RR must build a tunnel to maintain his access around the mountain. The tunnel co
ID: 1215439 • Letter: R
Question
RR must build a tunnel to maintain his access around the mountain. The tunnel could be fabricated of normal steel for an initial cost of $30,000 and should last for 15 years. Maintenance will cost $1,000 per year. Another option would be to use corrosion resistant steel, which will last for 15 years, with annual maintenance cost of $100. In 15 years there would be no salvage value for either bridge. RR pays combined federal and state taxes at the 48% marginal rate and uses straight-line depreciation. If the after tax MARR is 12%, what is the maximum amount that should be spent on the corrosion-resistant tunnel?
Explanation / Answer
Present worth of normal steel tunnel:
Initial cost = $30000
Life (n) = 15 years
Annual Maintenance cost = $1000
R = 12%
Present worth = initial cost + present value of annual maintenance cost
Present worth = 30000 + 1000*(1-1/(1+R)^n)/R
Present worth = 30000 + 1000*(1-1/1.12^15)/.12
Present worth =$36810.86
Corrosion steel tunnel:
Life (n) = 15 years
Annual Maintenance cost = $100
R = 12%
Present value of maintenance cost = 100*(1-1/(1+R)^n)/R = 100*(1-1/1.12^15)/.12 = $681.09
Thus,
Maximum cost of corrosion steel tunnel = 36810.86 - Present value of maintenance cost
Maximum cost of corrosion steel tunnel = 36810.86 – 681.09
Maximum initial cost of corrosion steel tunnel = $36129.77
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