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.)