A road is constructed at the capital cost of $6 million. At the end of Year 10, major improvements are to be made costing $17 million. At the end of Year 25, a replacement and upgrade is to be done at a cost of $29 million. At the end of year 40, the federal government issues a one-time tax credit in the amount of $12 million. Over a 50-year analysis period (assuming a 10% interest rate) what is the annualized cost to the nearest dollar?

The annualized cost is:

$299,272.

Explanation:

a) Data and Calculations:

Year 0  Capital cost of road construction = $6 million

Year 10 Major improvements cost = $17 million

Year 25 Replacement and upgrade cost = $29 million

Year 40 Federal government one-time tax credit = $12 million

Period of project analysis = 50 years

Cost of capital (discount rate) = 10%

Annualized cost at present value costs:

Amount spent  Discount Factor     Present value

$6 million           1                               $6,000,000

$17 million         0.386                          6,562,000

$29 million       0.092                          2,668,000

($12 million)      0.0222                         (266,400)

Total cost                                          $14,963,600

Annualized cost = $14,963,600/50 =  $299,272

b) The annualized cost for the road construction project, which is the annualized value of the net present costs of $14,963,600, is divided by 50.  Before obtaining the net present costs, the cash outflows, including the tax credit, are discounted to their present values, using the discount rate of 10%.  And then, the average of the cost is obtained by dividing the total net present cost into 50 years.

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