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8.1 A local government is considering promoting tourism in the city. It will cost $5,000 to develop a plan. The anticipated annual benefits and costs are as follows: Annual benefits: Increased local income and tax collections $117,400 Annual support service: Parking lot expansion, rest room, patrol car, and street repair $48,830 If the city government uses a discount rate of 6% and a study period of five years, is this tourism project justifiable according to the benefit–cost analysis?

Respuesta :

Answer:

This tourism project is justifiable.

Explanation:

Present value of benefits:

[tex]=\frac{117,400}{(1.06)} +\frac{117,400}{(1.06)^{2} } +\frac{117,400}{(1.06)^{3} } +\frac{117,400}{(1.06)^{4} } +\frac{117,400}{(1.06)^{5} }[/tex]

= $494,531.51

Present value of costs:

[tex]=5,000+\frac{48,830}{(1.06)} +\frac{48,830}{(1.06)^{2} } +\frac{48,830}{(1.06)^{3} } +\frac{48,830}{(1.06)^{4} } +\frac{48,830}{(1.06)^{5} }[/tex]

= $210,689.72

Benefit to cost ratio:

[tex]=\frac{Present\ value\ of\ benefits}{Present\ value\ of\ costs}[/tex]

[tex]=\frac{494,531.51}{210,689.72}[/tex]

= 2.35

Benefit to cost ratio > 1 ,

Therefore, this tourism project is justifiable.

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