## [answered] A machine has the first cost of \$60K.

A machine has the first cost of \$60K.? The net annual savings (which depends on the volume of throughput) and the salvage value at the end of its 8-year economic life (which depends on the progress in related technology) are given below:

??????????????????????????????????????????????????????????????????????????????? Volume of throughput

??????????????????????????????????????????????????????????????? High?????????????????????? Medium???????????????? Low

Probability??????????????????????????? 0.3????????????????????????? 0.6????????????????????????? 0.1

Annual Savings AS????????????? \$30K????????????????????? \$20K????????????????????? \$10K

??????????????????????????????????????????????????????????????? Rate of technological progress

??????????????????????????????????????????????? Incremental????????????????????????? Revolutionary

??????????????? Probability??????????? 0.75??????????????????????????????????????? 0.25

??????????????? Salvage S????????????? \$9K??????????????????????????????????????? \$3K

Assume that the progress in technology and the level of throughput volume are independent, and MARR is 10%.

a)??? Write the probability distribution of EAW, then compute the expected EAW, the standard deviation of EAW and the probability the there will be a loss in this investment. You may first write down the following formula:

EAW(10%) =??????????????????????????..

Then fill in the following table:? (Note: (A/P, 10%, 8) = 0.1874; (A/F, 10%, 8) = 0.0874)

?

?Combination:

??????????????? AS (\$K)????????? S(\$K)????????????? Prob??????????? EAW (\$K)????? Prob*EAW??????????????? Prob*EAW2

??????????????? 30?????????????????? 9????????????????????? 0.225????????? 19,543?????????? 4,397????????????????????????? 85,304,473

??????????????? ____?????????????? ____?????????????? ____?????????? _____??????????? _______??????????????????? ________

??????????????? ____?????????????? ____?????????????? ____?????????? _____??????????? _______??????????????????? ________

??????????????? 20?????????????????? 3????????????????????? 0.015????????? 9,018????????????? 1353?????????????????????????? 12,199,190

??????????????? 10?????????????????? 9????????????????????? 0.075????????? -457??????????????? -34????????????????????????????? 15,691

??????????????? 10?????????????????? 3????????????????????? 0.025????????? -982??????????????? -25???????????????????????????? 24,098?????????????????? ???????? ????? ?????????????????????????????? ???????????Sum:????????????? _______??????? ________ ???????????????????????

??????????????? E(EAW) ???

??????????????? SD(EAW)

Is this a good investment based on your own return/risk trade-off? Why or why not?? If the distribution of PW is approximately normal, what is the probability of loss?? (Table of Standard Normal distribution is given.)

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