Question

A firm has installed a manufacturing line for packaging materials. The firm plans to produce 50 tons of packing peanuts at $5000 per ton annually for 4 years, and then 80 tons of packing peanuts per year at $5500 per ton for the next 6 years. What is the present worth of the expected income? The firm's interest rate is 18% per year.

(I used the NPV fuction on Excel and got an answer of $1,466,286.23, but I am not sure how to find this without using this function)

Answer 1

Cash flows from year 1 to 4: $5,000 x 50 = $250,000.

Cash flows from year 5 to 10: $5.500 x 80 = 440,000.

Present values:

Year 1 = 250,000/(1.18)^1 = 211,864.4

Year 2 = 250,000/(1.18)^2 = 179,546.1

Year 3 = 250,000/(1.18)^3 = 152,157.7

Year 4 = 250,000/(1.18)^4 = 128,947.2

Year 5 = 440,000/(1.18)^5 = 192,328.1

Year 6 = 440,000/(1.18)^6 = 162,989.9

Year 7 = 440,000/(1.18)^7 = 138,127

Year 8 = 440,000/(1.18)^8 = 117,056.8

Year 9 = 440,000/(1.18)^9 = 99,200.67

Year 10 = 440,000/(1.18)^10 = 84,068.37

Net Present Value (sum of) = $1,466,286..23

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