Consider the following cash flow: Year Cash Flow -$ 29,800 13,900 15,000 11,400 1 2 3 a). What is the profitability index for the cash flows if the relevant discount rate is 9 percent? b) what is the profitability index if the discount rate is 14 percent? c) What is the profitability index if the discount rate is 21 percent?
Consider the following cash flow: Year Cash Flow -$ 29,800 13,900 15,000 11,400 1 2 3 a). What is the profitability index for the cash flows if the relevant discount rate is 9 percent? b) what is the profitability index if the discount rate is 14 percent? c) What is the profitability index if the discount rate is 21 percent?
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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![**Consider the following cash flow:**
| Year | Cash Flow |
|------|------------|
| 0 | -$29,800 |
| 1 | $13,900 |
| 2 | $15,000 |
| 3 | $11,400 |
**Questions:**
a) What is the profitability index for the cash flows if the relevant discount rate is 9 percent?
b) What is the profitability index if the discount rate is 14 percent?
c) What is the profitability index if the discount rate is 21 percent?
---
The cash flow table represents the yearly cash inflows and outflows for a hypothetical investment. The initial investment (Year 0) is -$29,800, indicating an outflow, followed by inflows of $13,900 in Year 1, $15,000 in Year 2, and $11,400 in Year 3.
The profitability index (PI) is calculated by dividing the present value of future cash inflows by the initial investment outlay. The present value of future cash inflows depends on the selected discount rate.
- If the discount rate is 9%, the profitability index (PI) is calculated as follows:
\[
\text{PI} = \frac{\text{PV of future cash inflows}}{\text{Initial Investment}}
\]
- If the discount rate is 14%, the same formula applies, with the cash flows discounted at 14%.
- Similarly, for a discount rate of 21%, the cash flows need to be discounted at 21%.
By calculating the present values of the cash inflows for each discount rate and comparing them to the initial investment, we can obtain the profitability index for each scenario.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce618159-930e-4ade-8eed-109751c2dc39%2Ff6164886-c563-400d-8b05-79db73e12d53%2Flac5g9t.png&w=3840&q=75)
Transcribed Image Text:**Consider the following cash flow:**
| Year | Cash Flow |
|------|------------|
| 0 | -$29,800 |
| 1 | $13,900 |
| 2 | $15,000 |
| 3 | $11,400 |
**Questions:**
a) What is the profitability index for the cash flows if the relevant discount rate is 9 percent?
b) What is the profitability index if the discount rate is 14 percent?
c) What is the profitability index if the discount rate is 21 percent?
---
The cash flow table represents the yearly cash inflows and outflows for a hypothetical investment. The initial investment (Year 0) is -$29,800, indicating an outflow, followed by inflows of $13,900 in Year 1, $15,000 in Year 2, and $11,400 in Year 3.
The profitability index (PI) is calculated by dividing the present value of future cash inflows by the initial investment outlay. The present value of future cash inflows depends on the selected discount rate.
- If the discount rate is 9%, the profitability index (PI) is calculated as follows:
\[
\text{PI} = \frac{\text{PV of future cash inflows}}{\text{Initial Investment}}
\]
- If the discount rate is 14%, the same formula applies, with the cash flows discounted at 14%.
- Similarly, for a discount rate of 21%, the cash flows need to be discounted at 21%.
By calculating the present values of the cash inflows for each discount rate and comparing them to the initial investment, we can obtain the profitability index for each scenario.
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