Corporate Finance Homework Assignment I
Answer All Questions (I will grade any two of them) Show all your work (use of formula, etc.) in solving the problems. You still need to show your work even if you use the financial calculator to get the answers.
1. Suppose you wish to plan for your newborn’s college tuition payment. You intend to make equal semiannual deposits into an account offering 4% compounded semiannually on the child’s 3rd through 13th birthdays. You expect that tuition payments will be $50,000 semiannually by the time the child is ready to enter college. Therefore, your goal is to make eight semiannual withdrawals of $50,000 each starting on the child’s 18th birthday, each withdrawal to be used for semiannual tuition. Assume the account continues to offer 4 percent per year compounded semiannually throughout the entire period of deposits and withdrawals. How much must each of the semiannual deposits be such that there will be enough money accumulated in the account to exactly meet the goal? [Suggestion: Draw the cash flow diagram to aid you in solving this problem.]
2. You are planning to save for retirement over the next 40 years. To do this, you will invest $500 per month in a stock account and $2,500 semiannually in a bond account. The return of the stock account is expected to be 6 percent per year, and the bond account will pay 4 percent per year. When you retire, you will combine your money into an account with a 5 percent per year return. How much can you withdraw each month from your account assuming a 25-year withdrawal period?
3. You are taking out a four-year loan of $30,000 from your bank. The interest rate is 5 percent per year, and the loan calls for equal monthly payments. How much principle is paid in the second month? How much total interest is paid after five months? (Draw an amortization table to answer the questions. Use of excel is highly encouraged.)
4. Bond J is a 4 percent coupon bond. Bond K is a 7 percent coupon bond. Both bonds have 10 years to maturity, make semiannual payments, and have a YTM of 6 percent. If interest rate (YTM) changes from 6 percent to 8 percent, what is the percentage price change of these bonds? What if the YTM suddenly falls from 6 percent to 4 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?
5. Rizzi Co. is growing quickly. The company just paid a $2 per share dividend and dividends are expected to grow at a 15%, 8% and 4% rate respectively for the next three years, with the growth rate falling off to a constant 3 percent thereafter. If the required return is 10 percent, what is the current share price?