Assignments: (100 points)
1. Calculating Present Value (5 points)– You have just received notification that you have won the $2 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you are around to collect), 80 years from now. What is the present value of your windfall if the appropriate discount rate is 9.1 percent?
2. Calculating Growth Rates and Future Value (5 points)– I 1985, the first US. Open Golf Championship was held. The winner’s prize was $150. In 2020, the winner’s check was $2.2 million. What was the annual percentage increase in the winner’s check over this period? If the winner’s prize increases at the same rate, what will it be in 2050?
3. Calculating Rates of Return (5 points)– Although appealing to more refined tastes, art as a collectible has not always performed so profitably. In 2010, Deutscher-Menzies sold Arkie under the Shower, a painting by renowned Australian painter Brett Whitely, at auction for $1,100,000. Unfortunately, the previous owner had purchased it three years earlier for $1,670,000. What was his annual rate of return on this painting?
4. Calculating Future Values (5 points)– You are scheduled to receive $10,000 in two years. When you receive it, you will invest it for six more years at 6.8% per year. How much will you have in eight years?
5. Calculate Present Value (5 points)– You have decided that you want to be a millionaire when you retire in 45 years. If you can earn an annual return of 11.8% percent, how much do you have to invest today? What if you can earn 5.9 percent?
6. Calculating Annuity Present Value (10 points) – Beginning three months from now, you want to be able to withdraw $3,000 each quarter from your bank account to cover college expenses over the next four years. If the account pays 0.57 percent interest per quarter, how much do you need to have in your bank account today to meet the expenses needs over the next four year?
7. Comparing cash flow streams (15 points) – You have just joined the investment banking firm of Dewey. Cheatum, and Howe. They have offered you two different salary arrangements. You can have $90,000 per year for the next two years, or you can have $77,000 per year for the next two years along with $20,000 signing bounce today. The bonus is paid immediately, and the salary is paid in equal amounts at the end of each month. If the interest rate is 7% compounded monthly, which do you prefer? (Show your calculations).
8. Calculation Annuity Values (25 points) – You are serving on a jury. A plaintiff is suing the city for injuries sustained after a freak street-sweeper accident. In the trial, doctors testified that it will be five years before the plaintiff is able to return to work. The jury has already decided in favor of the plaintiff. You are the foreperson of the jury and propose that the jury give the plaintiff an award to cover the following:
A. The present value of two years’ back pays. The plaintiff’s annual salary for the last two years Have been $43,000 and $46,000 respectively.
B. The present value of five years future salary will be $51,000 per year.
C. $150,000 for pain and suffering.
D. $20,000 court costs
Assume that the salary payments are equal to the amounts paid at the end of each month. If the interest rate you choose is EAR of 5.9%, what is the size of the settlement? If you were the plaintiff, would you like to see a higher or lower interest rate?
9. Coupon Rate (10 points) – Nikita Enterprises has a bond on the market making annual payments, with eight years to maturity, a par value of $1,000, and selling it for $962. At this price the bond’s yield is 5.1%. What must the coupon rate be on the bond?
10. Accrued Interest (15 points)– You purchase a bond with an invoice price of $1,053 and a par value of $1,000. The bond has a coupon rate of 5.3% and there are four months to the next semiannual coupon date. What is the clean price of the bond?
