Question

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 firm's interest rate is known to be 15%.

Answer 1

Answer:

salvage value is $16,368.34

Explanation:

given data

initial cost = $182,730

annualized capital cost = $42,442

service life = 7 year

interest rate = 15%

solution

we get here first present value that is

annual value  = rate ×  $\frac{present\ value}{(1 - (1+ r)^{-t})}$       .................1

put here value and we get

42,442 = 15% ×  $\frac{present\ value}{(1 - (1+ 0.15)^{-7})}$

solve it we get

present value = $176,576.5343  

so

present value = initial investment + salvage value     ..............2

we take here present value and initial investment will be negative

-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 = 16,368.34