Mini Case $4\mathrm{.}3$ Consider a company that has two potential projects. The first is an investment in the

replacement machine for already existing technology in the firm. The machine belongs to an older

generation, so it is not very efficient or eco$-$friendly. The investment costs are $100.$ The project results

in the following cash flows over the next five years: t$0=100,$ t$1=80,$b t$3=0,$ t$4=0$

The alternative project is an investment in a machine with brand new technology. The project results in

losses within the next two years, as a lot needs to be invested, but it generates profits in the following: t$0=-200,$ t$1=-150,$ t$2=60,$ t$4=400.$

years. The investment costs are $190.$ The cash flows of this project are as follows:

Assume that the appropriate discount rate is $r=4\%.$

a$)$ Which of the two projects maximizes the value of the company?

b$)$ Consider a manager who receives a fixed compensation of $18$ per annual, but also receives an

additional $($positive$)$ compensation per annual based on the current year's profit. The bonus is

$2\%$ of the current profit. Which project would the manager choose at time t$0$ if she only wants

to stay with the company for the next two years $($until the end of $t2)?$

c$)$ The shareholders think about changing the compensation system so that the manager gets an

additional compensation based on the net present value of the company paid out at the

beginning of the project. This additional compensation would be in addition to the

compensation package described in part $($b$).$

Assume that the manager only wants to stay with the company for the next $2$ years and the

firm's value stems only from the project. What percentage of the project's net present value

should the shareholders give to the manager, so that she decides to invest in the project that

maximizes the value of the company?