# explain whether and why the price to earnings ratio for Cord Chemical will increase or decrease.

1. Cord Chemical is a manufacturer of specialty chemicals. The firm, which does not currently pay a dividend, expects to earn \$4.00 per share next year. The firm plans to retain and reinvest 100 percent of earnings during each of the next three years to generate future earnings growth. Exactly four years from today (at date 4), the firm expects to pay its first ever dividend of \$5.40 per share from year 4 earnings of \$9.00 per share. From date 4 on, Cord expects that retained earnings can be reinvested in the firm at a return on equity (ROE) of 16 percent. The required rate of return on the company’s stock is 11.4 percent. Assuming that Cord Chemical will continue to retain the same fraction of earnings and to reinvest at the same ROE each year from date 4 on (in perpetuity), determine the current price of Cord’s stock and explain whether and why the price to earnings ratio for Cord Chemical will increase or decrease between date 0 and date 4. (15 points
2. ) 2. Elwood Dowd, who just turned 33, expects to retire in 35 years when he turns 68. Mr. Dowd expects to earn \$70,000 next year at his job as a licensed plumber. The yearly earnings for licensed plumbers are expected to grow at 4.2 percent per year over the next 35 years. Mr. Dowd plans to save for retirement by depositing 12 percent of his yearly income at the end of each year in a retirement savings account. Mr. Dowd expects to earn a yearly return on his retirement savings of 8.2 percent over the next 57 years. Mr. Dowd’s life expectancy is 57 years, so that he can expect to enjoy a 22-year retirement, with yearly withdrawals from the retirement account at the end of each of the 22 years following his retirement at age 68. Mr. Dowd would like for the yearly income stream that he receives during retirement to provide him with constant (the same) purchasing power during each year of his retirement. Consequently, the dollar amount of his retirement income must increase each year at the rate of inflation. Assuming that inflation is expected to be 3.8 percent per year, determine the maximum initial retirement income that Mr. Dowd can withdraw from the retirement account at the end of his first year in retirement. (15 points) 2
3. 3. On September 25, 2015 Bruno Stachel paid \$1135.96 for a U.S. Government bond having exactly 22 years to maturity. The bond has a coupon rate of 4.5 percent and a par value of \$1000, with the next coupon payment to bondholders scheduled for March 25, 2016. Assume that the Federal Reserve is sure to raise interest rates in December, before Mr. Stachel receives the next coupon payment from the bond. Due to the anticipated December increase in interest rates, Mr. Stachel will be able to reinvest all of the future coupon payments from the bond at a semiannually compounded rate of 4 percent. Determine the future amount to which the reinvested coupon payments from the bond will have grown by September 25, 2037 when the bond matures. (10 points)

1. 4. Last year, Cape Fear Energy raised (borrowed) \$100 million by issuing an innovative new bond that is being referred to as a “Triennial” bond. The Triennial bonds, which have a par value of \$1000, make an interest payment of \$120 once every three years in perpetuity, so the principal amount of the bond is never (not ever) returned to the bondholders. Assuming there are two years until the next triennial coupon payment of \$120 and that the required yearly rate of return on the Triennial bonds is 5.2 percent, determine the current value of one (and only one) of the Triennial bonds issued by Cape Fear Energy. (10 points)

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