What is the present value of a cash flow stream of $1,000 per year annually for 18 years that then grows at 5.0 percent per year forever when the discount rate is 11 percent? Note: Round intermediate calculations and final answer to 2 decimal places. Present value _
What is the present value of a cash flow stream of $1,000 per year annually for 18 years that then grows at 5.0 percent per year forever when the discount rate is 11 percent? Note: Round intermediate calculations and final answer to 2 decimal places. Present value _
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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![**Present Value Calculation of a Growing Cash Flow Stream**
In this example, we are tasked with determining the present value of a cash flow stream that begins at $1,000 per year for 18 years and then grows at a rate of 5.0% per year indefinitely. The discount rate provided is 11%.
**Problem Statement:**
What is the present value of a cash flow stream of $1,000 per year annually for 18 years that then grows at 5.0 percent per year forever when the discount rate is 11 percent?
**Instructions:**
Note: Round intermediate calculations and final answer to 2 decimal places.
**Calculation Worksheet:**
- Input Box:
- Label: Present value
- Input Field: User to enter their calculated present value
**Explanation:**
1. Calculate the present value of the fixed cash flows for the first 18 years.
2. Calculate the present value of the perpetuity starting in year 19, where the cash flow grows at 5.0% per year.
3. Sum these two present values to get the total present value of the cash flow stream.
Recommended formulas and steps for this calculation are primarily based on present value calculations for both a finite series of cash flows and a growing perpetuity.
**Formulae to Use:**
1. Present Value of an Annuity:
\[
PV_{\text{annuity}} = \frac{C \left(1 - (1 + r)^{-n}\right)}{r}
\]
Where:
- \( C \) = Cash flow per period
- \( r \) = Discount rate
- \( n \) = Number of periods
2. Present Value of a Growing Perpetuity starting after \( n \) periods:
\[
PV_{\text{perpetuity}} = \frac{C \times (1 + g)}{r - g} \times \frac{1}{(1 + r)^n}
\]
Where:
- \( C \) = Initial cash flow
- \( r \) = Discount rate
- \( g \) = Growth rate
- \( n \) = Number of periods after which perpetuity starts
After calculating the respective present values, sum them to get the total present value of the cash flow stream.
**Visualization:**
Although there are no graphs or diagrams in this content,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F816cc47c-f059-4914-940d-8196a7c7af6b%2Fe5982236-8d87-475c-94ea-8085a30a33ff%2F7bto3n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Present Value Calculation of a Growing Cash Flow Stream**
In this example, we are tasked with determining the present value of a cash flow stream that begins at $1,000 per year for 18 years and then grows at a rate of 5.0% per year indefinitely. The discount rate provided is 11%.
**Problem Statement:**
What is the present value of a cash flow stream of $1,000 per year annually for 18 years that then grows at 5.0 percent per year forever when the discount rate is 11 percent?
**Instructions:**
Note: Round intermediate calculations and final answer to 2 decimal places.
**Calculation Worksheet:**
- Input Box:
- Label: Present value
- Input Field: User to enter their calculated present value
**Explanation:**
1. Calculate the present value of the fixed cash flows for the first 18 years.
2. Calculate the present value of the perpetuity starting in year 19, where the cash flow grows at 5.0% per year.
3. Sum these two present values to get the total present value of the cash flow stream.
Recommended formulas and steps for this calculation are primarily based on present value calculations for both a finite series of cash flows and a growing perpetuity.
**Formulae to Use:**
1. Present Value of an Annuity:
\[
PV_{\text{annuity}} = \frac{C \left(1 - (1 + r)^{-n}\right)}{r}
\]
Where:
- \( C \) = Cash flow per period
- \( r \) = Discount rate
- \( n \) = Number of periods
2. Present Value of a Growing Perpetuity starting after \( n \) periods:
\[
PV_{\text{perpetuity}} = \frac{C \times (1 + g)}{r - g} \times \frac{1}{(1 + r)^n}
\]
Where:
- \( C \) = Initial cash flow
- \( r \) = Discount rate
- \( g \) = Growth rate
- \( n \) = Number of periods after which perpetuity starts
After calculating the respective present values, sum them to get the total present value of the cash flow stream.
**Visualization:**
Although there are no graphs or diagrams in this content,
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