6.1 and also 6.2 annual Worth Calculations
The AW method is frequently used because that comparing alternatives. As shown in chapter 4, AW way that allincomes and disbursements (irregular and also uniform) are converted right into an equivalent uniformannual (end-of-period) amount, i beg your pardon is the very same each period. The significant advantage the this method over all theother approaches is that it does not call for making the comparison over the the very least commonmultiple (LCM) the years once the alternatives have various lives. That is, the AW value of the alternate iscalculated because that one life bicycle only. Ifthe task is ongoing for much more than one cycle, the equivalent annual worth because that the nextcycle and all doing well cycles will be exactly the exact same as because that the first, noted allcash flows are the same for each cycle in constant-value dollars (discussed in Chapter12).
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The repeatability of the uniform annual series through various life cycles have the right to bedemonstrated through considering the cash-flow diagram in figure 6-1, which represents two lifecycles of one asset v a very first cost the $20,000, an yearly operating price of $8000, and also a3-year life.
The AW for one life bicycle (i.e., 3 years) would certainly be calculated as follows:
AW = -20,000 (A/P, 22%, 3) 8000 = -$17,793
The AW for 2 life cycles is calculation as
AW = -20,000 (A/P, 22%, 6) (20,000)(P/F, 22%, 3)(A/P, 22%, 6) 8000 = -$17,793
The AW value for the an initial life bike is precisely the same as the for 2 lifecycles. This exact same AW will be derived when three, four, or any type of other variety of lifecycles space evaluated. Thus, the AW for one life bike of an different representsthe equivalent uniform annual worth that that alternate every time the cycle isrepeated.
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When an asset has a terminal salvage value, there are numerous ways by which the AW canbe calculated. The two that will be disputed here room the rescue sinking fundmethod, i beg your pardon is represented by the basic equation:
AW = -P (A/P, i, n) + S (A/F, i, n)
And the funding recovery plus attention method, i m sorry is represented by
AW = -(P S) (A/P, i, n) Si
Their equivalence have the right to be demonstrated by considering an heritage which has a an initial cost of$20,000, an annual operating expense of $10,000 every year, and also a $5000 salvage worth at theend the its 5 year life. The yearly worth in ~ 12% per year by the very first method is:
AW = -20,000 (A/P, 12%, 5) 10,000 + 5000 (A/F,12%, 5) = -20,000 (0.27741) 10,000 + 5,000 (0.15741) = -$14,761
The annual worth by the second method is:
AW = -(20,000 - 5000) (A/P, 12%, 5) - 10,000 - 5000 (0.12) = -15,000 (0.27741) - 10,000 - 600 = -$14,761
Thus, the AW values room the very same by one of two people method, yet only the previous will be usedhereafter.