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marshall27
1 month ago
8

The owner of an interior lot has received notice that the city intends to place a sidewalk across his property. The lot measures

100' x 500'. The cost of the sidewalk is $40 per linear foot and the city will pick up 50% of the cost, with each homeowner picking up the difference. How much will this homeowner be charged in a special assessment tax to cover his cost of the sidewalk?
Business
1 answer:
marusya05 [3K]1 month ago
7 0

Answer:

He will incur a charge of $2000 due to a special assessment tax for the sidewalk.

Explanation:

The information provided indicates that the lot in question is an interior one, suggesting we should assess only one dimension of the property since the sidewalk is constructed at either the front or the rear.

The lot size is 100 feet in width and 500 feet in length.

The cost for constructing the sidewalk is $40 per linear foot.

The city will pay half of the total expense.

<p.to calculate="" the="" cost="" for="" width="" of="" lot:="">

100 feet multiplied by $40 equals $4000.

The city contributes 50% of the expense, meaning the homeowner is responsible for the remaining 50%.

Thus, the homeowner's share will be 50% of $4000, which is calculated as 0.5 times $4000, yielding $2000.

He will incur a charge of $2000 due to a special assessment tax for the sidewalk.

</p.to>
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1. For determining the net present value

Year    Cash flow     Discount factor @20%         Present value  

0         $75,000         1                                               $75,000

1          $20,000        0.8333333333                          $16,666.67

2         $25,000        0.6944444444                       $17,361.11

3         $30,000        0.5787037037                       $17,361.11

4         $50,000        0.4822530864                       $24,112.65

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NPV                                                                              $501.54                                      

The discount factor is to be calculated as follows:

= 1 ÷ (1 + rate) ^ years

2. The benefit-cost ratio is calculated by:

= Total Present Value ÷ Initial Investment

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= 1.01

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Year    Cash flow     Discount factor @20%         Present value  

0         $75,000         1                                               $75,000

1          $20,000        0.8064516129                     $16,129.03

2         $25,000        0.650364204                    $16,259.11

3         $30,000        0.5244872613                    $15,734.62

4         $50,000        0.4229735978                    $21,148.68

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