Question

Calculate the Net Present Value (NPV) of heating a home for 20 years if the heating bills total $1500/year. Heating costs are expected to escalate at a rate of 3%/year. Use a discount rate of 6%.

Answer 1

First thing we calculate sum of net present value by using Sum of G.P series formula;{ a(r^n-1)}/(r-1),where a is first year present Value discount rate in percentage point.

First year present value =1500/1.06=1415.09

As bills is increasing by 3% or 0.03and the bill become=1500*1.03

Second year bill present value=1500*1.03)/(1.06)^2

So r=1.03/1.06=103/106=0.97

Now using the mentioned formula using a=1415.09 and r=0.97

Net present value of heating home for 20, year={1415.09(0.97^20-1)/(0.97-1)={1415.09(0.54-1)}/(-0.03)

=1415.09*-0.46/-0.03=21,698.04~21698