The Empire Hotel is a full$-$service hotel in a large city. Empire is organized into three departments that are treated as investment centers. Budget information for the coming year for these three departments is shown as follows. The managers of each of the departments are evaluated and bonuses are awarded each year based on ROI.

Empire Hotel

Hotel Rooms Restaurants Health Spa

Average investment $ $8,219,000$ $ $4,827,000$ $ $1,212,000$

Sales revenue $ $10,000,000$ $ $2,000,000$ $ $600,000$

Operating expenses $8,729,0001,407,000498,000$

Operating earnings $ $1,271,000$ $

$593,000$

$ $102,000$

Required:

a$.$ Compute the ROI for each department. Use the DuPont method to analyze the return on sales and capital turnover.

Assume the Health Spa is considering installing new exercise equipment. Upon investigating, the manager of the division finds that the equipment would cost $$40,000$ and that operating earnings would increase by $$8,000$ per year as a result of the new equipment.

b$-1.$ What would be the ROI of investment in the new exercise equipment and Health Spa?

b$-2.$ Would the manager of the Health Spa be motivated to undertake such an investment?

c$-1.$ Compute the residual income for each department if the minimum required return for the Empire Hotel is $17$ percent.

c$-2.$ What would be the impact of the investment on the Health Spa's residual income?