ACME labs bought a new inspection device for $182,730. The accounting department has estimated that the device will have an annualized capital cost of $42,442 per year for its 7-year service life. What salvage value was assumed in calculating the capital cost

The salvage value taken is $16,368.34

Explanation:

ANSWER:

initial cost = $182,730

rate = 15%

n = 7 years

annualized capital cost = $42,442

salvage value = ?

first we will find the present worth.

annual worth = r * present worth / ( 1 - ( 1+ r) ^ - n)

42,442 = 15% * pw / ( 1 - (1+15%) ^ - 7)

42,442 = 0.15pw / ( 1 - (1.15) ^ -7)

42,442 = 0.15 pw / ( 1 - 0.37593)

42,442 = 0.15 pw / 0.6240

42,442 * 0.6240 = 0.15 pw

$26,486.48 = 0.15 pw

pw = $26,486.48 / 0.15

pw = $176,576.5343

pw also equals the initial investment + salvage value.

pw = initial investment + salvage value(p/f,i,n)

i = 15% , n = 7 years and pw will be taken negative here

-176,576.5343 = -182,730 + salvage value(p/f,15%,7)

-176,576.5343 +182,730 = salvage value(p/f,15%,7)

6,153.465 = salvage value * 0.3759

salvage value = 6,153.465 / 0.3759

salvage value = 16,368.34

so , the salvage value taken is $16,368.34

answer; swot analysis;