Question

Audio engineers at 3XT2 have determined that an anechoic additive will increase isolation and improve signal to noise by about 20%. To prep the site for the adhesive, you have to prime it and that costs you $35K separate from the additive. You have arranged to purchase the additive with a 5-year contract at $7K per year, starting 1 year from now. The annual price will increase by 12% per year starting in the sixth year and thereafter through year 13. Evaluated at 15%, the sound improvement better result in a net present worth profit of how much to negate the costs?

Answer 1

The correct answer is $83230

Step-by-step explanation:

Solution

Given that:

The Present worth of geometric series is shown below

= A *[1 - (1+g)^n /(1+i)^n] / (i-g)

Now,

The present cost of worth from EOY 5 to EOY 13 at EOY 4 = 7000 *[1 - (1+0.12)^9 /(1+0.15)^9] / (0.15-0.12)

Thus,

= 7000 *[1 - (1.12)^9 /(1.15)^9] / (0.03)

Which is,

= 7000 * 7.0572647

= 49400.85

Now, The NPW of all costs = 35000 + 7000*(P/A,15%,4) + 49400.85*(P/F,15%,4)

= 35000 + 7000*2.854978 + 49400.85*0.571753

= 83229.93

Therefore the sound improvement better result in a net present worth profit of how much to negate the costs is $83229.93 or 83230

Note: EOY = End of year.