## 7.6 Exercises

(***): A company is considering investing in new cloud storage equipment for their on-premises data center. The initial investment is $500,000 and the revenue from selling the cloud-based storage is expected to generate the following cash flows over the next four years: $125,000 (year 1), $145,000 (year 2), $165,000 (year 3), and $190,000 (year 4). The interest rate is 8%. However, there is a potential regulatory change that could increase the cost of capital to 10% starting in year 3. To account for this uncertainty, you are required to calculate the NPV under two scenarios: (1) The interest rate remains constant at 8% throughout the project’s life and (2) the interest rate changes to 10% starting in year 3 (i.e., 8% for year 1 and 2, 10% for year 3 and 4). Show your work in a way that demonstrates your understanding of the NPV formula and the effect of changing discount rates on cash flow projections. Based on your calculations, recommend whether the company should proceed with the project under each scenario.*Data Center Cloud Storage*(***): A non-profit organization is considering a community development project that requires an upfront investment of $300,000. The project is expected to generate the following cash flows over the next five years: $50,000 (year 1), $70,000 (year 2), $90,000 (year 3), $100,000 (year 4), and $120,000 (year 5). However, due to the project’s nature, there are significant uncertainties around the timing and size of the cash flows. If the project is delayed, each cash flow will be received a year later, and the amount for each year might decrease by 10%. Given those uncertainties, you are asked to calculate the Internal Rate of Return (IRR) under two scenarios: (1) The cash flows are received as listed without delay and (2) the project is delayed by one year, and each cash flow decreases by 10%. Compare the IRRs of both scenarios and recommend whether the non-profit should proceed with the project under either condition. Discuss why the IRR may be a useful decision-making tool in this context, considering the project’s uncertainties.*Community Development Project*(***): A municipality is evaluating two alternative projects for road maintenance, each with different initial costs and lifespans. Project A requires an initial investment of $1,200,000 and has a lifespan of 8 years. Project B requires an initial investment of $800,000 and has a lifespan of 5 years. Both projects are expected to provide equivalent service levels, but the municipality has a limited budget and needs to determine which project offers the better value over time. The discount rate for both projects is 6%. You are helping the municipality by calculating the annualization factor (AF) for each project in order to compare their costs on an annualized basis. In a first step, calculate the AF for both projects. Next, use the AF to calculate the equivalent annual cost for each project. Now, suppose that unforeseen circumstances lead to project A’s lifespan being extended by 2 years (making it 10 years) without an additional initial investment, and project B’s lifespan being shortened by 1 year (making it 4 years). Recalculate the AF and EAC under these new conditions, and explain the implications of these changes for the municipality’s decision-making process. Show all steps in calculating the annualization factor, including how you derived it using the present value of annuities formula. Clearly outline your reasoning for determining the EAC, and describe how changes in the lifespan of a project affect its annualized cost, making specific reference to the trade-offs between lifespan and upfront investment.*Municipal Road Maintenance Investment*