Question

Kermit is considering purchasing a new computer system. The purchase price is $138,448. 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 $8,026 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 $76,239 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

"Given"

Purchase Price	$138,448.00
	Loan (1/4 of Purchase Price)	$34,612	=138448*(1/4)
	Int	10%	Compounded annually
	Loan time period (equal annual payments)	3
	Salvage Value	$8,026.00
	Useful Life	5
	Annual Maintenance Cost	20,000.00
	Savings due to increased efficiencies	$76,239.00
	MARR	12%

Purchase Price	$138,448.00
Borrowed amount	$34,612
Down payment	$103,836	=138448 - 34612
Equal payment	$13,918	=$ 34,612/(P/A,10%,3)
		=$ 34,612/(2.48685199098422)

Net Present Value calculation:

Present value	=-103,836-13,918(P/A,12%,3)-20,000(P/A,12%,5)+76,239(P/A, 12%,5)+8,026(P/F,12%,5)
	=-103,836-13,918(2.401831)-20,000(3.604776)+76,239(3.604776)+8,026(0.5674)
Net Present Value	$70,018.27

So the net present worth for this new computer system = $70018

Workings:

P/A,12%,3	P/A,12%,5	P/F,12%,5
=((1+0.12)^3-1)/(0.12*(1.12)^3)	=((1+0.12)^5-1)/(0.12*(1.12)^5)	=1/(1+0.12)^5
$2.401831	$3.604776	$0.5674

P/A,10%,3

=((1+0.10)^3-1)/(0.10*(1.10)^3)

$2.48685199098422