Text_Problem_Sets

Text Problem Sets Chapter 5 Problem A3: (Bond valuation) General Electric made a coupon payment yesterday on its 6.75% bonds that mature in 8.5 years. If the required return on these bonds is 8% APR, what should be the market price of these bonds' Solution A3: A bond valuation formula for a bond with semiannual coupon payments is: B0= CPN21+r22N-1 r21+r22N+ 1,0001+r22N The semiannual coupon payments in this case will be $33.75 (= one-half of 6.75% of $1,000 = 67.5/2), and the semiannual required return is 4%. Using Equation shown above, the fair price of the bond—the present value of its expected future cash flows—is B0=(33.75)(1.04)17-1 0.041.0417+ 1,0001.0417 = (33.75) (0.947/0.077) + 513.67 = 415.081 + 513.610 = 928.45 (**It’s assumed that it’s a semi-annual bond with face value of $1000) Buying this bond for less than $928.45 would be a positive-NPV investment because it is worth more than it costs. Paying more than $928.45 would be a negative-NPV investment. At its fair price of exactly $928.45, buying the bond would be a zero-NPV investment. Problem A5: (Yield to maturity) New Jersey Lighting has a 7% coupon bond maturing in 17 years. The current market price of the bond is $975. What is the bond’s yield to maturity' Solution A5: The inputs are B0= 975, CPN/2 = 35.00 (one-half of 7.0% of $1,000), and 2N = 34. Putting these into Equation shown below, we have: 975= 35.001+r22N-1 r21+r22N+ 1,0001+r22N = 3.63% * 2 = 7.26% (**It’s assumed that it’s a semi-annual bond with face value of $1000) Problem A11: (Expected return) Northern States Power has a projected dividend of $3.60 next year. The current stock price is $50.50 per share. If the dividend is projected to grow at 3.5% annually, what is the expected return on Northern States stock' Solution A11: r=D1P0+g D1 = 3.60, P0 = 50.50, g = 3.5% (0.035) = 3.60 / 50.50 +0.035 = 0.071 + 0.035 = 0.106 = 10.6% expected return Problem A16: (Growth rate) Suppose Toshiba has a payout ratio of 55% and an expected return on its future investments of 15%. What is Toshiba’s expected growth rate' Solution A16: Expected Growth Rate = Expected Return*(1-Payout Ratio) = 15*(1-.55) =6.75% Problem B2: (Yield to maturity) GMAC’s 8.75% bonds closed yesterday at $952.50. If these bonds mature in 11 years, what is the yield to maturity of these bonds' What is their APY' Solution B2: The inputs are B0= 952.50, CPN/2 = 43.75 (one-half of 8.75% of $1,000), and 2N = 22. Putting these into Equation shown below, we have: 952.50= 43.751+r22N-1 r21+r22N+ 1,0001+r22N = 4.73% * 2 = 9.46% (**It’s assumed that it’s a semi-annual bond with face value of $1000) APY = [1.04375]2 – 1 = 0.0894 = 8.94% Chapter 7 Problem C3: (Fama-French Three-Factor Model) Using the Fama-French three-factor model, what are the expected returns for Ducca Computing and Lincoln Bank using this information' The riskless return is 4.3% RISK FACTOR | DUCCA COMPTUING FACTOR SENSITIVITY | LINCON BANK FACTOR SENSITITIVITY | EXPECTED FACTOR RETURN PREMIUMS | Market | 0.90 | 1.03 | 5.94% | Size | 0.24 | 0.15 | 4.92% | Book-to-market | -0.32 | 0.28 | 6.33% | Solution C3: Required Return for DUCCA Computing should be: = 4.3% + 0.90 (5.94%) + 0.24 (4.92%) + -0.32 (6.33%) = 0.043 + 0.05346 + 0.011808 – 0.020256 = 0.088012 = 8.8 % Required Return for LINCON Bank should be: = 4.3% + 1.03 (5.94%) + 0.15 (4.92%) +0.28 (6.33%) = 0.043 + 0.061182 + 0.00738 + 0.017724 = 0.129286 = 12.92% Reference Emery, D. R., Finnerty, J. D., & Stowe, J. D. (2007). Corporate Financial Management (3rd ed.). New York, NJ: Prentice Hall.