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?

Question

Business

Hollyn

16 January, 07:55

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?

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Answers (1)

Know the Answer?

Logan Vaughan · Answer 1

The correct answer is $83230

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.