NOTE:
- Please maintain at least 6 decimals while solving the question, and round to 2 decimals for the final answer.
- If using a financial calculator, please show all inputs used.
1. Assume it is now January 1, 2000, and you are offered the following deal: starting from year 2000, you will receive each year the amount of dollars equal to the year, i.e., $2000, $2001, $2002, etc., until year 3000 inclusive. Payments occur at the year end and the interest rate remains at 10% throughout the life of the investment, what is the most you would pay for this investment? How much would you pay for this deal if the payments cover only the years from 2000 to 2050 inclusive? What can you conclude from the comparison?
2. You plan to retire 24 years from now, and you expect that you will live 35 years after retiring. You want to have enough money upon reaching retirement age to withdraw $175,000 from the account at the beginning of each year you expect to live, and yet still have $1,000,000 left in the account at the time of your expected death. You plan to accumulate the retirement fund by making equal bi-weekly deposits at the end of each two week period for the next 24 years. You expect that you will be able to earn a quoted rate of 10%, compounded semi-annually on your deposits. However, you only expect to earn an EAR of 5% on your investment after you retire since you will choose to place the money in less risky investments. What equal bi-weekly deposits must you make to reach your retirement goal?
3. You have just been granted a business loan of $1,000,000. The terms of the loan requires that you pay off the loan in quarterly installments over a period of ten years. The bank is charging you an APR of 10%, compounded monthly.
a) Calculate the interest payment and construct a complete amortization schedule that breaks down the interest and principal repayment associated with each interest payment.
b) After five years, you put down a lump sum of $100,000 on the loan. You keep your payments thesame as in (a). By how much time have you shortened the life of your loan?
c) Using present value formulas you learned in class, show the interest and principal payment portions of the 32nd payment, and reconcile your result with the amortization schedule constructed in (a).
4. Rideau Auctions' dividends are expected to grow at 25% during the next year and then 8% per year indefinitely. The required return on this stock is 13%, and the stock currently sells for $85 per share. What is the value of the dividend per share that Rideau Auctions just paid?
5. A bond of MacKinnons Inc. has face value of $1000, pays 6% coupon semiannually, and has 20 years to maturity. The bond has a quoted price of 102.
a) What is the yield to maturity on MacKinnons' bond?
b) What is the current yield?
c) By how many percentage points would the price of MacKinnons' bond change if the market interest rates suddenly increase by 1%?
d) What will the market price of this bond be one year from now if the required yield on similar bonds falls to 2% in one year from now?
e) If you sell the bond in three and a half years from now at 102.7, what is your holding period yield?