Question

4-4 A government monument is expected to last forever. The first cost is $5,000,000. At the end of year 7 there will be a one-time remodeling cost of $300,000. At the end of every 12 years there will be a major remodeling cost of $500,000. Annual Operating& Maintenance Costs will total $15,000 for each year i-4% per year. a. Calculate the capitalized cost. b. Calculate the equivalent uniform annual cost (do not use the calculated capitalized cost in c. Draw the fully labeled cash flow diagram.

Answer 1

The following information about expenses incurred on remodeling of a monument is given: First cost $5,000,000 S300,000 cost (end of every 12 years) S500,000 $15,000 One-time remodeling cost (end of 7th year) Major remodeling Annual O&M cost 1 Life 4% infinity Capitalized long and is infinite in some cases cost (CC) is the present worth of an alternative whose project life is very Capitalized cost of a perpetual annual series (A) with a. interest rate (i) 1S Write the formula to calculate the capitalized cost of the project as follows Capitalized cost = First cost one-time remodelling cost (P/F,4%, 7)- remodelling cost (A/F,4%, 12) annual O&M cost 4% 4% =-S5,000,000 $300,000 (0.7599) - $500,000 (0.0666) $15,000 0.04 0.04 -$5,000,000-$227,970 S832,500-$375,000 -S6 ,435,470 Hence, the capitalized cost is-S6,435,470 b. Compute equivalent uniform annual worth cost as follows: EUAC -$5,000, 000 (0.04)- $300,000 (P/F. 4%, 7) (0.04)-$500, 000(A/F.4%, 12)-S15,000 -S200, 000-S300,000 (0.7599) (0.04)-S500,000 (0.0666)-$15,000 -$200,000-S9,118.8-$33,300-$15,000 -S257,418.8 Hence, the EUAC is-$257,418.8

c. The cash flow diagram is shown below 12 11 24 10 6- 15,000 15,000 15,000 15,000 15,000 15,000 15.000 15,000 15,000 5,000,000 15,000 15,00 15000 15.000 + $500,000 S500,000 300,000 As shown in the above diagram, $5,000,000 is the first cost, and $15,000 is per year cost. With this, $300,000 cost is incurred only in year 7. And $500,000 incurred after every 12 years