a. What is the present value of investment A at an annual discount rate of 21 percent? $(Round to the nearest cent.) b. What is the present value of investment B at an annual discount rate of 21 percent? $(Round to the nearest cent.) c. What is the present value of investment C at an annual discount rate of 21 percent? $(Round to the nearest cent.)
a. What is the present value of investment A at an annual discount rate of 21 percent? $(Round to the nearest cent.) b. What is the present value of investment B at an annual discount rate of 21 percent? $(Round to the nearest cent.) c. What is the present value of investment C at an annual discount rate of 21 percent? $(Round to the nearest cent.)
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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**Financial Calculations and Examples**
1. **Example 1 (circled 9)**:
\[ N = 5 \]
\[ I/Y = 21 \]
\[ PV = 35,690.77 \]
\[ PV = 32,185.83 \text{ PMT} = 11,000 \]
\[ PMT = 11,000 \]
\[ FV = 0 \]
2. **Example 2**:
\[
N = \frac{PV(0,21,5,11000,0)}{} \]
\[ N = 4 \]
\[ I/Y = 21 \]
\[ PV = 16,650.01 \]
\[ PMT = 0 \]
\[ PV = 35,690.77 \]
**Explanation:**
- **N**: Number of periods (typically years or months)
- **I/Y**: Interest rate per period
- **PV**: Present Value (initial investment)
- **PMT**: Payment made each period
- **FV**: Future Value (value at the end of the investment period)
These equations typically arise in scenarios involving loans, annuities, or investments, where individuals calculate the present or future value of a sum of money, given a specific interest rate and payment schedule.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ff6323c-cf7e-493a-b269-a8fbd92b416a%2Fd2c205a1-4471-47ee-ab1d-d5a8dbf491cc%2F0elrnya_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
**Financial Calculations and Examples**
1. **Example 1 (circled 9)**:
\[ N = 5 \]
\[ I/Y = 21 \]
\[ PV = 35,690.77 \]
\[ PV = 32,185.83 \text{ PMT} = 11,000 \]
\[ PMT = 11,000 \]
\[ FV = 0 \]
2. **Example 2**:
\[
N = \frac{PV(0,21,5,11000,0)}{} \]
\[ N = 4 \]
\[ I/Y = 21 \]
\[ PV = 16,650.01 \]
\[ PMT = 0 \]
\[ PV = 35,690.77 \]
**Explanation:**
- **N**: Number of periods (typically years or months)
- **I/Y**: Interest rate per period
- **PV**: Present Value (initial investment)
- **PMT**: Payment made each period
- **FV**: Future Value (value at the end of the investment period)
These equations typically arise in scenarios involving loans, annuities, or investments, where individuals calculate the present or future value of a sum of money, given a specific interest rate and payment schedule.
---
![### Present Value of Annuities and Complex Cash Flows
You are given three investment alternatives to analyze. The cash flows from these three investments are as follows:
**Investment Table:**
| End of Year | Investment A | Investment B | Investment C |
|-------------|--------------|--------------|--------------|
| 1 | $11,000 | - | $16,000 |
| 2 | $11,000 | - | - |
| 3 | $11,000 | - | - |
| 4 | $11,000 | - | - |
| 5 | $11,000 | $11,000 | $48,000 |
| 6 | $11,000 | $11,000 | - |
| 7 | $11,000 | $11,000 | - |
| 8 | - | $11,000 | - |
---
**Questions:**
a. What is the present value of investment A at an annual discount rate of 21 percent?
*(Round to the nearest cent.)*
$\_\_\_\__
b. What is the present value of investment B at an annual discount rate of 21 percent?
*(Round to the nearest cent.)*
$\_\_\_\__
c. What is the present value of investment C at an annual discount rate of 21 percent?
*(Round to the nearest cent.)*
$\_\_\_\__
---
Please ensure to calculate the present value of each cash flow for each investment, then sum these present values to get the total present value of the investment. Use the formula for present value:
\[ PV = \frac{CF}{(1 + r)^n} \]
where:
- \( PV \) = Present Value
- \( CF \) = Cash Flow in year \( n \)
- \( r \) = discount rate
- \( n \) = year
For example, for the first cash flow of Investment A in year 1, you would calculate:
\[ PV_1 = \frac{11,000}{(1 + 0.21)^1} \]
Continue this calculation for each cash flow and sum all the present values to get the total present value for each investment.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ff6323c-cf7e-493a-b269-a8fbd92b416a%2Fd2c205a1-4471-47ee-ab1d-d5a8dbf491cc%2Fm2qpwg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Present Value of Annuities and Complex Cash Flows
You are given three investment alternatives to analyze. The cash flows from these three investments are as follows:
**Investment Table:**
| End of Year | Investment A | Investment B | Investment C |
|-------------|--------------|--------------|--------------|
| 1 | $11,000 | - | $16,000 |
| 2 | $11,000 | - | - |
| 3 | $11,000 | - | - |
| 4 | $11,000 | - | - |
| 5 | $11,000 | $11,000 | $48,000 |
| 6 | $11,000 | $11,000 | - |
| 7 | $11,000 | $11,000 | - |
| 8 | - | $11,000 | - |
---
**Questions:**
a. What is the present value of investment A at an annual discount rate of 21 percent?
*(Round to the nearest cent.)*
$\_\_\_\__
b. What is the present value of investment B at an annual discount rate of 21 percent?
*(Round to the nearest cent.)*
$\_\_\_\__
c. What is the present value of investment C at an annual discount rate of 21 percent?
*(Round to the nearest cent.)*
$\_\_\_\__
---
Please ensure to calculate the present value of each cash flow for each investment, then sum these present values to get the total present value of the investment. Use the formula for present value:
\[ PV = \frac{CF}{(1 + r)^n} \]
where:
- \( PV \) = Present Value
- \( CF \) = Cash Flow in year \( n \)
- \( r \) = discount rate
- \( n \) = year
For example, for the first cash flow of Investment A in year 1, you would calculate:
\[ PV_1 = \frac{11,000}{(1 + 0.21)^1} \]
Continue this calculation for each cash flow and sum all the present values to get the total present value for each investment.
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