A 50-room motel is for sale in Houston and is being considered by the Lone Star Motel Chain as an investment. The current owners indicate that the occupancy of the motel averages 80 percent each day of the year that the motel is open. The motel is open 300 days per year. Each room
rents for $$\$ 75$$ per day, and variable cash operating costs are $$\$ 10$$ per day that the room is occupied. Fixed annual cash operating costs are $$\$ 100,000$$.
An acquisition price of $$\$ 2,000,000$$ is being offered by Lone Star. The chain plans on keeping the motel for 14 years and then disposing of it. Because the market for motels is so difficult to predict, Lone Star estimates the salvage value to be zero at the time of disposal. Depreciation will be taken on a straightline basis for tax purposes. In making the following computations, assume that there will be no tax consequences of the sale in 14 years. The chain's tax rate is estimated at 35 percent for all years.
a. Determine the after-tax net present value of the motel to Lone Star, assuming a cost of capital rate of 13 percent.
b. What is the highest level that the discount rate can be and still allow this project to be considered acceptable by Lone Star? If this discount rate exceeds the highest rate shown in the table ( 20 percent), simply state this fact and provide supporting computations and reasons.
c. How small can the net after-tax cash flows be and still allow the project to be considered acceptable by Lone Star, assuming a cost of capital rate of 13 percent?
d. What is the shortest number of years for which the net after-tax cash flows can be received and still have the project be considered acceptable?
e. Assume that the answer to part (c) is $$\$ 217,425$$. If all costs remain as they are currently stated and the motel continues to stay open 300 days per year, approximately how many rooms would have to be rented each night to achieve this level of cash flows?