Question

You have created a novel reusable water bottle filtration system. When presenting it to the client, you have decided to do a present value/ present worth analysis, over 5 years with an interest rate of 20%. It includes a rebuild cost (representing the filter replacement) of $33 at year 4. Please assume all costs are positive and all benefits are negative.

a. What is the present value/present worth of the rebuild (filter replacement)?

Answer 1

Solution

Back-up Theory

Given the interest rate of r% or equivalently i in decimal form [i.e., r = 10% => i = 0.1], the discounting factor for the nth year hence = 1/(1 + i)ⁿ ..................................................................... (1)

Present value of a return P in nth year hence = P_n = P x {1/(1 + i)ⁿ}.................................................... (2)

Now to work out the solution,

In the given scenario, P = 33, n = 4 and r = 20 or i = 0.2

So, vide (2),

present value/present worth of the rebuild (filter replacement)

= 33/1.2⁴

= 33/2.0736

= 15.91.

Thus, present value/present worth of the rebuild (filter replacement) = $15.91 Answer

DONE