An annuity that goes on indefinitely is called a perpetuity. The payments of a perpetuity constitute a/an -Select- series. The equation is: PV of a perpetuity = PMT I A -Select- ✓stock with no maturity is an example of a perpetuity. Quantitative Problem: You own a security that provides an annual dividend of $155 forever. The security's annual return is 8%. What is the present value of this security? Round your answer to the nearest cent. $
An annuity that goes on indefinitely is called a perpetuity. The payments of a perpetuity constitute a/an -Select- series. The equation is: PV of a perpetuity = PMT I A -Select- ✓stock with no maturity is an example of a perpetuity. Quantitative Problem: You own a security that provides an annual dividend of $155 forever. The security's annual return is 8%. What is the present value of this security? Round your answer 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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![An annuity that goes on indefinitely is called a **perpetuity**. The payments of a perpetuity constitute a/an [Select] series. The equation is:
\[ \text{PV of a perpetuity} = \frac{\text{PMT}}{i} \]
A [Select] stock with no maturity is an example of a perpetuity.
**Quantitative Problem:** You own a security that provides an annual dividend of $155 forever. The security’s annual return is 8%. What is the present value of this security? Round your answer to the nearest cent.
\$ [Input box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d494b17-8b36-49e0-a6a1-3408f9cee0a7%2F7d376fa0-912e-4ce3-8cf9-bc40ec89e736%2Fh8picq5_processed.png&w=3840&q=75)
Transcribed Image Text:An annuity that goes on indefinitely is called a **perpetuity**. The payments of a perpetuity constitute a/an [Select] series. The equation is:
\[ \text{PV of a perpetuity} = \frac{\text{PMT}}{i} \]
A [Select] stock with no maturity is an example of a perpetuity.
**Quantitative Problem:** You own a security that provides an annual dividend of $155 forever. The security’s annual return is 8%. What is the present value of this security? Round your answer to the nearest cent.
\$ [Input box]
![### Analysis of Uneven, or Nonconstant, Cash Flows
Many financial decisions require the analysis of **uneven, or nonconstant, cash flows**. For example, stock dividends typically increase over time, and investments in capital equipment almost always generate uneven cash flows. The term cash flow (CFₜ) refers to cash flows, while payment (PMT) designates regular, constant cash flows coming at regular intervals.
#### Present Value of an Uneven Cash Flow Stream
The present value (PV) of an uneven cash flow stream is the sum of the present values (PVs) of the individual cash flows. The equation is:
\[
PV = \frac{CF_1}{(1 + I)^1} + \frac{CF_2}{(1 + I)^2} + \cdots + \frac{CF_N}{(1 + I)^N} = \sum_{t=1}^{N} \frac{CF_t}{(1 + I)^t}
\]
#### Future Value of an Uneven Cash Flow Stream
Similarly, the future value of an uneven cash flow stream is the sum of the future values (FVs) of the individual cash flows. Many calculators have an NFV key that lets you obtain the FV. However, if your calculator doesn't have a net future value (NFV) key, you can calculate the NFV as follows:
\[
NFV = NPV \times (1 + I)^N
\]
You can also find the interest rate of the uneven cash flow stream with a financial calculator by solving for the interest rate using the internal rate of return (IRR) key.
### Quantitative Problem
You own a security with the cash flows shown below:
- Cash Flow Timeline:
- Year 0: $0
- Year 1: $700
- Year 2: $350
- Year 3: $250
- Year 4: $300
If you require an annual return of 10%, what is the present value of this cash flow stream? Do not round intermediate calculations. Round your answer to the nearest cent.
\[ \$ \_\_\_ \]
In this timeline, the cash flows are represented as vertical lines at each year, where the height of the line corresponds to the amount of cash flow received in that year.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d494b17-8b36-49e0-a6a1-3408f9cee0a7%2F7d376fa0-912e-4ce3-8cf9-bc40ec89e736%2Fzujaphh_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of Uneven, or Nonconstant, Cash Flows
Many financial decisions require the analysis of **uneven, or nonconstant, cash flows**. For example, stock dividends typically increase over time, and investments in capital equipment almost always generate uneven cash flows. The term cash flow (CFₜ) refers to cash flows, while payment (PMT) designates regular, constant cash flows coming at regular intervals.
#### Present Value of an Uneven Cash Flow Stream
The present value (PV) of an uneven cash flow stream is the sum of the present values (PVs) of the individual cash flows. The equation is:
\[
PV = \frac{CF_1}{(1 + I)^1} + \frac{CF_2}{(1 + I)^2} + \cdots + \frac{CF_N}{(1 + I)^N} = \sum_{t=1}^{N} \frac{CF_t}{(1 + I)^t}
\]
#### Future Value of an Uneven Cash Flow Stream
Similarly, the future value of an uneven cash flow stream is the sum of the future values (FVs) of the individual cash flows. Many calculators have an NFV key that lets you obtain the FV. However, if your calculator doesn't have a net future value (NFV) key, you can calculate the NFV as follows:
\[
NFV = NPV \times (1 + I)^N
\]
You can also find the interest rate of the uneven cash flow stream with a financial calculator by solving for the interest rate using the internal rate of return (IRR) key.
### Quantitative Problem
You own a security with the cash flows shown below:
- Cash Flow Timeline:
- Year 0: $0
- Year 1: $700
- Year 2: $350
- Year 3: $250
- Year 4: $300
If you require an annual return of 10%, what is the present value of this cash flow stream? Do not round intermediate calculations. Round your answer to the nearest cent.
\[ \$ \_\_\_ \]
In this timeline, the cash flows are represented as vertical lines at each year, where the height of the line corresponds to the amount of cash flow received in that year.
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