Chrome Company is considering the purchase of a machine for $24,000 that would reduce operating costs by $4,000 per year for 8 years. The machine will have no salvage value (residual value) at the end of its 8-year useful life. The company's required rate of return is 11%. What is the net present value of the investment in the machine? (Select the answer that is
Chrome Company is considering the purchase of a machine for $24,000 that would reduce operating costs by $4,000 per year for 8 years. The machine will have no salvage value (residual value) at the end of its 8-year useful life. The company's required rate of return is 11%. What is the net present value of the investment in the machine? (Select the answer that is
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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![### Investment Analysis for Chrome Company: Net Present Value Calculation
**Scenario:**
Chrome Company is contemplating the acquisition of a machine costing $24,000. This machine is projected to reduce operating costs by $4,000 annually for a period of 8 years. It’s important to note that the machine will not have any salvage value (residual value) at the conclusion of its 8-year lifespan. The enterprise has set a required rate of return (discount rate) at 11%.
**Question:**
What is the net present value (NPV) of the investment in the machine?
**Given Data:**
- Initial Investment: $24,000
- Annual Operating Cost Savings: $4,000
- Useful Life: 8 years
- Salvage Value: $0
- Discount Rate: 11%
**Formula for Net Present Value (NPV):**
\[
\text{NPV} = \sum_{t=1}^{n} \frac{R_t}{(1 + r)^t} - C_0
\]
where:
- \( R_t \) = net cash inflow during the period t
- \( r \) = discount rate (11% or 0.11)
- \( t \) = number of time periods (years)
- \( C_0 \) = initial investment cost
**Calculation Process:**
1. Calculate the present value of the annual savings for each of the 8 years.
2. Sum the present values.
3. Subtract the initial investment cost from the sum of present values.
**Steps:**
1. Determine the present value factor for each year using the formula \[ \frac{1}{(1 + r)^t} \].
2. Multiply the annual savings by the present value factor for each year.
3. Sum the results to obtain the total present value of savings.
4. Subtract the initial investment to get the NPV.
**Detailed Explanation:**
To be provided on the educational platform, a step-by-step calculation would involve creating a table to display the present value factor for each year, the multiplication results of the factor and annual savings, and the final summation of these values.
---
**Graph/Diagram Explanation (if applicable):**
In this context, no graph or diagram is provided in the image. However, typically, educators might include a time-value-of-money table or a cash flow diagram to illustrate the process of determining the N](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7038cbde-5259-4f1b-ade8-fa8f6320a6eb%2F7b696cd2-9388-4022-bb04-2a7df81c3cfc%2Fxrj5on_processed.png&w=3840&q=75)
Transcribed Image Text:### Investment Analysis for Chrome Company: Net Present Value Calculation
**Scenario:**
Chrome Company is contemplating the acquisition of a machine costing $24,000. This machine is projected to reduce operating costs by $4,000 annually for a period of 8 years. It’s important to note that the machine will not have any salvage value (residual value) at the conclusion of its 8-year lifespan. The enterprise has set a required rate of return (discount rate) at 11%.
**Question:**
What is the net present value (NPV) of the investment in the machine?
**Given Data:**
- Initial Investment: $24,000
- Annual Operating Cost Savings: $4,000
- Useful Life: 8 years
- Salvage Value: $0
- Discount Rate: 11%
**Formula for Net Present Value (NPV):**
\[
\text{NPV} = \sum_{t=1}^{n} \frac{R_t}{(1 + r)^t} - C_0
\]
where:
- \( R_t \) = net cash inflow during the period t
- \( r \) = discount rate (11% or 0.11)
- \( t \) = number of time periods (years)
- \( C_0 \) = initial investment cost
**Calculation Process:**
1. Calculate the present value of the annual savings for each of the 8 years.
2. Sum the present values.
3. Subtract the initial investment cost from the sum of present values.
**Steps:**
1. Determine the present value factor for each year using the formula \[ \frac{1}{(1 + r)^t} \].
2. Multiply the annual savings by the present value factor for each year.
3. Sum the results to obtain the total present value of savings.
4. Subtract the initial investment to get the NPV.
**Detailed Explanation:**
To be provided on the educational platform, a step-by-step calculation would involve creating a table to display the present value factor for each year, the multiplication results of the factor and annual savings, and the final summation of these values.
---
**Graph/Diagram Explanation (if applicable):**
In this context, no graph or diagram is provided in the image. However, typically, educators might include a time-value-of-money table or a cash flow diagram to illustrate the process of determining the N
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