A road resurfacing project costs $250,000, lasts 5 years and saves $150,000 annually in patching costs....

A road resurfacing project costs $250,000, lasts 5 years and saves $150,000 annually in patching costs. MARR is 12%. Determine the future worth (in $).

Expert Solution

Cost = $250,000

MARR = 12%

Net cost after 5 years would be [Cost * (1 + MARR)^^Years] = [250,000 * (1 + 0.12)^⁵] = 440,585.4

Saving per year = $150,000

Savings in first year can be deposited in bank for 4 years, saving of second year can be deposited for 3 years and so on....

Future value can be calculated as: [Savings * (1 + MARR)^^{Year for which amount is deposited}]

Future value of saving of first year is = [150,000 * (1 + 0.12)^⁴] = 236,027.9

Future value of saving of second year is = [150,000 * (1 + 0.12)^³] = 210,739.2

Future value of saving of third year is = [150,000 * (1 + 0.12)^²] = 188,160

Future value of saving of forth year is = [150,000 * (1 + 0.12)^¹] = 168,000

Future value of saving of fifth year is = [150,000 * (1 + 0.12)^⁰] = 150,000

Sum of future value for 5 years is 236,027.9 + 210,739.2 + 188,160 + 168,000 + 150,000 = 952,927.1

Future value of project = Sum of future value - Net cost after 5 year = 952,927.1 - 440,585.4 = 512,341.7

Rahul Sunny answered 2 years ago

A road resurfacing project costs $200,000, lasts 5 years and saves $100,000 annually in patching costs....

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