For my exmaple, we have machine A with an initial cost of 15K and O&M of 2k per year for the next 4 years. After 4 years, the O&M rise to $2.7k per year. No salvage value and life span of 20 years. 10% interest. What's the present worth of machine A?
It is easier for me to understand the problem by first stating that all cost out of pocket is negative. Since we do not have any salvage value in this problem, it will all be negative.
Here are my thoughts:
The cost of purchase the machine is out of pocket. 2k per year of O&M for first 4 year, at an uniform rate which is annual. 2.7k after the 4 years.
My equation came out to :
Present (A) = -15k - 2k (P/A, 10%, 4) - 2.7k (P/A, 10%, 16)
However at the solution, they added one more variable that I do not understand why.
Present (A) = 15k + 2k (P/A, 10%, 4) + 2.7k (P/A, 10%, 16) * (P/F,10%,4)
Please explain to me why do we need the last part (P/F,10%,4)? to get the present value of machine A.