we want to donate a marble birdbath to the city park as a memorial to cats. we a

Question

we want to donate a marble birdbath to the city park as a memorial to cats. we also want to set up a perpetual care fund to cover future expenses "forever". the initial cost of the bath is $5000. routine annual operating costs are $200 per year, but every fifth year the cost will be $500 to cover major cleaning and maintenance as well as operation. a) what is the capitalized cost of this project if the interest rate it 8%? b) hoe much is the present worth of this project if it is to be demolished after 75 years? the final $500 payment in the 75th year will cover the year's operating cost and the site reclamation. explain your work please

Explanation / Answer

The first thing we need to do is calculate the net present value for given perpetuity.
a) Initial investment is in its NPV
b) Next we break the $500 cost every five year to $200 and $300
Interest rate is assumed to be 8% per annum

Calculating NPV
For $200 we have NPV = $200 / .08 = $2500
For $300 we have NPV = $300/ (1.085-1) = $639.21 (post for help on this formula, its basic though)

Toal NPV = $5000 + $2500 + $639.21 = $8139.21....ans of (a)

Project is demolished after 75 years

NPV for $200 = (1/0.8)*[200 - 200/1.0875] = $2492.21

NPV for $300 = (1/1.085-1)*{300 - 300/1.0875] = $637.01

Total NPV = $5000+$2492.21+$637.01 = $8129.22

NOTE : The formulas used above are fairly simple to find as well as derive. Post to get help on those.

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