Two business alternators (shown in Table below) are competing with one another.

Question

Two business alternators (shown in Table below) are competing with one another. The first Alternative A is a four year project, while the second Alternative B is an eight year project. Interest rate is 10% How must this be solved Solve each PW independently at their individual time frames and compare Solve each PW at the LCM and compare Solve each AW independently at their individual time frames and compare Both i and iii Both ii and iii Trick Question - this can't be solved Solve and show which Alternative is the desirable Alternative (using any method/tool you deem appropriate and correct)

Explanation / Answer

a) Choose the fifth option v) Both ii and iii

Since the projects have unequal lives they may give contradictory results with regard to the IRR(rate of return) generated by them and the Present worth(PW) therefore a common LCM time frame is chosen and the PWs are calculated over this common time frame(8 years here) for both projects and compared.The PWs calculated this way shall concur with the rate of returns obtained.High PW shall be associated with high IRR and low  PW shall be associated with low IRR.

The AW(Annual Worth) are the cash flows that each project generates per year since the comparison is year by year therefore the time frame matches and the AWs could be compared to reach a decision as to which project to choose(choose one with higher AW).

b)

Since the PW of project B is higher as compared to project A(95,911.26>80,479.53) therefore Alternative B is more desirable.

Annual cash flow=190,000-64,500=125,500 Annual cash flow=250,000-138,300=111,700 rate 10.00% CF=Cash Flow rate 10.00% CF=Cash Flow Project A PV oF CF(A) Project B PV oF CF(B) t CF(A) (=CF(A)/(1.1)^t t CF(B) (=CF(B)/(1.1)^t 0 -3,50,000 -350000.00 0 -5,00,000 -500000 1 1,25,500 114090.91 1 1,11,700 101545.45 2 1,25,500 103719.01 2 1,11,700 92314.05 3 1,25,500 94290.01 3 1,11,700 83921.86 4 -2,24,500 -153336.52 4 1,11,700 76292.60 5 1,25,500 77925.63 5 1,11,700 69356.91 6 1,25,500 70841.48 6 1,11,700 63051.74 7 1,25,500 64401.34 7 1,11,700 57319.76 8 1,25,500 58546.68 8 1,11,700 52108.87 PW(sum above PVs) $                           80,478.53 PW(sum above PVs) $                                95,911.26

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