18. A public relations company hired by the City of El Paso to increase tourism

Question

18. A public relations company hired by the City of El Paso to increase tourism to the Sun City proposed that the city build the world's only roller coaster that travels through two different countries. The idea is to build the ride along the Rio Grande River and have part of the tracks in the US and part in Mex ico. The ride would be built such that coaster cars could be launched from either side of the border, but riders would get off at the same point where they got on. After the ride becomes operational, tourism revenue is projected to be Si million initially (i.e. at time zero), S1.05 million after the first month, $1.1025 million after the second month and amounts increasing by 5% each month through the first year. At an interest rate of 12% per year compounded monthly, the present worth (time 0) of the tourism revenue generated by the ride is closest to a. b. c. d. $15.59 million $16.59 million S17.59 million Over $18 million

Explanation / Answer

Option (b).

Monthly (nominal) interest rate = 12%/12 = 1%

Number of months = 12

Present worth is computed as follows. Note that

(i) Revenue in month N = Revenue in month (N - 1) x 1.05

(ii) PV Factor in month N = (1.01)-N

Month Revenue ($million) PV Factor @1% Discounted Revenue ($million) (A) (B) (A) x (B) 0 1.0000 1.0000 1.00 1 1.0500 0.9901 1.04 2 1.1025 0.9803 1.08 3 1.1576 0.9706 1.12 4 1.2155 0.9610 1.17 5 1.2763 0.9515 1.21 6 1.3401 0.9420 1.26 7 1.4071 0.9327 1.31 8 1.4775 0.9235 1.36 9 1.5513 0.9143 1.42 10 1.6289 0.9053 1.47 11 1.7103 0.8963 1.53 12 1.7959 0.8874 1.59 Present Worth ($million) = 16.59

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