Week_2_Text_Problems

Individual Assignment: Text Problem Sets February 17 2010, Ch. 5: Problems A1. (Bond valuation) A $1,000 face value bond has a remaining maturity of 10 years and a required return of 9%. The bond’s coupon rate is 7.4%. What is the fair value of this bond' {draw:frame} {draw:rect} {draw:frame} 1,000 x3.7 % =37 # of periods =10years 2 =20 periods the price= 481.29+ 414.64 =$895.94 10 x 2 r= 9% /2PV =BMT= 7.4 % x 1.000/2 = 37 FV =1,000 PV = $895.94 Expected dividend in next year (D1) = $5.60 Dividend expected growth rate (g) = 6% per year Required Return on Stock ( R) = 10% Current Market Value of a Share (P0) = D1 / (R – g) Current Market Value of a Share (P0) = $5.60 / (0.10 – 0.06) Current Market Value of a Share (P0) = $5.60 / 0.04 Current Market Value of a Share (P0) = $140 A12. (Required return for a preferred stock) James River $3.38 preferred is selling for $45.25. The preferred dividends is now growing. What is the required return on James River preferred stock' Required Return = Dividend/Market Price Dividend = $3.38 Market Price = $45.25 Required Return = $3.38 / $45.25 Required Return = 7.47% A14.(Stock Valuation) Suppose Toyota has nonmaturing (perpetual) preferred stock outstanding that pays a $1.00 quarterly dividend and has a required return of 12% APR (3% per quarterly). What is the stock worth' Perpetual Quarterly Preferred Dividend (D) = $1.00 Annual Dividend ($1.00 x 4.00) = $4.00 Annual Percentage Rate (APR) = 12% Preferred Stock Value (P0) = (D / R) Preferred Stock Value (P0) = ($4.00 / 0.12) Preferred Stock Value (P0) = $33.33 B16 Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock Exchange. Suppose PhilEl’s bonds have identical coupon rates of 9.125% but that one issue matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment was made yesterday. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond' 1 Year Maturity n = 1 x 2 = 2 r = 8% / 2 = 4% PV = ' PMT = 9.125% x 1,000 / 2 = $45.62 FV = $1,000 PV = $1,010.61 7 Year Maturity n = 7 x 2 = 14 r = 8% / 2 = 4% PV = ' PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000 PV = $1,059.42 10 Year Maturity n = 15 x 2 = 30 r = 8% / 2 = 4% PV = ' PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000 PV = -$1,097.27 Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%. What is the fair price of each bond now' 1Year Maturity n = 1 x 2 = 2 r = 7% / 2 = 3.5% PV = n/a PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000 PV = $1,020.18 7 Year Maturity n = 7 x 2 = 14 r = 7% / 2 = 3.5% PV = n/a PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000 PV = $1,116.03 10 Year Maturity n = 15 x 2 = 30 r = 7% / 2 = 3.5% PV = n/a PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000 PV = $1,195.42 Suppose that the yield to maturity for all of these bonds changed instantaneously again, this time to 9%. Now what is the fair price of each bond' 1 Year Maturity n = 1 x 2 = 2 r = 9% / 2 = 4.5% PV = n/a PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000 PV = $1,001.17 7 Year Maturity n = 7 x 2 = 14 r = 9% / 2 = 4.5% PV = n/a PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000 PV = $1,006.39 10 Year Maturity n = 15 x 2 = 30 r = 9% / 2 = 4.5% PV = n/a PMT = 9.125% x 1,000 / 2 = $45.625 FV = $1,000 PV = $1,010.18 B18. (Default risk) You buy a very risky bond that promises a 9.5% coupon and return of the $1,000 principal in 10 years. You pay only $500 for the bond. You receive the coupon payments for three years and the bond defaults. After liquidating the firm, the bondholders receive a distribution of $150 per bond at the end of 3.5 years. What is the realized return on your investment' Part