Question

A company is considering expanding their production capabilities with a new machine that costs $67,000 and has a projected lifespan of 9 years. They estimate the increased production will provide a constant $8,000 per year of additional income. Money can earn 1.8% per year, compounded continuously. Should the company buy the machine? $ _____ over the life of the machine

Answer 1

Answer:

I = 1.8% per year compounded continuously

n = 365 days

effective rate = (1 + i / n) ^ n - 1

er = (1 + 1.8% / 365) ^ 365 - 1

er = (1 + 0.000049315) ^ 365 - 1

er = (1.000049315) ^ 365 - 1

er = 1.0181625- 1

er = 0.0181625

er = 0.181625%

initial cost = $67000

n = 9 years

we need to find the present worth and if it is positive the company should buy the machine.

pw = initial cost + constant income(p/a,i,n)

pw = -67000 + 8000 (p/a,0.181625%,9)

pw = -67000+ 8000 * 8.9188

pw = -67000 + 71350.4

pw =$4350.4

since the pw of the machine is positive , therefore the company should purchase from the machine.