Problem 1
Below you are presented with a series of present and future values, annual compounding interest rates and the number of years between the present and future values. For each set of values calculate the missing term (highlighted in yellow):
| |
Present Value
|
Interest Rate
|
# Years
|
Future Value
|
|
Example:
|
$10,000
|
7.5%
|
20
|
$ 42,479
|
| |
|
|
|
|
|
a.
|
$10,000
|
5.0%
|
20
|
|
|
b.
|
$10,000
|
10.0%
|
20
|
|
|
c.
|
|
8.0%
|
5
|
$ 50,000
|
|
d.
|
|
8.0%
|
10
|
$ 50,000
|
|
e.
|
$25,000
|
|
5
|
$ 50,000
|
Problem 2
You won a lottery which pays $10,000 per year for 10 years (at the end of each year). Assuming a discount rate of 8% calculate the present value of your expected winnings. Enter and/or calculate the cells highlighted in yellow:
Use the PV function of Excel to calculate the present value. Confirm that this is the same as your above calculation. (Note, the output of Excel's PV function is negative so you'll need to put a negative sign in front of it.)
Problem 3
Calculate the following (assume all payments are made at the end of the year)
What is the value today of a $10,000 payment made in perpetuity assuming a 8% discount rate?
Assume the same perpetuity as above but the payments will not begin for another five years. What is the present value of such a perpetuity?
What is the present value of a 5 year annuity which pays $10,000 per year and with an interest rate of 8%?
Problem 4
What is the relationship between the present value and time? Explain
What is the relationship between present value and the discount rate? Explain
Problem 5
You are told you will receive the following cash payments at the end of the next three years:
Year 1: $10,000
Year 2: $25,000
Year 3: $50,000
Assuming a discount rate of 12%, what is present value of all payments?