An improvement to the roadwat is desired from a Philmont Scout Ranch to Springer

Question

An improvement to the roadwat is desired from a Philmont Scout Ranch to Springer iin northeastern New Mexico. Alternative N (for North) costs $2,400,000 initially and $155,000/year thereafter. Route SA will cost $4,200,000 initially and $88,000/year thereafter. Route SB is the same as SA with wider lanes and shoulders. It costs $5200000 initially with maintenance at $125000/year. USer costs considering time, operation, and safety are $625,000 for N, $410,000 for SA and $310,000 for SB. The salvage value for N, SA, SB after 20 years are 20% of initial cost, respectively. Using a MARR of 7 percent and a 20-year study period, which should be constructed?

a. Use an incremental B/C analysis.

b. Use a B-C analysis.

c. Which route is preffered if 0% interest is used?

Explanation / Answer

Dear,

In a given scenario, following are the options and its number in tabular form,

For your easy understanding, I have given Alphbatical Identification to each variable. I have kept Present Value data in details for easy reference.

I would prefer to answer option b first, from which option can easily be arrived.

b. Cost Benifit Analysis considering 7% as MARR for 20 Years.

The net benefit is user cost less yearly maitenance cost. Now project life is for 20 Years, we have to cosinder the time value of money. For e.g N Route is giving yearly benifit of $ 470,000 but future period has interest component in it. So will have to remove the it and called as discounting. For which PV tables need to be used. Conitnuing above,

There are two stream of cash flows, one year user cost is revenue which is netted with Yearly maitenance cost. Another stream is salvage value i.e. Terminal value. Both add up together makes project cash inflow. But yearly cash inflows will be multiplie with PVA Factor and terminal value will be multiplied with PV Factor.

There is only one cash outflow of initial expenditure, assuming it is spend at the begining of the year PV Factor for the same is 1. Hence, resultant calculations are as follows,

Hence it can be concluded in terms of Cost benifit Analysis, Route N is to be selected as it gives highest positive CB.

a. Use of Incremental CB analysis,

It is simple to do the incremental analysis from above. Lets keep route N as base, Route SA give incremental loss of $ 32,75,032 (i.e. difference between Loss of $ 5,72,012 Profit of $ 27,03,020). Simliarly, SB gives incremental loss of $ -29,71,790. Further, this can be substaintiated with the following calculations, (N Route as a base),

So, incremental CB analysis stands still as per cost benifit analysis.

c. Preferable route if 0% MARR.

In this scenario, 0% MARR is nothing but no time value hence every number is considered in absolute value i.e. ignoring time value. Resultant calculation will be as follows,

Hope this would explains and answers your questions thoroughly.

N Route Route SA Route SB Initial Cost ($) - [A] 24,00,000    42,00,000    52,00,000 Given Maitenance Cost ($) - [B]     1,55,000 88,000      1,25,000 Given No. Of Years 20 20 20 Salvage Value % at end of Life 20% 20% 20% Given Salvage Value - [C = A*20%]     4,80,000      8,40,000    10,40,000 Calculated Revenue (User Cost PM) ($) - [D]     6,25,000      4,10,000      3,10,000 Given Net Yearly Benefit [E = D-B]     4,70,000      3,22,000      1,85,000 Calcualed Cost of Capital [F] 7% 7% 7% PVA Factor @ 7% for 20 Years [G] (From PV Tables) 10.59 10.59 10.59 PV Factor @ 7% for 20th Year [H] (From PV tables) 0.258 0.258 0.258

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