An auto manufacturer is considering adding new automation to their assembly line to reduce production costs. The manufacturer is confident that capital costs to get the new equipment "in service" will be $4,000,000, with a salvage value of $40,000 after a 9 year useful life. The manufacturer is less confident about the annual savings that will occur as a result of automation and cannot accurately assess the probability of the various outcomes. The manufacturer estimates the annual savings will be in the range of:
Pessimistic $460,000
Most likely $660,000
Optimistic $840,000
Required:
1. Using an MARR of 12%, and the Beta distribution, determine the mean NOW for the investment. Express your answer in $ to the nearest $1,000

Check the explanation

Explanation:

As per the beta distribution, the average revenue per year = (Pessimistic +4*Most Likely +Optimistic) / 6

Avg revenue per year = (460000 + 4*660000 + 840000) / 6 = 656666.67

MARR = 12%, life = 9 yrs

NPW = -4000000 + 656666.67 * (P/A,12%,9) + 40000 * (P/F,12%,9)

= -4000000 + 656666.67 * 5.32824 + 40000 * 0.36061

= 7498877.6+14424.4

= -433415.60

= -433000 (nearest 1000)

-6410000 (nearest 1000)

Explanation:

For the beta distribution, the average revenue per year =              (Pessimistic +4*Most Likely +Optimistic) / 6

Avg revenue per year = (460000 + 4*660000 + 840000) / 6 = 656666.67

MARR = 12%, life = 9 yrs

NPW = -4000000 + 656666.67 * (P/A,12%,9) + 40000 * (P/F,12%,9)

= -4000000 + 656666.67 * 5.32824 + 40000 * 0.36061

= -6409511.847

= -6410000 (nearest 1000)

d. all of the above are true.