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13 September, 17:50

You spend $1,000 on new equipment for your manufacturing company. Given that the interest rate is 5%, and you earn the following benefits, compute the Present Worth of the following series of payments.

Year Benefit ($)

1 500

2 600

3 700

4 800

5 900

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Answers (1)
  1. 13 September, 18:09
    0
    Present Worth of the given series of Payments would be $2,988.43.

    Explanation:

    C₁ = $500

    C₂ = $600

    C₃ = $700

    C₄ = $800

    C₅ = $900

    r = 5% = 0.05

    n₁ = 1

    n₂ = 2

    n₃ = 3

    n₄ = 4

    n₅ = 5

    PV₁ = ?

    PV₂ = ?

    PV₃ = ?

    PV₄ = ?

    PV₅ = ?

    PV₁ = C₁ / (1 + r) ⁿ₁

    PV₁ = 500 / (1 + 0.05) ¹

    PV₁ = $476.19

    PV₂ = C₂ / (1 + r) ⁿ₂

    PV₂ = 600 / (1 + 0.05) ²

    PV₂ = $544.22

    PV₃ = C₃ / (1 + r) ⁿ₃

    PV₃ = 700 / (1 + 0.05) ³

    PV₃ = $604.69

    PV₄ = C₄ / (1 + r) ⁿ₄

    PV₄ = 800 / (1 + 0.05) ⁴

    PV₄ = $658.16

    PV₅ = C₅ / (1 + r) ⁿ₅

    PV₅ = 900 / (1 + 0.05) ⁵

    PV₅ = $705.17

    Now add all the present values of Cash Flows, we get;

    PV₁ + PV₂ + PV₃ + PV₄ + PV₅

    = $476.19 + $544.22 + $604.69 + $658.16 + $705.17

    = $2,988.43

    Hence the Present Values of all the Cash Flows is $2,988.43 which is more than the Investment of $1,000. So the new equipment for manufacturing company should be purchased.
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