$8.$ Individual Problems $5-6$

In early $2008,$ you purchased and remodeled a $120-$room hotel to handle the increased number of conventions coming to town. By mid$-2008,$ it became apparent that the recession would kill the demand for conventions. Now, you forecast that you will be able to sell only $10,000$ room$-$nights, which cost $$40$ per room per night to service. You spent $$25\mathrm{.}00$ million on the hotel in $2008,$ and your cost of capital is $20\%.$ The current going price to sell the hotel is $$20$ million.

If the estimated demand is $10,000$ room$-$nights, the break$-$even price is

$$per room, per night. $($Hint: Remember that the cost of capital is the opportunity cost, or true cost, of making an investment.$)$