Question

A power plant that supplies a community with electricity costs $1 billion to build, lasts 25 years, and has an annual operating cost of $0.2 billion; it costs $0.1 billion to decommission the plant at the end of its lifetime (25 years). (Assume that the construction costs and the operating costs are paid at the beginning of the period, and that the decommissioning cost is paid at the end of the life of the plant.) The annual discount rate is r, with discount factor ρ = 1 1+r . Write the formula for the present value of the cost of providing this community with electricity for 100 years, including the decommissioning costs. (Hint: First find the present value of providing one unit of electricity for 25 years. Denote this magnitude as Z. Then find the present value of incurring this cost, Z, 4 times: in periods 0, 25, 50, and 75.)

Answer 1

Present value of Costs for providing community with electricity for 25 years (in Billion $)

Z = 1 + 0.2/r*(1-1/(1+r)^25)*(1+r) + 0.1/(1+r)^25

This cost will be incurred at time 0, 25, 50 and 75

So,

Present value of Costs for providing community with electricity for 25 years (in Billion $)

= Z+Z/(1+r)^25+Z/(1+r)^50+Z/(1+r)^75

= (1 + 0.2/r*(1-1/(1+r)^25)*(1+r) + 0.1/(1+r)^25)* (1+1/(1+r)^25+1/(1+r)^50+1/(1+r)^75)

which is the required formula for the present value of the cost of providing this community with electricity for 100 years