For the above projects find the cross$-$over point, i$.$e$.$ the discount rate where NPV$$s are equal. Draw a rough draft of the two NPV profiles. Hint: figure out the NPV at a zero$-$discount rate. $$ At a discount rate of $12\%,$ which project$($s$)$ would you select? $$ At a discount rate of $20\%,$ which project$($s$)$ would you select? Bottom$-$straddle strategy.

$(10)$ Points The Big Company ${?}^{TM}$ is considering two pieces of machinery that perform the same repetitive task. The two

alternatives available provide the following set of after$-$tax net cash flows. Assuming a required rate of return of $10\%$ :

$(1)$ Calculate the NPV for each project.

$(2)$ Calculate the IRR for each project.

$(3)$ Calculate the uniform annual series $($UAS$)$ or the equivalent annual

annuity $($EAA$)$ for each project.

$(4)$ Compare the two projects using the replacement chain method $($i$.$e$.$ find

the replacement chain value$).$ Which project would you select?

$(5)$ Calculate the discounted payback. $($ii$)$ Convert this to a rate of return.

If the projects are mutually exclusive, and can be reproduced which

project do you select? Explain.