A hotel called the Lodge Hotel could be operated as it is or renovated. Calculate the NPV of both options. Incorporate tax implications and the risk and opportunities of high inflation.

The Lodge Hotel has been in operation for $13$ years and has a remaining useful life of $10$ years. The hotel is currently available for acquisition at a price of $$24$ million, and it is estimated that the hotel could be sold for $$30$ million after $10$ years. The projected annual net cash revenues from operating the hotel are as follows:

Year $1$: $$3,200,000$

Year $2$: $$3,400,000$

Year $3$: $$4,100,000$

Year $4-10$: $$4,600,000$ per year

The estimated annual operating expenses, including salaries, maintenance, utilities, and other costs, amount to $$1,400,000$ fixed, and a variable cost portion amounting at $10\%$ of net revenue. The hotel's tax rate is $21\%,$ and the required rate of return for the project is $12\%.$

To meet Luxury scale standards, LRH plans to invest $$18$ million in renovating and upgrading the hotel. The renovation is expected to take two years and be completed before the hotel commences operations. During the renovation period, there will be no cash inflows from the hotel. If they choose to renovate, it is estimated that the hotel could be sold for $$42$ million after $10$ years. Additionally, the useful life should they choose to renovate will be extended from $10$ years to $25$ years.

Once the hotel is operational, the projected net cash flows from operating the renovated Horizon Luxury Hotel are as follows:

Year $3$: $$5,500,000$

Year $4$: $$6,200,000$

Year $5-10$: $$6,500,000$ per year

The estimated annual operating expenses for the "new" Horizon Luxury Hotel amount to $$1,800,000$ fixed and $8\%$ variable cost portion. The tax rate and required rate of return for the project remain the same.

Additional Information:

a$)$ Depreciation: Straight$-$line depreciation will be used for both the existing hotel and the new hotel over their respective useful lives. Depreciation expense is calculated by dividing the initial investment $($purchase price plus renovation cost$)$ by the remaining useful life.

b$)$ Working Capital: An additional $$800,000$ investment in working capital is required for either option. This investment is expected to be fully recovered at the end of the project.

Required:

$(1)$ Calculate the Net Present Value $($NPV$)$ for both options $($operating the hotel as it is or renovating$)$ and recommend the most financially viable option.

$(2)$ Prepare a comprehensive report summarizing your analysis, including a comparison of the two options and your recommendation based on the NPV results.

$(3)$ Discuss the tax implications of your NPV analysis. How would the results be affected if there were no taxes?

$(4)$ Assess the risks and opportunities of the inflation rate increasing to $20\%$