A medium$-$sized firm is considering outsourcing its logistics operations to an external manager. The manager$$s efforts to optimize costs and performance are not directly observable by the firm, leading to a potential shirking problem. To mitigate this risk, the firm can invest in monitoring software that tracks the manager$$s activities.$$

$$ The cost of the monitoring software is $$160,000$ per year.

$$ Without monitoring, the firm estimates that the manager has a $30\%$ probability of shirking, which would result in a $15\%$ reduction in the division's annual profit.

$$ With the monitoring software in place, the probability of shirking reduces to $10\%.$

$$ The division$$s annual profit is $$4$ million.

Should the firm invest in the monitoring software? What is the net benefit of implementing the monitoring software?

a$.$ No; $-$$$40,000$

b$.$ Yes; $$30,000$

c$.$ Yes; $$40,000$

d$.$ Yes; $$20,000$

e$.$ No; $-$$$30,000$