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erma4kov [3.2K]
2 years ago
10

A new highway is to be constructed.

Business
1 answer:
baherus [9]2 years ago
6 0

Answer:

Desing B

<u><em>Total Present worth</em></u>     $  502.485,35‬

<u><em>Annual worth:</em></u>              $    49,722.003

Option 2:

<u><em>Total Present worth</em></u>     $  666.441,33‬

<u><em>Annual worth:</em></u>              $   53,845.798

Explanation:

<h2>Desing A</h2>

$85 x 5280     =   448,800

$4 x 3 x 5280  =     63,360

$8000 x 4        = <u>    32,000  </u>

total cost:                544,160‬

Annual cost:

11,800 + 300 = 12,100

PV of the annual maintenance:

C \times \frac{1-(1+r)^{-time} }{rate} = PV\\

C 12,100.00

time 16

rate 0.06

12100 \times \frac{1-(1+0.06)^{-16} }{0.06} = PV\\

PV $122,281.3328

<u><em>Present worth:</em></u>

total cost to construct  544,160‬ + maintenance $122,281.33 = 666.441,33

<u><em>Annual worth:</em></u>

PV \div \frac{1-(1+r)^{-time} }{rate} = C\\

PV 544,160

time 16

rate 0.06

544160 \div \frac{1-(1+0.06)^{-16} }{0.06} = C\\

C  $ 53,845.798

<h2>Desing B</h2>

a mile is equivalent to 5,280 foot

paviment $40 x 5,280 = $ 211,200

sood ditched 2 per foot x 5,280 foot per mile x $1.40 = $ 12,038.4

pipe culvert 2,200 x 2 = 4,400

Total value to construct: 227.638,4‬

PV of maintenance:

replacement 2,400 x 2 = 4,800 (in 8 years)

\frac{Maturity}{(1 + rate)^{time} } = PV  

Maturity  $4,800.0000

time  8.00

rate  0.06000

\frac{4800}{(1 + 0.06)^{8} } = PV  

PV   3,011.5794

maintenance $2,900

culverts 2 x $ 230 = $ 460

ditch 1.45 x 5,280 x 2 = $ 15,312

Total yearly cost: 18.672‬

PV of this annuity over 16 years:

C \times \frac{1-(1+r)^{-time} }{rate} = PV\\

C 18,672.00

time 16

rate 0.06

18672 \times \frac{1-(1+0.06)^{-16} }{0.06} = PV\\

PV $188,697.2765

PV of the replacement bituminous concrete

\frac{Maturity}{(1 + rate)^{time} } = PV  

Maturity  $211,200.0000

time  16.00

rate  0.06000

\frac{211200}{(1 + 0.06)^{16} } = PV  

PV   83,138.0951

<u><em>Present worth:</em></u>

Total value to construct: $  227.638,4‬ +

yearly cost PB                 $  188,697.28 +

concrete replacement    $ 83,138.0951

culvert replacement:       $<u>   3,011.58      </u>

Total Present worth        502.485,35‬

<u><em>Annual worth:</em></u>

PV \div \frac{1-(1+r)^{-time} }{rate} = C\\

502485.35 \div \frac{1-(1+0.06)^{-16} }{0.06} = C\\

C  $ 49,722.003

<em><u /></em>

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