A warehouse built at a cost of $60000 has to be renovated every year with sum of $1500. If Money is Worth 6% p.a compounded annually. What is the capitalized cost of the warehouse
To determine the capitalized cost of the warehouse, we must calculate the present value of the infinite series of renovation costs, which constitutes a perpetuity, and then add the initial building cost.
The perpetuity present value formula is:
PV = C / r
where:
PV = Present Value of the perpetuity
C = Annual cost of maintenance
r = Annual interest rate (expressed as a decimal)
Given:
C = $1,500 (annual cost of renovations)
r = 6% or 0.06 (interest rate)
Let's calculate the present value of the renovation costs:
PV = $1500 / 0.06 = $25,000
This $25,000 is the present value of all future renovation costs.
The capitalized cost of the warehouse is the sum of its initial construction cost and the present value of all future renovation costs.
Initial Construction Cost = $60,000
Present Value of Renovations = $25,000
Capitalized Cost = Initial Construction Cost + Present Value of Renovations
Capitalized Cost = $60,000 + $25,000
Capitalized Cost = $85,000
Therefore, the capitalized cost of the warehouse, including the initial cost and the present value of perpetual renovations, is $85,000.