.76. We thus have: We cannot solve this algebraically for YTM. We need to use trial and error or your calculator. Set P/Y=2 N I/Y PV PMT 20 ??? -111.76 3.375 Solving this for I/Y, we find that YTM is 5.23% 3.USING RISK-FREE RATE AND A SPREAD Since we don’t have any information aboutthe risk-free rates or spreads, we can’t use this method. ttC1Face ValuePrice = 1 - (1+r)(1+r)r20203.3751100111.76 = 1 - (1+r)(1+r)r
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