Two plans have been proposed for a high speed passenger rail line between Cincin

Question

Two plans have been proposed for a high speed passenger rail line between Cincinnati and Cleveland. The plans are summarized in the table below. Costs and benefits are in millions of dollars. Use benefit-cost ratio analysis with an interest rate of 10% Plan A Plan B Eco. Life (Years) 40 20 Salvage Value $15 $12 Annual Benefits $25 $22 Annual M & O Cost $5 $3 Initial Cost $ 300 $ 160 Use increment analysis, Use Net Present Worth and Annual Worth to determine which, if either, of the plans should be accepted. Compare between Net Present Worth and Annual Worth in the analysis of benefit- cost ratio.

Explanation / Answer

Plan A Initial cost -300 Annual benefits 25 Less:Annual M&O costs 5 Net Annual benefits 20 PVoA @10%,40Yrs. 9.779051 Present value of Net annual benefits(20*9.779051) 195.58102 Salvage value)15*0.022095 3.31425 Net Present Worth(A)(-300+195.581+3.31425) -101.10475 Plan B Initial cost -160 Annual benefits 22 Less:Annual M&O costs 3 Net Annual benefits 19 PVoA @10%, 20Yrs. 8.513564 Present value of Net annual benefits(19*8.513564) 161.757716 Salvage value(12*0.148644) 1.783728 Net Present Worth(B)(-160+161.7577+1.783728) 3.541444 Incremental NPW of B 101.05+3.54144 104.59144 Plan B has an incremental NPW of 104.59144 Mn. Over Plan A Benefit -Cost ratio Plan A Plan B Cost 300 160 PV of Benefits 198.89527 163.541444 Benefit /Cost ratio(%) 66.30 102.21 Plan B should be accepted as per NPW analysis

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