I have this problem with the solution.

I can't understand why in the problem, they didn't use as PV of the extruder 350000...

Please help...

Problem:

The XYZ Corporation is planning to purchase an extruder. The purchase price of the extruder is $350,000. The company plans to make a down payment of 25% of the first cost of the extruder and to make a 7-year, 10%, yearly payment loan for the rest of the first cost of the extruder. XYZ believes that the extruder can be sold for $75,000 at the end of its 15-year service life.

The new extruder will increase the company's annual income by $90,000. Maintenance and operating costs are expected to be $4,000 during the first year and to increase by $1,200 each year. XYZ uses a before-tax MARR of 12% for its preliminary economic studies.

What is the net present worth (NPW) of this investment to XYZ?

Solution:

P = $350,000. S = $75,000. M&O = $4,000. M&OG = $1,200.

Uniform Annual Benefit = $90,000

MARR = 12%.

Down Payment = 0.25 × 350,000 = $87,500.

Loan = 350,000 - 87,500 = $262,500.

Interest rate for the loan = 10%.

Loan Payments, A = 262,500 (A/P, 10%, 7) = 262,500 (0.2054) = $53,917.50.

NPW = Present Worth of Benefits - Present Worth of Costs

= {90,0000(P/A,12%,15) + 75,000(P/F,12%,15)}- {53,917.50 (P/A,12%,7) + 4,000(P/A,12%,15) + 1,200 (P/G, 12%,15) + 87,500 }

= {90,0000(6.811) + 75,000(0.1827)}- {53,917.50 (4.564)+ 4,000(6.811) + 1,200 (33.920) + 87,500}

= 626, 692.5 – 401,527.5 = $225,165.

The correct answer isanswer $225,165