Question

Kermit is considering purchasing a new computer system. The purchase price is $112208. Kermit will borrow one-fourth of the purchase price from a bank at 10 percent per year compounded annually. The loan is to be repaid using equal annual payments over a 3-year period. The computer system is expected to last 5 years and has a salvage value of $6656 at that time. Over the 5-year period, Kermit expects to pay a technician $20,000 per year to maintain the system but will save $65760 per year through increased efficiencies. Kermit uses a MARR of 12 percent to evaluate investments. What is the net present worth for this new computer system?

Enter your answer in this format: 12345

Answer 1

ANSWER:

Initial cost = $112,208

Loan amount = 1/4 * 112,208 = $28,052

installment to be paid for 3 years = r * loan amount / (1 - (1 +r) ^ -n )

where r = 10% and n = 3 years

installment to be paid for 3 years = 10% * 28,052 / ( 1 - ( 1 + 10%) ^ - 3)

installment to be paid for 3 years = 2,805.2 / ( 1 - (1.1) ^ -3)

installment to be paid for 3 years = 2,805.2 / (1 - 0.7513)

installment to be paid for 3 years = 2,805.2 / 0.2486

installment to be paid for 3 years = $11,280.12

salvage value = $6,656

technician costs = $20,000

benefits = $65,760

pw of system = initial cost + installment to be paid(p/a,i,n) + salvage value(p/f,i,n) + technician costs(p/a,i,n) + benefits(p/a,i,n)

where i = 12% and n = 5 years and for installment it is 3 years and every cost apart from benefits and salvage value will be negative.

pw of system = -112,208 - 11,280.12(p/a,12%,3) + 6,656(p/f,12%,5) - 20,000(p/a,12%,5) + 65,760(p/a,12%,5)

pw of system = -112,208 - 11,280.12 * 2.402 + 6,656 * 0.5674 - 20,000 * 3.605 + 65,760 * 3.605

pw of system = -112,208 - 27,094.86 + 3,776.614 - 72,100 + 237,064.8

pw of system = $29,438.56