6.16 A mall with two levels is under construction. The plan is to install only n
ID: 2619671 • Letter: 6
Question
6.16 A mall with two levels is under construction. The plan is to install only nine esca- lators at the start, although the ultimate design calls for 16. The question arises as to whether to provide necessary facilities (stair supports, wiring conduits, motor foundations, etc.) that would permit the installation of the additional escalators at the mere cost of their purchase and installation or to defer investment in these facilities until the escalators need to be installed Option 1. Provide these facilities now for all seven future escalators at $200,000 ·Option 2, Defer the investment in the facility as needed. Install two more esca- lators in two years, three more in five years, and the last two in eight years. The installation of these facilities at the time they are required is estimated to cost $100,000 in year 2, $160,000 in year 5, and $140,000 in year 8 Additional annual expenses are estimated at $3000 for each escalator facility in- stalled. At an interest rate of 12%, compare the net present worth of each option over eight yearsExplanation / Answer
We will use the following formula to find the present value
Present value = 1 / ((1 + r)n
Where r is the rate of interest and n is the number of years
Hence the present worth of Option 2 is lower and hence the mall should select Option 2
Year 0 1 2 3 4 5 6 7 8 Total Option 1 Setup cost 200000 Annual cost @ $3000 per escalator facility 21000 21000 21000 21000 21000 21000 21000 21000 Total cost -------------(A) 200000 21000 21000 21000 21000 21000 21000 21000 21000 PV factor @ 12% 1 / (1+0.12)^0 1 / (1+0.12)^1 1 / (1+0.12)^2 1 / (1+0.12)^3 1 / (1+0.12)^4 1 / (1+0.12)^5 1 / (1+0.12)^6 1 / (1+0.12)^7 1 / (1+0.12)^8 PV factor --------------(B) 1.0000 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 NPV -------------------(A x B) 200000.0000 18750.0000 16741.0714 14947.3852 13345.8796 11915.9640 10639.2535 9499.3335 8481.5478 304320.44Related Questions
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