1. If the interest rate is 10 percent, the present value of $200 paid one year from now equal’s ______.
2. If the interest rate is 5 percent, the present value of $200 paid one year from now equals’ ______. If the $200 is received in two years, the present value will equal ______.
3. If interest rates increase, the present value of a fixed payment in the future ______.
4. The present value of lottery winnings paid over a 20-year period will ______ (rise/fall) with a rise in interest rates.
5. Investments in Solar Energy. Proponents of solar energy point to the vast savings that come in the long run from using a free source of energy (the sun) rather than paying high prices for electricity. Unfortunately, solar energy systems typically have large up-front expenses to install the system. Use the concept of present value to show that solar energy systems are more likely to be profitable when interest rates are low.
6. Real Interest Rates and Opportunity Cost. When real interest rates are high, so is the opportunity cost of funds. What does this statement mean?
7. Present Value. A lottery pays a winner $1 million a year for 20 years (starting in year 1). What is the present value of this sum at an interest rate of 8 percent? You can do this by hand (not recommended) or in an Excel spreadsheet. Here is how: Enter 1 in cells A1 through A20. In cell C3, enter @NPV (.08, A1:A20) and press enter. This will give you the result. What happens to the present value of the lottery if the interest rate falls to 5 percent?
8. Pension Funds and Interest Rates. Many firms have pension funds that have fixed dollar obligations to their retirees. For financial purposes, firms must estimate the present value of these obligations to determine how much they truly owe their retirees. What happens to the value of these obligations as interest rates fall? Why?