Question

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

Answer 1

Present Worth of the given series of Payments would be $2,988.43.

Step-by-step 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.