Question

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? $

Answer 1

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

Step-by-step 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

`(Salvage )/((1 + rate)^(time) ) = PV`

Salvage $720,000.00

time 20 years

rate 0.07000

`(720000)/((1 + 0.07)^(20) ) = PV`

PV 186,061.68

Present value of an annuity with geometric progression:

`(1-(1+g)^(n)* (1+r)^(-n) )/(r - g)`

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:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV $ 9,690,684

time 20 years

rate 0.07

`9690683.75 / (1-(1+0.07)^(-20) )/(0.07) = C\\`

C $ 236,384.129

divided among 1,500,000 visitors:

$ 0.16 dollars per visitor