Problem $7-38.$ Intercontinental has several hotels and resorts in the South Pacific. For one of these hotels, management expects occupancy rates to be $95\%$ in December, January, and February; $85\%$ in November, March, and April; and $70\%$ the rest of the year. This hotel has $300$ rooms and the average room rental is $$250$ per night. Of this, on average $10\%$ is received as a deposit the month before the stay, $60\%$ is received in the month of the stay, and $28\%$ is collected the month after. The remaining $2\%$ is never collected.

Most of the costs of running the hotel are fixed. The variable costs are only $$30$ per occupied room per night. Fixed salaries $($including benefits$)$ run $$400,000$ per month, depreciation is $$350,000$ a month, other fixed operating costs are $$120,000$ per month, and interest expense is $$600,000$ per month. Variable costs and salaries are paid in the month they are incurred, depreciation is recorded at the end of each quarter, other fixed operating costs are paid as incurred, and interest is paid semi$-$annually cach June and December.

Prepare a monthly cash budget for this Intercontinental hotel for the entire ycar. For simplicity, assume that there are $30$ days in each month.

How much would the hotel's amnal profit increase if oceupancy rate increased by $5\%$ during the off$-$season $($that is$,$ from $70\%$ to $75\%$ in each of the months from May$-$October$).$