Analysis:

The NPV is a negative value, indicating that the project is not expected to generate a profit in the long run, and may not align with the company's financial goals.

Based on the NPV calculation, Zelo Corporation should not undertake the project. The investment is not expected to yield a return that exceeds the discount rate, and would not be considered a profitable investment.$$

Explanation:

Net Present Value $($NPV$)$: is a financial metric that compares the present value of a project's future cash flows to the initial investment. A positive NPV indicates that the project is likely to be profitable, while a negative NPV suggests it may not be profitable.$$

The Time Value of Money $($TVM$)$ is the concept that a sum of money is worth more today than in the future, due to its potential earning capacity. TVM is used in NPV calculations to account for the fact that future cash flows are not worth as much as current cash flows.$$

When Zelo Corporation considers the TVM concept, they are essentially recognizing that the $$25,000$ annual cash inflows over $5$ years are not as valuable as the $$100,000$ investment made today. The NPV calculation demonstrates that the present value of the future cash inflows is less than the initial investment, meaning the project is not expected to be profitable.$$

Reasoning:

Financial Goals:

Zelo Corporation should prioritize investments that align with their financial goals. By analyzing the NPV$,$ the company can assess whether a project is likely to generate a return that meets their financial requirements.$$

Opportunity Cost:

The TVM concept also helps Zelo Corporation consider the opportunity cost of investing in this project. The money invested in this project could potentially be used for other projects or investments that could yield a higher return.$$

Decision$-$Making:

The NPV calculation provides a clear and objective basis for making financial decisions. By understanding the potential profitability of a project, Zelo Corporation can make more informed decisions about their investment strategies.$$

Decision$-$Making Guidance $($Deciding betwee

n Lump Sum and Annuity$)$:

The TVM concept is crucial when deciding between a lump sum payment and an annuity $($a series of payments over time$).$