The Ocean City water park is considering the purchase of a new log flume ride. The cost to purchase the equipment is $3,500,000$ and it will cost an additional $250,000$ to have it installed. The equipment has an expected life of $6$ years, and it will be depreciated using a MACRS $7-$year class life. Management expects to run about $150$ rides per day, with each ride averaging $25$ riders. The season will last for $120$ days per year. In the first year, the ticket price per rider is expected to be $$4\mathrm{.}00,$ and it will be increased by $4\%$ per year. The variable cost per rider will be $$1\mathrm{.}40,$ and total fixed costs will be $$320,000$ per year. After six years, the ride will be dismantled at a cost of $$115,000$ and the parts will be sold for $$450,000.$ The cost of capital is $12\%,$ and its marginal tax rate is $35\%.$

a$)$ Calculate the initial outlay, annual after$-$tax cash flow for each year and the terminal cash flow.

b$)$ Calculate the NPV$,$ IRR, and MIRR of the new equipment. Is the project acceptable?

c$)$ Create a Data Table that shows NPV$,$ IRR, and MIRR for MACRS classes of $3,5,7,10,15$ and $20$ years. What do you conclude about the speed of depreciation and the profitability of an investment?

d$)$Using the Goal Seek tool, calculate the minimum ticket price that must be charged in the first year in order to make the project acceptable.