ash Flow $1,000 t Rate/Period 6% of Periods 5 Value using a Time Line 1 2 ws Value of Each Cash Flow
ash Flow $1,000 t Rate/Period 6% of Periods 5 Value using a Time Line 1 2 ws Value of Each Cash Flow
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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Question
![**Single Cash Flow: Present Value Calculation**
**Inputs:**
- **Single Cash Flow:** $1,000
- **Discount Rate/Period:** 6%
- **Number of Periods:** 5
---
**Present Value using a Time Line**
| Period | 0 | 1 | 2 | 3 | 4 | 5 |
|--------|---|---|---|---|---|---|
| Cash Flows | | | | | | |
| Present Value of Each Cash Flow | | | | | | |
| **Present Value** | | | | | | |
**Present Value using the Formula**
| **Present Value** | [Calculate Here] |
**Present Value using the PV Function**
| **Present Value** | [Calculate Here] |
---
**Explanation:**
This table helps calculate the present value of a single cash flow of $1,000 over 5 periods with a 6% discount rate. The present value can be calculated using either a time line, a mathematical formula, or the PV function in spreadsheet software.
1. **Using a Time Line:** Track the cash flow across 5 periods to determine the present value after discounting each period's cash flow.
2. **Using the Formula:** Apply the present value formula:
\[
PV = \frac{CF}{(1 + r)^n}
\]
where \( CF \) is the cash flow, \( r \) is the discount rate, and \( n \) is the number of periods.
3. **Using the PV Function:** Utilize the function available in software like Excel for quick calculation of present value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6ea49f2-aec0-47e4-ae21-0e0a47907cd1%2Fc8100f75-754b-469b-aef8-37c890b42eda%2Funib8dv_processed.png&w=3840&q=75)
Transcribed Image Text:**Single Cash Flow: Present Value Calculation**
**Inputs:**
- **Single Cash Flow:** $1,000
- **Discount Rate/Period:** 6%
- **Number of Periods:** 5
---
**Present Value using a Time Line**
| Period | 0 | 1 | 2 | 3 | 4 | 5 |
|--------|---|---|---|---|---|---|
| Cash Flows | | | | | | |
| Present Value of Each Cash Flow | | | | | | |
| **Present Value** | | | | | | |
**Present Value using the Formula**
| **Present Value** | [Calculate Here] |
**Present Value using the PV Function**
| **Present Value** | [Calculate Here] |
---
**Explanation:**
This table helps calculate the present value of a single cash flow of $1,000 over 5 periods with a 6% discount rate. The present value can be calculated using either a time line, a mathematical formula, or the PV function in spreadsheet software.
1. **Using a Time Line:** Track the cash flow across 5 periods to determine the present value after discounting each period's cash flow.
2. **Using the Formula:** Apply the present value formula:
\[
PV = \frac{CF}{(1 + r)^n}
\]
where \( CF \) is the cash flow, \( r \) is the discount rate, and \( n \) is the number of periods.
3. **Using the PV Function:** Utilize the function available in software like Excel for quick calculation of present value.
![### Present Value Calculation Example
1. A cash flow of $1,000.00 will be received in period 5. For this cash flow, the appropriate discount rate per period is 6.0%. What is the present value of this single cash flow? Use worksheet "Single-PV".
To find the present value (PV) of a future cash flow, you can use the formula:
\[ PV = \frac{FV}{(1 + r)^n} \]
Where:
- \( PV \) is the present value
- \( FV \) is the future value ($1,000.00 in this case)
- \( r \) is the discount rate per period (0.06 in this case)
- \( n \) is the number of periods (5 in this case)
By substituting the given values:
\[ PV = \frac{1000}{(1 + 0.06)^5} \]
Calculate this to find the present value of the cash flow. Use the "Single-PV" worksheet for detailed steps and calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6ea49f2-aec0-47e4-ae21-0e0a47907cd1%2Fc8100f75-754b-469b-aef8-37c890b42eda%2Fnevqmil_processed.png&w=3840&q=75)
Transcribed Image Text:### Present Value Calculation Example
1. A cash flow of $1,000.00 will be received in period 5. For this cash flow, the appropriate discount rate per period is 6.0%. What is the present value of this single cash flow? Use worksheet "Single-PV".
To find the present value (PV) of a future cash flow, you can use the formula:
\[ PV = \frac{FV}{(1 + r)^n} \]
Where:
- \( PV \) is the present value
- \( FV \) is the future value ($1,000.00 in this case)
- \( r \) is the discount rate per period (0.06 in this case)
- \( n \) is the number of periods (5 in this case)
By substituting the given values:
\[ PV = \frac{1000}{(1 + 0.06)^5} \]
Calculate this to find the present value of the cash flow. Use the "Single-PV" worksheet for detailed steps and calculations.
Expert Solution
Step 1
Present value refer to the concept of determining the value of money on current date is comparatively more than it will be in the near future.
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