Lincoln Park Zoo in Chicago is considering a renovation that will improve some physical facilities at a cost of $1,800,000. Addition of new species will cost another $310,000. Additional maintenance, food, and animal care and replacement will cost $145,000 in the 1st year, increasing by 3 % each year thereafter. The zoo has been in operation since 1868 and is expected to continue indefinitely; however, it is common to use a 20-year planning horizon on all new investments. Salvage value on facilities after 20 years will be 40 % of initial cost. Interest is 7 %. An estimated 1.5 million visits per year are made to the zoo, and the cost remains free year-round. How much additional benefit per visit, on average, must the visitors perceive to justify the renovation? $

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TomShelby TomShelby · Answer 1 · 2019-11-05T14:46:57+01:00

Answer:

The visitors should perceive an additional benefit of $ 0.16 dollars per visit to justify the renovation

Explanation:

F0

physical facilities: 1,800,000

new speciest cost: 310,000

total 2, 110,000

present value of the salvage value:

Salvage value: 1,800,000 x 40% = 720,000

[tex]\frac{Salvage }{(1 + rate)^{time} } = PV[/tex]

Salvage $720,000.00

time 20 years

rate 0.07000

[tex]\frac{720000}{(1 + 0.07)^{20} } = PV[/tex]

PV 186,061.68

Present value of an annuity with geometric progression:

[tex]\frac{1-(1+g)^{n}\times (1+r)^{-n} }{r - g}[/tex]

C 145,000 maintenance, food and animal care cost

g= increase by 3% each year: 0.03

r = cost of capital = 0.07

n = 20 years

7,766,745.43

Present worth:

2,110,000 + 7,766,745.43 - 186,061.68 = 9690683,75

Now, we need to know the equivalent annual cost and divide by the expected visitors:

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

PV $ 9,690,684

time 20 years

rate 0.07

[tex]9690683.75 \div \frac{1-(1+0.07)^{-20} }{0.07} = C\\[/tex]

C $ 236,384.129

divided among 1,500,000 visitors:

$ 0.16 dollars per visitor