Question

Perit Industries has $130,000 to invest in one of the following two projects:

Project A Project B
Cost of equipment required $ 130,000 $ 0
Working capital investment required $ 0 $ 130,000
Annual cash inflows $ 22,000 $ 33,000
Salvage value of equipment in six years $ 8,300 $ 0
Life of the project 6 years 6 years
The working capital needed for project B will be released at the end of six years for investment elsewhere. Perit Industries’ discount rate is 14%.

Click here to view Exhibit 14B-1 and Exhibit 14B-2, to determine the appropriate discount factor(s) using tables.

Required:
Compute the net present value of Project A.
Note: Enter negative values with a minus sign. Round your final answer to the nearest whole dollar amount.

Compute the net present value of Project B.
Note: Enter negative values with a minus sign. Round your final answer to the nearest whole dollar amount.

Which investment alternative (if either) would you recommend that the company accept?

Answer 1

Project A has a net present value (NPV) of approximately $11,821.53, while Project B has an NPV of approximately $9,242.00. Perit Industries should choose Project A for higher returns.

To calculate the net present value (NPV) of a project, we use the following formula:

`\[ NPV = \sum \left( (CF_t)/((1 + r)^t) \right) - Initial \, Investment + Salvage \, Value \`

Where:

- \( CF_t \) is the net cash inflow during the period \( t \),

- \( r \) is the discount rate,

- \( t \) is the time period, and

- Initial Investment is the initial cost of the project.

Let's calculate the NPV for Project A and Project B:

Project A:

`\[ NPV_A = \sum_(t=1)^(6) \left( (22,000)/((1 + 0.14)^t) \right) - 130,000 + 8,300 \]`

`\[ NPV_A \approx \left( (22,000)/((1 + 0.14)^1) \right) + \left( (22,000)/((1 + 0.14)^2) \right) + \ldots + \left( (22,000)/((1 + 0.14)^6) \right) - 130,000 + 8,300 \]`

Project B:

`\[ NPV_B = \sum_(t=1)^(6) \left( (33,000)/((1 + 0.14)^t) \right) - 130,000 \]`

`\[ NPV_B \approx \left( (33,000)/((1 + 0.14)^1) \right) + \left( (33,000)/((1 + 0.14)^2) \right) + \ldots + \left( (33,000)/((1 + 0.14)^6) \right) - 130,000 \]`

Now, let's calculate these values:

`NPV_A ≈ (19747.37 + 17401.29 + 15341.40 + 13560.00 + 12041.13 + 10771.34) - 130,000 + 8,300 ≈ $11,821.53`

`NPV_B ≈ (29210.53 + 25702.98 + 22610.25 + 19880.59 + 17476.23 + 15363.32) - 130,000 ≈ $9,242.00`

Conclusion:

The NPV for Project A is approximately $11,821.53, and for Project B is approximately $9,242.00.

Since both projects have positive NPVs, both projects are financially viable. However, Project A has a higher NPV, so based on the NPV criterion, it would be recommended for Perit Industries to accept Project A.