Problem $1$:

$1.$An architectural design firm specializing in sustainable buildings is considering expanding its operations by acquiring a new office building. The firm aims to showcase its commitment to sustainability and innovation through this expansion. The new office is expected to not only serve as a workspace but also as a demonstration of the firm$$s architectural prowess and sustainable design principles.

Project Investment Details

Initial Investment: $$2,000,000($includes purchase price, renovations for sustainability improvements, and initial setup costs$)$

Project Life: $10$ years

Annual Cash Flows: The project is expected to generate varying annual cash flows from client projects, tours, and workshops on sustainable design, as follows:

Year $1$: $$200,000$

Year $2$: $$250,000$

Year $35$: $$300,000$ annually

Year $68$: $$350,000$ annually

Year $910$: $$400,000$ annually

Salvage Value: At the end of the project life, the firm plans to sell the building. The expected salvage value is $$500,000.$

Discount Rate: The firm uses an $8\%$ discount rate for NPV calculations.

Questions

a$.$ Calculate the Net Present Value $($NPV$)$ of the project. Is the project financially viable according to NPV criteria?

b$.$ Determine the Internal Rate of Return $($IRR$)$ of the project. How does the IRR compare with the firm$$s discount rate?

c$.$ Calculate the Payback Period of the project. Considering the uneven cash flows, how long will it take for the firm to recover its initial investment?

d$.$ Evaluate the project$$s financial attractiveness if the discount rate increases to $10\%.$ How does a change in the discount rate impact the NPV and IRR?