7/24/2019 Pop Quiz Solution

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EIN6357: Advanced Engineering Economy

POP QUIZ (will not be graded)

First Name:__________________________ Last Name:______________________

The folloing to !ro"ects are availa#le for investment over a 3 year !eriod $reven%eachieved in the !revio%s year is reinvested in the same !ro"ect&:

The first !ro"ect gives yo% an '() ret%rn on yo%r investment in the first year*

+() in the second year and +() in the third year* #%t re,%ires !aying a fee of -.(at the end of the third year/

The second !ro"ect gives yo% a .() ret%rn on yo%r investment each year* #%t

re,%ires !aying a fee of -5( at the end of the third year/

a& 0%!!ose that yo% initially have -1((/ 2o m%ch money ill yo% have at the end ofthe third year if yo% invest -1(( in the first !ro"ect 2o m%ch money ill yo% have

at the end of the third year if yo% invest -1(( in the second !ro"ect 4hich !ro"ecto%ld yo% !refer

At the end of the first year

project 1 gives !1""#(1$%"&)#(1$'"&)' !*" + !'1,-'

project ' gives !1""#(1$*"&). !/" + !''*-*

Project ' is preferred-

#& 4hat minimal initial investment is needed to !artici!ate in the first !ro"ect $find a#rea even !oint ass%ring that yo% ill #e a#le to !ay the fee at the end of the third

year& 4hat minimal initial investment is needed to !artici!ate in the second !ro"ect0%!!osing that yo% have only -17* hich of to !ro"ects o%ld yo% !refer

0et 1 and ' be initial brea2even invest3ents for projects 1 and '4

respectively-

5or project 14 1 is fo6nd fro3

1#(1$%"&)#(1$'"&)' *" + "4

1 + !1/-*

5or project '4 ' is fo6nd fro3

'#(1$*"&). /" + "4

1 + !1%-'

If !17 is initially available4 only the first project is preferred-