A town has to resurface a section of its roads. There\'s two options: gravel or

Question

A town has to resurface a section of its roads. There's two options: gravel or going through another company that uses another surfacing technique. The gravel has an initial cost of $200,000 to put down and it costs $15,000 to grade the road on an annual basis. The other surfacing technique costs $300,000 to install, but only requires $45,000 maintenance once every five years. The gravel road will last ten years while the new sufacing technique will last 15 years. The town's cost of capital is 9%. Which road surfacing option should the town choose (use time value of money)?

I'm not sure what to do with this question because the town isn't making money through any of this. All of it is money spent; there are no cash inflows. So, I'm assuming you're just trying to figure out which option would end up at less of a loss? How do you go about doing that? I've not done a problem like this before using time value of money.

Explanation / Answer

To solve this first of all we have to bring it to a single base, that is we have to consider it for 30 years to make a apple to apple to cpmarison:

The present value of future cashoutflows is less in case of gravel that is -354,105 compared to -377,249 .

Gravel surfacing PV of cash flows Other surfacing PV of cash flows Initial cost -                200,000 -                200,000 -                  300,000 -                   300,000 Maintenance cost 1 -                  15,000 -                  13,761                                -                                    -   2 -                  15,000 -                  12,625                                -                                    -   3 -                  15,000 -                  11,583                                -                                    -   4 -                  15,000 -                  10,626                                -                                    -   5 -                  15,000 -                    9,749 -                    45,000 -                      29,247 6 -                  15,000 -                    8,944                                -                                    -   7 -                  15,000 -                    8,206                                -                                    -   8 -                  15,000 -                    7,528                                -                                    -   9 -                  15,000 -                    6,906                                -                                    -   10 -                  15,000 -                    6,336 -                    45,000 -                      19,008 11 -                  15,000 -                    5,813                                -                                    -   12 -                  15,000 -                    5,333                                -                                    -   13 -                  15,000 -                    4,893                                -                                    -   14 -                  15,000 -                    4,489                                -                                    -   15 -                  15,000 -                    4,118 -                    45,000 -                      12,354 16 -                  15,000 -                    3,778                                -                                    -   17 -                  15,000 -                    3,466                                -                                    -   18 -                  15,000 -                    3,180                                -                                    -   19 -                  15,000 -                    2,917                                -                                    -   20 -                  15,000 -                    2,676 -                    45,000 -                        8,029 21 -                  15,000 -                    2,455                                -                                    -   22 -                  15,000 -                    2,253                                -                                    -   23 -                  15,000 -                    2,067                                -                                    -   24 -                  15,000 -                    1,896                                -                                    -   25 -                  15,000 -                    1,740 -                    45,000 -                        5,219 26 -                  15,000 -                    1,596                                -                                    -   27 -                  15,000 -                    1,464                                -                                    -   28 -                  15,000 -                    1,343                                -                                    -   29 -                  15,000 -                    1,232                                -                                    -   30 -                  15,000 -                    1,131 -                    45,000 -                        3,392 Total - -354,105 - -377,249

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