Question

You are working on an assembly line and you want to find out how confident by 90% that the project will be a good investment? The MARR is 12%. Optimistic Most Likely Pessimistic Initial Cost $40,000 $32,000 $49,000 Annual Cost $17,000 $24,000 $25,000 Annual Revenue $30,000 $37,000 $35,000 Salvage Value (PV) $8,000 $5,000 $5,000 Life Cycle 25 years 15 years 15 years Probablity 65% 75% 55%

Answer 1

ANSWER

Present Worth of optimistic project is

PW₁ = -40000-17000*(P/A, 12%,25)+8000*(P/F,12%, 25) +30000*(P/F,12%, 25) = -40000-17000*7.843+8000*.0588+30000*.0588 (From Annuity table for discrete compounding)

        = -$171096.6

The probability rate of optimistic project = 65%

Therefore, the expected PW₁ = -171096.6*65/100= -$111212.79

Similarly present worth of most likely project is

PW₂ = -32000-24000*(P/A, 12%,15)+5000*(P/F,12%, 15) +37000*(P/F,12%, 15) = -32000-24000*6.811+5000*.1827+37000*.1827

                = -$187790.6

Probability rate of most likely project = 75%

expected PW₂ = -187790.6*75/100=-$140842.95

& present worth of pessimistic project is

PW₃ = -49000-25000*(P/A, 12%,15)+5000*(P/F,12%, 15) +35000*(P/F,12%, 15) = -49000-25000*6.811+5000*.1827+35000*.1827

                 = -$211967

Probability rate of pessimistic project = 55%

expected PW₃ = -211967*55/100=-$116581.85

As expected PW₁ value is highest, the optimistic project should be a good investment.

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