Question

A company that manufactures air-operated drain valve assemblies currently has $150,000 available to pay for plastic components over a 5-year period. If the company spent only $42,000 in year 1, what uniform annual amount can the company spend in each of the next 4 years to deplete the entire budget? Let i = 15% per year.

The uniform annual amount the company can spend is $?

Answer 1

The uniform annual amount is computed as follows:

Current Amount = Amount in year 1 / (1 + rate) + Uniform Annual Amount / (1 + rate)² + Uniform Annual Amount / (1 + rate)³ + Uniform Annual Amount / (1 + rate)⁴ + Uniform Annual Amount / (1 + rate)⁵

$ 150,000 = $ 42,000 / 1.15 + Uniform Annual Amount / 1.15² + Uniform Annual Amount / 1.15³ + Uniform Annual Amount / 1.15⁴ + Uniform Annual Amount / 1.15⁵

$ 150,000 - $ 36,521.73913 = Uniform Annual Amount / 1.15² + Uniform Annual Amount / 1.15³ + Uniform Annual Amount / 1.15⁴ + Uniform Annual Amount / 1.15⁵

$ 113,478.2609 = Uniform annual amount x 0.756143667 + Uniform annual amount x 0.657516232 + Uniform annual amount x 0.571753246 + Uniform annual amount x 0.497176735

$ 113,478.2609 = Uniform annual amount x (0.756143667 + 0.657516232 + 0.571753246 + 0.497176735)

$ 113,478.2609 = Uniform annual amount x 2.48258988

Uniform annual amount = $ 113,478.2609 / 2.48258988

Uniform annual amount = $ 45,709.6284