Pln 20TS Problem 8 A patriotic group of firefighters is planning to erect a perm
ID: 2771231 • Letter: P
Question
Pln 20TS Problem 8 A patriotic group of firefighters is planning to erect a permanent monument in L.A. city to honor those killed in the line of duty. What is the present worth (capitalized cost) for this project? Assume an i-10%. You must draw the cash flow diagram. Score: /16 points In the table below, you can find all the associated costs for the project Year Year 0 Year 10 Per year, for n oo First one on year 8, then every 8 years $350,000 Initial Investment One time reinvestment100,000 15,000 100 000 Annual cost Major Maintenance CostsExplanation / Answer
a. Present worth of initial investment = 350,000 (as it is being made at year 0)
b. Present worth of one time reinvestment = amount/(1+i)^n i = 10%, n = 10 years
= 100,000/1.1^10 = $38,554.33
c. Annual cost is in the form of a perpetuity. Its present worth = Amount/i = 15,000/0.10 = 150,000
d. Maintenance costs = 100,000 every 8 years.
Its present worth will be calculated using the formula: amount/(1+i)^n. The assumption being made here is that the maintainance costs will continue till perpetuity (at the interval of every 8 years). Its present worth calculation is shown below:
Total presnt worth of the monument = a+b+c+d = 350,000+38,544.33+150,000+87,444.02 = $625,988.40
Year Amount i 1+i Present worth 8 100,000 0.1 1.1 46,650.74 16 100,000 21,762.91 24 100,000 10,152.56 32 100,000 4,736.24 40 100,000 2,209.49 48 100,000 1,030.74 56 100,000 480.85 64 100,000 224.32 72 100,000 104.65 80 100,000 48.82 88 100,000 22.77 96 100,000 10.62 104 100,000 4.96 112 100,000 2.31 120 100,000 1.08 128 100,000 0.50 136 100,000 0.23 144 100,000 0.11 152 100,000 0.05 160 100,000 0.02 168 100,000 0.01 176 100,000 0.01 184 100,000 0.00 192 100,000 0.00 200 100,000 0.00 208 100,000 0.00 216 100,000 0.00 224 100,000 0.00 232 100,000 0.00 Total 87,444.02