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:
|
Present Value |
Interest Rate |
# Years |
Future Value |
| Example: |
$10,000 |
7.5% |
20 |
$ 42,479 |
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| a. |
$10,000 |
5.0% |
20 |
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| 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 (starting at the beginning of next year). Assuming a discount rate of 8% calculate the present value of your expected winnings.
a. Enter and/or calculate the cells highlighted in yellow (as an example, Year 1 has been calculated):
| Year |
Annual Payment |
Present Value Factor (PVF) |
Present Value (PV) |
| 0 |
|
|
$ 9,259 |
| 1 |
$10,000 |
0.926 |
$ 9,259 |
| 2 |
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| 9 |
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| 10 |
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b. "Use the PV function of Excel to calculate the present value.
To use this function (which is already entered in the green cell below), indicate the rate (""RATE""), number of periods (""NPER"") and the annual payment (""PMT"") by entering these amounts in the cells highlighted in yellow as indicated below. (As a check, the two calculations from parts a and b should be identical.):"
Problem 3
Calculate the following (assume all payments are made at the end of the year)
a. What is the value today of a $7,500 payment made in perpetuity assuming a 12% discount rate?
b. Assume the same perpetuity as above but the payments will not begin for another five years. What is the present value, today, of such a perpetuity?
c. Use the PV function within Excel to calculate the present value of a 5 year annuity which pays $7,500 per year (starting next year) and with an interest rate of 12%? (Note, as a check, your answer in part (a) minus your answer in part (b) should equal your answer in part (c).
Problem 4
Answer the following questions:
a. What is the relationship between the present value and time? Explain
b. What is the relationship between present value and the discount rate? Explain
Problem 5
"At the end of each year specified below you will be receiving the indicated payment. Assume a discount rate of 16%. What is the Present Value of each payment and what is the total Present Value of all three payments combined?
Year 1: $10,000
Year 2: $25,000
Year 3: $50,000"
Attachment:- Assignment TVM.xlsx