4. (10 points) A machine has the first cost of $60K. The net annual savings (whi

Question

4. (10 points) 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 Volume of throughput 0.6 the progress in related technology) are given below Low 0.1 SIOK Medium High 0.3 Probability Annual Savings AS S30K S20K Rate of technological progress Revolutionary 0.25 S3K Incremental Probability 0.75 Salvage S S9K Assume that the progress in technology and the level of throughput volume are independent, and MARR is 10%. 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: E.411( 10%) = a) Then fill in the following table: (Note: (AP. 102. 8) 0.1874; (ME 10%, 8)-0.0874) Combination Prob EAW 85,304,473 30 0.225 19.543 4.397 20 0.15 0.075 457 0.025 -982 1353 34 9.018 12,199,190 15,691 24,098 10 Sum: E(EAW) = SDEAW)- distribution of PW is approximately normal, what is the probability of loss? (Table of Standard b) Is this a good investment based on your own return/tis trade off? Why or why not? If the Normal distribution is giyen.)

Explanation / Answer

Soln : Probability is being calculated in each case by taking case with high*incremental, high* revolutionary

EAW is calculated by using the formula = EAB-EAC

EAB = $30k and EAC = (initial cost-salvage value)*(A/P, 10%,8) + S*MARR

Please refer the table here for probability distribution

Standard deviation ,s can be calculated using excel formula STD(values) = 24.35%

Expected EAW = summation of column prob*EAW = $11.41k

(b) As we can see that expected EAW =11.41, it is more on positive side hemce, investment is worth in this case.

Annual Savings Salavage Value Prob EAW prob*EAW prob*EAW^2 30.00 9.00 0.2250 19.5426 4.3971 85.9305 30 3 0.075 19.0182 1.4264 27.1269 20 9.00 0.45 9.5426 4.2942 40.9775 20 3 0.15 9.0182 1.3527 12.1992 10 9.00 0.075 -0.4574 -0.0343 0.0157 10 3 0.025 -0.9818 -0.0245 0.0241 Sum 11.4115 166.2739

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