Problem 06.004 Annual Worth and Capital Recovery Calculations A delivery car had

Question

Problem 06.004 Annual Worth and Capital Recovery Calculations A delivery car had a first cost of $38,000, an annual operating cost of $14,000, and an estimated $5500 salvage value after its 6-year life. Due to an economic slowdown, the car will be retained for only 4 years and must be sold now as a used vehicle. At an interest rate of 9% per year, what must the market value of the used vehicle be in order for its AW value to be the same as the Aw if it had been kept for its full life cycle? eBook nt The market value of the used vehicle is determined to be $ Print References

Explanation / Answer

The equivalent uniform annual worth of the car if it had been kept for 6 years is calculated as

AW = $ 38,000 ( A/P, 9%, 6 years ) + $ 14,000 - $ 5,000 (A/F, 9% , 6 years )

AW = $ 38,000 * 0.222920 + $ 14,000 - $ 5000 * 0.132920

AW = $ 21,806.36

The equivalent uniform annual worth of the car if it had been kept for 4 years is calculated as

AW = $ 38,000 ( A/P, 9%, 4 years ) + $ 14,000 - Salvage value (A/F, 9% , 4 years )

The annual worth in 6 years = Annual worth in 4 years

$ 21,806.36 = $ 38,000 ( A/P, 9%, 4 years ) + $ 14,000 - Market value (A/F, 9% , 4 years )

$ 21,806.36 =  $ 38,000 * 0.308669 + $ 14,000 - Market value * 0.218669

$ 21,806.36 = $ 25,729.42 - Market value * 0.218669

Market value = $ 17,940.64

The market value of the used car is determined to be $ 17,940.64

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