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**Unformatted text preview: **SOLUTIONS TO PRACTICE FINAL #1 Honors Corporate Finance INSTRUCTIONS 1. There are 8 questions on the exam for a total of 75 points 2. For full credit on a question, please show your work and write the answer in the space provided. Please use the back of the page if you need additional space. Remember: Read each question carefully. The questions are not in order of difficulty. If you get stuck, just go on to the next question. 1 1. (8 pts) Suppose that a 1-year, zero-coupon bond has a price of $96.15 per $100 of face value. A 2-year, zero-coupon bond has a price of $90.70 per $100 of face value. A 3-year zero-coupon bond has a price of $85.16 per $100 of face value. Throughout this problem, assume annual compounding. (a) (2 pts) What is the annual rate you can lock in now for lending between years one and two? Note that year one is next year, while year two is two years from now. Let f 1 be the forward rate between years one and two, then (1 + r 1 )(1 + f 1 ) = (1 + r 2 ) 2 f 1 = (1 + r 2 ) 2 1 + r 1 (1) The prices P 1 and P 2 of the one- and two-year zero-coupon bond with face value F are P 1 = F 1 + r 1 ; P 2 = F (1 + r 2 ) 2 which shows that 1 + r 1 = F P 1 ; (1 + r 2 ) 2 = F P 2 Plug these expressions into ( ?? ) above to see that f 1 = P 1 P 2- 1 = 96 . 15 90 . 70- 1 = 6 . 01% (b) (2 pts) What is the annual rate you can lock in now for lending between years two and three? Similarly to above, f 2 = P 2 P 3- 1 = 90 . 70 85 . 16- 1 = 6 . 51% (c) (4 pts) Calculate the price of an annual coupon bond with a coupon rate of 5% and a face value of $1000, with 3 years to maturity. We can think of the cash flows of the coupon bond as cashflows from a portfolio of 50 one-year, 50 two-year and 1050 three-year zero-coupon bonds of face value $1 , so the price P of the coupon bond is P = 50 96 . 15 100 + 50 90 . 70 100 + 1050 85 . 16 100 = 48 . 075 + 45 . 35 + 894 . 18 = 987 . 605 2 2. (5 pts) You purchased 200 shares of stock LOR on January 1, 2000 for $15 each. The following table shows the price per share and the dividend per share for the next four years. Assume dividends are paid at the end of the year (for example, LOR sold for a price of $16 and paid a dividend of $2 on December 31, 2000). Price Dividend 2000 $16 $2 2001 $18 $2 2002 $17 $3 2003 $15 $3 Assuming all dividends are reinvested into LOR, calculate the annual holding period return over this period....

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