Question

"A manufacturing company is considering a new investment in a machine that will cost $173,000 and has a maintenance cost of $5,700 that occurs every 2 years starting at the end of year 2. Assuming that this equipment will last infinitely under these conditions, what is the capitalized equivalent cost of this investment at the rate of 13.3%? Enter your answer as a positive number."

Answer 1

The question clearly states that the present investment for the project is $173,000 and the maintenance cost biennially is $5700. The yearly rate is given as 13.3% or 0.133

Since the rate is on per year basis, we’ll have to convert it two per 2 years interest rate. We’ll do this using Effective Annual Rate method.

Effective annual rate (EIR) = [1+(Rate/no of compounding periods)]^{no of compounding periods}

EIR = 0.133 = [1+(R/2)]²

R = 0.1288 = 12.88%

Now, we’ll find the Capitalized equivalent cost of the investment. This case entails an initial investment followed by biennial maintenance cost of $5700.

Present value of Annuity (maintenance cost) = 5700/0.1288 = $44,254.66

Present value of Initial investment = $173,000

Total equivalent cost = $173,000 + $44,254.66 = $217,254.66