a: Calculating Realized Return on Investment Rate: Present Value of the Bond $500.00 Par Value of the Bond $1,000 Annual Coupon Rate 9.50% Number of Years to Maturity 3.5 years *Values per Excel Function* (rate) Number of years to Maturity =3.5 Present Value of the Bond (PV) =500.00 Future Value (Parvalue of the Bond ) (FV) = -1,000 Realized Return on Investment (Rate) = 37.34% The firm does far better than expected and bondholders receive all of the promised interest and principal payments. What is the realized return on your investment' (b) Calculating Realized Return on Investment Rate: Present Value of the Bond = $500.00 Par Value of the Bond = $1,000 Annual Coupon Rate = 9.50% Number of Years to Maturity 10 years Number of years to Maturity =10 Annual Coupon Payment (PMT) ($1000 * 9.50%) =-95 Present Value of the Bond (PV) =500.00 Future Value (or) Parvalue of the Bond (FV) =-1,000 Realized Rate of Return on Investment (Rate) =0.2242 Realized Return on Investment (Rate) =22.42% B20. (Constant growth model) Medtrans is a profitable firm that is not paying a dividend on its common stock. James Weber, an analyst for A. G. Edwards, believes that Medtrans will begin paying a $1.00 per share dividend in two years and that the dividend will increase 6% annually thereafter. Bret Kimes, one of James’ colleagues at the same firm, is less optimistic. Bret thinks that Medtrans will begin paying a dividend in four years, that the dividend will be $1.00, and that it will grow at 4% annually. James and Bret agree that the required return for Medtrans is 13%. What value would James estimate for this firm' Dividend Paid in 2 years (D2) = $1.00 Dividend growth rate (g) = 6% Required Rate of Return (R ) = 13% Medtrans Stock Value (P2) = D3 / (R - g) Medtrans Stock Value (P2) = D2 (1+g) / (0.13 - 0.06) Medtrans Stock Value (P2) = $1.00 (1.06) / 0.07 Medtrans Stock Value (P2) = $1.06 / 0.07 Medtrans Stock Value = $15.14 What value would Bret assign to the Medtrans stock' Medtrans Stock Value (P4) = D5 / (R - g) Medtrans Stock Value (P4) = D5 (1+g) / (0.13 - 0.04) Medtrans Stock Value (P4) = $1.00 (1.04) / 0.09 Medtrans Stock Value (P4) = $1.04 / 0.09 Medtrans Stock Value = $11.55 Ch. 7: Problem C1. (Beta and required return) The riskless return is currently 6%, and Chicago Gear has estimated the contingent returns given here. What is Chicago Gear’s beta' Expected Return on Stock Market E(Rstock market) = [(0.20 * -0.10) + (0.35 * 0.10) + (0.30 * 0.15) + (0.15 * 0.25) Expected Return on Stock Market E(Rstock market) = (-0.02 + 0.035 + 0.045 + 0.0375) Expected Return on Chicago Gear E(Rchicago gear) = [(0.20 * -0.15) + (0.35 * 0.15) + (0.30 * 0.25) + (0.15 * 0.35)] Expected Return on Chicago Gear E(Rchicago gear) = (-0.03 + 0.0525 + 0.075 + 0.0525) Expected Return on Chicago Gear E(Rchicago gear) =15% b) Calculating Chicago Gear’s Beta (ßChicago gear): Average Realized Return on Chicago Gear = (-0.15 + 0.15 + 0.25 + 0.35) / 4 Average Realized Return on Chicago Gear = 15% Expected Return on Chicago Gear E(Rchicago gear) = 15% Risk-free Return (Rf) = 6% 0.15 = 0.06 + Beta (ß) * (0.15 - 0.06) 0.15 = 0.06 + ß * 0.09 0.15 - 0.06 = ß * 0.09 0.09 = ß * 0.09 ß * 0.09 = 0.09 ß = 0.09 / 0.09 What is Chicago Gear’s required return according to the CAPM' Required Return (RE) = Rf + ß (RM - Rf) Required Return of Chicago Gear's Required Return (Rchicago gear's) = 0.06 + 1 (0.15 - 0.06) Required Return of Chicago Gear's Required Return (Rchicago gear's) = 0.06 + 1 (0.09) Required Return of Chicago Gear's Required Return (Rchicago gear's) = 0.06 + 0.09 Required Return of Chicago Gear's Required Return (Rchicago gear's) = 15%